Active sensing in the categorization of visual patterns

PubMed Central

Yang, Scott Cheng-Hsin; Lengyel, Máté; Wolpert, Daniel M

2016-01-01

Interpreting visual scenes typically requires us to accumulate information from multiple locations in a scene. Using a novel gaze-contingent paradigm in a visual categorization task, we show that participants' scan paths follow an active sensing strategy that incorporates information already acquired about the scene and knowledge of the statistical structure of patterns. Intriguingly, categorization performance was markedly improved when locations were revealed to participants by an optimal Bayesian active sensor algorithm. By using a combination of a Bayesian ideal observer and the active sensor algorithm, we estimate that a major portion of this apparent suboptimality of fixation locations arises from prior biases, perceptual noise and inaccuracies in eye movements, and the central process of selecting fixation locations is around 70% efficient in our task. Our results suggest that participants select eye movements with the goal of maximizing information about abstract categories that require the integration of information from multiple locations. DOI: http://dx.doi.org/10.7554/eLife.12215.001 PMID:26880546

Task-based data-acquisition optimization for sparse image reconstruction systems

NASA Astrophysics Data System (ADS)

Chen, Yujia; Lou, Yang; Kupinski, Matthew A.; Anastasio, Mark A.

2017-03-01

Conventional wisdom dictates that imaging hardware should be optimized by use of an ideal observer (IO) that exploits full statistical knowledge of the class of objects to be imaged, without consideration of the reconstruction method to be employed. However, accurate and tractable models of the complete object statistics are often difficult to determine in practice. Moreover, in imaging systems that employ compressive sensing concepts, imaging hardware and (sparse) image reconstruction are innately coupled technologies. We have previously proposed a sparsity-driven ideal observer (SDIO) that can be employed to optimize hardware by use of a stochastic object model that describes object sparsity. The SDIO and sparse reconstruction method can therefore be "matched" in the sense that they both utilize the same statistical information regarding the class of objects to be imaged. To efficiently compute SDIO performance, the posterior distribution is estimated by use of computational tools developed recently for variational Bayesian inference. Subsequently, the SDIO test statistic can be computed semi-analytically. The advantages of employing the SDIO instead of a Hotelling observer are systematically demonstrated in case studies in which magnetic resonance imaging (MRI) data acquisition schemes are optimized for signal detection tasks.

Structural and parameteric uncertainty quantification in cloud microphysics parameterization schemes

NASA Astrophysics Data System (ADS)

van Lier-Walqui, M.; Morrison, H.; Kumjian, M. R.; Prat, O. P.; Martinkus, C.

2017-12-01

Atmospheric model parameterization schemes employ approximations to represent the effects of unresolved processes. These approximations are a source of error in forecasts, caused in part by considerable uncertainty about the optimal value of parameters within each scheme -- parameteric uncertainty. Furthermore, there is uncertainty regarding the best choice of the overarching structure of the parameterization scheme -- structrual uncertainty. Parameter estimation can constrain the first, but may struggle with the second because structural choices are typically discrete. We address this problem in the context of cloud microphysics parameterization schemes by creating a flexible framework wherein structural and parametric uncertainties can be simultaneously constrained. Our scheme makes no assuptions about drop size distribution shape or the functional form of parametrized process rate terms. Instead, these uncertainties are constrained by observations using a Markov Chain Monte Carlo sampler within a Bayesian inference framework. Our scheme, the Bayesian Observationally-constrained Statistical-physical Scheme (BOSS), has flexibility to predict various sets of prognostic drop size distribution moments as well as varying complexity of process rate formulations. We compare idealized probabilistic forecasts from versions of BOSS with varying levels of structural complexity. This work has applications in ensemble forecasts with model physics uncertainty, data assimilation, and cloud microphysics process studies.

From Neutron Star Observables to the Equation of State. II. Bayesian Inference of Equation of State Pressures

NASA Astrophysics Data System (ADS)

Raithel, Carolyn A.; Özel, Feryal; Psaltis, Dimitrios

2017-08-01

One of the key goals of observing neutron stars is to infer the equation of state (EoS) of the cold, ultradense matter in their interiors. Here, we present a Bayesian statistical method of inferring the pressures at five fixed densities, from a sample of mock neutron star masses and radii. We show that while five polytropic segments are needed for maximum flexibility in the absence of any prior knowledge of the EoS, regularizers are also necessary to ensure that simple underlying EoS are not over-parameterized. For ideal data with small measurement uncertainties, we show that the pressure at roughly twice the nuclear saturation density, {ρ }{sat}, can be inferred to within 0.3 dex for many realizations of potential sources of uncertainties. The pressures of more complicated EoS with significant phase transitions can also be inferred to within ˜30%. We also find that marginalizing the multi-dimensional parameter space of pressure to infer a mass-radius relation can lead to biases of nearly 1 km in radius, toward larger radii. Using the full, five-dimensional posterior likelihoods avoids this bias.

eGSM: A extended Sky Model of Diffuse Radio Emission

NASA Astrophysics Data System (ADS)

Kim, Doyeon; Liu, Adrian; Switzer, Eric

2018-01-01

Both cosmic microwave background and 21cm cosmology observations must contend with astrophysical foreground contaminants in the form of diffuse radio emission. For precise cosmological measurements, these foregrounds must be accurately modeled over the entire sky Ideally, such full-sky models ought to be primarily motivated by observations. Yet in practice, these observations are limited, with data sets that are observed not only in a heterogenous fashion, but also over limited frequency ranges. Previously, the Global Sky Model (GSM) took some steps towards solving the problem of incomplete observational data by interpolating over multi-frequency maps using principal component analysis (PCA).In this poster, we present an extended version of GSM (called eGSM) that includes the following improvements: 1) better zero-level calibration 2) incorporation of non-uniform survey resolutions and sky coverage 3) the ability to quantify uncertainties in sky models 4) the ability to optimally select spectral models using Bayesian Evidence techniques.

Improving the Accuracy of Planet Occurrence Rates from Kepler Using Approximate Bayesian Computation

NASA Astrophysics Data System (ADS)

Hsu, Danley C.; Ford, Eric B.; Ragozzine, Darin; Morehead, Robert C.

2018-05-01

We present a new framework to characterize the occurrence rates of planet candidates identified by Kepler based on hierarchical Bayesian modeling, approximate Bayesian computing (ABC), and sequential importance sampling. For this study, we adopt a simple 2D grid in planet radius and orbital period as our model and apply our algorithm to estimate occurrence rates for Q1–Q16 planet candidates orbiting solar-type stars. We arrive at significantly increased planet occurrence rates for small planet candidates (R p < 1.25 R ⊕) at larger orbital periods (P > 80 day) compared to the rates estimated by the more common inverse detection efficiency method (IDEM). Our improved methodology estimates that the occurrence rate density of small planet candidates in the habitable zone of solar-type stars is {1.6}-0.5+1.2 per factor of 2 in planet radius and orbital period. Additionally, we observe a local minimum in the occurrence rate for strong planet candidates marginalized over orbital period between 1.5 and 2 R ⊕ that is consistent with previous studies. For future improvements, the forward modeling approach of ABC is ideally suited to incorporating multiple populations, such as planets, astrophysical false positives, and pipeline false alarms, to provide accurate planet occurrence rates and uncertainties. Furthermore, ABC provides a practical statistical framework for answering complex questions (e.g., frequency of different planetary architectures) and providing sound uncertainties, even in the face of complex selection effects, observational biases, and follow-up strategies. In summary, ABC offers a powerful tool for accurately characterizing a wide variety of astrophysical populations.

A conceptual model for site-level ecology of the giant gartersnake (Thamnophis gigas) in the Sacramento Valley, California

USGS Publications Warehouse

Halstead, Brian J.; Wylie, Glenn D.; Casazza, Michael L.; Hansen, Eric C.; Scherer, Rick D.; Patterson, Laura C.

2015-08-14

Bayesian networks further provide a clear visual display of the model that facilitates understanding among various stakeholders (Marcot and others, 2001; Uusitalo , 2007). Empirical data and expert judgment can be combined, as continuous or categorical variables, to update knowledge about the system (Marcot and others, 2001; Uusitalo , 2007). Importantly, Bayesian network models allow inference from causes to consequences, but also from consequences to causes, so that data can inform the states of nodes (values of different random variables) in either direction (Marcot and others, 2001; Uusitalo , 2007). Because they can incorporate both decision nodes that represent management actions and utility nodes that quantify the costs and benefits of outcomes, Bayesian networks are ideally suited to risk analysis and adaptive management (Nyberg and others, 2006; Howes and others, 2010). Thus, Bayesian network models are useful in situations where empirical data are not available, such as questions concerning the responses of giant gartersnakes to management.

A Computational Observer For Performing Contrast-Detail Analysis Of Ultrasound Images

NASA Astrophysics Data System (ADS)

Lopez, H.; Loew, M. H.

1988-06-01

Contrast-Detail (C/D) analysis allows the quantitative determination of an imaging system's ability to display a range of varying-size targets as a function of contrast. Using this technique, a contrast-detail plot is obtained which can, in theory, be used to compare image quality from one imaging system to another. The C/D plot, however, is usually obtained by using data from human observer readings. We have shown earlier(7) that the performance of human observers in the task of threshold detection of simulated lesions embedded in random ultrasound noise is highly inaccurate and non-reproducible for untrained observers. We present an objective, computational method for the determination of the C/D curve for ultrasound images. This method utilizes digital images of the C/D phantom developed at CDRH, and lesion-detection algorithms that simulate the Bayesian approach using the likelihood function for an ideal observer. We present the results of this method, and discuss the relationship to the human observer and to the comparability of image quality between systems.

Obtaining parsimonious hydraulic conductivity fields using head and transport observations: A Bayesian geostatistical parameter estimation approach

NASA Astrophysics Data System (ADS)

Fienen, M.; Hunt, R.; Krabbenhoft, D.; Clemo, T.

2009-08-01

Flow path delineation is a valuable tool for interpreting the subsurface hydrogeochemical environment. Different types of data, such as groundwater flow and transport, inform different aspects of hydrogeologic parameter values (hydraulic conductivity in this case) which, in turn, determine flow paths. This work combines flow and transport information to estimate a unified set of hydrogeologic parameters using the Bayesian geostatistical inverse approach. Parameter flexibility is allowed by using a highly parameterized approach with the level of complexity informed by the data. Despite the effort to adhere to the ideal of minimal a priori structure imposed on the problem, extreme contrasts in parameters can result in the need to censor correlation across hydrostratigraphic bounding surfaces. These partitions segregate parameters into facies associations. With an iterative approach in which partitions are based on inspection of initial estimates, flow path interpretation is progressively refined through the inclusion of more types of data. Head observations, stable oxygen isotopes (18O/16O ratios), and tritium are all used to progressively refine flow path delineation on an isthmus between two lakes in the Trout Lake watershed, northern Wisconsin, United States. Despite allowing significant parameter freedom by estimating many distributed parameter values, a smooth field is obtained.

Obtaining parsimonious hydraulic conductivity fields using head and transport observations: A Bayesian geostatistical parameter estimation approach

USGS Publications Warehouse

Fienen, M.; Hunt, R.; Krabbenhoft, D.; Clemo, T.

2009-01-01

Flow path delineation is a valuable tool for interpreting the subsurface hydrogeochemical environment. Different types of data, such as groundwater flow and transport, inform different aspects of hydrogeologic parameter values (hydraulic conductivity in this case) which, in turn, determine flow paths. This work combines flow and transport information to estimate a unified set of hydrogeologic parameters using the Bayesian geostatistical inverse approach. Parameter flexibility is allowed by using a highly parameterized approach with the level of complexity informed by the data. Despite the effort to adhere to the ideal of minimal a priori structure imposed on the problem, extreme contrasts in parameters can result in the need to censor correlation across hydrostratigraphic bounding surfaces. These partitions segregate parameters into facies associations. With an iterative approach in which partitions are based on inspection of initial estimates, flow path interpretation is progressively refined through the inclusion of more types of data. Head observations, stable oxygen isotopes (18O/16O ratios), and tritium are all used to progressively refine flow path delineation on an isthmus between two lakes in the Trout Lake watershed, northern Wisconsin, United States. Despite allowing significant parameter freedom by estimating many distributed parameter values, a smooth field is obtained.

Bayesian flood forecasting methods: A review

NASA Astrophysics Data System (ADS)

Han, Shasha; Coulibaly, Paulin

2017-08-01

Over the past few decades, floods have been seen as one of the most common and largely distributed natural disasters in the world. If floods could be accurately forecasted in advance, then their negative impacts could be greatly minimized. It is widely recognized that quantification and reduction of uncertainty associated with the hydrologic forecast is of great importance for flood estimation and rational decision making. Bayesian forecasting system (BFS) offers an ideal theoretic framework for uncertainty quantification that can be developed for probabilistic flood forecasting via any deterministic hydrologic model. It provides suitable theoretical structure, empirically validated models and reasonable analytic-numerical computation method, and can be developed into various Bayesian forecasting approaches. This paper presents a comprehensive review on Bayesian forecasting approaches applied in flood forecasting from 1999 till now. The review starts with an overview of fundamentals of BFS and recent advances in BFS, followed with BFS application in river stage forecasting and real-time flood forecasting, then move to a critical analysis by evaluating advantages and limitations of Bayesian forecasting methods and other predictive uncertainty assessment approaches in flood forecasting, and finally discusses the future research direction in Bayesian flood forecasting. Results show that the Bayesian flood forecasting approach is an effective and advanced way for flood estimation, it considers all sources of uncertainties and produces a predictive distribution of the river stage, river discharge or runoff, thus gives more accurate and reliable flood forecasts. Some emerging Bayesian forecasting methods (e.g. ensemble Bayesian forecasting system, Bayesian multi-model combination) were shown to overcome limitations of single model or fixed model weight and effectively reduce predictive uncertainty. In recent years, various Bayesian flood forecasting approaches have been developed and widely applied, but there is still room for improvements. Future research in the context of Bayesian flood forecasting should be on assimilation of various sources of newly available information and improvement of predictive performance assessment methods.

An assessment of Gallistel's (2012) rationalistic account of extinction phenomena.

PubMed

Miller, Ralph R

2012-05-01

Gallistel (2012) asserts that animals use rationalistic reasoning (i.e., information theory and Bayesian inference) to make decisions that underlie select extinction phenomena. Rational processes are presumed to lead to evolutionarily optimal behavior. Thus, Gallistel's model is a type of optimality theory. But optimality theory is only a theory, a theory about an ideal organism, and its predictions frequently deviate appreciably from observed behavior of animals in the laboratory and the real world. That is, behavior of animals is often far from optimal, as is evident in many behavioral phenomena. Hence, appeals to optimality theory to explain, rather than illuminate, actual behavior are misguided. Copyright © 2012 Elsevier B.V. All rights reserved.

BUMPER: the Bayesian User-friendly Model for Palaeo-Environmental Reconstruction

NASA Astrophysics Data System (ADS)

Holden, Phil; Birks, John; Brooks, Steve; Bush, Mark; Hwang, Grace; Matthews-Bird, Frazer; Valencia, Bryan; van Woesik, Robert

2017-04-01

We describe the Bayesian User-friendly Model for Palaeo-Environmental Reconstruction (BUMPER), a Bayesian transfer function for inferring past climate and other environmental variables from microfossil assemblages. The principal motivation for a Bayesian approach is that the palaeoenvironment is treated probabilistically, and can be updated as additional data become available. Bayesian approaches therefore provide a reconstruction-specific quantification of the uncertainty in the data and in the model parameters. BUMPER is fully self-calibrating, straightforward to apply, and computationally fast, requiring 2 seconds to build a 100-taxon model from a 100-site training-set on a standard personal computer. We apply the model's probabilistic framework to generate thousands of artificial training-sets under ideal assumptions. We then use these to demonstrate both the general applicability of the model and the sensitivity of reconstructions to the characteristics of the training-set, considering assemblage richness, taxon tolerances, and the number of training sites. We demonstrate general applicability to real data, considering three different organism types (chironomids, diatoms, pollen) and different reconstructed variables. In all of these applications an identically configured model is used, the only change being the input files that provide the training-set environment and taxon-count data.

Bayesian neural adjustment of inhibitory control predicts emergence of problem stimulant use.

PubMed

Harlé, Katia M; Stewart, Jennifer L; Zhang, Shunan; Tapert, Susan F; Yu, Angela J; Paulus, Martin P

2015-11-01

Bayesian ideal observer models quantify individuals' context- and experience-dependent beliefs and expectations about their environment, which provides a powerful approach (i) to link basic behavioural mechanisms to neural processing; and (ii) to generate clinical predictors for patient populations. Here, we focus on (ii) and determine whether individual differences in the neural representation of the need to stop in an inhibitory task can predict the development of problem use (i.e. abuse or dependence) in individuals experimenting with stimulants. One hundred and fifty-seven non-dependent occasional stimulant users, aged 18-24, completed a stop-signal task while undergoing functional magnetic resonance imaging. These individuals were prospectively followed for 3 years and evaluated for stimulant use and abuse/dependence symptoms. At follow-up, 38 occasional stimulant users met criteria for a stimulant use disorder (problem stimulant users), while 50 had discontinued use (desisted stimulant users). We found that those individuals who showed greater neural responses associated with Bayesian prediction errors, i.e. the difference between actual and expected need to stop on a given trial, in right medial prefrontal cortex/anterior cingulate cortex, caudate, anterior insula, and thalamus were more likely to exhibit problem use 3 years later. Importantly, these computationally based neural predictors outperformed clinical measures and non-model based neural variables in predicting clinical status. In conclusion, young adults who show exaggerated brain processing underlying whether to 'stop' or to 'go' are more likely to develop stimulant abuse. Thus, Bayesian cognitive models provide both a computational explanation and potential predictive biomarkers of belief processing deficits in individuals at risk for stimulant addiction. © The Author (2015). Published by Oxford University Press on behalf of the Guarantors of Brain. All rights reserved. For Permissions, please email: journals.permissions@oup.com.

Bayesian Modal Estimation of the Four-Parameter Item Response Model in Real, Realistic, and Idealized Data Sets.

PubMed

Waller, Niels G; Feuerstahler, Leah

2017-01-01

In this study, we explored item and person parameter recovery of the four-parameter model (4PM) in over 24,000 real, realistic, and idealized data sets. In the first analyses, we fit the 4PM and three alternative models to data from three Minnesota Multiphasic Personality Inventory-Adolescent form factor scales using Bayesian modal estimation (BME). Our results indicated that the 4PM fits these scales better than simpler item Response Theory (IRT) models. Next, using the parameter estimates from these real data analyses, we estimated 4PM item parameters in 6,000 realistic data sets to establish minimum sample size requirements for accurate item and person parameter recovery. Using a factorial design that crossed discrete levels of item parameters, sample size, and test length, we also fit the 4PM to an additional 18,000 idealized data sets to extend our parameter recovery findings. Our combined results demonstrated that 4PM item parameters and parameter functions (e.g., item response functions) can be accurately estimated using BME in moderate to large samples (N ⩾ 5, 000) and person parameters can be accurately estimated in smaller samples (N ⩾ 1, 000). In the supplemental files, we report annotated [Formula: see text] code that shows how to estimate 4PM item and person parameters in [Formula: see text] (Chalmers, 2012 ).

Bayesian approach to MSD-based analysis of particle motion in live cells.

PubMed

Monnier, Nilah; Guo, Syuan-Ming; Mori, Masashi; He, Jun; Lénárt, Péter; Bathe, Mark

2012-08-08

Quantitative tracking of particle motion using live-cell imaging is a powerful approach to understanding the mechanism of transport of biological molecules, organelles, and cells. However, inferring complex stochastic motion models from single-particle trajectories in an objective manner is nontrivial due to noise from sampling limitations and biological heterogeneity. Here, we present a systematic Bayesian approach to multiple-hypothesis testing of a general set of competing motion models based on particle mean-square displacements that automatically classifies particle motion, properly accounting for sampling limitations and correlated noise while appropriately penalizing model complexity according to Occam's Razor to avoid over-fitting. We test the procedure rigorously using simulated trajectories for which the underlying physical process is known, demonstrating that it chooses the simplest physical model that explains the observed data. Further, we show that computed model probabilities provide a reliability test for the downstream biological interpretation of associated parameter values. We subsequently illustrate the broad utility of the approach by applying it to disparate biological systems including experimental particle trajectories from chromosomes, kinetochores, and membrane receptors undergoing a variety of complex motions. This automated and objective Bayesian framework easily scales to large numbers of particle trajectories, making it ideal for classifying the complex motion of large numbers of single molecules and cells from high-throughput screens, as well as single-cell-, tissue-, and organism-level studies. Copyright © 2012 Biophysical Society. Published by Elsevier Inc. All rights reserved.

Improving the Calibration of the SN Ia Anchor Datasets with a Bayesian Hierarchal Model

NASA Astrophysics Data System (ADS)

Currie, Miles; Rubin, David

2018-01-01

Inter-survey calibration remains one of the largest systematic uncertainties in SN Ia cosmology today. Ideally, each survey would measure their system throughputs and observe well characterized spectrophotometric standard stars, but many important surveys have not done so. For these surveys, we calibrate using tertiary survey stars tied to SDSS and Pan-STARRS. We improve on previous efforts by taking the spatially variable response of each telescope/camera into account, and using improved color transformations in the surveys’ natural instrumental photometric system. We use a global hierarchical model of the data, automatically providing a covariance matrix of magnitude offsets and bandpass shifts which reduces the systematic uncertainty in inter-survey calibration, thereby providing better cosmological constraints.

Enhancing Flood Prediction Reliability Using Bayesian Model Averaging

NASA Astrophysics Data System (ADS)

Liu, Z.; Merwade, V.

2017-12-01

Uncertainty analysis is an indispensable part of modeling the hydrology and hydrodynamics of non-idealized environmental systems. Compared to reliance on prediction from one model simulation, using on ensemble of predictions that consider uncertainty from different sources is more reliable. In this study, Bayesian model averaging (BMA) is applied to Black River watershed in Arkansas and Missouri by combining multi-model simulations to get reliable deterministic water stage and probabilistic inundation extent predictions. The simulation ensemble is generated from 81 LISFLOOD-FP subgrid model configurations that include uncertainty from channel shape, channel width, channel roughness and discharge. Model simulation outputs are trained with observed water stage data during one flood event, and BMA prediction ability is validated for another flood event. Results from this study indicate that BMA does not always outperform all members in the ensemble, but it provides relatively robust deterministic flood stage predictions across the basin. Station based BMA (BMA_S) water stage prediction has better performance than global based BMA (BMA_G) prediction which is superior to the ensemble mean prediction. Additionally, high-frequency flood inundation extent (probability greater than 60%) in BMA_G probabilistic map is more accurate than the probabilistic flood inundation extent based on equal weights.

Human Visual Search Does Not Maximize the Post-Saccadic Probability of Identifying Targets

PubMed Central

Morvan, Camille; Maloney, Laurence T.

2012-01-01

Researchers have conjectured that eye movements during visual search are selected to minimize the number of saccades. The optimal Bayesian eye movement strategy minimizing saccades does not simply direct the eye to whichever location is judged most likely to contain the target but makes use of the entire retina as an information gathering device during each fixation. Here we show that human observers do not minimize the expected number of saccades in planning saccades in a simple visual search task composed of three tokens. In this task, the optimal eye movement strategy varied, depending on the spacing between tokens (in the first experiment) or the size of tokens (in the second experiment), and changed abruptly once the separation or size surpassed a critical value. None of our observers changed strategy as a function of separation or size. Human performance fell far short of ideal, both qualitatively and quantitatively. PMID:22319428

Template optimization and transfer in perceptual learning.

PubMed

Kurki, Ilmari; Hyvärinen, Aapo; Saarinen, Jussi

2016-08-01

We studied how learning changes the processing of a low-level Gabor stimulus, using a classification-image method (psychophysical reverse correlation) and a task where observers discriminated between slight differences in the phase (relative alignment) of a target Gabor in visual noise. The method estimates the internal "template" that describes how the visual system weights the input information for decisions. One popular idea has been that learning makes the template more like an ideal Bayesian weighting; however, the evidence has been indirect. We used a new regression technique to directly estimate the template weight change and to test whether the direction of reweighting is significantly different from an optimal learning strategy. The subjects trained the task for six daily sessions, and we tested the transfer of training to a target in an orthogonal orientation. Strong learning and partial transfer were observed. We tested whether task precision (difficulty) had an effect on template change and transfer: Observers trained in either a high-precision (small, 60° phase difference) or a low-precision task (180°). Task precision did not have an effect on the amount of template change or transfer, suggesting that task precision per se does not determine whether learning generalizes. Classification images show that training made observers use more task-relevant features and unlearn some irrelevant features. The transfer templates resembled partially optimized versions of templates in training sessions. The template change direction resembles ideal learning significantly but not completely. The amount of template change was highly correlated with the amount of learning.

The Scientific Method, Diagnostic Bayes, and How to Detect Epistemic Errors

NASA Astrophysics Data System (ADS)

Vrugt, J. A.

2015-12-01

In the past decades, Bayesian methods have found widespread application and use in environmental systems modeling. Bayes theorem states that the posterior probability, P(H|D) of a hypothesis, H is proportional to the product of the prior probability, P(H) of this hypothesis and the likelihood, L(H|hat{D}) of the same hypothesis given the new/incoming observations, \\hat {D}. In science and engineering, H often constitutes some numerical simulation model, D = F(x,.) which summarizes using algebraic, empirical, and differential equations, state variables and fluxes, all our theoretical and/or practical knowledge of the system of interest, and x are the d unknown parameters which are subject to inference using some data, \\hat {D} of the observed system response. The Bayesian approach is intimately related to the scientific method and uses an iterative cycle of hypothesis formulation (model), experimentation and data collection, and theory/hypothesis refinement to elucidate the rules that govern the natural world. Unfortunately, model refinement has proven to be very difficult in large part because of the poor diagnostic power of residual based likelihood functions tep{gupta2008}. This has inspired te{vrugt2013} to advocate the use of 'likelihood-free' inference using approximate Bayesian computation (ABC). This approach uses one or more summary statistics, S(\\hat {D}) of the original data, \\hat {D} designed ideally to be sensitive only to one particular process in the model. Any mismatch between the observed and simulated summary metrics is then easily linked to a specific model component. A recurrent issue with the application of ABC is self-sufficiency of the summary statistics. In theory, S(.) should contain as much information as the original data itself, yet complex systems rarely admit sufficient statistics. In this article, we propose to combine the ideas of ABC and regular Bayesian inference to guarantee that no information is lost in diagnostic model evaluation. This hybrid approach, coined diagnostic Bayes, uses the summary metrics as prior distribution and original data in the likelihood function, or P(x|\\hat {D}) ∝ P(x|S(\\hat {D})) L(x|\\hat {D}). A case study illustrates the ability of the proposed methodology to diagnose epistemic errors and provide guidance on model refinement.

Bayesian data analysis in observational comparative effectiveness research: rationale and examples.

PubMed

Olson, William H; Crivera, Concetta; Ma, Yi-Wen; Panish, Jessica; Mao, Lian; Lynch, Scott M

2013-11-01

Many comparative effectiveness research and patient-centered outcomes research studies will need to be observational for one or both of two reasons: first, randomized trials are expensive and time-consuming; and second, only observational studies can answer some research questions. It is generally recognized that there is a need to increase the scientific validity and efficiency of observational studies. Bayesian methods for the design and analysis of observational studies are scientifically valid and offer many advantages over frequentist methods, including, importantly, the ability to conduct comparative effectiveness research/patient-centered outcomes research more efficiently. Bayesian data analysis is being introduced into outcomes studies that we are conducting. Our purpose here is to describe our view of some of the advantages of Bayesian methods for observational studies and to illustrate both realized and potential advantages by describing studies we are conducting in which various Bayesian methods have been or could be implemented.

Uncertainty aggregation and reduction in structure-material performance prediction

NASA Astrophysics Data System (ADS)

Hu, Zhen; Mahadevan, Sankaran; Ao, Dan

2018-02-01

An uncertainty aggregation and reduction framework is presented for structure-material performance prediction. Different types of uncertainty sources, structural analysis model, and material performance prediction model are connected through a Bayesian network for systematic uncertainty aggregation analysis. To reduce the uncertainty in the computational structure-material performance prediction model, Bayesian updating using experimental observation data is investigated based on the Bayesian network. It is observed that the Bayesian updating results will have large error if the model cannot accurately represent the actual physics, and that this error will be propagated to the predicted performance distribution. To address this issue, this paper proposes a novel uncertainty reduction method by integrating Bayesian calibration with model validation adaptively. The observation domain of the quantity of interest is first discretized into multiple segments. An adaptive algorithm is then developed to perform model validation and Bayesian updating over these observation segments sequentially. Only information from observation segments where the model prediction is highly reliable is used for Bayesian updating; this is found to increase the effectiveness and efficiency of uncertainty reduction. A composite rotorcraft hub component fatigue life prediction model, which combines a finite element structural analysis model and a material damage model, is used to demonstrate the proposed method.

Convergence among cave catfishes: long-branch attraction and a Bayesian relative rates test.

PubMed

Wilcox, T P; García de León, F J; Hendrickson, D A; Hillis, D M

2004-06-01

Convergence has long been of interest to evolutionary biologists. Cave organisms appear to be ideal candidates for studying convergence in morphological, physiological, and developmental traits. Here we report apparent convergence in two cave-catfishes that were described on morphological grounds as congeners: Prietella phreatophila and Prietella lundbergi. We collected mitochondrial DNA sequence data from 10 species of catfishes, representing five of the seven genera in Ictaluridae, as well as seven species from a broad range of siluriform outgroups. Analysis of the sequence data under parsimony supports a monophyletic Prietella. However, both maximum-likelihood and Bayesian analyses support polyphyly of the genus, with P. lundbergi sister to Ictalurus and P. phreatophila sister to Ameiurus. The topological difference between parsimony and the other methods appears to result from long-branch attraction between the Prietella species. Similarly, the sequence data do not support several other relationships within Ictaluridae supported by morphology. We develop a new Bayesian method for examining variation in molecular rates of evolution across a phylogeny.

Reliable evaluation of the quantal determinants of synaptic efficacy using Bayesian analysis

PubMed Central

Beato, M.

2013-01-01

Communication between neurones in the central nervous system depends on synaptic transmission. The efficacy of synapses is determined by pre- and postsynaptic factors that can be characterized using quantal parameters such as the probability of neurotransmitter release, number of release sites, and quantal size. Existing methods of estimating the quantal parameters based on multiple probability fluctuation analysis (MPFA) are limited by their requirement for long recordings to acquire substantial data sets. We therefore devised an algorithm, termed Bayesian Quantal Analysis (BQA), that can yield accurate estimates of the quantal parameters from data sets of as small a size as 60 observations for each of only 2 conditions of release probability. Computer simulations are used to compare its performance in accuracy with that of MPFA, while varying the number of observations and the simulated range in release probability. We challenge BQA with realistic complexities characteristic of complex synapses, such as increases in the intra- or intersite variances, and heterogeneity in release probabilities. Finally, we validate the method using experimental data obtained from electrophysiological recordings to show that the effect of an antagonist on postsynaptic receptors is correctly characterized by BQA by a specific reduction in the estimates of quantal size. Since BQA routinely yields reliable estimates of the quantal parameters from small data sets, it is ideally suited to identify the locus of synaptic plasticity for experiments in which repeated manipulations of the recording environment are unfeasible. PMID:23076101

BATSE gamma-ray burst line search. 2: Bayesian consistency methodology

NASA Technical Reports Server (NTRS)

Band, D. L.; Ford, L. A.; Matteson, J. L.; Briggs, M.; Paciesas, W.; Pendleton, G.; Preece, R.; Palmer, D.; Teegarden, B.; Schaefer, B.

1994-01-01

We describe a Bayesian methodology to evaluate the consistency between the reported Ginga and Burst and Transient Source Experiment (BATSE) detections of absorption features in gamma-ray burst spectra. Currently no features have been detected by BATSE, but this methodology will still be applicable if and when such features are discovered. The Bayesian methodology permits the comparison of hypotheses regarding the two detectors' observations and makes explicit the subjective aspects of our analysis (e.g., the quantification of our confidence in detector performance). We also present non-Bayesian consistency statistics. Based on preliminary calculations of line detectability, we find that both the Bayesian and non-Bayesian techniques show that the BATSE and Ginga observations are consistent given our understanding of these detectors.

Precisely and Accurately Inferring Single-Molecule Rate Constants

PubMed Central

Kinz-Thompson, Colin D.; Bailey, Nevette A.; Gonzalez, Ruben L.

2017-01-01

The kinetics of biomolecular systems can be quantified by calculating the stochastic rate constants that govern the biomolecular state versus time trajectories (i.e., state trajectories) of individual biomolecules. To do so, the experimental signal versus time trajectories (i.e., signal trajectories) obtained from observing individual biomolecules are often idealized to generate state trajectories by methods such as thresholding or hidden Markov modeling. Here, we discuss approaches for idealizing signal trajectories and calculating stochastic rate constants from the resulting state trajectories. Importantly, we provide an analysis of how the finite length of signal trajectories restrict the precision of these approaches, and demonstrate how Bayesian inference-based versions of these approaches allow rigorous determination of this precision. Similarly, we provide an analysis of how the finite lengths and limited time resolutions of signal trajectories restrict the accuracy of these approaches, and describe methods that, by accounting for the effects of the finite length and limited time resolution of signal trajectories, substantially improve this accuracy. Collectively, therefore, the methods we consider here enable a rigorous assessment of the precision, and a significant enhancement of the accuracy, with which stochastic rate constants can be calculated from single-molecule signal trajectories. PMID:27793280

Value of evidence from syndromic surveillance with cumulative evidence from multiple data streams with delayed reporting.

PubMed

Struchen, R; Vial, F; Andersson, M G

2017-04-26

Delayed reporting of health data may hamper the early detection of infectious diseases in surveillance systems. Furthermore, combining multiple data streams, e.g. aiming at improving a system's sensitivity, can be challenging. In this study, we used a Bayesian framework where the result is presented as the value of evidence, i.e. the likelihood ratio for the evidence under outbreak versus baseline conditions. Based on a historical data set of routinely collected cattle mortality events, we evaluated outbreak detection performance (sensitivity, time to detection, in-control run length) under the Bayesian approach among three scenarios: presence of delayed data reporting, but not accounting for it; presence of delayed data reporting accounted for; and absence of delayed data reporting (i.e. an ideal system). Performance on larger and smaller outbreaks was compared with a classical approach, considering syndromes separately or combined. We found that the Bayesian approach performed better than the classical approach, especially for the smaller outbreaks. Furthermore, the Bayesian approach performed similarly well in the scenario where delayed reporting was accounted for to the scenario where it was absent. We argue that the value of evidence framework may be suitable for surveillance systems with multiple syndromes and delayed reporting of data.

Bayesian ensemble refinement by replica simulations and reweighting.

PubMed

Hummer, Gerhard; Köfinger, Jürgen

2015-12-28

We describe different Bayesian ensemble refinement methods, examine their interrelation, and discuss their practical application. With ensemble refinement, the properties of dynamic and partially disordered (bio)molecular structures can be characterized by integrating a wide range of experimental data, including measurements of ensemble-averaged observables. We start from a Bayesian formulation in which the posterior is a functional that ranks different configuration space distributions. By maximizing this posterior, we derive an optimal Bayesian ensemble distribution. For discrete configurations, this optimal distribution is identical to that obtained by the maximum entropy "ensemble refinement of SAXS" (EROS) formulation. Bayesian replica ensemble refinement enhances the sampling of relevant configurations by imposing restraints on averages of observables in coupled replica molecular dynamics simulations. We show that the strength of the restraints should scale linearly with the number of replicas to ensure convergence to the optimal Bayesian result in the limit of infinitely many replicas. In the "Bayesian inference of ensembles" method, we combine the replica and EROS approaches to accelerate the convergence. An adaptive algorithm can be used to sample directly from the optimal ensemble, without replicas. We discuss the incorporation of single-molecule measurements and dynamic observables such as relaxation parameters. The theoretical analysis of different Bayesian ensemble refinement approaches provides a basis for practical applications and a starting point for further investigations.

Bayesian ensemble refinement by replica simulations and reweighting

NASA Astrophysics Data System (ADS)

Hummer, Gerhard; Köfinger, Jürgen

2015-12-01

We describe different Bayesian ensemble refinement methods, examine their interrelation, and discuss their practical application. With ensemble refinement, the properties of dynamic and partially disordered (bio)molecular structures can be characterized by integrating a wide range of experimental data, including measurements of ensemble-averaged observables. We start from a Bayesian formulation in which the posterior is a functional that ranks different configuration space distributions. By maximizing this posterior, we derive an optimal Bayesian ensemble distribution. For discrete configurations, this optimal distribution is identical to that obtained by the maximum entropy "ensemble refinement of SAXS" (EROS) formulation. Bayesian replica ensemble refinement enhances the sampling of relevant configurations by imposing restraints on averages of observables in coupled replica molecular dynamics simulations. We show that the strength of the restraints should scale linearly with the number of replicas to ensure convergence to the optimal Bayesian result in the limit of infinitely many replicas. In the "Bayesian inference of ensembles" method, we combine the replica and EROS approaches to accelerate the convergence. An adaptive algorithm can be used to sample directly from the optimal ensemble, without replicas. We discuss the incorporation of single-molecule measurements and dynamic observables such as relaxation parameters. The theoretical analysis of different Bayesian ensemble refinement approaches provides a basis for practical applications and a starting point for further investigations.

Efficient Bayesian hierarchical functional data analysis with basis function approximations using Gaussian-Wishart processes.

PubMed

Yang, Jingjing; Cox, Dennis D; Lee, Jong Soo; Ren, Peng; Choi, Taeryon

2017-12-01

Functional data are defined as realizations of random functions (mostly smooth functions) varying over a continuum, which are usually collected on discretized grids with measurement errors. In order to accurately smooth noisy functional observations and deal with the issue of high-dimensional observation grids, we propose a novel Bayesian method based on the Bayesian hierarchical model with a Gaussian-Wishart process prior and basis function representations. We first derive an induced model for the basis-function coefficients of the functional data, and then use this model to conduct posterior inference through Markov chain Monte Carlo methods. Compared to the standard Bayesian inference that suffers serious computational burden and instability in analyzing high-dimensional functional data, our method greatly improves the computational scalability and stability, while inheriting the advantage of simultaneously smoothing raw observations and estimating the mean-covariance functions in a nonparametric way. In addition, our method can naturally handle functional data observed on random or uncommon grids. Simulation and real studies demonstrate that our method produces similar results to those obtainable by the standard Bayesian inference with low-dimensional common grids, while efficiently smoothing and estimating functional data with random and high-dimensional observation grids when the standard Bayesian inference fails. In conclusion, our method can efficiently smooth and estimate high-dimensional functional data, providing one way to resolve the curse of dimensionality for Bayesian functional data analysis with Gaussian-Wishart processes. © 2017, The International Biometric Society.

Human observers have optimal introspective access to perceptual processes even for visually masked stimuli

PubMed Central

Peters, Megan A K; Lau, Hakwan

2015-01-01

Many believe that humans can ‘perceive unconsciously’ – that for weak stimuli, briefly presented and masked, above-chance discrimination is possible without awareness. Interestingly, an online survey reveals that most experts in the field recognize the lack of convincing evidence for this phenomenon, and yet they persist in this belief. Using a recently developed bias-free experimental procedure for measuring subjective introspection (confidence), we found no evidence for unconscious perception; participants’ behavior matched that of a Bayesian ideal observer, even though the stimuli were visually masked. This surprising finding suggests that the thresholds for subjective awareness and objective discrimination are effectively the same: if objective task performance is above chance, there is likely conscious experience. These findings shed new light on decades-old methodological issues regarding what it takes to consider a neurobiological or behavioral effect to be 'unconscious,' and provide a platform for rigorously investigating unconscious perception in future studies. DOI: http://dx.doi.org/10.7554/eLife.09651.001 PMID:26433023

Accounting for uncertainty in the historical response rate of the standard treatment in single-arm two-stage designs based on Bayesian power functions.

PubMed

Matano, Francesca; Sambucini, Valeria

2016-11-01

In phase II single-arm studies, the response rate of the experimental treatment is typically compared with a fixed target value that should ideally represent the true response rate for the standard of care therapy. Generally, this target value is estimated through previous data, but the inherent variability in the historical response rate is not taken into account. In this paper, we present a Bayesian procedure to construct single-arm two-stage designs that allows to incorporate uncertainty in the response rate of the standard treatment. In both stages, the sample size determination criterion is based on the concepts of conditional and predictive Bayesian power functions. Different kinds of prior distributions, which play different roles in the designs, are introduced, and some guidelines for their elicitation are described. Finally, some numerical results about the performance of the designs are provided and a real data example is illustrated. Copyright © 2016 John Wiley & Sons, Ltd. Copyright © 2016 John Wiley & Sons, Ltd.

Informative Bayesian Type A uncertainty evaluation, especially applicable to a small number of observations

NASA Astrophysics Data System (ADS)

Cox, M.; Shirono, K.

2017-10-01

A criticism levelled at the Guide to the Expression of Uncertainty in Measurement (GUM) is that it is based on a mixture of frequentist and Bayesian thinking. In particular, the GUM’s Type A (statistical) uncertainty evaluations are frequentist, whereas the Type B evaluations, using state-of-knowledge distributions, are Bayesian. In contrast, making the GUM fully Bayesian implies, among other things, that a conventional objective Bayesian approach to Type A uncertainty evaluation for a number n of observations leads to the impractical consequence that n must be at least equal to 4, thus presenting a difficulty for many metrologists. This paper presents a Bayesian analysis of Type A uncertainty evaluation that applies for all n ≥slant 2 , as in the frequentist analysis in the current GUM. The analysis is based on assuming that the observations are drawn from a normal distribution (as in the conventional objective Bayesian analysis), but uses an informative prior based on lower and upper bounds for the standard deviation of the sampling distribution for the quantity under consideration. The main outcome of the analysis is a closed-form mathematical expression for the factor by which the standard deviation of the mean observation should be multiplied to calculate the required standard uncertainty. Metrological examples are used to illustrate the approach, which is straightforward to apply using a formula or look-up table.

Spatio-temporal interpolation of precipitation during monsoon periods in Pakistan

NASA Astrophysics Data System (ADS)

Hussain, Ijaz; Spöck, Gunter; Pilz, Jürgen; Yu, Hwa-Lung

2010-08-01

Spatio-temporal estimation of precipitation over a region is essential to the modeling of hydrologic processes for water resources management. The changes of magnitude and space-time heterogeneity of rainfall observations make space-time estimation of precipitation a challenging task. In this paper we propose a Box-Cox transformed hierarchical Bayesian multivariate spatio-temporal interpolation method for the skewed response variable. The proposed method is applied to estimate space-time monthly precipitation in the monsoon periods during 1974-2000, and 27-year monthly average precipitation data are obtained from 51 stations in Pakistan. The results of transformed hierarchical Bayesian multivariate spatio-temporal interpolation are compared to those of non-transformed hierarchical Bayesian interpolation by using cross-validation. The software developed by [11] is used for Bayesian non-stationary multivariate space-time interpolation. It is observed that the transformed hierarchical Bayesian method provides more accuracy than the non-transformed hierarchical Bayesian method.

Quantifying Uncertainty in Near Surface Electromagnetic Imaging Using Bayesian Methods

NASA Astrophysics Data System (ADS)

Blatter, D. B.; Ray, A.; Key, K.

2017-12-01

Geoscientists commonly use electromagnetic methods to image the Earth's near surface. Field measurements of EM fields are made (often with the aid an artificial EM source) and then used to infer near surface electrical conductivity via a process known as inversion. In geophysics, the standard inversion tool kit is robust and can provide an estimate of the Earth's near surface conductivity that is both geologically reasonable and compatible with the measured field data. However, standard inverse methods struggle to provide a sense of the uncertainty in the estimate they provide. This is because the task of finding an Earth model that explains the data to within measurement error is non-unique - that is, there are many, many such models; but the standard methods provide only one "answer." An alternative method, known as Bayesian inversion, seeks to explore the full range of Earth model parameters that can adequately explain the measured data, rather than attempting to find a single, "ideal" model. Bayesian inverse methods can therefore provide a quantitative assessment of the uncertainty inherent in trying to infer near surface conductivity from noisy, measured field data. This study applies a Bayesian inverse method (called trans-dimensional Markov chain Monte Carlo) to transient airborne EM data previously collected over Taylor Valley - one of the McMurdo Dry Valleys in Antarctica. Our results confirm the reasonableness of previous estimates (made using standard methods) of near surface conductivity beneath Taylor Valley. In addition, we demonstrate quantitatively the uncertainty associated with those estimates. We demonstrate that Bayesian inverse methods can provide quantitative uncertainty to estimates of near surface conductivity.

A Bayesian observer replicates convexity context effects in figure-ground perception.

PubMed

Goldreich, Daniel; Peterson, Mary A

2012-01-01

Peterson and Salvagio (2008) demonstrated convexity context effects in figure-ground perception. Subjects shown displays consisting of unfamiliar alternating convex and concave regions identified the convex regions as foreground objects progressively more frequently as the number of regions increased; this occurred only when the concave regions were homogeneously colored. The origins of these effects have been unclear. Here, we present a two-free-parameter Bayesian observer that replicates convexity context effects. The Bayesian observer incorporates two plausible expectations regarding three-dimensional scenes: (1) objects tend to be convex rather than concave, and (2) backgrounds tend (more than foreground objects) to be homogeneously colored. The Bayesian observer estimates the probability that a depicted scene is three-dimensional, and that the convex regions are figures. It responds stochastically by sampling from its posterior distributions. Like human observers, the Bayesian observer shows convexity context effects only for images with homogeneously colored concave regions. With optimal parameter settings, it performs similarly to the average human subject on the four display types tested. We propose that object convexity and background color homogeneity are environmental regularities exploited by human visual perception; vision achieves figure-ground perception by interpreting ambiguous images in light of these and other expected regularities in natural scenes.

Rational integration of noisy evidence and prior semantic expectations in sentence interpretation.

PubMed

Gibson, Edward; Bergen, Leon; Piantadosi, Steven T

2013-05-14

Sentence processing theories typically assume that the input to our language processing mechanisms is an error-free sequence of words. However, this assumption is an oversimplification because noise is present in typical language use (for instance, due to a noisy environment, producer errors, or perceiver errors). A complete theory of human sentence comprehension therefore needs to explain how humans understand language given imperfect input. Indeed, like many cognitive systems, language processing mechanisms may even be "well designed"--in this case for the task of recovering intended meaning from noisy utterances. In particular, comprehension mechanisms may be sensitive to the types of information that an idealized statistical comprehender would be sensitive to. Here, we evaluate four predictions about such a rational (Bayesian) noisy-channel language comprehender in a sentence comprehension task: (i) semantic cues should pull sentence interpretation towards plausible meanings, especially if the wording of the more plausible meaning is close to the observed utterance in terms of the number of edits; (ii) this process should asymmetrically treat insertions and deletions due to the Bayesian "size principle"; such nonliteral interpretation of sentences should (iii) increase with the perceived noise rate of the communicative situation and (iv) decrease if semantically anomalous meanings are more likely to be communicated. These predictions are borne out, strongly suggesting that human language relies on rational statistical inference over a noisy channel.

A Bayesian Markov-chain-based heteroscedastic regression model for the analysis of 18O-labeled mass spectra.

PubMed

Zhu, Qi; Burzykowski, Tomasz

2011-03-01

To reduce the influence of the between-spectra variability on the results of peptide quantification, one can consider the (18)O-labeling approach. Ideally, with such labeling technique, a mass shift of 4 Da of the isotopic distributions of peptides from the labeled sample is induced, which allows one to distinguish the two samples and to quantify the relative abundance of the peptides. It is worth noting, however, that the presence of small quantities of (16)O and (17)O atoms during the labeling step can cause incomplete labeling. In practice, ignoring incomplete labeling may result in the biased estimation of the relative abundance of the peptide in the compared samples. A Markov model was developed to address this issue (Zhu, Valkenborg, Burzykowski. J. Proteome Res. 9, 2669-2677, 2010). The model assumed that the peak intensities were normally distributed with heteroscedasticity using a power-of-the-mean variance funtion. Such a dependence has been observed in practice. Alternatively, we formulate the model within the Bayesian framework. This opens the possibility to further extend the model by the inclusion of random effects that can be used to capture the biological/technical variability of the peptide abundance. The operational characteristics of the model were investigated by applications to real-life mass-spectrometry data sets and a simulation study. © American Society for Mass Spectrometry, 2011

Rational integration of noisy evidence and prior semantic expectations in sentence interpretation

PubMed Central

Gibson, Edward; Bergen, Leon; Piantadosi, Steven T.

2013-01-01

Sentence processing theories typically assume that the input to our language processing mechanisms is an error-free sequence of words. However, this assumption is an oversimplification because noise is present in typical language use (for instance, due to a noisy environment, producer errors, or perceiver errors). A complete theory of human sentence comprehension therefore needs to explain how humans understand language given imperfect input. Indeed, like many cognitive systems, language processing mechanisms may even be “well designed”–in this case for the task of recovering intended meaning from noisy utterances. In particular, comprehension mechanisms may be sensitive to the types of information that an idealized statistical comprehender would be sensitive to. Here, we evaluate four predictions about such a rational (Bayesian) noisy-channel language comprehender in a sentence comprehension task: (i) semantic cues should pull sentence interpretation towards plausible meanings, especially if the wording of the more plausible meaning is close to the observed utterance in terms of the number of edits; (ii) this process should asymmetrically treat insertions and deletions due to the Bayesian “size principle”; such nonliteral interpretation of sentences should (iii) increase with the perceived noise rate of the communicative situation and (iv) decrease if semantically anomalous meanings are more likely to be communicated. These predictions are borne out, strongly suggesting that human language relies on rational statistical inference over a noisy channel. PMID:23637344

Using Bayesian Networks for Candidate Generation in Consistency-based Diagnosis

NASA Technical Reports Server (NTRS)

Narasimhan, Sriram; Mengshoel, Ole

2008-01-01

Consistency-based diagnosis relies heavily on the assumption that discrepancies between model predictions and sensor observations can be detected accurately. When sources of uncertainty like sensor noise and model abstraction exist robust schemes have to be designed to make a binary decision on whether predictions are consistent with observations. This risks the occurrence of false alarms and missed alarms when an erroneous decision is made. Moreover when multiple sensors (with differing sensing properties) are available the degree of match between predictions and observations can be used to guide the search for fault candidates. In this paper we propose a novel approach to handle this problem using Bayesian networks. In the consistency- based diagnosis formulation, automatically generated Bayesian networks are used to encode a probabilistic measure of fit between predictions and observations. A Bayesian network inference algorithm is used to compute most probable fault candidates.

An overview of quantitative approaches in Gestalt perception.

PubMed

Jäkel, Frank; Singh, Manish; Wichmann, Felix A; Herzog, Michael H

2016-09-01

Gestalt psychology is often criticized as lacking quantitative measurements and precise mathematical models. While this is true of the early Gestalt school, today there are many quantitative approaches in Gestalt perception and the special issue of Vision Research "Quantitative Approaches in Gestalt Perception" showcases the current state-of-the-art. In this article we give an overview of these current approaches. For example, ideal observer models are one of the standard quantitative tools in vision research and there is a clear trend to try and apply this tool to Gestalt perception and thereby integrate Gestalt perception into mainstream vision research. More generally, Bayesian models, long popular in other areas of vision research, are increasingly being employed to model perceptual grouping as well. Thus, although experimental and theoretical approaches to Gestalt perception remain quite diverse, we are hopeful that these quantitative trends will pave the way for a unified theory. Copyright © 2016 Elsevier Ltd. All rights reserved.

Order priors for Bayesian network discovery with an application to malware phylogeny

DOE PAGES

Oyen, Diane; Anderson, Blake; Sentz, Kari; ...

2017-09-15

Here, Bayesian networks have been used extensively to model and discover dependency relationships among sets of random variables. We learn Bayesian network structure with a combination of human knowledge about the partial ordering of variables and statistical inference of conditional dependencies from observed data. Our approach leverages complementary information from human knowledge and inference from observed data to produce networks that reflect human beliefs about the system as well as to fit the observed data. Applying prior beliefs about partial orderings of variables is an approach distinctly different from existing methods that incorporate prior beliefs about direct dependencies (or edges)more » in a Bayesian network. We provide an efficient implementation of the partial-order prior in a Bayesian structure discovery learning algorithm, as well as an edge prior, showing that both priors meet the local modularity requirement necessary for an efficient Bayesian discovery algorithm. In benchmark studies, the partial-order prior improves the accuracy of Bayesian network structure learning as well as the edge prior, even though order priors are more general. Our primary motivation is in characterizing the evolution of families of malware to aid cyber security analysts. For the problem of malware phylogeny discovery, we find that our algorithm, compared to existing malware phylogeny algorithms, more accurately discovers true dependencies that are missed by other algorithms.« less

Order priors for Bayesian network discovery with an application to malware phylogeny

DOE Office of Scientific and Technical Information (OSTI.GOV)

Oyen, Diane; Anderson, Blake; Sentz, Kari

Here, Bayesian networks have been used extensively to model and discover dependency relationships among sets of random variables. We learn Bayesian network structure with a combination of human knowledge about the partial ordering of variables and statistical inference of conditional dependencies from observed data. Our approach leverages complementary information from human knowledge and inference from observed data to produce networks that reflect human beliefs about the system as well as to fit the observed data. Applying prior beliefs about partial orderings of variables is an approach distinctly different from existing methods that incorporate prior beliefs about direct dependencies (or edges)more » in a Bayesian network. We provide an efficient implementation of the partial-order prior in a Bayesian structure discovery learning algorithm, as well as an edge prior, showing that both priors meet the local modularity requirement necessary for an efficient Bayesian discovery algorithm. In benchmark studies, the partial-order prior improves the accuracy of Bayesian network structure learning as well as the edge prior, even though order priors are more general. Our primary motivation is in characterizing the evolution of families of malware to aid cyber security analysts. For the problem of malware phylogeny discovery, we find that our algorithm, compared to existing malware phylogeny algorithms, more accurately discovers true dependencies that are missed by other algorithms.« less

Bayesian estimates of the incidence of rare cancers in Europe.

PubMed

Botta, Laura; Capocaccia, Riccardo; Trama, Annalisa; Herrmann, Christian; Salmerón, Diego; De Angelis, Roberta; Mallone, Sandra; Bidoli, Ettore; Marcos-Gragera, Rafael; Dudek-Godeau, Dorota; Gatta, Gemma; Cleries, Ramon

2018-04-21

The RARECAREnet project has updated the estimates of the burden of the 198 rare cancers in each European country. Suspecting that scant data could affect the reliability of statistical analysis, we employed a Bayesian approach to estimate the incidence of these cancers. We analyzed about 2,000,000 rare cancers diagnosed in 2000-2007 provided by 83 population-based cancer registries from 27 European countries. We considered European incidence rates (IRs), calculated over all the data available in RARECAREnet, as a valid a priori to merge with country-specific observed data. Therefore we provided (1) Bayesian estimates of IRs and the yearly numbers of cases of rare cancers in each country; (2) the expected time (T) in years needed to observe one new case; and (3) practical criteria to decide when to use the Bayesian approach. Bayesian and classical estimates did not differ much; substantial differences (>10%) ranged from 77 rare cancers in Iceland to 14 in England. The smaller the population the larger the number of rare cancers needing a Bayesian approach. Bayesian estimates were useful for cancers with fewer than 150 observed cases in a country during the study period; this occurred mostly when the population of the country is small. For the first time the Bayesian estimates of IRs and the yearly expected numbers of cases for each rare cancer in each individual European country were calculated. Moreover, the indicator T is useful to convey incidence estimates for exceptionally rare cancers and in small countries; it far exceeds the professional lifespan of a medical doctor. Copyright © 2018 Elsevier Ltd. All rights reserved.

Geomagnetic field secular variation in Pacific Ocean: A Bayesian reference curve based on Holocene Hawaiian lava flows

NASA Astrophysics Data System (ADS)

Tema, E.; Herrero-Bervera, E.; Lanos, Ph.

2017-11-01

Hawaii is an ideal place for reconstructing the past variations of the Earth's magnetic field in the Pacific Ocean thanks to the almost continuous volcanic activity during the last 10 000 yrs. We present here an updated compilation of palaeomagnetic data from historic and radiocarbon dated Hawaiian lava flows available for the last ten millennia. A total of 278 directional and 66 intensity reference data have been used for the calculation of the first full geomagnetic field reference secular variation (SV) curves for central Pacific covering the last ten millennia. The obtained SV curves are calculated following recent advances on curve building based on the Bayesian statistics and are well constrained for the last five millennia while for older periods their error envelopes are wide due to the scarce number of reference data. The new Bayesian SV curves show three clear intensity maxima during the last 3000 yrs that are accompanied by sharp directional changes. Such short-term variations of the geomagnetic field could be interpreted as archaeomagnetic jerks and could be an interesting feature of the geomagnetic field variation in the Pacific Ocean that should be further explored by new data.

Covariate Balance in Bayesian Propensity Score Approaches for Observational Studies

ERIC Educational Resources Information Center

Chen, Jianshen; Kaplan, David

2015-01-01

Bayesian alternatives to frequentist propensity score approaches have recently been proposed. However, few studies have investigated their covariate balancing properties. This article compares a recently developed two-step Bayesian propensity score approach to the frequentist approach with respect to covariate balance. The effects of different…

Dynamic Bayesian Network Modeling of Game Based Diagnostic Assessments. CRESST Report 837

ERIC Educational Resources Information Center

Levy, Roy

2014-01-01

Digital games offer an appealing environment for assessing student proficiencies, including skills and misconceptions in a diagnostic setting. This paper proposes a dynamic Bayesian network modeling approach for observations of student performance from an educational video game. A Bayesian approach to model construction, calibration, and use in…

Dynamic Bayesian wavelet transform: New methodology for extraction of repetitive transients

NASA Astrophysics Data System (ADS)

Wang, Dong; Tsui, Kwok-Leung

2017-05-01

Thanks to some recent research works, dynamic Bayesian wavelet transform as new methodology for extraction of repetitive transients is proposed in this short communication to reveal fault signatures hidden in rotating machine. The main idea of the dynamic Bayesian wavelet transform is to iteratively estimate posterior parameters of wavelet transform via artificial observations and dynamic Bayesian inference. First, a prior wavelet parameter distribution can be established by one of many fast detection algorithms, such as the fast kurtogram, the improved kurtogram, the enhanced kurtogram, the sparsogram, the infogram, continuous wavelet transform, discrete wavelet transform, wavelet packets, multiwavelets, empirical wavelet transform, empirical mode decomposition, local mean decomposition, etc.. Second, artificial observations can be constructed based on one of many metrics, such as kurtosis, the sparsity measurement, entropy, approximate entropy, the smoothness index, a synthesized criterion, etc., which are able to quantify repetitive transients. Finally, given artificial observations, the prior wavelet parameter distribution can be posteriorly updated over iterations by using dynamic Bayesian inference. More importantly, the proposed new methodology can be extended to establish the optimal parameters required by many other signal processing methods for extraction of repetitive transients.

Bayesian Retrieval of Complete Posterior PDFs of Oceanic Rain Rate From Microwave Observations

NASA Technical Reports Server (NTRS)

Chiu, J. Christine; Petty, Grant W.

2005-01-01

This paper presents a new Bayesian algorithm for retrieving surface rain rate from Tropical Rainfall Measurements Mission (TRMM) Microwave Imager (TMI) over the ocean, along with validations against estimates from the TRMM Precipitation Radar (PR). The Bayesian approach offers a rigorous basis for optimally combining multichannel observations with prior knowledge. While other rain rate algorithms have been published that are based at least partly on Bayesian reasoning, this is believed to be the first self-contained algorithm that fully exploits Bayes Theorem to yield not just a single rain rate, but rather a continuous posterior probability distribution of rain rate. To advance our understanding of theoretical benefits of the Bayesian approach, we have conducted sensitivity analyses based on two synthetic datasets for which the true conditional and prior distribution are known. Results demonstrate that even when the prior and conditional likelihoods are specified perfectly, biased retrievals may occur at high rain rates. This bias is not the result of a defect of the Bayesian formalism but rather represents the expected outcome when the physical constraint imposed by the radiometric observations is weak, due to saturation effects. It is also suggested that the choice of the estimators and the prior information are both crucial to the retrieval. In addition, the performance of our Bayesian algorithm is found to be comparable to that of other benchmark algorithms in real-world applications, while having the additional advantage of providing a complete continuous posterior probability distribution of surface rain rate.

Bayesian accounts of covert selective attention: A tutorial review.

PubMed

Vincent, Benjamin T

2015-05-01

Decision making and optimal observer models offer an important theoretical approach to the study of covert selective attention. While their probabilistic formulation allows quantitative comparison to human performance, the models can be complex and their insights are not always immediately apparent. Part 1 establishes the theoretical appeal of the Bayesian approach, and introduces the way in which probabilistic approaches can be applied to covert search paradigms. Part 2 presents novel formulations of Bayesian models of 4 important covert attention paradigms, illustrating optimal observer predictions over a range of experimental manipulations. Graphical model notation is used to present models in an accessible way and Supplementary Code is provided to help bridge the gap between model theory and practical implementation. Part 3 reviews a large body of empirical and modelling evidence showing that many experimental phenomena in the domain of covert selective attention are a set of by-products. These effects emerge as the result of observers conducting Bayesian inference with noisy sensory observations, prior expectations, and knowledge of the generative structure of the stimulus environment.

Flood quantile estimation at ungauged sites by Bayesian networks

NASA Astrophysics Data System (ADS)

Mediero, L.; Santillán, D.; Garrote, L.

2012-04-01

Estimating flood quantiles at a site for which no observed measurements are available is essential for water resources planning and management. Ungauged sites have no observations about the magnitude of floods, but some site and basin characteristics are known. The most common technique used is the multiple regression analysis, which relates physical and climatic basin characteristic to flood quantiles. Regression equations are fitted from flood frequency data and basin characteristics at gauged sites. Regression equations are a rigid technique that assumes linear relationships between variables and cannot take the measurement errors into account. In addition, the prediction intervals are estimated in a very simplistic way from the variance of the residuals in the estimated model. Bayesian networks are a probabilistic computational structure taken from the field of Artificial Intelligence, which have been widely and successfully applied to many scientific fields like medicine and informatics, but application to the field of hydrology is recent. Bayesian networks infer the joint probability distribution of several related variables from observations through nodes, which represent random variables, and links, which represent causal dependencies between them. A Bayesian network is more flexible than regression equations, as they capture non-linear relationships between variables. In addition, the probabilistic nature of Bayesian networks allows taking the different sources of estimation uncertainty into account, as they give a probability distribution as result. A homogeneous region in the Tagus Basin was selected as case study. A regression equation was fitted taking the basin area, the annual maximum 24-hour rainfall for a given recurrence interval and the mean height as explanatory variables. Flood quantiles at ungauged sites were estimated by Bayesian networks. Bayesian networks need to be learnt from a huge enough data set. As observational data are reduced, a stochastic generator of synthetic data was developed. Synthetic basin characteristics were randomised, keeping the statistical properties of observed physical and climatic variables in the homogeneous region. The synthetic flood quantiles were stochastically generated taking the regression equation as basis. The learnt Bayesian network was validated by the reliability diagram, the Brier Score and the ROC diagram, which are common measures used in the validation of probabilistic forecasts. Summarising, the flood quantile estimations through Bayesian networks supply information about the prediction uncertainty as a probability distribution function of discharges is given as result. Therefore, the Bayesian network model has application as a decision support for water resources and planning management.

Model-Based Individualized Treatment of Chemotherapeutics: Bayesian Population Modeling and Dose Optimization

PubMed Central

Jayachandran, Devaraj; Laínez-Aguirre, José; Rundell, Ann; Vik, Terry; Hannemann, Robert; Reklaitis, Gintaras; Ramkrishna, Doraiswami

2015-01-01

6-Mercaptopurine (6-MP) is one of the key drugs in the treatment of many pediatric cancers, auto immune diseases and inflammatory bowel disease. 6-MP is a prodrug, converted to an active metabolite 6-thioguanine nucleotide (6-TGN) through enzymatic reaction involving thiopurine methyltransferase (TPMT). Pharmacogenomic variation observed in the TPMT enzyme produces a significant variation in drug response among the patient population. Despite 6-MP’s widespread use and observed variation in treatment response, efforts at quantitative optimization of dose regimens for individual patients are limited. In addition, research efforts devoted on pharmacogenomics to predict clinical responses are proving far from ideal. In this work, we present a Bayesian population modeling approach to develop a pharmacological model for 6-MP metabolism in humans. In the face of scarcity of data in clinical settings, a global sensitivity analysis based model reduction approach is used to minimize the parameter space. For accurate estimation of sensitive parameters, robust optimal experimental design based on D-optimality criteria was exploited. With the patient-specific model, a model predictive control algorithm is used to optimize the dose scheduling with the objective of maintaining the 6-TGN concentration within its therapeutic window. More importantly, for the first time, we show how the incorporation of information from different levels of biological chain-of response (i.e. gene expression-enzyme phenotype-drug phenotype) plays a critical role in determining the uncertainty in predicting therapeutic target. The model and the control approach can be utilized in the clinical setting to individualize 6-MP dosing based on the patient’s ability to metabolize the drug instead of the traditional standard-dose-for-all approach. PMID:26226448

Perceptual learning through optimization of attentional weighting: human versus optimal Bayesian learner

NASA Technical Reports Server (NTRS)

Eckstein, Miguel P.; Abbey, Craig K.; Pham, Binh T.; Shimozaki, Steven S.

2004-01-01

Human performance in visual detection, discrimination, identification, and search tasks typically improves with practice. Psychophysical studies suggest that perceptual learning is mediated by an enhancement in the coding of the signal, and physiological studies suggest that it might be related to the plasticity in the weighting or selection of sensory units coding task relevant information (learning through attention optimization). We propose an experimental paradigm (optimal perceptual learning paradigm) to systematically study the dynamics of perceptual learning in humans by allowing comparisons to that of an optimal Bayesian algorithm and a number of suboptimal learning models. We measured improvement in human localization (eight-alternative forced-choice with feedback) performance of a target randomly sampled from four elongated Gaussian targets with different orientations and polarities and kept as a target for a block of four trials. The results suggest that the human perceptual learning can occur within a lapse of four trials (<1 min) but that human learning is slower and incomplete with respect to the optimal algorithm (23.3% reduction in human efficiency from the 1st-to-4th learning trials). The greatest improvement in human performance, occurring from the 1st-to-2nd learning trial, was also present in the optimal observer, and, thus reflects a property inherent to the visual task and not a property particular to the human perceptual learning mechanism. One notable source of human inefficiency is that, unlike the ideal observer, human learning relies more heavily on previous decisions than on the provided feedback, resulting in no human learning on trials following a previous incorrect localization decision. Finally, the proposed theory and paradigm provide a flexible framework for future studies to evaluate the optimality of human learning of other visual cues and/or sensory modalities.

Learning Bayesian Networks from Correlated Data

NASA Astrophysics Data System (ADS)

Bae, Harold; Monti, Stefano; Montano, Monty; Steinberg, Martin H.; Perls, Thomas T.; Sebastiani, Paola

2016-05-01

Bayesian networks are probabilistic models that represent complex distributions in a modular way and have become very popular in many fields. There are many methods to build Bayesian networks from a random sample of independent and identically distributed observations. However, many observational studies are designed using some form of clustered sampling that introduces correlations between observations within the same cluster and ignoring this correlation typically inflates the rate of false positive associations. We describe a novel parameterization of Bayesian networks that uses random effects to model the correlation within sample units and can be used for structure and parameter learning from correlated data without inflating the Type I error rate. We compare different learning metrics using simulations and illustrate the method in two real examples: an analysis of genetic and non-genetic factors associated with human longevity from a family-based study, and an example of risk factors for complications of sickle cell anemia from a longitudinal study with repeated measures.

Sparse Bayesian Inference and the Temperature Structure of the Solar Corona

DOE Office of Scientific and Technical Information (OSTI.GOV)

Warren, Harry P.; Byers, Jeff M.; Crump, Nicholas A.

Measuring the temperature structure of the solar atmosphere is critical to understanding how it is heated to high temperatures. Unfortunately, the temperature of the upper atmosphere cannot be observed directly, but must be inferred from spectrally resolved observations of individual emission lines that span a wide range of temperatures. Such observations are “inverted” to determine the distribution of plasma temperatures along the line of sight. This inversion is ill posed and, in the absence of regularization, tends to produce wildly oscillatory solutions. We introduce the application of sparse Bayesian inference to the problem of inferring the temperature structure of themore » solar corona. Within a Bayesian framework a preference for solutions that utilize a minimum number of basis functions can be encoded into the prior and many ad hoc assumptions can be avoided. We demonstrate the efficacy of the Bayesian approach by considering a test library of 40 assumed temperature distributions.« less

A hierarchical Bayesian approach to adaptive vision testing: A case study with the contrast sensitivity function.

PubMed

Gu, Hairong; Kim, Woojae; Hou, Fang; Lesmes, Luis Andres; Pitt, Mark A; Lu, Zhong-Lin; Myung, Jay I

2016-01-01

Measurement efficiency is of concern when a large number of observations are required to obtain reliable estimates for parametric models of vision. The standard entropy-based Bayesian adaptive testing procedures addressed the issue by selecting the most informative stimulus in sequential experimental trials. Noninformative, diffuse priors were commonly used in those tests. Hierarchical adaptive design optimization (HADO; Kim, Pitt, Lu, Steyvers, & Myung, 2014) further improves the efficiency of the standard Bayesian adaptive testing procedures by constructing an informative prior using data from observers who have already participated in the experiment. The present study represents an empirical validation of HADO in estimating the human contrast sensitivity function. The results show that HADO significantly improves the accuracy and precision of parameter estimates, and therefore requires many fewer observations to obtain reliable inference about contrast sensitivity, compared to the method of quick contrast sensitivity function (Lesmes, Lu, Baek, & Albright, 2010), which uses the standard Bayesian procedure. The improvement with HADO was maintained even when the prior was constructed from heterogeneous populations or a relatively small number of observers. These results of this case study support the conclusion that HADO can be used in Bayesian adaptive testing by replacing noninformative, diffuse priors with statistically justified informative priors without introducing unwanted bias.

A hierarchical Bayesian approach to adaptive vision testing: A case study with the contrast sensitivity function

PubMed Central

Gu, Hairong; Kim, Woojae; Hou, Fang; Lesmes, Luis Andres; Pitt, Mark A.; Lu, Zhong-Lin; Myung, Jay I.

2016-01-01

Measurement efficiency is of concern when a large number of observations are required to obtain reliable estimates for parametric models of vision. The standard entropy-based Bayesian adaptive testing procedures addressed the issue by selecting the most informative stimulus in sequential experimental trials. Noninformative, diffuse priors were commonly used in those tests. Hierarchical adaptive design optimization (HADO; Kim, Pitt, Lu, Steyvers, & Myung, 2014) further improves the efficiency of the standard Bayesian adaptive testing procedures by constructing an informative prior using data from observers who have already participated in the experiment. The present study represents an empirical validation of HADO in estimating the human contrast sensitivity function. The results show that HADO significantly improves the accuracy and precision of parameter estimates, and therefore requires many fewer observations to obtain reliable inference about contrast sensitivity, compared to the method of quick contrast sensitivity function (Lesmes, Lu, Baek, & Albright, 2010), which uses the standard Bayesian procedure. The improvement with HADO was maintained even when the prior was constructed from heterogeneous populations or a relatively small number of observers. These results of this case study support the conclusion that HADO can be used in Bayesian adaptive testing by replacing noninformative, diffuse priors with statistically justified informative priors without introducing unwanted bias. PMID:27105061

Robust cue integration: a Bayesian model and evidence from cue-conflict studies with stereoscopic and figure cues to slant.

PubMed

Knill, David C

2007-05-23

Most research on depth cue integration has focused on stimulus regimes in which stimuli contain the small cue conflicts that one might expect to normally arise from sensory noise. In these regimes, linear models for cue integration provide a good approximation to system performance. This article focuses on situations in which large cue conflicts can naturally occur in stimuli. We describe a Bayesian model for nonlinear cue integration that makes rational inferences about scenes across the entire range of possible cue conflicts. The model derives from the simple intuition that multiple properties of scenes or causal factors give rise to the image information associated with most cues. To make perceptual inferences about one property of a scene, an ideal observer must necessarily take into account the possible contribution of these other factors to the information provided by a cue. In the context of classical depth cues, large cue conflicts most commonly arise when one or another cue is generated by an object or scene that violates the strongest form of constraint that makes the cue informative. For example, when binocularly viewing a slanted trapezoid, the slant interpretation of the figure derived by assuming that the figure is rectangular may conflict greatly with the slant suggested by stereoscopic disparities. An optimal Bayesian estimator incorporates the possibility that different constraints might apply to objects in the world and robustly integrates cues with large conflicts by effectively switching between different internal models of the prior constraints underlying one or both cues. We performed two experiments to test the predictions of the model when applied to estimating surface slant from binocular disparities and the compression cue (the aspect ratio of figures in an image). The apparent weight that subjects gave to the compression cue decreased smoothly as a function of the conflict between the cues but did not shrink to zero; that is, subjects did not fully veto the compression cue at large cue conflicts. A Bayesian model that assumes a mixed prior distribution of figure shapes in the world, with a large proportion being very regular and a smaller proportion having random shapes, provides a good quantitative fit for subjects' performance. The best fitting model parameters are consistent with the sensory noise to be expected in measurements of figure shape, further supporting the Bayesian model as an account of robust cue integration.

Bayesian Adaptive Lasso for Ordinal Regression with Latent Variables

ERIC Educational Resources Information Center

Feng, Xiang-Nan; Wu, Hao-Tian; Song, Xin-Yuan

2017-01-01

We consider an ordinal regression model with latent variables to investigate the effects of observable and latent explanatory variables on the ordinal responses of interest. Each latent variable is characterized by correlated observed variables through a confirmatory factor analysis model. We develop a Bayesian adaptive lasso procedure to conduct…

Traffic Video Image Segmentation Model Based on Bayesian and Spatio-Temporal Markov Random Field

NASA Astrophysics Data System (ADS)

Zhou, Jun; Bao, Xu; Li, Dawei; Yin, Yongwen

2017-10-01

Traffic video image is a kind of dynamic image and its background and foreground is changed at any time, which results in the occlusion. In this case, using the general method is more difficult to get accurate image segmentation. A segmentation algorithm based on Bayesian and Spatio-Temporal Markov Random Field is put forward, which respectively build the energy function model of observation field and label field to motion sequence image with Markov property, then according to Bayesian' rule, use the interaction of label field and observation field, that is the relationship of label field’s prior probability and observation field’s likelihood probability, get the maximum posterior probability of label field’s estimation parameter, use the ICM model to extract the motion object, consequently the process of segmentation is finished. Finally, the segmentation methods of ST - MRF and the Bayesian combined with ST - MRF were analyzed. Experimental results: the segmentation time in Bayesian combined with ST-MRF algorithm is shorter than in ST-MRF, and the computing workload is small, especially in the heavy traffic dynamic scenes the method also can achieve better segmentation effect.

The utility of Bayesian predictive probabilities for interim monitoring of clinical trials

PubMed Central

Connor, Jason T.; Ayers, Gregory D; Alvarez, JoAnn

2014-01-01

Background Bayesian predictive probabilities can be used for interim monitoring of clinical trials to estimate the probability of observing a statistically significant treatment effect if the trial were to continue to its predefined maximum sample size. Purpose We explore settings in which Bayesian predictive probabilities are advantageous for interim monitoring compared to Bayesian posterior probabilities, p-values, conditional power, or group sequential methods. Results For interim analyses that address prediction hypotheses, such as futility monitoring and efficacy monitoring with lagged outcomes, only predictive probabilities properly account for the amount of data remaining to be observed in a clinical trial and have the flexibility to incorporate additional information via auxiliary variables. Limitations Computational burdens limit the feasibility of predictive probabilities in many clinical trial settings. The specification of prior distributions brings additional challenges for regulatory approval. Conclusions The use of Bayesian predictive probabilities enables the choice of logical interim stopping rules that closely align with the clinical decision making process. PMID:24872363

Applications of Bayesian Statistics to Problems in Gamma-Ray Bursts

NASA Technical Reports Server (NTRS)

Meegan, Charles A.

1997-01-01

This presentation will describe two applications of Bayesian statistics to Gamma Ray Bursts (GRBS). The first attempts to quantify the evidence for a cosmological versus galactic origin of GRBs using only the observations of the dipole and quadrupole moments of the angular distribution of bursts. The cosmological hypothesis predicts isotropy, while the galactic hypothesis is assumed to produce a uniform probability distribution over positive values for these moments. The observed isotropic distribution indicates that the Bayes factor for the cosmological hypothesis over the galactic hypothesis is about 300. Another application of Bayesian statistics is in the estimation of chance associations of optical counterparts with galaxies. The Bayesian approach is preferred to frequentist techniques here because the Bayesian approach easily accounts for galaxy mass distributions and because one can incorporate three disjoint hypotheses: (1) bursts come from galactic centers, (2) bursts come from galaxies in proportion to luminosity, and (3) bursts do not come from external galaxies. This technique was used in the analysis of the optical counterpart to GRB970228.

Bayesian statistics: estimating plant demographic parameters

Treesearch

James S. Clark; Michael Lavine

2001-01-01

There are times when external information should be brought tobear on an ecological analysis. experiments are never conducted in a knowledge-free context. The inference we draw from an observation may depend on everything else we know about the process. Bayesian analysis is a method that brings outside evidence into the analysis of experimental and observational data...

A Bayesian Approach to Person Fit Analysis in Item Response Theory Models. Research Report.

ERIC Educational Resources Information Center

Glas, Cees A. W.; Meijer, Rob R.

A Bayesian approach to the evaluation of person fit in item response theory (IRT) models is presented. In a posterior predictive check, the observed value on a discrepancy variable is positioned in its posterior distribution. In a Bayesian framework, a Markov Chain Monte Carlo procedure can be used to generate samples of the posterior distribution…

Extracting a Whisper from the DIN: A Bayesian-Inductive Approach to Learning an Anticipatory Model of Cavitation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kercel, S.W.

1999-11-07

For several reasons, Bayesian parameter estimation is superior to other methods for inductively learning a model for an anticipatory system. Since it exploits prior knowledge, the analysis begins from a more advantageous starting point than other methods. Also, since "nuisance parameters" can be removed from the Bayesian analysis, the description of the model need not be as complete as is necessary for such methods as matched filtering. In the limit of perfectly random noise and a perfect description of the model, the signal-to-noise ratio improves as the square root of the number of samples in the data. Even with themore » imperfections of real-world data, Bayesian methods approach this ideal limit of performance more closely than other methods. These capabilities provide a strategy for addressing a major unsolved problem in pump operation: the identification of precursors of cavitation. Cavitation causes immediate degradation of pump performance and ultimate destruction of the pump. However, the most efficient point to operate a pump is just below the threshold of cavitation. It might be hoped that a straightforward method to minimize pump cavitation damage would be to simply adjust the operating point until the inception of cavitation is detected and then to slightly readjust the operating point to let the cavitation vanish. However, due to the continuously evolving state of the fluid moving through the pump, the threshold of cavitation tends to wander. What is needed is to anticipate cavitation, and this requires the detection and identification of precursor features that occur just before cavitation starts.« less

Predicting the Future as Bayesian Inference: People Combine Prior Knowledge with Observations when Estimating Duration and Extent

ERIC Educational Resources Information Center

Griffiths, Thomas L.; Tenenbaum, Joshua B.

2011-01-01

Predicting the future is a basic problem that people have to solve every day and a component of planning, decision making, memory, and causal reasoning. In this article, we present 5 experiments testing a Bayesian model of predicting the duration or extent of phenomena from their current state. This Bayesian model indicates how people should…

The disagreement between the ideal observer and human observers in hardware and software imaging system optimization: theoretical explanations and evidence

NASA Astrophysics Data System (ADS)

He, Xin

2017-03-01

The ideal observer is widely used in imaging system optimization. One practical question remains open: do the ideal and human observers have the same preference in system optimization and evaluation? Based on the ideal observer's mathematical properties proposed by Barrett et. al. and the empirical properties of human observers investigated by Myers et. al., I attempt to pursue the general rules regarding the applicability of the ideal observer in system optimization. Particularly, in software optimization, the ideal observer pursues data conservation while humans pursue data presentation or perception. In hardware optimization, the ideal observer pursues a system with the maximum total information, while humans pursue a system with the maximum selected (e.g., certain frequency bands) information. These different objectives may result in different system optimizations between human and the ideal observers. Thus, an ideal observer optimized system is not necessarily optimal for humans. I cite empirical evidence in search and detection tasks, in hardware and software evaluation, in X-ray CT, pinhole imaging, as well as emission computed tomography to corroborate the claims. (Disclaimer: the views expressed in this work do not necessarily represent those of the FDA)

The rat approximates an ideal detector of changes in rates of reward: implications for the law of effect.

PubMed

Gallistel, C R; Mark, T A; King, A P; Latham, P E

2001-10-01

Rats responded on 2 levers delivering brain stimulation reward on concurrent variable interval schedules. Following many successive sessions with unchanging relative rates of reward, subjects adjusted to an eventual change slowly and showed spontaneous reversions at the beginning of subsequent sessions. When changes in rates of reward occurred between and within every session, subjects adjusted to them about as rapidly as they could in principle do so, as shown by comparison to a Bayesian model of an ideal detector. This and other features of the adjustments to frequent changes imply that the behavioral effect of reinforcement depends on the subject's perception of incomes and changes in incomes rather than on the strengthening and weakening of behaviors in accord with their past effects or expected results. Models for the process by which perceived incomes determine stay durations and for the process that detects changes in rates are developed.

Learning coefficient of generalization error in Bayesian estimation and vandermonde matrix-type singularity.

PubMed

Aoyagi, Miki; Nagata, Kenji

2012-06-01

The term algebraic statistics arises from the study of probabilistic models and techniques for statistical inference using methods from algebra and geometry (Sturmfels, 2009 ). The purpose of our study is to consider the generalization error and stochastic complexity in learning theory by using the log-canonical threshold in algebraic geometry. Such thresholds correspond to the main term of the generalization error in Bayesian estimation, which is called a learning coefficient (Watanabe, 2001a , 2001b ). The learning coefficient serves to measure the learning efficiencies in hierarchical learning models. In this letter, we consider learning coefficients for Vandermonde matrix-type singularities, by using a new approach: focusing on the generators of the ideal, which defines singularities. We give tight new bound values of learning coefficients for the Vandermonde matrix-type singularities and the explicit values with certain conditions. By applying our results, we can show the learning coefficients of three-layered neural networks and normal mixture models.

Poisson point process modeling for polyphonic music transcription.

PubMed

Peeling, Paul; Li, Chung-fai; Godsill, Simon

2007-04-01

Peaks detected in the frequency domain spectrum of a musical chord are modeled as realizations of a nonhomogeneous Poisson point process. When several notes are superimposed to make a chord, the processes for individual notes combine to give another Poisson process, whose likelihood is easily computable. This avoids a data association step linking individual harmonics explicitly with detected peaks in the spectrum. The likelihood function is ideal for Bayesian inference about the unknown note frequencies in a chord. Here, maximum likelihood estimation of fundamental frequencies shows very promising performance on real polyphonic piano music recordings.

Bayesian probabilistic approach for inverse source determination from limited and noisy chemical or biological sensor concentration measurements

NASA Astrophysics Data System (ADS)

Yee, Eugene

2007-04-01

Although a great deal of research effort has been focused on the forward prediction of the dispersion of contaminants (e.g., chemical and biological warfare agents) released into the turbulent atmosphere, much less work has been directed toward the inverse prediction of agent source location and strength from the measured concentration, even though the importance of this problem for a number of practical applications is obvious. In general, the inverse problem of source reconstruction is ill-posed and unsolvable without additional information. It is demonstrated that a Bayesian probabilistic inferential framework provides a natural and logically consistent method for source reconstruction from a limited number of noisy concentration data. In particular, the Bayesian approach permits one to incorporate prior knowledge about the source as well as additional information regarding both model and data errors. The latter enables a rigorous determination of the uncertainty in the inference of the source parameters (e.g., spatial location, emission rate, release time, etc.), hence extending the potential of the methodology as a tool for quantitative source reconstruction. A model (or, source-receptor relationship) that relates the source distribution to the concentration data measured by a number of sensors is formulated, and Bayesian probability theory is used to derive the posterior probability density function of the source parameters. A computationally efficient methodology for determination of the likelihood function for the problem, based on an adjoint representation of the source-receptor relationship, is described. Furthermore, we describe the application of efficient stochastic algorithms based on Markov chain Monte Carlo (MCMC) for sampling from the posterior distribution of the source parameters, the latter of which is required to undertake the Bayesian computation. The Bayesian inferential methodology for source reconstruction is validated against real dispersion data for two cases involving contaminant dispersion in highly disturbed flows over urban and complex environments where the idealizations of horizontal homogeneity and/or temporal stationarity in the flow cannot be applied to simplify the problem. Furthermore, the methodology is applied to the case of reconstruction of multiple sources.

A Test of Bayesian Observer Models of Processing in the Eriksen Flanker Task

ERIC Educational Resources Information Center

White, Corey N.; Brown, Scott; Ratcliff, Roger

2012-01-01

Two Bayesian observer models were recently proposed to account for data from the Eriksen flanker task, in which flanking items interfere with processing of a central target. One model assumes that interference stems from a perceptual bias to process nearby items as if they are compatible, and the other assumes that the interference is due to…

Bayesian parameter estimation for chiral effective field theory

NASA Astrophysics Data System (ADS)

Wesolowski, Sarah; Furnstahl, Richard; Phillips, Daniel; Klco, Natalie

2016-09-01

The low-energy constants (LECs) of a chiral effective field theory (EFT) interaction in the two-body sector are fit to observable data using a Bayesian parameter estimation framework. By using Bayesian prior probability distributions (pdfs), we quantify relevant physical expectations such as LEC naturalness and include them in the parameter estimation procedure. The final result is a posterior pdf for the LECs, which can be used to propagate uncertainty resulting from the fit to data to the final observable predictions. The posterior pdf also allows an empirical test of operator redundancy and other features of the potential. We compare results of our framework with other fitting procedures, interpreting the underlying assumptions in Bayesian probabilistic language. We also compare results from fitting all partial waves of the interaction simultaneously to cross section data compared to fitting to extracted phase shifts, appropriately accounting for correlations in the data. Supported in part by the NSF and DOE.

Bayesian least squares deconvolution

NASA Astrophysics Data System (ADS)

Asensio Ramos, A.; Petit, P.

2015-11-01

Aims: We develop a fully Bayesian least squares deconvolution (LSD) that can be applied to the reliable detection of magnetic signals in noise-limited stellar spectropolarimetric observations using multiline techniques. Methods: We consider LSD under the Bayesian framework and we introduce a flexible Gaussian process (GP) prior for the LSD profile. This prior allows the result to automatically adapt to the presence of signal. We exploit several linear algebra identities to accelerate the calculations. The final algorithm can deal with thousands of spectral lines in a few seconds. Results: We demonstrate the reliability of the method with synthetic experiments and we apply it to real spectropolarimetric observations of magnetic stars. We are able to recover the magnetic signals using a small number of spectral lines, together with the uncertainty at each velocity bin. This allows the user to consider if the detected signal is reliable. The code to compute the Bayesian LSD profile is freely available.

The Brightness of Colour

PubMed Central

Corney, David; Haynes, John-Dylan; Rees, Geraint; Lotto, R. Beau

2009-01-01

Background The perception of brightness depends on spatial context: the same stimulus can appear light or dark depending on what surrounds it. A less well-known but equally important contextual phenomenon is that the colour of a stimulus can also alter its brightness. Specifically, stimuli that are more saturated (i.e. purer in colour) appear brighter than stimuli that are less saturated at the same luminance. Similarly, stimuli that are red or blue appear brighter than equiluminant yellow and green stimuli. This non-linear relationship between stimulus intensity and brightness, called the Helmholtz-Kohlrausch (HK) effect, was first described in the nineteenth century but has never been explained. Here, we take advantage of the relative simplicity of this ‘illusion’ to explain it and contextual effects more generally, by using a simple Bayesian ideal observer model of the human visual ecology. We also use fMRI brain scans to identify the neural correlates of brightness without changing the spatial context of the stimulus, which has complicated the interpretation of related fMRI studies. Results Rather than modelling human vision directly, we use a Bayesian ideal observer to model human visual ecology. We show that the HK effect is a result of encoding the non-linear statistical relationship between retinal images and natural scenes that would have been experienced by the human visual system in the past. We further show that the complexity of this relationship is due to the response functions of the cone photoreceptors, which themselves are thought to represent an efficient solution to encoding the statistics of images. Finally, we show that the locus of the response to the relationship between images and scenes lies in the primary visual cortex (V1), if not earlier in the visual system, since the brightness of colours (as opposed to their luminance) accords with activity in V1 as measured with fMRI. Conclusions The data suggest that perceptions of brightness represent a robust visual response to the likely sources of stimuli, as determined, in this instance, by the known statistical relationship between scenes and their retinal responses. While the responses of the early visual system (receptors in this case) may represent specifically the statistics of images, post receptor responses are more likely represent the statistical relationship between images and scenes. A corollary of this suggestion is that the visual cortex is adapted to relate the retinal image to behaviour given the statistics of its past interactions with the sources of retinal images: the visual cortex is adapted to the signals it receives from the eyes, and not directly to the world beyond. PMID:19333398

Fast genomic predictions via Bayesian G-BLUP and multilocus models of threshold traits including censored Gaussian data.

PubMed

Kärkkäinen, Hanni P; Sillanpää, Mikko J

2013-09-04

Because of the increased availability of genome-wide sets of molecular markers along with reduced cost of genotyping large samples of individuals, genomic estimated breeding values have become an essential resource in plant and animal breeding. Bayesian methods for breeding value estimation have proven to be accurate and efficient; however, the ever-increasing data sets are placing heavy demands on the parameter estimation algorithms. Although a commendable number of fast estimation algorithms are available for Bayesian models of continuous Gaussian traits, there is a shortage for corresponding models of discrete or censored phenotypes. In this work, we consider a threshold approach of binary, ordinal, and censored Gaussian observations for Bayesian multilocus association models and Bayesian genomic best linear unbiased prediction and present a high-speed generalized expectation maximization algorithm for parameter estimation under these models. We demonstrate our method with simulated and real data. Our example analyses suggest that the use of the extra information present in an ordered categorical or censored Gaussian data set, instead of dichotomizing the data into case-control observations, increases the accuracy of genomic breeding values predicted by Bayesian multilocus association models or by Bayesian genomic best linear unbiased prediction. Furthermore, the example analyses indicate that the correct threshold model is more accurate than the directly used Gaussian model with a censored Gaussian data, while with a binary or an ordinal data the superiority of the threshold model could not be confirmed.

Fast Genomic Predictions via Bayesian G-BLUP and Multilocus Models of Threshold Traits Including Censored Gaussian Data

PubMed Central

Kärkkäinen, Hanni P.; Sillanpää, Mikko J.

2013-01-01

Because of the increased availability of genome-wide sets of molecular markers along with reduced cost of genotyping large samples of individuals, genomic estimated breeding values have become an essential resource in plant and animal breeding. Bayesian methods for breeding value estimation have proven to be accurate and efficient; however, the ever-increasing data sets are placing heavy demands on the parameter estimation algorithms. Although a commendable number of fast estimation algorithms are available for Bayesian models of continuous Gaussian traits, there is a shortage for corresponding models of discrete or censored phenotypes. In this work, we consider a threshold approach of binary, ordinal, and censored Gaussian observations for Bayesian multilocus association models and Bayesian genomic best linear unbiased prediction and present a high-speed generalized expectation maximization algorithm for parameter estimation under these models. We demonstrate our method with simulated and real data. Our example analyses suggest that the use of the extra information present in an ordered categorical or censored Gaussian data set, instead of dichotomizing the data into case-control observations, increases the accuracy of genomic breeding values predicted by Bayesian multilocus association models or by Bayesian genomic best linear unbiased prediction. Furthermore, the example analyses indicate that the correct threshold model is more accurate than the directly used Gaussian model with a censored Gaussian data, while with a binary or an ordinal data the superiority of the threshold model could not be confirmed. PMID:23821618

Application of Multiple Imputation for Missing Values in Three-Way Three-Mode Multi-Environment Trial Data

PubMed Central

Tian, Ting; McLachlan, Geoffrey J.; Dieters, Mark J.; Basford, Kaye E.

2015-01-01

It is a common occurrence in plant breeding programs to observe missing values in three-way three-mode multi-environment trial (MET) data. We proposed modifications of models for estimating missing observations for these data arrays, and developed a novel approach in terms of hierarchical clustering. Multiple imputation (MI) was used in four ways, multiple agglomerative hierarchical clustering, normal distribution model, normal regression model, and predictive mean match. The later three models used both Bayesian analysis and non-Bayesian analysis, while the first approach used a clustering procedure with randomly selected attributes and assigned real values from the nearest neighbour to the one with missing observations. Different proportions of data entries in six complete datasets were randomly selected to be missing and the MI methods were compared based on the efficiency and accuracy of estimating those values. The results indicated that the models using Bayesian analysis had slightly higher accuracy of estimation performance than those using non-Bayesian analysis but they were more time-consuming. However, the novel approach of multiple agglomerative hierarchical clustering demonstrated the overall best performances. PMID:26689369

Application of Multiple Imputation for Missing Values in Three-Way Three-Mode Multi-Environment Trial Data.

PubMed

Tian, Ting; McLachlan, Geoffrey J; Dieters, Mark J; Basford, Kaye E

2015-01-01

It is a common occurrence in plant breeding programs to observe missing values in three-way three-mode multi-environment trial (MET) data. We proposed modifications of models for estimating missing observations for these data arrays, and developed a novel approach in terms of hierarchical clustering. Multiple imputation (MI) was used in four ways, multiple agglomerative hierarchical clustering, normal distribution model, normal regression model, and predictive mean match. The later three models used both Bayesian analysis and non-Bayesian analysis, while the first approach used a clustering procedure with randomly selected attributes and assigned real values from the nearest neighbour to the one with missing observations. Different proportions of data entries in six complete datasets were randomly selected to be missing and the MI methods were compared based on the efficiency and accuracy of estimating those values. The results indicated that the models using Bayesian analysis had slightly higher accuracy of estimation performance than those using non-Bayesian analysis but they were more time-consuming. However, the novel approach of multiple agglomerative hierarchical clustering demonstrated the overall best performances.

Practical differences among probabilities, possibilities, and credibilities

NASA Astrophysics Data System (ADS)

Grandin, Jean-Francois; Moulin, Caroline

2002-03-01

This paper presents some important differences that exist between theories, which allow the uncertainty management in data fusion. The main comparative results illustrated in this paper are the followings: Incompatibility between decisions got from probabilities and credibilities is highlighted. In the dynamic frame, as remarked in [19] or [17], belief and plausibility of Dempster-Shafer model do not frame the Bayesian probability. This framing can however be obtained by the Modified Dempster-Shafer approach. It also can be obtained in the Bayesian framework either by simulation techniques, or with a studentization. The uncommitted in the Dempster-Shafer way, e.g. the mass accorded to the ignorance, gives a mechanism similar to the reliability in the Bayesian model. Uncommitted mass in Dempster-Shafer theory or reliability in Bayes theory act like a filter that weakens extracted information, and improves robustness to outliners. So, it is logical to observe on examples like the one presented particularly by D.M. Buede, a faster convergence of a Bayesian method that doesn't take into account the reliability, in front of Dempster-Shafer method which uses uncommitted mass. But, on Bayesian masses, if reliability is taken into account, at the same level that the uncommited, e.g. F=1-m, we observe an equivalent rate for convergence. When Dempster-Shafer and Bayes operator are informed by uncertainty, faster or lower convergence can be exhibited on non Bayesian masses. This is due to positive or negative synergy between information delivered by sensors. This effect is a direct consequence of non additivity when considering non Bayesian masses. Unknowledge of the prior in bayesian techniques can be quickly compensated by information accumulated as time goes on by a set of sensors. All these results are presented on simple examples, and developed when necessary.

Determination of confidence limits for experiments with low numbers of counts. [Poisson-distributed photon counts from astrophysical sources

NASA Technical Reports Server (NTRS)

Kraft, Ralph P.; Burrows, David N.; Nousek, John A.

1991-01-01

Two different methods, classical and Bayesian, for determining confidence intervals involving Poisson-distributed data are compared. Particular consideration is given to cases where the number of counts observed is small and is comparable to the mean number of background counts. Reasons for preferring the Bayesian over the classical method are given. Tables of confidence limits calculated by the Bayesian method are provided for quick reference.

BUMPER v1.0: a Bayesian user-friendly model for palaeo-environmental reconstruction

NASA Astrophysics Data System (ADS)

Holden, Philip B.; Birks, H. John B.; Brooks, Stephen J.; Bush, Mark B.; Hwang, Grace M.; Matthews-Bird, Frazer; Valencia, Bryan G.; van Woesik, Robert

2017-02-01

We describe the Bayesian user-friendly model for palaeo-environmental reconstruction (BUMPER), a Bayesian transfer function for inferring past climate and other environmental variables from microfossil assemblages. BUMPER is fully self-calibrating, straightforward to apply, and computationally fast, requiring ˜ 2 s to build a 100-taxon model from a 100-site training set on a standard personal computer. We apply the model's probabilistic framework to generate thousands of artificial training sets under ideal assumptions. We then use these to demonstrate the sensitivity of reconstructions to the characteristics of the training set, considering assemblage richness, taxon tolerances, and the number of training sites. We find that a useful guideline for the size of a training set is to provide, on average, at least 10 samples of each taxon. We demonstrate general applicability to real data, considering three different organism types (chironomids, diatoms, pollen) and different reconstructed variables. An identically configured model is used in each application, the only change being the input files that provide the training-set environment and taxon-count data. The performance of BUMPER is shown to be comparable with weighted average partial least squares (WAPLS) in each case. Additional artificial datasets are constructed with similar characteristics to the real data, and these are used to explore the reasons for the differing performances of the different training sets.

The surprisingly high human efficiency at learning to recognize faces

PubMed Central

Peterson, Matthew F.; Abbey, Craig K.; Eckstein, Miguel P.

2009-01-01

We investigated the ability of humans to optimize face recognition performance through rapid learning of individual relevant features. We created artificial faces with discriminating visual information heavily concentrated in single features (nose, eyes, chin or mouth). In each of 2500 learning blocks a feature was randomly selected and retained over the course of four trials, during which observers identified randomly sampled, noisy face images. Observers learned the discriminating feature through indirect feedback, leading to large performance gains. Performance was compared to a learning Bayesian ideal observer, resulting in unexpectedly high learning compared to previous studies with simpler stimuli. We explore various explanations and conclude that the higher learning measured with faces cannot be driven by adaptive eye movement strategies but can be mostly accounted for by suboptimalities in human face discrimination when observers are uncertain about the discriminating feature. We show that an initial bias of humans to use specific features to perform the task even though they are informed that each of four features is equally likely to be the discriminatory feature would lead to seemingly supra-optimal learning. We also examine the possibility of inefficient human integration of visual information across the spatially distributed facial features. Together, the results suggest that humans can show large performance improvement effects in discriminating faces as they learn to identify the feature containing the discriminatory information. PMID:19000918

Bayesian network modeling applied to coastal geomorphology: lessons learned from a decade of experimentation and application

NASA Astrophysics Data System (ADS)

Plant, N. G.; Thieler, E. R.; Gutierrez, B.; Lentz, E. E.; Zeigler, S. L.; Van Dongeren, A.; Fienen, M. N.

2016-12-01

We evaluate the strengths and weaknesses of Bayesian networks that have been used to address scientific and decision-support questions related to coastal geomorphology. We will provide an overview of coastal geomorphology research that has used Bayesian networks and describe what this approach can do and when it works (or fails to work). Over the past decade, Bayesian networks have been formulated to analyze the multi-variate structure and evolution of coastal morphology and associated human and ecological impacts. The approach relates observable system variables to each other by estimating discrete correlations. The resulting Bayesian-networks make predictions that propagate errors, conduct inference via Bayes rule, or both. In scientific applications, the model results are useful for hypothesis testing, using confidence estimates to gage the strength of tests while applications to coastal resource management are aimed at decision-support, where the probabilities of desired ecosystems outcomes are evaluated. The range of Bayesian-network applications to coastal morphology includes emulation of high-resolution wave transformation models to make oceanographic predictions, morphologic response to storms and/or sea-level rise, groundwater response to sea-level rise and morphologic variability, habitat suitability for endangered species, and assessment of monetary or human-life risk associated with storms. All of these examples are based on vast observational data sets, numerical model output, or both. We will discuss the progression of our experiments, which has included testing whether the Bayesian-network approach can be implemented and is appropriate for addressing basic and applied scientific problems and evaluating the hindcast and forecast skill of these implementations. We will present and discuss calibration/validation tests that are used to assess the robustness of Bayesian-network models and we will compare these results to tests of other models. This will demonstrate how Bayesian networks are used to extract new insights about coastal morphologic behavior, assess impacts to societal and ecological systems, and communicate probabilistic predictions to decision makers.

Bayesian Estimation and Inference Using Stochastic Electronics

PubMed Central

Thakur, Chetan Singh; Afshar, Saeed; Wang, Runchun M.; Hamilton, Tara J.; Tapson, Jonathan; van Schaik, André

2016-01-01

In this paper, we present the implementation of two types of Bayesian inference problems to demonstrate the potential of building probabilistic algorithms in hardware using single set of building blocks with the ability to perform these computations in real time. The first implementation, referred to as the BEAST (Bayesian Estimation and Stochastic Tracker), demonstrates a simple problem where an observer uses an underlying Hidden Markov Model (HMM) to track a target in one dimension. In this implementation, sensors make noisy observations of the target position at discrete time steps. The tracker learns the transition model for target movement, and the observation model for the noisy sensors, and uses these to estimate the target position by solving the Bayesian recursive equation online. We show the tracking performance of the system and demonstrate how it can learn the observation model, the transition model, and the external distractor (noise) probability interfering with the observations. In the second implementation, referred to as the Bayesian INference in DAG (BIND), we show how inference can be performed in a Directed Acyclic Graph (DAG) using stochastic circuits. We show how these building blocks can be easily implemented using simple digital logic gates. An advantage of the stochastic electronic implementation is that it is robust to certain types of noise, which may become an issue in integrated circuit (IC) technology with feature sizes in the order of tens of nanometers due to their low noise margin, the effect of high-energy cosmic rays and the low supply voltage. In our framework, the flipping of random individual bits would not affect the system performance because information is encoded in a bit stream. PMID:27047326

Bayesian Estimation and Inference Using Stochastic Electronics.

PubMed

Thakur, Chetan Singh; Afshar, Saeed; Wang, Runchun M; Hamilton, Tara J; Tapson, Jonathan; van Schaik, André

2016-01-01

In this paper, we present the implementation of two types of Bayesian inference problems to demonstrate the potential of building probabilistic algorithms in hardware using single set of building blocks with the ability to perform these computations in real time. The first implementation, referred to as the BEAST (Bayesian Estimation and Stochastic Tracker), demonstrates a simple problem where an observer uses an underlying Hidden Markov Model (HMM) to track a target in one dimension. In this implementation, sensors make noisy observations of the target position at discrete time steps. The tracker learns the transition model for target movement, and the observation model for the noisy sensors, and uses these to estimate the target position by solving the Bayesian recursive equation online. We show the tracking performance of the system and demonstrate how it can learn the observation model, the transition model, and the external distractor (noise) probability interfering with the observations. In the second implementation, referred to as the Bayesian INference in DAG (BIND), we show how inference can be performed in a Directed Acyclic Graph (DAG) using stochastic circuits. We show how these building blocks can be easily implemented using simple digital logic gates. An advantage of the stochastic electronic implementation is that it is robust to certain types of noise, which may become an issue in integrated circuit (IC) technology with feature sizes in the order of tens of nanometers due to their low noise margin, the effect of high-energy cosmic rays and the low supply voltage. In our framework, the flipping of random individual bits would not affect the system performance because information is encoded in a bit stream.

An approach to quantifying the efficiency of a Bayesian filter

USDA-ARS?s Scientific Manuscript database

Data assimilation is defined as the Bayesian conditioning of uncertain model simulations on observations for the purpose of reducing uncertainty about model states. Practical data assimilation applications require that simplifying assumptions be made about the prior and posterior state distributions...

Analysis of the Bayesian Cramér-Rao lower bound in astrometry. Studying the impact of prior information in the location of an object

NASA Astrophysics Data System (ADS)

Echeverria, Alex; Silva, Jorge F.; Mendez, Rene A.; Orchard, Marcos

2016-10-01

Context. The best precision that can be achieved to estimate the location of a stellar-like object is a topic of permanent interest in the astrometric community. Aims: We analyze bounds for the best position estimation of a stellar-like object on a CCD detector array in a Bayesian setting where the position is unknown, but where we have access to a prior distribution. In contrast to a parametric setting where we estimate a parameter from observations, the Bayesian approach estimates a random object (I.e., the position is a random variable) from observations that are statistically dependent on the position. Methods: We characterize the Bayesian Cramér-Rao (CR) that bounds the minimum mean square error (MMSE) of the best estimator of the position of a point source on a linear CCD-like detector, as a function of the properties of detector, the source, and the background. Results: We quantify and analyze the increase in astrometric performance from the use of a prior distribution of the object position, which is not available in the classical parametric setting. This gain is shown to be significant for various observational regimes, in particular in the case of faint objects or when the observations are taken under poor conditions. Furthermore, we present numerical evidence that the MMSE estimator of this problem tightly achieves the Bayesian CR bound. This is a remarkable result, demonstrating that all the performance gains presented in our analysis can be achieved with the MMSE estimator. Conclusions: The Bayesian CR bound can be used as a benchmark indicator of the expected maximum positional precision of a set of astrometric measurements in which prior information can be incorporated. This bound can be achieved through the conditional mean estimator, in contrast to the parametric case where no unbiased estimator precisely reaches the CR bound.

Bayesian inversion of refraction seismic traveltime data

NASA Astrophysics Data System (ADS)

Ryberg, T.; Haberland, Ch

2018-03-01

We apply a Bayesian Markov chain Monte Carlo (McMC) formalism to the inversion of refraction seismic, traveltime data sets to derive 2-D velocity models below linear arrays (i.e. profiles) of sources and seismic receivers. Typical refraction data sets, especially when using the far-offset observations, are known as having experimental geometries which are very poor, highly ill-posed and far from being ideal. As a consequence, the structural resolution quickly degrades with depth. Conventional inversion techniques, based on regularization, potentially suffer from the choice of appropriate inversion parameters (i.e. number and distribution of cells, starting velocity models, damping and smoothing constraints, data noise level, etc.) and only local model space exploration. McMC techniques are used for exhaustive sampling of the model space without the need of prior knowledge (or assumptions) of inversion parameters, resulting in a large number of models fitting the observations. Statistical analysis of these models allows to derive an average (reference) solution and its standard deviation, thus providing uncertainty estimates of the inversion result. The highly non-linear character of the inversion problem, mainly caused by the experiment geometry, does not allow to derive a reference solution and error map by a simply averaging procedure. We present a modified averaging technique, which excludes parts of the prior distribution in the posterior values due to poor ray coverage, thus providing reliable estimates of inversion model properties even in those parts of the models. The model is discretized by a set of Voronoi polygons (with constant slowness cells) or a triangulated mesh (with interpolation within the triangles). Forward traveltime calculations are performed by a fast, finite-difference-based eikonal solver. The method is applied to a data set from a refraction seismic survey from Northern Namibia and compared to conventional tomography. An inversion test for a synthetic data set from a known model is also presented.

Bayesian hierarchical model of ceftriaxone resistance proportions among Salmonella serotype Heidelberg infections.

PubMed

Gu, Weidong; Medalla, Felicita; Hoekstra, Robert M

2018-02-01

The National Antimicrobial Resistance Monitoring System (NARMS) at the Centers for Disease Control and Prevention tracks resistance among Salmonella infections. The annual number of Salmonella isolates of a particular serotype from states may be small, making direct estimation of resistance proportions unreliable. We developed a Bayesian hierarchical model to improve estimation by borrowing strength from relevant sampling units. We illustrate the models with different specifications of spatio-temporal interaction using 2004-2013 NARMS data for ceftriaxone-resistant Salmonella serotype Heidelberg. Our results show that Bayesian estimates of resistance proportions were smoother than observed values, and the difference between predicted and observed proportions was inversely related to the number of submitted isolates. The model with interaction allowed for tracking of annual changes in resistance proportions at the state level. We demonstrated that Bayesian hierarchical models provide a useful tool to examine spatio-temporal patterns of small sample size such as those found in NARMS. Published by Elsevier Ltd.

Estimating the hatchery fraction of a natural population: a Bayesian approach

USGS Publications Warehouse

Barber, Jarrett J.; Gerow, Kenneth G.; Connolly, Patrick J.; Singh, Sarabdeep

2011-01-01

There is strong and growing interest in estimating the proportion of hatchery fish that are in a natural population (the hatchery fraction). In a sample of fish from the relevant population, some are observed to be marked, indicating their origin as hatchery fish. The observed proportion of marked fish is usually less than the actual hatchery fraction, since the observed proportion is determined by the proportion originally marked, differential survival (usually lower) of marked fish relative to unmarked hatchery fish, and rates of mark retention and detection. Bayesian methods can work well in a setting such as this, in which empirical data are limited but for which there may be considerable expert judgment regarding these values. We explored a Bayesian estimation of the hatchery fraction using Monte Carlo–Markov chain methods. Based on our findings, we created an interactive Excel tool to implement the algorithm, which we have made available for free.

Calibrating Bayesian Network Representations of Social-Behavioral Models

DOE Office of Scientific and Technical Information (OSTI.GOV)

Whitney, Paul D.; Walsh, Stephen J.

2010-04-08

While human behavior has long been studied, recent and ongoing advances in computational modeling present opportunities for recasting research outcomes in human behavior. In this paper we describe how Bayesian networks can represent outcomes of human behavior research. We demonstrate a Bayesian network that represents political radicalization research – and show a corresponding visual representation of aspects of this research outcome. Since Bayesian networks can be quantitatively compared with external observations, the representation can also be used for empirical assessments of the research which the network summarizes. For a political radicalization model based on published research, we show this empiricalmore » comparison with data taken from the Minorities at Risk Organizational Behaviors database.« less

A BAYESIAN STATISTICAL APPROACH FOR THE EVALUATION OF CMAQ

EPA Science Inventory

Bayesian statistical methods are used to evaluate Community Multiscale Air Quality (CMAQ) model simulations of sulfate aerosol over a section of the eastern US for 4-week periods in summer and winter 2001. The observed data come from two U.S. Environmental Protection Agency data ...

Bayesian nonparametric clustering in phylogenetics: modeling antigenic evolution in influenza.

PubMed

Cybis, Gabriela B; Sinsheimer, Janet S; Bedford, Trevor; Rambaut, Andrew; Lemey, Philippe; Suchard, Marc A

2018-01-30

Influenza is responsible for up to 500,000 deaths every year, and antigenic variability represents much of its epidemiological burden. To visualize antigenic differences across many viral strains, antigenic cartography methods use multidimensional scaling on binding assay data to map influenza antigenicity onto a low-dimensional space. Analysis of such assay data ideally leads to natural clustering of influenza strains of similar antigenicity that correlate with sequence evolution. To understand the dynamics of these antigenic groups, we present a framework that jointly models genetic and antigenic evolution by combining multidimensional scaling of binding assay data, Bayesian phylogenetic machinery and nonparametric clustering methods. We propose a phylogenetic Chinese restaurant process that extends the current process to incorporate the phylogenetic dependency structure between strains in the modeling of antigenic clusters. With this method, we are able to use the genetic information to better understand the evolution of antigenicity throughout epidemics, as shown in applications of this model to H1N1 influenza. Copyright © 2017 John Wiley & Sons, Ltd. Copyright © 2017 John Wiley & Sons, Ltd.

Evolution of Associative Learning in Chemical Networks

PubMed Central

McGregor, Simon; Vasas, Vera; Husbands, Phil; Fernando, Chrisantha

2012-01-01

Organisms that can learn about their environment and modify their behaviour appropriately during their lifetime are more likely to survive and reproduce than organisms that do not. While associative learning – the ability to detect correlated features of the environment – has been studied extensively in nervous systems, where the underlying mechanisms are reasonably well understood, mechanisms within single cells that could allow associative learning have received little attention. Here, using in silico evolution of chemical networks, we show that there exists a diversity of remarkably simple and plausible chemical solutions to the associative learning problem, the simplest of which uses only one core chemical reaction. We then asked to what extent a linear combination of chemical concentrations in the network could approximate the ideal Bayesian posterior of an environment given the stimulus history so far? This Bayesian analysis revealed the ‘memory traces’ of the chemical network. The implication of this paper is that there is little reason to believe that a lack of suitable phenotypic variation would prevent associative learning from evolving in cell signalling, metabolic, gene regulatory, or a mixture of these networks in cells. PMID:23133353

The impact of using informative priors in a Bayesian cost-effectiveness analysis: an application of endovascular versus open surgical repair for abdominal aortic aneurysms in high-risk patients.

PubMed

McCarron, C Elizabeth; Pullenayegum, Eleanor M; Thabane, Lehana; Goeree, Ron; Tarride, Jean-Eric

2013-04-01

Bayesian methods have been proposed as a way of synthesizing all available evidence to inform decision making. However, few practical applications of the use of Bayesian methods for combining patient-level data (i.e., trial) with additional evidence (e.g., literature) exist in the cost-effectiveness literature. The objective of this study was to compare a Bayesian cost-effectiveness analysis using informative priors to a standard non-Bayesian nonparametric method to assess the impact of incorporating additional information into a cost-effectiveness analysis. Patient-level data from a previously published nonrandomized study were analyzed using traditional nonparametric bootstrap techniques and bivariate normal Bayesian models with vague and informative priors. Two different types of informative priors were considered to reflect different valuations of the additional evidence relative to the patient-level data (i.e., "face value" and "skeptical"). The impact of using different distributions and valuations was assessed in a sensitivity analysis. Models were compared in terms of incremental net monetary benefit (INMB) and cost-effectiveness acceptability frontiers (CEAFs). The bootstrapping and Bayesian analyses using vague priors provided similar results. The most pronounced impact of incorporating the informative priors was the increase in estimated life years in the control arm relative to what was observed in the patient-level data alone. Consequently, the incremental difference in life years originally observed in the patient-level data was reduced, and the INMB and CEAF changed accordingly. The results of this study demonstrate the potential impact and importance of incorporating additional information into an analysis of patient-level data, suggesting this could alter decisions as to whether a treatment should be adopted and whether more information should be acquired.

Identification of transmissivity fields using a Bayesian strategy and perturbative approach

NASA Astrophysics Data System (ADS)

Zanini, Andrea; Tanda, Maria Giovanna; Woodbury, Allan D.

2017-10-01

The paper deals with the crucial problem of the groundwater parameter estimation that is the basis for efficient modeling and reclamation activities. A hierarchical Bayesian approach is developed: it uses the Akaike's Bayesian Information Criteria in order to estimate the hyperparameters (related to the covariance model chosen) and to quantify the unknown noise variance. The transmissivity identification proceeds in two steps: the first, called empirical Bayesian interpolation, uses Y* (Y = lnT) observations to interpolate Y values on a specified grid; the second, called empirical Bayesian update, improve the previous Y estimate through the addition of hydraulic head observations. The relationship between the head and the lnT has been linearized through a perturbative solution of the flow equation. In order to test the proposed approach, synthetic aquifers from literature have been considered. The aquifers in question contain a variety of boundary conditions (both Dirichelet and Neuman type) and scales of heterogeneities (σY2 = 1.0 and σY2 = 5.3). The estimated transmissivity fields were compared to the true one. The joint use of Y* and head measurements improves the estimation of Y considering both degrees of heterogeneity. Even if the variance of the strong transmissivity field can be considered high for the application of the perturbative approach, the results show the same order of approximation of the non-linear methods proposed in literature. The procedure allows to compute the posterior probability distribution of the target quantities and to quantify the uncertainty in the model prediction. Bayesian updating has advantages related both to the Monte-Carlo (MC) and non-MC approaches. In fact, as the MC methods, Bayesian updating allows computing the direct posterior probability distribution of the target quantities and as non-MC methods it has computational times in the order of seconds.

Bayesian characterization of uncertainty in species interaction strengths.

PubMed

Wolf, Christopher; Novak, Mark; Gitelman, Alix I

2017-06-01

Considerable effort has been devoted to the estimation of species interaction strengths. This effort has focused primarily on statistical significance testing and obtaining point estimates of parameters that contribute to interaction strength magnitudes, leaving the characterization of uncertainty associated with those estimates unconsidered. We consider a means of characterizing the uncertainty of a generalist predator's interaction strengths by formulating an observational method for estimating a predator's prey-specific per capita attack rates as a Bayesian statistical model. This formulation permits the explicit incorporation of multiple sources of uncertainty. A key insight is the informative nature of several so-called non-informative priors that have been used in modeling the sparse data typical of predator feeding surveys. We introduce to ecology a new neutral prior and provide evidence for its superior performance. We use a case study to consider the attack rates in a New Zealand intertidal whelk predator, and we illustrate not only that Bayesian point estimates can be made to correspond with those obtained by frequentist approaches, but also that estimation uncertainty as described by 95% intervals is more useful and biologically realistic using the Bayesian method. In particular, unlike in bootstrap confidence intervals, the lower bounds of the Bayesian posterior intervals for attack rates do not include zero when a predator-prey interaction is in fact observed. We conclude that the Bayesian framework provides a straightforward, probabilistic characterization of interaction strength uncertainty, enabling future considerations of both the deterministic and stochastic drivers of interaction strength and their impact on food webs.

Final Report, DOE Early Career Award: Predictive modeling of complex physical systems: new tools for statistical inference, uncertainty quantification, and experimental design

DOE Office of Scientific and Technical Information (OSTI.GOV)

Marzouk, Youssef

Predictive simulation of complex physical systems increasingly rests on the interplay of experimental observations with computational models. Key inputs, parameters, or structural aspects of models may be incomplete or unknown, and must be developed from indirect and limited observations. At the same time, quantified uncertainties are needed to qualify computational predictions in the support of design and decision-making. In this context, Bayesian statistics provides a foundation for inference from noisy and limited data, but at prohibitive computional expense. This project intends to make rigorous predictive modeling *feasible* in complex physical systems, via accelerated and scalable tools for uncertainty quantification, Bayesianmore » inference, and experimental design. Specific objectives are as follows: 1. Develop adaptive posterior approximations and dimensionality reduction approaches for Bayesian inference in high-dimensional nonlinear systems. 2. Extend accelerated Bayesian methodologies to large-scale {\\em sequential} data assimilation, fully treating nonlinear models and non-Gaussian state and parameter distributions. 3. Devise efficient surrogate-based methods for Bayesian model selection and the learning of model structure. 4. Develop scalable simulation/optimization approaches to nonlinear Bayesian experimental design, for both parameter inference and model selection. 5. Demonstrate these inferential tools on chemical kinetic models in reacting flow, constructing and refining thermochemical and electrochemical models from limited data. Demonstrate Bayesian filtering on canonical stochastic PDEs and in the dynamic estimation of inhomogeneous subsurface properties and flow fields.« less

Information loss in approximately bayesian data assimilation: a comparison of generative and discriminative approaches to estimating agricultural yield

USDA-ARS?s Scientific Manuscript database

Data assimilation and regression are two commonly used methods for predicting agricultural yield from remote sensing observations. Data assimilation is a generative approach because it requires explicit approximations of the Bayesian prior and likelihood to compute the probability density function...

Spectral Bayesian Knowledge Tracing

ERIC Educational Resources Information Center

Falakmasir, Mohammad; Yudelson, Michael; Ritter, Steve; Koedinger, Ken

2015-01-01

Bayesian Knowledge Tracing (BKT) has been in wide use for modeling student skill acquisition in Intelligent Tutoring Systems (ITS). BKT tracks and updates student's latent mastery of a skill as a probability distribution of a binary variable. BKT does so by accounting for observed student successes in applying the skill correctly, where success is…

Ideal AFROC and FROC observers.

PubMed

Khurd, Parmeshwar; Liu, Bin; Gindi, Gene

2010-02-01

Detection of multiple lesions in images is a medically important task and free-response receiver operating characteristic (FROC) analyses and its variants, such as alternative FROC (AFROC) analyses, are commonly used to quantify performance in such tasks. However, ideal observers that optimize FROC or AFROC performance metrics have not yet been formulated in the general case. If available, such ideal observers may turn out to be valuable for imaging system optimization and in the design of computer aided diagnosis techniques for lesion detection in medical images. In this paper, we derive ideal AFROC and FROC observers. They are ideal in that they maximize, amongst all decision strategies, the area, or any partial area, under the associated AFROC or FROC curve. Calculation of observer performance for these ideal observers is computationally quite complex. We can reduce this complexity by considering forms of these observers that use false positive reports derived from signal-absent images only. We also consider a Bayes risk analysis for the multiple-signal detection task with an appropriate definition of costs. A general decision strategy that minimizes Bayes risk is derived. With particular cost constraints, this general decision strategy reduces to the decision strategy associated with the ideal AFROC or FROC observer.

Modular Bayesian Networks with Low-Power Wearable Sensors for Recognizing Eating Activities.

PubMed

Kim, Kee-Hoon; Cho, Sung-Bae

2017-12-11

Recently, recognizing a user's daily activity using a smartphone and wearable sensors has become a popular issue. However, in contrast with the ideal definition of an experiment, there could be numerous complex activities in real life with respect to its various background and contexts: time, space, age, culture, and so on. Recognizing these complex activities with limited low-power sensors, considering the power and memory constraints of the wearable environment and the user's obtrusiveness at once is not an easy problem, although it is very crucial for the activity recognizer to be practically useful. In this paper, we recognize activity of eating, which is one of the most typical examples of a complex activity, using only daily low-power mobile and wearable sensors. To organize the related contexts systemically, we have constructed the context model based on activity theory and the "Five W's", and propose a Bayesian network with 88 nodes to predict uncertain contexts probabilistically. The structure of the proposed Bayesian network is designed by a modular and tree-structured approach to reduce the time complexity and increase the scalability. To evaluate the proposed method, we collected the data with 10 different activities from 25 volunteers of various ages, occupations, and jobs, and have obtained 79.71% accuracy, which outperforms other conventional classifiers by 7.54-14.4%. Analyses of the results showed that our probabilistic approach could also give approximate results even when one of contexts or sensor values has a very heterogeneous pattern or is missing.

Development and comparison in uncertainty assessment based Bayesian modularization method in hydrological modeling

NASA Astrophysics Data System (ADS)

Li, Lu; Xu, Chong-Yu; Engeland, Kolbjørn

2013-04-01

SummaryWith respect to model calibration, parameter estimation and analysis of uncertainty sources, various regression and probabilistic approaches are used in hydrological modeling. A family of Bayesian methods, which incorporates different sources of information into a single analysis through Bayes' theorem, is widely used for uncertainty assessment. However, none of these approaches can well treat the impact of high flows in hydrological modeling. This study proposes a Bayesian modularization uncertainty assessment approach in which the highest streamflow observations are treated as suspect information that should not influence the inference of the main bulk of the model parameters. This study includes a comprehensive comparison and evaluation of uncertainty assessments by our new Bayesian modularization method and standard Bayesian methods using the Metropolis-Hastings (MH) algorithm with the daily hydrological model WASMOD. Three likelihood functions were used in combination with standard Bayesian method: the AR(1) plus Normal model independent of time (Model 1), the AR(1) plus Normal model dependent on time (Model 2) and the AR(1) plus Multi-normal model (Model 3). The results reveal that the Bayesian modularization method provides the most accurate streamflow estimates measured by the Nash-Sutcliffe efficiency and provide the best in uncertainty estimates for low, medium and entire flows compared to standard Bayesian methods. The study thus provides a new approach for reducing the impact of high flows on the discharge uncertainty assessment of hydrological models via Bayesian method.

Bayesian methods for characterizing unknown parameters of material models

DOE PAGES

Emery, J. M.; Grigoriu, M. D.; Field Jr., R. V.

2016-02-04

A Bayesian framework is developed for characterizing the unknown parameters of probabilistic models for material properties. In this framework, the unknown parameters are viewed as random and described by their posterior distributions obtained from prior information and measurements of quantities of interest that are observable and depend on the unknown parameters. The proposed Bayesian method is applied to characterize an unknown spatial correlation of the conductivity field in the definition of a stochastic transport equation and to solve this equation by Monte Carlo simulation and stochastic reduced order models (SROMs). As a result, the Bayesian method is also employed tomore » characterize unknown parameters of material properties for laser welds from measurements of peak forces sustained by these welds.« less

Bayesian methods for characterizing unknown parameters of material models

DOE Office of Scientific and Technical Information (OSTI.GOV)

Emery, J. M.; Grigoriu, M. D.; Field Jr., R. V.

A Bayesian framework is developed for characterizing the unknown parameters of probabilistic models for material properties. In this framework, the unknown parameters are viewed as random and described by their posterior distributions obtained from prior information and measurements of quantities of interest that are observable and depend on the unknown parameters. The proposed Bayesian method is applied to characterize an unknown spatial correlation of the conductivity field in the definition of a stochastic transport equation and to solve this equation by Monte Carlo simulation and stochastic reduced order models (SROMs). As a result, the Bayesian method is also employed tomore » characterize unknown parameters of material properties for laser welds from measurements of peak forces sustained by these welds.« less

Bayesian Inference in the Modern Design of Experiments

NASA Technical Reports Server (NTRS)

DeLoach, Richard

2008-01-01

This paper provides an elementary tutorial overview of Bayesian inference and its potential for application in aerospace experimentation in general and wind tunnel testing in particular. Bayes Theorem is reviewed and examples are provided to illustrate how it can be applied to objectively revise prior knowledge by incorporating insights subsequently obtained from additional observations, resulting in new (posterior) knowledge that combines information from both sources. A logical merger of Bayesian methods and certain aspects of Response Surface Modeling is explored. Specific applications to wind tunnel testing, computational code validation, and instrumentation calibration are discussed.

Bayesian Decision Support

NASA Astrophysics Data System (ADS)

Berliner, M.

2017-12-01

Bayesian statistical decision theory offers a natural framework for decision-policy making in the presence of uncertainty. Key advantages of the approach include efficient incorporation of information and observations. However, in complicated settings it is very difficult, perhaps essentially impossible, to formalize the mathematical inputs needed in the approach. Nevertheless, using the approach as a template is useful for decision support; that is, organizing and communicating our analyses. Bayesian hierarchical modeling is valuable in quantifying and managing uncertainty such cases. I review some aspects of the idea emphasizing statistical model development and use in the context of sea-level rise.

Nutritional status and the influence of TV consumption on female body size ideals in populations recently exposed to the media.

PubMed

Jucker, Jean-Luc; Thornborrow, Tracey; Beierholm, Ulrik; Burt, D Michael; Barton, Robert A; Evans, Elizabeth H; Jamieson, Mark A; Tovée, Martin J; Boothroyd, Lynda G

2017-08-16

Television consumption influences perceptions of attractive female body size. However, cross-cultural research examining media influence on body ideals is typically confounded by differences in the availability of reliable and diverse foodstuffs. 112 participants were recruited from 3 Nicaraguan villages that differed in television consumption and nutritional status, such that the contribution of both factors could be revealed. Participants completed a female figure preference task, reported their television consumption, and responded to several measures assessing nutritional status. Communities with higher television consumption and/or higher nutritional status preferred thinner female bodies than communities with lower television consumption and/or lower nutritional status. Bayesian mixed models estimated the plausible range of effects for television consumption, nutritional status, and other relevant variables on individual preferences. The model explained all meaningful differences between our low-nutrition villages, and television consumption, after sex, was the most likely of these predictors to contribute to variation in preferences (probability mass >95% when modelling only variables with zero-order associations with preferences, but only 90% when modelling all possible predictors). In contrast, we found no likely link with nutritional status. We thus found evidence that where media access and nutritional status are confounded, media is the more likely predictor of body ideals.

Wavelet-Bayesian inference of cosmic strings embedded in the cosmic microwave background

NASA Astrophysics Data System (ADS)

McEwen, J. D.; Feeney, S. M.; Peiris, H. V.; Wiaux, Y.; Ringeval, C.; Bouchet, F. R.

2017-12-01

Cosmic strings are a well-motivated extension to the standard cosmological model and could induce a subdominant component in the anisotropies of the cosmic microwave background (CMB), in addition to the standard inflationary component. The detection of strings, while observationally challenging, would provide a direct probe of physics at very high-energy scales. We develop a framework for cosmic string inference from observations of the CMB made over the celestial sphere, performing a Bayesian analysis in wavelet space where the string-induced CMB component has distinct statistical properties to the standard inflationary component. Our wavelet-Bayesian framework provides a principled approach to compute the posterior distribution of the string tension Gμ and the Bayesian evidence ratio comparing the string model to the standard inflationary model. Furthermore, we present a technique to recover an estimate of any string-induced CMB map embedded in observational data. Using Planck-like simulations, we demonstrate the application of our framework and evaluate its performance. The method is sensitive to Gμ ∼ 5 × 10-7 for Nambu-Goto string simulations that include an integrated Sachs-Wolfe contribution only and do not include any recombination effects, before any parameters of the analysis are optimized. The sensitivity of the method compares favourably with other techniques applied to the same simulations.

A Bayesian hierarchical approach to comparative audit for carotid surgery.

PubMed

Kuhan, G; Marshall, E C; Abidia, A F; Chetter, I C; McCollum, P T

2002-12-01

the aim of this study was to illustrate how a Bayesian hierarchical modelling approach can aid the reliable comparison of outcome rates between surgeons. retrospective analysis of prospective and retrospective data. binary outcome data (death/stroke within 30 days), together with information on 15 possible risk factors specific for CEA were available on 836 CEAs performed by four vascular surgeons from 1992-99. The median patient age was 68 (range 38-86) years and 60% were men. the model was developed using the WinBUGS software. After adjusting for patient-level risk factors, a cross-validatory approach was adopted to identify "divergent" performance. A ranking exercise was also carried out. the overall observed 30-day stroke/death rate was 3.9% (33/836). The model found diabetes, stroke and heart disease to be significant risk factors. There was no significant difference between the predicted and observed outcome rates for any surgeon (Bayesian p -value>0.05). Each surgeon had a median rank of 3 with associated 95% CI 1.0-5.0, despite the variability of observed stroke/death rate from 2.9-4.4%. After risk adjustment, there was very little residual between-surgeon variability in outcome rate. Bayesian hierarchical models can help to accurately quantify the uncertainty associated with surgeons' performance and rank.

Bayesian Network Meta-Analysis for Unordered Categorical Outcomes with Incomplete Data

ERIC Educational Resources Information Center

Schmid, Christopher H.; Trikalinos, Thomas A.; Olkin, Ingram

2014-01-01

We develop a Bayesian multinomial network meta-analysis model for unordered (nominal) categorical outcomes that allows for partially observed data in which exact event counts may not be known for each category. This model properly accounts for correlations of counts in mutually exclusive categories and enables proper comparison and ranking of…

A Comparison of Imputation Methods for Bayesian Factor Analysis Models

ERIC Educational Resources Information Center

Merkle, Edgar C.

2011-01-01

Imputation methods are popular for the handling of missing data in psychology. The methods generally consist of predicting missing data based on observed data, yielding a complete data set that is amiable to standard statistical analyses. In the context of Bayesian factor analysis, this article compares imputation under an unrestricted…

Prediction of Individual Serum Infliximab Concentrations in Inflammatory Bowel Disease by a Bayesian Dashboard System.

PubMed

Eser, Alexander; Primas, Christian; Reinisch, Sieglinde; Vogelsang, Harald; Novacek, Gottfried; Mould, Diane R; Reinisch, Walter

2018-01-30

Despite a robust exposure-response relationship of infliximab in inflammatory bowel disease (IBD), attempts to adjust dosing to individually predicted serum concentrations of infliximab (SICs) are lacking. Compared with labor-intensive conventional software for pharmacokinetic (PK) modeling (eg, NONMEM) dashboards are easy-to-use programs incorporating complex Bayesian statistics to determine individual pharmacokinetics. We evaluated various infliximab detection assays and the number of samples needed to precisely forecast individual SICs using a Bayesian dashboard. We assessed long-term infliximab retention in patients being dosed concordantly versus discordantly with Bayesian dashboard recommendations. Three hundred eighty-two serum samples from 117 adult IBD patients on infliximab maintenance therapy were analyzed by 3 commercially available assays. Data from each assay was modeled using NONMEM and a Bayesian dashboard. PK parameter precision and residual variability were assessed. Forecast concentrations from both systems were compared with observed concentrations. Infliximab retention was assessed by prediction for dose intensification via Bayesian dashboard versus real-life practice. Forecast precision of SICs varied between detection assays. At least 3 SICs from a reliable assay are needed for an accurate forecast. The Bayesian dashboard performed similarly to NONMEM to predict SICs. Patients dosed concordantly with Bayesian dashboard recommendations had a significantly longer median drug survival than those dosed discordantly (51.5 versus 4.6 months, P < .0001). The Bayesian dashboard helps to assess the diagnostic performance of infliximab detection assays. Three, not single, SICs provide sufficient information for individualized dose adjustment when incorporated into the Bayesian dashboard. Treatment adjusted to forecasted SICs is associated with longer drug retention of infliximab. © 2018, The American College of Clinical Pharmacology.

Online Variational Bayesian Filtering-Based Mobile Target Tracking in Wireless Sensor Networks

PubMed Central

Zhou, Bingpeng; Chen, Qingchun; Li, Tiffany Jing; Xiao, Pei

2014-01-01

The received signal strength (RSS)-based online tracking for a mobile node in wireless sensor networks (WSNs) is investigated in this paper. Firstly, a multi-layer dynamic Bayesian network (MDBN) is introduced to characterize the target mobility with either directional or undirected movement. In particular, it is proposed to employ the Wishart distribution to approximate the time-varying RSS measurement precision's randomness due to the target movement. It is shown that the proposed MDBN offers a more general analysis model via incorporating the underlying statistical information of both the target movement and observations, which can be utilized to improve the online tracking capability by exploiting the Bayesian statistics. Secondly, based on the MDBN model, a mean-field variational Bayesian filtering (VBF) algorithm is developed to realize the online tracking of a mobile target in the presence of nonlinear observations and time-varying RSS precision, wherein the traditional Bayesian filtering scheme cannot be directly employed. Thirdly, a joint optimization between the real-time velocity and its prior expectation is proposed to enable online velocity tracking in the proposed online tacking scheme. Finally, the associated Bayesian Cramer–Rao Lower Bound (BCRLB) analysis and numerical simulations are conducted. Our analysis unveils that, by exploiting the potential state information via the general MDBN model, the proposed VBF algorithm provides a promising solution to the online tracking of a mobile node in WSNs. In addition, it is shown that the final tracking accuracy linearly scales with its expectation when the RSS measurement precision is time-varying. PMID:25393784

Bayesian Forecasting Tool to Predict the Need for Antidote in Acute Acetaminophen Overdose.

PubMed

Desrochers, Julie; Wojciechowski, Jessica; Klein-Schwartz, Wendy; Gobburu, Jogarao V S; Gopalakrishnan, Mathangi

2017-08-01

Acetaminophen (APAP) overdose is the leading cause of acute liver injury in the United States. Patients with elevated plasma acetaminophen concentrations (PACs) require hepatoprotective treatment with N-acetylcysteine (NAC). These patients have been primarily risk-stratified using the Rumack-Matthew nomogram. Previous studies of acute APAP overdoses found that the nomogram failed to accurately predict the need for the antidote. The objectives of this study were to develop a population pharmacokinetic (PK) model for APAP following acute overdose and evaluate the utility of population PK model-based Bayesian forecasting in NAC administration decisions. Limited APAP concentrations from a retrospective cohort of acute overdosed subjects from the Maryland Poison Center were used to develop the population PK model and to investigate the effect of type of APAP products and other prognostic factors. The externally validated population PK model was used a prior for Bayesian forecasting to predict the individual PK profile when one or two observed PACs were available. The utility of Bayesian forecasted APAP concentration-time profiles inferred from one (first) or two (first and second) PAC observations were also tested in their ability to predict the observed NAC decisions. A one-compartment model with first-order absorption and elimination adequately described the data with single activated charcoal and APAP products as significant covariates on absorption and bioavailability. The Bayesian forecasted individual concentration-time profiles had acceptable bias (6.2% and 9.8%) and accuracy (40.5% and 41.9%) when either one or two PACs were considered, respectively. The sensitivity and negative predictive value of the Bayesian forecasted NAC decisions using one PAC were 84% and 92.6%, respectively. The population PK analysis provided a platform for acceptably predicting an individual's concentration-time profile following acute APAP overdose with at least one PAC, and the individual's covariate profile, and can potentially be used for making early NAC administration decisions. © 2017 Pharmacotherapy Publications, Inc.

Bayesian Techniques for Comparing Time-dependent GRMHD Simulations to Variable Event Horizon Telescope Observations

NASA Astrophysics Data System (ADS)

Kim, Junhan; Marrone, Daniel P.; Chan, Chi-Kwan; Medeiros, Lia; Özel, Feryal; Psaltis, Dimitrios

2016-12-01

The Event Horizon Telescope (EHT) is a millimeter-wavelength, very-long-baseline interferometry (VLBI) experiment that is capable of observing black holes with horizon-scale resolution. Early observations have revealed variable horizon-scale emission in the Galactic Center black hole, Sagittarius A* (Sgr A*). Comparing such observations to time-dependent general relativistic magnetohydrodynamic (GRMHD) simulations requires statistical tools that explicitly consider the variability in both the data and the models. We develop here a Bayesian method to compare time-resolved simulation images to variable VLBI data, in order to infer model parameters and perform model comparisons. We use mock EHT data based on GRMHD simulations to explore the robustness of this Bayesian method and contrast it to approaches that do not consider the effects of variability. We find that time-independent models lead to offset values of the inferred parameters with artificially reduced uncertainties. Moreover, neglecting the variability in the data and the models often leads to erroneous model selections. We finally apply our method to the early EHT data on Sgr A*.

BAYESIAN TECHNIQUES FOR COMPARING TIME-DEPENDENT GRMHD SIMULATIONS TO VARIABLE EVENT HORIZON TELESCOPE OBSERVATIONS

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kim, Junhan; Marrone, Daniel P.; Chan, Chi-Kwan

2016-12-01

The Event Horizon Telescope (EHT) is a millimeter-wavelength, very-long-baseline interferometry (VLBI) experiment that is capable of observing black holes with horizon-scale resolution. Early observations have revealed variable horizon-scale emission in the Galactic Center black hole, Sagittarius A* (Sgr A*). Comparing such observations to time-dependent general relativistic magnetohydrodynamic (GRMHD) simulations requires statistical tools that explicitly consider the variability in both the data and the models. We develop here a Bayesian method to compare time-resolved simulation images to variable VLBI data, in order to infer model parameters and perform model comparisons. We use mock EHT data based on GRMHD simulations to explore themore » robustness of this Bayesian method and contrast it to approaches that do not consider the effects of variability. We find that time-independent models lead to offset values of the inferred parameters with artificially reduced uncertainties. Moreover, neglecting the variability in the data and the models often leads to erroneous model selections. We finally apply our method to the early EHT data on Sgr A*.« less

Using Bayesian Adaptive Trial Designs for Comparative Effectiveness Research: A Virtual Trial Execution.

PubMed

Luce, Bryan R; Connor, Jason T; Broglio, Kristine R; Mullins, C Daniel; Ishak, K Jack; Saunders, Elijah; Davis, Barry R

2016-09-20

Bayesian and adaptive clinical trial designs offer the potential for more efficient processes that result in lower sample sizes and shorter trial durations than traditional designs. To explore the use and potential benefits of Bayesian adaptive clinical trial designs in comparative effectiveness research. Virtual execution of ALLHAT (Antihypertensive and Lipid-Lowering Treatment to Prevent Heart Attack Trial) as if it had been done according to a Bayesian adaptive trial design. Comparative effectiveness trial of antihypertensive medications. Patient data sampled from the more than 42 000 patients enrolled in ALLHAT with publicly available data. Number of patients randomly assigned between groups, trial duration, observed numbers of events, and overall trial results and conclusions. The Bayesian adaptive approach and original design yielded similar overall trial conclusions. The Bayesian adaptive trial randomly assigned more patients to the better-performing group and would probably have ended slightly earlier. This virtual trial execution required limited resampling of ALLHAT patients for inclusion in RE-ADAPT (REsearch in ADAptive methods for Pragmatic Trials). Involvement of a data monitoring committee and other trial logistics were not considered. In a comparative effectiveness research trial, Bayesian adaptive trial designs are a feasible approach and potentially generate earlier results and allocate more patients to better-performing groups. National Heart, Lung, and Blood Institute.

"A Bayesian sensitivity analysis to evaluate the impact of unmeasured confounding with external data: a real world comparative effectiveness study in osteoporosis".

PubMed

Zhang, Xiang; Faries, Douglas E; Boytsov, Natalie; Stamey, James D; Seaman, John W

2016-09-01

Observational studies are frequently used to assess the effectiveness of medical interventions in routine clinical practice. However, the use of observational data for comparative effectiveness is challenged by selection bias and the potential of unmeasured confounding. This is especially problematic for analyses using a health care administrative database, in which key clinical measures are often not available. This paper provides an approach to conducting a sensitivity analyses to investigate the impact of unmeasured confounding in observational studies. In a real world osteoporosis comparative effectiveness study, the bone mineral density (BMD) score, an important predictor of fracture risk and a factor in the selection of osteoporosis treatments, is unavailable in the data base and lack of baseline BMD could potentially lead to significant selection bias. We implemented Bayesian twin-regression models, which simultaneously model both the observed outcome and the unobserved unmeasured confounder, using information from external sources. A sensitivity analysis was also conducted to assess the robustness of our conclusions to changes in such external data. The use of Bayesian modeling in this study suggests that the lack of baseline BMD did have a strong impact on the analysis, reversing the direction of the estimated effect (odds ratio of fracture incidence at 24 months: 0.40 vs. 1.36, with/without adjusting for unmeasured baseline BMD). The Bayesian twin-regression models provide a flexible sensitivity analysis tool to quantitatively assess the impact of unmeasured confounding in observational studies. Copyright © 2016 John Wiley & Sons, Ltd. Copyright © 2016 John Wiley & Sons, Ltd.

Exoplanet Biosignatures: Future Directions

PubMed Central

Bains, William; Cronin, Leroy; DasSarma, Shiladitya; Danielache, Sebastian; Domagal-Goldman, Shawn; Kacar, Betul; Kiang, Nancy Y.; Lenardic, Adrian; Reinhard, Christopher T.; Moore, William; Schwieterman, Edward W.; Shkolnik, Evgenya L.; Smith, Harrison B.

2018-01-01

Abstract We introduce a Bayesian method for guiding future directions for detection of life on exoplanets. We describe empirical and theoretical work necessary to place constraints on the relevant likelihoods, including those emerging from better understanding stellar environment, planetary climate and geophysics, geochemical cycling, the universalities of physics and chemistry, the contingencies of evolutionary history, the properties of life as an emergent complex system, and the mechanisms driving the emergence of life. We provide examples for how the Bayesian formalism could guide future search strategies, including determining observations to prioritize or deciding between targeted searches or larger lower resolution surveys to generate ensemble statistics and address how a Bayesian methodology could constrain the prior probability of life with or without a positive detection. Key Words: Exoplanets—Biosignatures—Life detection—Bayesian analysis. Astrobiology 18, 779–824. PMID:29938538

Sequential Inverse Problems Bayesian Principles and the Logistic Map Example

NASA Astrophysics Data System (ADS)

Duan, Lian; Farmer, Chris L.; Moroz, Irene M.

2010-09-01

Bayesian statistics provides a general framework for solving inverse problems, but is not without interpretation and implementation problems. This paper discusses difficulties arising from the fact that forward models are always in error to some extent. Using a simple example based on the one-dimensional logistic map, we argue that, when implementation problems are minimal, the Bayesian framework is quite adequate. In this paper the Bayesian Filter is shown to be able to recover excellent state estimates in the perfect model scenario (PMS) and to distinguish the PMS from the imperfect model scenario (IMS). Through a quantitative comparison of the way in which the observations are assimilated in both the PMS and the IMS scenarios, we suggest that one can, sometimes, measure the degree of imperfection.

Population forecasts for Bangladesh, using a Bayesian methodology.

PubMed

Mahsin, Md; Hossain, Syed Shahadat

2012-12-01

Population projection for many developing countries could be quite a challenging task for the demographers mostly due to lack of availability of enough reliable data. The objective of this paper is to present an overview of the existing methods for population forecasting and to propose an alternative based on the Bayesian statistics, combining the formality of inference. The analysis has been made using Markov Chain Monte Carlo (MCMC) technique for Bayesian methodology available with the software WinBUGS. Convergence diagnostic techniques available with the WinBUGS software have been applied to ensure the convergence of the chains necessary for the implementation of MCMC. The Bayesian approach allows for the use of observed data and expert judgements by means of appropriate priors, and a more realistic population forecasts, along with associated uncertainty, has been possible.

Exoplanet Biosignatures: Future Directions.

PubMed

Walker, Sara I; Bains, William; Cronin, Leroy; DasSarma, Shiladitya; Danielache, Sebastian; Domagal-Goldman, Shawn; Kacar, Betul; Kiang, Nancy Y; Lenardic, Adrian; Reinhard, Christopher T; Moore, William; Schwieterman, Edward W; Shkolnik, Evgenya L; Smith, Harrison B

2018-06-01

We introduce a Bayesian method for guiding future directions for detection of life on exoplanets. We describe empirical and theoretical work necessary to place constraints on the relevant likelihoods, including those emerging from better understanding stellar environment, planetary climate and geophysics, geochemical cycling, the universalities of physics and chemistry, the contingencies of evolutionary history, the properties of life as an emergent complex system, and the mechanisms driving the emergence of life. We provide examples for how the Bayesian formalism could guide future search strategies, including determining observations to prioritize or deciding between targeted searches or larger lower resolution surveys to generate ensemble statistics and address how a Bayesian methodology could constrain the prior probability of life with or without a positive detection. Key Words: Exoplanets-Biosignatures-Life detection-Bayesian analysis. Astrobiology 18, 779-824.

Exoplanet Biosignatures: A Framework for Their Assessment.

PubMed

Catling, David C; Krissansen-Totton, Joshua; Kiang, Nancy Y; Crisp, David; Robinson, Tyler D; DasSarma, Shiladitya; Rushby, Andrew J; Del Genio, Anthony; Bains, William; Domagal-Goldman, Shawn

2018-04-20

Finding life on exoplanets from telescopic observations is an ultimate goal of exoplanet science. Life produces gases and other substances, such as pigments, which can have distinct spectral or photometric signatures. Whether or not life is found with future data must be expressed with probabilities, requiring a framework of biosignature assessment. We present a framework in which we advocate using biogeochemical "Exo-Earth System" models to simulate potential biosignatures in spectra or photometry. Given actual observations, simulations are used to find the Bayesian likelihoods of those data occurring for scenarios with and without life. The latter includes "false positives" wherein abiotic sources mimic biosignatures. Prior knowledge of factors influencing planetary inhabitation, including previous observations, is combined with the likelihoods to give the Bayesian posterior probability of life existing on a given exoplanet. Four components of observation and analysis are necessary. (1) Characterization of stellar (e.g., age and spectrum) and exoplanetary system properties, including "external" exoplanet parameters (e.g., mass and radius), to determine an exoplanet's suitability for life. (2) Characterization of "internal" exoplanet parameters (e.g., climate) to evaluate habitability. (3) Assessment of potential biosignatures within the environmental context (components 1-2), including corroborating evidence. (4) Exclusion of false positives. We propose that resulting posterior Bayesian probabilities of life's existence map to five confidence levels, ranging from "very likely" (90-100%) to "very unlikely" (<10%) inhabited. Key Words: Bayesian statistics-Biosignatures-Drake equation-Exoplanets-Habitability-Planetary science. Astrobiology 18, xxx-xxx.

Efficiency of the human observer detecting random signals in random backgrounds

PubMed Central

Park, Subok; Clarkson, Eric; Kupinski, Matthew A.; Barrett, Harrison H.

2008-01-01

The efficiencies of the human observer and the channelized-Hotelling observer relative to the ideal observer for signal-detection tasks are discussed. Both signal-known-exactly (SKE) tasks and signal-known-statistically (SKS) tasks are considered. Signal location is uncertain for the SKS tasks, and lumpy backgrounds are used for background uncertainty in both cases. Markov chain Monte Carlo methods are employed to determine ideal-observer performance on the detection tasks. Psychophysical studies are conducted to compute human-observer performance on the same tasks. Efficiency is computed as the squared ratio of the detectabilities of the observer of interest to the ideal observer. Human efficiencies are approximately 2.1% and 24%, respectively, for the SKE and SKS tasks. The results imply that human observers are not affected as much as the ideal observer by signal-location uncertainty even though the ideal observer outperforms the human observer for both tasks. Three different simplified pinhole imaging systems are simulated, and the humans and the model observers rank the systems in the same order for both the SKE and the SKS tasks. PMID:15669610

Bayesian statistics in radionuclide metrology: measurement of a decaying source

NASA Astrophysics Data System (ADS)

Bochud, François O.; Bailat, Claude J.; Laedermann, Jean-Pascal

2007-08-01

The most intuitive way of defining a probability is perhaps through the frequency at which it appears when a large number of trials are realized in identical conditions. The probability derived from the obtained histogram characterizes the so-called frequentist or conventional statistical approach. In this sense, probability is defined as a physical property of the observed system. By contrast, in Bayesian statistics, a probability is not a physical property or a directly observable quantity, but a degree of belief or an element of inference. The goal of this paper is to show how Bayesian statistics can be used in radionuclide metrology and what its advantages and disadvantages are compared with conventional statistics. This is performed through the example of an yttrium-90 source typically encountered in environmental surveillance measurement. Because of the very low activity of this kind of source and the small half-life of the radionuclide, this measurement takes several days, during which the source decays significantly. Several methods are proposed to compute simultaneously the number of unstable nuclei at a given reference time, the decay constant and the background. Asymptotically, all approaches give the same result. However, Bayesian statistics produces coherent estimates and confidence intervals in a much smaller number of measurements. Apart from the conceptual understanding of statistics, the main difficulty that could deter radionuclide metrologists from using Bayesian statistics is the complexity of the computation.

Finite‐fault Bayesian inversion of teleseismic body waves

USGS Publications Warehouse

Clayton, Brandon; Hartzell, Stephen; Moschetti, Morgan P.; Minson, Sarah E.

2017-01-01

Inverting geophysical data has provided fundamental information about the behavior of earthquake rupture. However, inferring kinematic source model parameters for finite‐fault ruptures is an intrinsically underdetermined problem (the problem of nonuniqueness), because we are restricted to finite noisy observations. Although many studies use least‐squares techniques to make the finite‐fault problem tractable, these methods generally lack the ability to apply non‐Gaussian error analysis and the imposition of nonlinear constraints. However, the Bayesian approach can be employed to find a Gaussian or non‐Gaussian distribution of all probable model parameters, while utilizing nonlinear constraints. We present case studies to quantify the resolving power and associated uncertainties using only teleseismic body waves in a Bayesian framework to infer the slip history for a synthetic case and two earthquakes: the 2011 Mw 7.1 Van, east Turkey, earthquake and the 2010 Mw 7.2 El Mayor–Cucapah, Baja California, earthquake. In implementing the Bayesian method, we further present two distinct solutions to investigate the uncertainties by performing the inversion with and without velocity structure perturbations. We find that the posterior ensemble becomes broader when including velocity structure variability and introduces a spatial smearing of slip. Using the Bayesian framework solely on teleseismic body waves, we find rake is poorly constrained by the observations and rise time is poorly resolved when slip amplitude is low.

Bayesian inference of a historical bottleneck in a heavily exploited marine mammal.

PubMed

Hoffman, J I; Grant, S M; Forcada, J; Phillips, C D

2011-10-01

Emerging Bayesian analytical approaches offer increasingly sophisticated means of reconstructing historical population dynamics from genetic data, but have been little applied to scenarios involving demographic bottlenecks. Consequently, we analysed a large mitochondrial and microsatellite dataset from the Antarctic fur seal Arctocephalus gazella, a species subjected to one of the most extreme examples of uncontrolled exploitation in history when it was reduced to the brink of extinction by the sealing industry during the late eighteenth and nineteenth centuries. Classical bottleneck tests, which exploit the fact that rare alleles are rapidly lost during demographic reduction, yielded ambiguous results. In contrast, a strong signal of recent demographic decline was detected using both Bayesian skyline plots and Approximate Bayesian Computation, the latter also allowing derivation of posterior parameter estimates that were remarkably consistent with historical observations. This was achieved using only contemporary samples, further emphasizing the potential of Bayesian approaches to address important problems in conservation and evolutionary biology. © 2011 Blackwell Publishing Ltd.

Bayesian conditional-independence modeling of the AIDS epidemic in England and Wales

NASA Astrophysics Data System (ADS)

Gilks, Walter R.; De Angelis, Daniela; Day, Nicholas E.

We describe the use of conditional-independence modeling, Bayesian inference and Markov chain Monte Carlo, to model and project the HIV-AIDS epidemic in homosexual/bisexual males in England and Wales. Complexity in this analysis arises through selectively missing data, indirectly observed underlying processes, and measurement error. Our emphasis is on presentation and discussion of the concepts, not on the technicalities of this analysis, which can be found elsewhere [D. De Angelis, W.R. Gilks, N.E. Day, Bayesian projection of the the acquired immune deficiency syndrome epidemic (with discussion), Applied Statistics, in press].

Probabilistic Inference: Task Dependency and Individual Differences of Probability Weighting Revealed by Hierarchical Bayesian Modeling

PubMed Central

Boos, Moritz; Seer, Caroline; Lange, Florian; Kopp, Bruno

2016-01-01

Cognitive determinants of probabilistic inference were examined using hierarchical Bayesian modeling techniques. A classic urn-ball paradigm served as experimental strategy, involving a factorial two (prior probabilities) by two (likelihoods) design. Five computational models of cognitive processes were compared with the observed behavior. Parameter-free Bayesian posterior probabilities and parameter-free base rate neglect provided inadequate models of probabilistic inference. The introduction of distorted subjective probabilities yielded more robust and generalizable results. A general class of (inverted) S-shaped probability weighting functions had been proposed; however, the possibility of large differences in probability distortions not only across experimental conditions, but also across individuals, seems critical for the model's success. It also seems advantageous to consider individual differences in parameters of probability weighting as being sampled from weakly informative prior distributions of individual parameter values. Thus, the results from hierarchical Bayesian modeling converge with previous results in revealing that probability weighting parameters show considerable task dependency and individual differences. Methodologically, this work exemplifies the usefulness of hierarchical Bayesian modeling techniques for cognitive psychology. Theoretically, human probabilistic inference might be best described as the application of individualized strategic policies for Bayesian belief revision. PMID:27303323

Structural mapping in statistical word problems: A relational reasoning approach to Bayesian inference.

PubMed

Johnson, Eric D; Tubau, Elisabet

2017-06-01

Presenting natural frequencies facilitates Bayesian inferences relative to using percentages. Nevertheless, many people, including highly educated and skilled reasoners, still fail to provide Bayesian responses to these computationally simple problems. We show that the complexity of relational reasoning (e.g., the structural mapping between the presented and requested relations) can help explain the remaining difficulties. With a non-Bayesian inference that required identical arithmetic but afforded a more direct structural mapping, performance was universally high. Furthermore, reducing the relational demands of the task through questions that directed reasoners to use the presented statistics, as compared with questions that prompted the representation of a second, similar sample, also significantly improved reasoning. Distinct error patterns were also observed between these presented- and similar-sample scenarios, which suggested differences in relational-reasoning strategies. On the other hand, while higher numeracy was associated with better Bayesian reasoning, higher-numerate reasoners were not immune to the relational complexity of the task. Together, these findings validate the relational-reasoning view of Bayesian problem solving and highlight the importance of considering not only the presented task structure, but also the complexity of the structural alignment between the presented and requested relations.

A Bayesian Approach for Summarizing and Modeling Time-Series Exposure Data with Left Censoring.

PubMed

Houseman, E Andres; Virji, M Abbas

2017-08-01

Direct reading instruments are valuable tools for measuring exposure as they provide real-time measurements for rapid decision making. However, their use is limited to general survey applications in part due to issues related to their performance. Moreover, statistical analysis of real-time data is complicated by autocorrelation among successive measurements, non-stationary time series, and the presence of left-censoring due to limit-of-detection (LOD). A Bayesian framework is proposed that accounts for non-stationary autocorrelation and LOD issues in exposure time-series data in order to model workplace factors that affect exposure and estimate summary statistics for tasks or other covariates of interest. A spline-based approach is used to model non-stationary autocorrelation with relatively few assumptions about autocorrelation structure. Left-censoring is addressed by integrating over the left tail of the distribution. The model is fit using Markov-Chain Monte Carlo within a Bayesian paradigm. The method can flexibly account for hierarchical relationships, random effects and fixed effects of covariates. The method is implemented using the rjags package in R, and is illustrated by applying it to real-time exposure data. Estimates for task means and covariates from the Bayesian model are compared to those from conventional frequentist models including linear regression, mixed-effects, and time-series models with different autocorrelation structures. Simulations studies are also conducted to evaluate method performance. Simulation studies with percent of measurements below the LOD ranging from 0 to 50% showed lowest root mean squared errors for task means and the least biased standard deviations from the Bayesian model compared to the frequentist models across all levels of LOD. In the application, task means from the Bayesian model were similar to means from the frequentist models, while the standard deviations were different. Parameter estimates for covariates were significant in some frequentist models, but in the Bayesian model their credible intervals contained zero; such discrepancies were observed in multiple datasets. Variance components from the Bayesian model reflected substantial autocorrelation, consistent with the frequentist models, except for the auto-regressive moving average model. Plots of means from the Bayesian model showed good fit to the observed data. The proposed Bayesian model provides an approach for modeling non-stationary autocorrelation in a hierarchical modeling framework to estimate task means, standard deviations, quantiles, and parameter estimates for covariates that are less biased and have better performance characteristics than some of the contemporary methods. Published by Oxford University Press on behalf of the British Occupational Hygiene Society 2017.

Prediction and assimilation of surf-zone processes using a Bayesian network: Part II: Inverse models

USGS Publications Warehouse

Plant, Nathaniel G.; Holland, K. Todd

2011-01-01

A Bayesian network model has been developed to simulate a relatively simple problem of wave propagation in the surf zone (detailed in Part I). Here, we demonstrate that this Bayesian model can provide both inverse modeling and data-assimilation solutions for predicting offshore wave heights and depth estimates given limited wave-height and depth information from an onshore location. The inverse method is extended to allow data assimilation using observational inputs that are not compatible with deterministic solutions of the problem. These inputs include sand bar positions (instead of bathymetry) and estimates of the intensity of wave breaking (instead of wave-height observations). Our results indicate that wave breaking information is essential to reduce prediction errors. In many practical situations, this information could be provided from a shore-based observer or from remote-sensing systems. We show that various combinations of the assimilated inputs significantly reduce the uncertainty in the estimates of water depths and wave heights in the model domain. Application of the Bayesian network model to new field data demonstrated significant predictive skill (R2 = 0.7) for the inverse estimate of a month-long time series of offshore wave heights. The Bayesian inverse results include uncertainty estimates that were shown to be most accurate when given uncertainty in the inputs (e.g., depth and tuning parameters). Furthermore, the inverse modeling was extended to directly estimate tuning parameters associated with the underlying wave-process model. The inverse estimates of the model parameters not only showed an offshore wave height dependence consistent with results of previous studies but the uncertainty estimates of the tuning parameters also explain previously reported variations in the model parameters.

Bayesian State-Space Modelling of Conventional Acoustic Tracking Provides Accurate Descriptors of Home Range Behavior in a Small-Bodied Coastal Fish Species

PubMed Central

Alós, Josep; Palmer, Miquel; Balle, Salvador; Arlinghaus, Robert

2016-01-01

State-space models (SSM) are increasingly applied in studies involving biotelemetry-generated positional data because they are able to estimate movement parameters from positions that are unobserved or have been observed with non-negligible observational error. Popular telemetry systems in marine coastal fish consist of arrays of omnidirectional acoustic receivers, which generate a multivariate time-series of detection events across the tracking period. Here we report a novel Bayesian fitting of a SSM application that couples mechanistic movement properties within a home range (a specific case of random walk weighted by an Ornstein-Uhlenbeck process) with a model of observational error typical for data obtained from acoustic receiver arrays. We explored the performance and accuracy of the approach through simulation modelling and extensive sensitivity analyses of the effects of various configurations of movement properties and time-steps among positions. Model results show an accurate and unbiased estimation of the movement parameters, and in most cases the simulated movement parameters were properly retrieved. Only in extreme situations (when fast swimming speeds are combined with pooling the number of detections over long time-steps) the model produced some bias that needs to be accounted for in field applications. Our method was subsequently applied to real acoustic tracking data collected from a small marine coastal fish species, the pearly razorfish, Xyrichtys novacula. The Bayesian SSM we present here constitutes an alternative for those used to the Bayesian way of reasoning. Our Bayesian SSM can be easily adapted and generalized to any species, thereby allowing studies in freely roaming animals on the ecological and evolutionary consequences of home ranges and territory establishment, both in fishes and in other taxa. PMID:27119718

Impact assessment of extreme storm events using a Bayesian network

USGS Publications Warehouse

den Heijer, C.(Kees); Knipping, Dirk T.J.A.; Plant, Nathaniel G.; van Thiel de Vries, Jaap S. M.; Baart, Fedor; van Gelder, Pieter H. A. J. M.

2012-01-01

This paper describes an investigation on the usefulness of Bayesian Networks in the safety assessment of dune coasts. A network has been created that predicts the erosion volume based on hydraulic boundary conditions and a number of cross-shore profile indicators. Field measurement data along a large part of the Dutch coast has been used to train the network. Corresponding storm impact on the dunes was calculated with an empirical dune erosion model named duros+. Comparison between the Bayesian Network predictions and the original duros+ results, here considered as observations, results in a skill up to 0.88, provided that the training data covers the range of predictions. Hence, the predictions from a deterministic model (duros+) can be captured in a probabilistic model (Bayesian Network) such that both the process knowledge and uncertainties can be included in impact and vulnerability assessments.

Modular Bayesian Networks with Low-Power Wearable Sensors for Recognizing Eating Activities

PubMed Central

Kim, Kee-Hoon

2017-01-01

Recently, recognizing a user’s daily activity using a smartphone and wearable sensors has become a popular issue. However, in contrast with the ideal definition of an experiment, there could be numerous complex activities in real life with respect to its various background and contexts: time, space, age, culture, and so on. Recognizing these complex activities with limited low-power sensors, considering the power and memory constraints of the wearable environment and the user’s obtrusiveness at once is not an easy problem, although it is very crucial for the activity recognizer to be practically useful. In this paper, we recognize activity of eating, which is one of the most typical examples of a complex activity, using only daily low-power mobile and wearable sensors. To organize the related contexts systemically, we have constructed the context model based on activity theory and the “Five W’s”, and propose a Bayesian network with 88 nodes to predict uncertain contexts probabilistically. The structure of the proposed Bayesian network is designed by a modular and tree-structured approach to reduce the time complexity and increase the scalability. To evaluate the proposed method, we collected the data with 10 different activities from 25 volunteers of various ages, occupations, and jobs, and have obtained 79.71% accuracy, which outperforms other conventional classifiers by 7.54–14.4%. Analyses of the results showed that our probabilistic approach could also give approximate results even when one of contexts or sensor values has a very heterogeneous pattern or is missing. PMID:29232937

Virtual Representation of IID Observations in Bayesian Belief Networks

DTIC Science & Technology

1994-04-01

programs for structuring and using Bayesian inference include ERGO ( Noetic Systems, Inc., 1991) and HUGIN (Andersen, Jensen, Olesen, & Jensen, 1989...Nichols, S.. Chipman, & R. Brennan (Eds.), Cognitively diagnostic assessment. Hillsdale, NJ: Erlbaum. Noetic Systems, Inc. (1991). ERGO [computer...Dr Geore Eageiard Jr Chicago IL 60612 US Naval Academy Division of Educational Studies Annapolis MD 21402-5002 Emory University Dr Janice Gifford 210

The Approximate Bayesian Computation methods in the localization of the atmospheric contamination source

NASA Astrophysics Data System (ADS)

Kopka, P.; Wawrzynczak, A.; Borysiewicz, M.

2015-09-01

In many areas of application, a central problem is a solution to the inverse problem, especially estimation of the unknown model parameters to model the underlying dynamics of a physical system precisely. In this situation, the Bayesian inference is a powerful tool to combine observed data with prior knowledge to gain the probability distribution of searched parameters. We have applied the modern methodology named Sequential Approximate Bayesian Computation (S-ABC) to the problem of tracing the atmospheric contaminant source. The ABC is technique commonly used in the Bayesian analysis of complex models and dynamic system. Sequential methods can significantly increase the efficiency of the ABC. In the presented algorithm, the input data are the on-line arriving concentrations of released substance registered by distributed sensor network from OVER-LAND ATMOSPHERIC DISPERSION (OLAD) experiment. The algorithm output are the probability distributions of a contamination source parameters i.e. its particular location, release rate, speed and direction of the movement, start time and duration. The stochastic approach presented in this paper is completely general and can be used in other fields where the parameters of the model bet fitted to the observable data should be found.

Reducing the Uncertainty in Atlantic Meridional Overturning Circulation Projections Using Bayesian Model Averaging

NASA Astrophysics Data System (ADS)

Olson, R.; An, S. I.

2016-12-01

Atlantic Meridional Overturning Circulation (AMOC) in the ocean might slow down in the future, which can lead to a host of climatic effects in North Atlantic and throughout the world. Despite improvements in climate models and availability of new observations, AMOC projections remain uncertain. Here we constrain CMIP5 multi-model ensemble output with observations of a recently developed AMOC index to provide improved Bayesian predictions of future AMOC. Specifically, we first calculate yearly AMOC index loosely based on Rahmstorf et al. (2015) for years 1880—2004 for both observations, and the CMIP5 models for which relevant output is available. We then assign a weight to each model based on a Bayesian Model Averaging method that accounts for differential model skill in terms of both mean state and variability. We include the temporal autocorrelation in climate model errors, and account for the uncertainty in the parameters of our statistical model. We use the weights to provide future weighted projections of AMOC, and compare them to un-weighted ones. Our projections use bootstrapping to account for uncertainty in internal AMOC variability. We also perform spectral and other statistical analyses to show that AMOC index variability, both in models and in observations, is consistent with red noise. Our results improve on and complement previous work by using a new ensemble of climate models, a different observational metric, and an improved Bayesian weighting method that accounts for differential model skill at reproducing internal variability. Reference: Rahmstorf, S., Box, J. E., Feulner, G., Mann, M. E., Robinson, A., Rutherford, S., & Schaffernicht, E. J. (2015). Exceptional twentieth-century slowdown in atlantic ocean overturning circulation. Nature Climate Change, 5(5), 475-480. doi:10.1038/nclimate2554

Unraveling multiple changes in complex climate time series using Bayesian inference

NASA Astrophysics Data System (ADS)

Berner, Nadine; Trauth, Martin H.; Holschneider, Matthias

2016-04-01

Change points in time series are perceived as heterogeneities in the statistical or dynamical characteristics of observations. Unraveling such transitions yields essential information for the understanding of the observed system. The precise detection and basic characterization of underlying changes is therefore of particular importance in environmental sciences. We present a kernel-based Bayesian inference approach to investigate direct as well as indirect climate observations for multiple generic transition events. In order to develop a diagnostic approach designed to capture a variety of natural processes, the basic statistical features of central tendency and dispersion are used to locally approximate a complex time series by a generic transition model. A Bayesian inversion approach is developed to robustly infer on the location and the generic patterns of such a transition. To systematically investigate time series for multiple changes occurring at different temporal scales, the Bayesian inversion is extended to a kernel-based inference approach. By introducing basic kernel measures, the kernel inference results are composed into a proxy probability to a posterior distribution of multiple transitions. Thus, based on a generic transition model a probability expression is derived that is capable to indicate multiple changes within a complex time series. We discuss the method's performance by investigating direct and indirect climate observations. The approach is applied to environmental time series (about 100 a), from the weather station in Tuscaloosa, Alabama, and confirms documented instrumentation changes. Moreover, the approach is used to investigate a set of complex terrigenous dust records from the ODP sites 659, 721/722 and 967 interpreted as climate indicators of the African region of the Plio-Pleistocene period (about 5 Ma). The detailed inference unravels multiple transitions underlying the indirect climate observations coinciding with established global climate events.

Performance evaluation of contrast-detail in full field digital mammography systems using ideal (Hotelling) observer vs. conventional automated analysis of CDMAM images for quality control of contrast-detail characteristics.

PubMed

Delakis, Ioannis; Wise, Robert; Morris, Lauren; Kulama, Eugenia

2015-11-01

The purpose of this work was to evaluate the contrast-detail performance of full field digital mammography (FFDM) systems using ideal (Hotelling) observer Signal-to-Noise Ratio (SNR) methodology and ascertain whether it can be considered an alternative to the conventional, automated analysis of CDMAM phantom images. Five FFDM units currently used in the national breast screening programme were evaluated, which differed with respect to age, detector, Automatic Exposure Control (AEC) and target/filter combination. Contrast-detail performance was analysed using CDMAM and ideal observer SNR methodology. The ideal observer SNR was calculated for input signal originating from gold discs of varying thicknesses and diameters, and then used to estimate the threshold gold thickness for each diameter as per CDMAM analysis. The variability of both methods and the dependence of CDMAM analysis on phantom manufacturing discrepancies also investigated. Results from both CDMAM and ideal observer methodologies were informative differentiators of FFDM systems' contrast-detail performance, displaying comparable patterns with respect to the FFDM systems' type and age. CDMAM results suggested higher threshold gold thickness values compared with the ideal observer methodology, especially for small-diameter details, which can be attributed to the behaviour of the CDMAM phantom used in this study. In addition, ideal observer methodology results showed lower variability than CDMAM results. The Ideal observer SNR methodology can provide a useful metric of the FFDM systems' contrast detail characteristics and could be considered a surrogate for conventional, automated analysis of CDMAM images. Copyright © 2015 Associazione Italiana di Fisica Medica. Published by Elsevier Ltd. All rights reserved.

Geostatistics and Bayesian updating for transmissivity estimation in a multiaquifer system in Manitoba, Canada.

PubMed

Kennedy, Paula L; Woodbury, Allan D

2002-01-01

In ground water flow and transport modeling, the heterogeneous nature of porous media has a considerable effect on the resulting flow and solute transport. Some method of generating the heterogeneous field from a limited dataset of uncertain measurements is required. Bayesian updating is one method that interpolates from an uncertain dataset using the statistics of the underlying probability distribution function. In this paper, Bayesian updating was used to determine the heterogeneous natural log transmissivity field for a carbonate and a sandstone aquifer in southern Manitoba. It was determined that the transmissivity in m2/sec followed a natural log normal distribution for both aquifers with a mean of -7.2 and - 8.0 for the carbonate and sandstone aquifers, respectively. The variograms were calculated using an estimator developed by Li and Lake (1994). Fractal nature was not evident in the variogram from either aquifer. The Bayesian updating heterogeneous field provided good results even in cases where little data was available. A large transmissivity zone in the sandstone aquifer was created by the Bayesian procedure, which is not a reflection of any deterministic consideration, but is a natural outcome of updating a prior probability distribution function with observations. The statistical model returns a result that is very reasonable; that is homogeneous in regions where little or no information is available to alter an initial state. No long range correlation trends or fractal behavior of the log-transmissivity field was observed in either aquifer over a distance of about 300 km.

Understanding causality and uncertainty in volcanic observations: An example of forecasting eruptive activity on Soufrière Hills Volcano, Montserrat

NASA Astrophysics Data System (ADS)

Sheldrake, T. E.; Aspinall, W. P.; Odbert, H. M.; Wadge, G.; Sparks, R. S. J.

2017-07-01

Following a cessation in eruptive activity it is important to understand how a volcano will behave in the future and when it may next erupt. Such an assessment can be based on the volcano's long-term pattern of behaviour and insights into its current state via monitoring observations. We present a Bayesian network that integrates these two strands of evidence to forecast future eruptive scenarios using expert elicitation. The Bayesian approach provides a framework to quantify the magmatic causes in terms of volcanic effects (i.e., eruption and unrest). In October 2013, an expert elicitation was performed to populate a Bayesian network designed to help forecast future eruptive (in-)activity at Soufrière Hills Volcano. The Bayesian network was devised to assess the state of the shallow magmatic system, as a means to forecast the future eruptive activity in the context of the long-term behaviour at similar dome-building volcanoes. The findings highlight coherence amongst experts when interpreting the current behaviour of the volcano, but reveal considerable ambiguity when relating this to longer patterns of volcanism at dome-building volcanoes, as a class. By asking questions in terms of magmatic causes, the Bayesian approach highlights the importance of using short-term unrest indicators from monitoring data as evidence in long-term forecasts at volcanoes. Furthermore, it highlights potential biases in the judgements of volcanologists and identifies sources of uncertainty in terms of magmatic causes rather than scenario-based outcomes.

The place of the ideal observer in medical ethics.

PubMed

Churchill, L R

1983-01-01

The idea of an ideal observer is frequently employed in ethical reasoning and has recently been introduced into medical ethics. The contemporary use of this idea, however, is deeply flawed. It ignores important social and personal dimensions of ethics. By espousing a perspective of observation removed from history and community, the ideal observer notion encourages a pretense of objectivity and overlooks the distortions of distance. If taken seriously as a model for choice, the ideal observer is incoherent, as it dispenses with the concrete moral agent and the locus of choice. Adam Smith's 'impartial spectator' is examined as a more adequate statement of the need for appreciating diverse perspectives in ethical choices.

Robust Bayesian Experimental Design for Conceptual Model Discrimination

NASA Astrophysics Data System (ADS)

Pham, H. V.; Tsai, F. T. C.

2015-12-01

A robust Bayesian optimal experimental design under uncertainty is presented to provide firm information for model discrimination, given the least number of pumping wells and observation wells. Firm information is the maximum information of a system can be guaranteed from an experimental design. The design is based on the Box-Hill expected entropy decrease (EED) before and after the experiment design and the Bayesian model averaging (BMA) framework. A max-min programming is introduced to choose the robust design that maximizes the minimal Box-Hill EED subject to that the highest expected posterior model probability satisfies a desired probability threshold. The EED is calculated by the Gauss-Hermite quadrature. The BMA method is used to predict future observations and to quantify future observation uncertainty arising from conceptual and parametric uncertainties in calculating EED. Monte Carlo approach is adopted to quantify the uncertainty in the posterior model probabilities. The optimal experimental design is tested by a synthetic 5-layer anisotropic confined aquifer. Nine conceptual groundwater models are constructed due to uncertain geological architecture and boundary condition. High-performance computing is used to enumerate all possible design solutions in order to identify the most plausible groundwater model. Results highlight the impacts of scedasticity in future observation data as well as uncertainty sources on potential pumping and observation locations.

Classic maximum entropy recovery of the average joint distribution of apparent FRET efficiency and fluorescence photons for single-molecule burst measurements.

PubMed

DeVore, Matthew S; Gull, Stephen F; Johnson, Carey K

2012-04-05

We describe a method for analysis of single-molecule Förster resonance energy transfer (FRET) burst measurements using classic maximum entropy. Classic maximum entropy determines the Bayesian inference for the joint probability describing the total fluorescence photons and the apparent FRET efficiency. The method was tested with simulated data and then with DNA labeled with fluorescent dyes. The most probable joint distribution can be marginalized to obtain both the overall distribution of fluorescence photons and the apparent FRET efficiency distribution. This method proves to be ideal for determining the distance distribution of FRET-labeled biomolecules, and it successfully predicts the shape of the recovered distributions.

A Bayesian Model of the Memory Colour Effect.

PubMed

Witzel, Christoph; Olkkonen, Maria; Gegenfurtner, Karl R

2018-01-01

According to the memory colour effect, the colour of a colour-diagnostic object is not perceived independently of the object itself. Instead, it has been shown through an achromatic adjustment method that colour-diagnostic objects still appear slightly in their typical colour, even when they are colourimetrically grey. Bayesian models provide a promising approach to capture the effect of prior knowledge on colour perception and to link these effects to more general effects of cue integration. Here, we model memory colour effects using prior knowledge about typical colours as priors for the grey adjustments in a Bayesian model. This simple model does not involve any fitting of free parameters. The Bayesian model roughly captured the magnitude of the measured memory colour effect for photographs of objects. To some extent, the model predicted observed differences in memory colour effects across objects. The model could not account for the differences in memory colour effects across different levels of realism in the object images. The Bayesian model provides a particularly simple account of memory colour effects, capturing some of the multiple sources of variation of these effects.

A Bayesian Model of the Memory Colour Effect

PubMed Central

Olkkonen, Maria; Gegenfurtner, Karl R.

2018-01-01

According to the memory colour effect, the colour of a colour-diagnostic object is not perceived independently of the object itself. Instead, it has been shown through an achromatic adjustment method that colour-diagnostic objects still appear slightly in their typical colour, even when they are colourimetrically grey. Bayesian models provide a promising approach to capture the effect of prior knowledge on colour perception and to link these effects to more general effects of cue integration. Here, we model memory colour effects using prior knowledge about typical colours as priors for the grey adjustments in a Bayesian model. This simple model does not involve any fitting of free parameters. The Bayesian model roughly captured the magnitude of the measured memory colour effect for photographs of objects. To some extent, the model predicted observed differences in memory colour effects across objects. The model could not account for the differences in memory colour effects across different levels of realism in the object images. The Bayesian model provides a particularly simple account of memory colour effects, capturing some of the multiple sources of variation of these effects. PMID:29760874

BAYESIAN ESTIMATION OF THERMONUCLEAR REACTION RATES

DOE Office of Scientific and Technical Information (OSTI.GOV)

Iliadis, C.; Anderson, K. S.; Coc, A.

The problem of estimating non-resonant astrophysical S -factors and thermonuclear reaction rates, based on measured nuclear cross sections, is of major interest for nuclear energy generation, neutrino physics, and element synthesis. Many different methods have been applied to this problem in the past, almost all of them based on traditional statistics. Bayesian methods, on the other hand, are now in widespread use in the physical sciences. In astronomy, for example, Bayesian statistics is applied to the observation of extrasolar planets, gravitational waves, and Type Ia supernovae. However, nuclear physics, in particular, has been slow to adopt Bayesian methods. We presentmore » astrophysical S -factors and reaction rates based on Bayesian statistics. We develop a framework that incorporates robust parameter estimation, systematic effects, and non-Gaussian uncertainties in a consistent manner. The method is applied to the reactions d(p, γ ){sup 3}He, {sup 3}He({sup 3}He,2p){sup 4}He, and {sup 3}He( α , γ ){sup 7}Be, important for deuterium burning, solar neutrinos, and Big Bang nucleosynthesis.« less

Hierarchical Bayesian sparse image reconstruction with application to MRFM.

PubMed

Dobigeon, Nicolas; Hero, Alfred O; Tourneret, Jean-Yves

2009-09-01

This paper presents a hierarchical Bayesian model to reconstruct sparse images when the observations are obtained from linear transformations and corrupted by an additive white Gaussian noise. Our hierarchical Bayes model is well suited to such naturally sparse image applications as it seamlessly accounts for properties such as sparsity and positivity of the image via appropriate Bayes priors. We propose a prior that is based on a weighted mixture of a positive exponential distribution and a mass at zero. The prior has hyperparameters that are tuned automatically by marginalization over the hierarchical Bayesian model. To overcome the complexity of the posterior distribution, a Gibbs sampling strategy is proposed. The Gibbs samples can be used to estimate the image to be recovered, e.g., by maximizing the estimated posterior distribution. In our fully Bayesian approach, the posteriors of all the parameters are available. Thus, our algorithm provides more information than other previously proposed sparse reconstruction methods that only give a point estimate. The performance of the proposed hierarchical Bayesian sparse reconstruction method is illustrated on synthetic data and real data collected from a tobacco virus sample using a prototype MRFM instrument.

Bayesian Approach to the Joint Inversion of Gravity and Magnetic Data, with Application to the Ismenius Area of Mars

NASA Technical Reports Server (NTRS)

Jewell, Jeffrey B.; Raymond, C.; Smrekar, S.; Millbury, C.

2004-01-01

This viewgraph presentation reviews a Bayesian approach to the inversion of gravity and magnetic data with specific application to the Ismenius Area of Mars. Many inverse problems encountered in geophysics and planetary science are well known to be non-unique (i.e. inversion of gravity the density structure of a body). In hopes of reducing the non-uniqueness of solutions, there has been interest in the joint analysis of data. An example is the joint inversion of gravity and magnetic data, with the assumption that the same physical anomalies generate both the observed magnetic and gravitational anomalies. In this talk, we formulate the joint analysis of different types of data in a Bayesian framework and apply the formalism to the inference of the density and remanent magnetization structure for a local region in the Ismenius area of Mars. The Bayesian approach allows prior information or constraints in the solutions to be incorporated in the inversion, with the "best" solutions those whose forward predictions most closely match the data while remaining consistent with assumed constraints. The application of this framework to the inversion of gravity and magnetic data on Mars reveals two typical challenges - the forward predictions of the data have a linear dependence on some of the quantities of interest, and non-linear dependence on others (termed the "linear" and "non-linear" variables, respectively). For observations with Gaussian noise, a Bayesian approach to inversion for "linear" variables reduces to a linear filtering problem, with an explicitly computable "error" matrix. However, for models whose forward predictions have non-linear dependencies, inference is no longer given by such a simple linear problem, and moreover, the uncertainty in the solution is no longer completely specified by a computable "error matrix". It is therefore important to develop methods for sampling from the full Bayesian posterior to provide a complete and statistically consistent picture of model uncertainty, and what has been learned from observations. We will discuss advanced numerical techniques, including Monte Carlo Markov

Case studies in Bayesian microbial risk assessments.

PubMed

Kennedy, Marc C; Clough, Helen E; Turner, Joanne

2009-12-21

The quantification of uncertainty and variability is a key component of quantitative risk analysis. Recent advances in Bayesian statistics make it ideal for integrating multiple sources of information, of different types and quality, and providing a realistic estimate of the combined uncertainty in the final risk estimates. We present two case studies related to foodborne microbial risks. In the first, we combine models to describe the sequence of events resulting in illness from consumption of milk contaminated with VTEC O157. We used Monte Carlo simulation to propagate uncertainty in some of the inputs to computer models describing the farm and pasteurisation process. Resulting simulated contamination levels were then assigned to consumption events from a dietary survey. Finally we accounted for uncertainty in the dose-response relationship and uncertainty due to limited incidence data to derive uncertainty about yearly incidences of illness in young children. Options for altering the risk were considered by running the model with different hypothetical policy-driven exposure scenarios. In the second case study we illustrate an efficient Bayesian sensitivity analysis for identifying the most important parameters of a complex computer code that simulated VTEC O157 prevalence within a managed dairy herd. This was carried out in 2 stages, first to screen out the unimportant inputs, then to perform a more detailed analysis on the remaining inputs. The method works by building a Bayesian statistical approximation to the computer code using a number of known code input/output pairs (training runs). We estimated that the expected total number of children aged 1.5-4.5 who become ill due to VTEC O157 in milk is 8.6 per year, with 95% uncertainty interval (0,11.5). The most extreme policy we considered was banning on-farm pasteurisation of milk, which reduced the estimate to 6.4 with 95% interval (0,11). In the second case study the effective number of inputs was reduced from 30 to 7 in the screening stage, and just 2 inputs were found to explain 82.8% of the output variance. A combined total of 500 runs of the computer code were used. These case studies illustrate the use of Bayesian statistics to perform detailed uncertainty and sensitivity analyses, integrating multiple information sources in a way that is both rigorous and efficient.

Survival Bayesian Estimation of Exponential-Gamma Under Linex Loss Function

NASA Astrophysics Data System (ADS)

Rizki, S. W.; Mara, M. N.; Sulistianingsih, E.

2017-06-01

This paper elaborates a research of the cancer patients after receiving a treatment in cencored data using Bayesian estimation under Linex Loss function for Survival Model which is assumed as an exponential distribution. By giving Gamma distribution as prior and likelihood function produces a gamma distribution as posterior distribution. The posterior distribution is used to find estimatior {\\hat{λ }}BL by using Linex approximation. After getting {\\hat{λ }}BL, the estimators of hazard function {\\hat{h}}BL and survival function {\\hat{S}}BL can be found. Finally, we compare the result of Maximum Likelihood Estimation (MLE) and Linex approximation to find the best method for this observation by finding smaller MSE. The result shows that MSE of hazard and survival under MLE are 2.91728E-07 and 0.000309004 and by using Bayesian Linex worths 2.8727E-07 and 0.000304131, respectively. It concludes that the Bayesian Linex is better than MLE.

Robust Learning of High-dimensional Biological Networks with Bayesian Networks

NASA Astrophysics Data System (ADS)

Nägele, Andreas; Dejori, Mathäus; Stetter, Martin

Structure learning of Bayesian networks applied to gene expression data has become a potentially useful method to estimate interactions between genes. However, the NP-hardness of Bayesian network structure learning renders the reconstruction of the full genetic network with thousands of genes unfeasible. Consequently, the maximal network size is usually restricted dramatically to a small set of genes (corresponding with variables in the Bayesian network). Although this feature reduction step makes structure learning computationally tractable, on the downside, the learned structure might be adversely affected due to the introduction of missing genes. Additionally, gene expression data are usually very sparse with respect to the number of samples, i.e., the number of genes is much greater than the number of different observations. Given these problems, learning robust network features from microarray data is a challenging task. This chapter presents several approaches tackling the robustness issue in order to obtain a more reliable estimation of learned network features.

Bayesian truncation errors in chiral effective field theory: model checking and accounting for correlations

NASA Astrophysics Data System (ADS)

Melendez, Jordan; Wesolowski, Sarah; Furnstahl, Dick

2017-09-01

Chiral effective field theory (EFT) predictions are necessarily truncated at some order in the EFT expansion, which induces an error that must be quantified for robust statistical comparisons to experiment. A Bayesian model yields posterior probability distribution functions for these errors based on expectations of naturalness encoded in Bayesian priors and the observed order-by-order convergence pattern of the EFT. As a general example of a statistical approach to truncation errors, the model was applied to chiral EFT for neutron-proton scattering using various semi-local potentials of Epelbaum, Krebs, and Meißner (EKM). Here we discuss how our model can learn correlation information from the data and how to perform Bayesian model checking to validate that the EFT is working as advertised. Supported in part by NSF PHY-1614460 and DOE NUCLEI SciDAC DE-SC0008533.

Asteroid orbital error analysis: Theory and application

NASA Technical Reports Server (NTRS)

Muinonen, K.; Bowell, Edward

1992-01-01

We present a rigorous Bayesian theory for asteroid orbital error estimation in which the probability density of the orbital elements is derived from the noise statistics of the observations. For Gaussian noise in a linearized approximation the probability density is also Gaussian, and the errors of the orbital elements at a given epoch are fully described by the covariance matrix. The law of error propagation can then be applied to calculate past and future positional uncertainty ellipsoids (Cappellari et al. 1976, Yeomans et al. 1987, Whipple et al. 1991). To our knowledge, this is the first time a Bayesian approach has been formulated for orbital element estimation. In contrast to the classical Fisherian school of statistics, the Bayesian school allows a priori information to be formally present in the final estimation. However, Bayesian estimation does give the same results as Fisherian estimation when no priori information is assumed (Lehtinen 1988, and reference therein).

Probing Intrinsic Properties of Short Gamma-Ray Bursts with Gravitational Waves.

PubMed

Fan, Xilong; Messenger, Christopher; Heng, Ik Siong

2017-11-03

Progenitors of short gamma-ray bursts are thought to be neutron stars coalescing with their companion black hole or neutron star, which are one of the main gravitational wave sources. We have devised a Bayesian framework for combining gamma-ray burst and gravitational wave information that allows us to probe short gamma-ray burst luminosities. We show that combined short gamma-ray burst and gravitational wave observations not only improve progenitor distance and inclination angle estimates, they also allow the isotropic luminosities of short gamma-ray bursts to be determined without the need for host galaxy or light-curve information. We characterize our approach by simulating 1000 joint short gamma-ray burst and gravitational wave detections by Advanced LIGO and Advanced Virgo. We show that ∼90% of the simulations have uncertainties on short gamma-ray burst isotropic luminosity estimates that are within a factor of two of the ideal scenario, where the distance is known exactly. Therefore, isotropic luminosities can be confidently determined for short gamma-ray bursts observed jointly with gravitational waves detected by Advanced LIGO and Advanced Virgo. Planned enhancements to Advanced LIGO will extend its range and likely produce several joint detections of short gamma-ray bursts and gravitational waves. Third-generation gravitational wave detectors will allow for isotropic luminosity estimates for the majority of the short gamma-ray burst population within a redshift of z∼1.

Bayesian Logic Programs for Plan Recognition and Machine Reading

DTIC Science & Technology

2012-12-01

models is that they can handle both uncertainty and structured/ relational data. As a result, they are widely used in domains like social network...data. As a result, they are widely used in domains like social net- work analysis, biological data analysis, and natural language processing. Bayesian...the Story Understanding data set. (b) The logical representation of the observations. (c) The set of ground rules obtained from logical abduction

A comparison of Monte Carlo-based Bayesian parameter estimation methods for stochastic models of genetic networks

PubMed Central

Zaikin, Alexey; Míguez, Joaquín

2017-01-01

We compare three state-of-the-art Bayesian inference methods for the estimation of the unknown parameters in a stochastic model of a genetic network. In particular, we introduce a stochastic version of the paradigmatic synthetic multicellular clock model proposed by Ullner et al., 2007. By introducing dynamical noise in the model and assuming that the partial observations of the system are contaminated by additive noise, we enable a principled mechanism to represent experimental uncertainties in the synthesis of the multicellular system and pave the way for the design of probabilistic methods for the estimation of any unknowns in the model. Within this setup, we tackle the Bayesian estimation of a subset of the model parameters. Specifically, we compare three Monte Carlo based numerical methods for the approximation of the posterior probability density function of the unknown parameters given a set of partial and noisy observations of the system. The schemes we assess are the particle Metropolis-Hastings (PMH) algorithm, the nonlinear population Monte Carlo (NPMC) method and the approximate Bayesian computation sequential Monte Carlo (ABC-SMC) scheme. We present an extensive numerical simulation study, which shows that while the three techniques can effectively solve the problem there are significant differences both in estimation accuracy and computational efficiency. PMID:28797087

Bayesian Analysis for Risk Assessment of Selected Medical Events in Support of the Integrated Medical Model Effort

NASA Technical Reports Server (NTRS)

Gilkey, Kelly M.; Myers, Jerry G.; McRae, Michael P.; Griffin, Elise A.; Kallrui, Aditya S.

2012-01-01

The Exploration Medical Capability project is creating a catalog of risk assessments using the Integrated Medical Model (IMM). The IMM is a software-based system intended to assist mission planners in preparing for spaceflight missions by helping them to make informed decisions about medical preparations and supplies needed for combating and treating various medical events using Probabilistic Risk Assessment. The objective is to use statistical analyses to inform the IMM decision tool with estimated probabilities of medical events occurring during an exploration mission. Because data regarding astronaut health are limited, Bayesian statistical analysis is used. Bayesian inference combines prior knowledge, such as data from the general U.S. population, the U.S. Submarine Force, or the analog astronaut population located at the NASA Johnson Space Center, with observed data for the medical condition of interest. The posterior results reflect the best evidence for specific medical events occurring in flight. Bayes theorem provides a formal mechanism for combining available observed data with data from similar studies to support the quantification process. The IMM team performed Bayesian updates on the following medical events: angina, appendicitis, atrial fibrillation, atrial flutter, dental abscess, dental caries, dental periodontal disease, gallstone disease, herpes zoster, renal stones, seizure, and stroke.

Montblanc1: GPU accelerated radio interferometer measurement equations in support of Bayesian inference for radio observations

NASA Astrophysics Data System (ADS)

Perkins, S. J.; Marais, P. C.; Zwart, J. T. L.; Natarajan, I.; Tasse, C.; Smirnov, O.

2015-09-01

We present Montblanc, a GPU implementation of the Radio interferometer measurement equation (RIME) in support of the Bayesian inference for radio observations (BIRO) technique. BIRO uses Bayesian inference to select sky models that best match the visibilities observed by a radio interferometer. To accomplish this, BIRO evaluates the RIME multiple times, varying sky model parameters to produce multiple model visibilities. χ2 values computed from the model and observed visibilities are used as likelihood values to drive the Bayesian sampling process and select the best sky model. As most of the elements of the RIME and χ2 calculation are independent of one another, they are highly amenable to parallel computation. Additionally, Montblanc caters for iterative RIME evaluation to produce multiple χ2 values. Modified model parameters are transferred to the GPU between each iteration. We implemented Montblanc as a Python package based upon NVIDIA's CUDA architecture. As such, it is easy to extend and implement different pipelines. At present, Montblanc supports point and Gaussian morphologies, but is designed for easy addition of new source profiles. Montblanc's RIME implementation is performant: On an NVIDIA K40, it is approximately 250 times faster than MEQTREES on a dual hexacore Intel E5-2620v2 CPU. Compared to the OSKAR simulator's GPU-implemented RIME components it is 7.7 and 12 times faster on the same K40 for single and double-precision floating point respectively. However, OSKAR's RIME implementation is more general than Montblanc's BIRO-tailored RIME. Theoretical analysis of Montblanc's dominant CUDA kernel suggests that it is memory bound. In practice, profiling shows that is balanced between compute and memory, as much of the data required by the problem is retained in L1 and L2 caches.

Bayesian Modeling of Perceived Surface Slant from Actively-Generated and Passively-Observed Optic Flow

PubMed Central

Caudek, Corrado; Fantoni, Carlo; Domini, Fulvio

2011-01-01

We measured perceived depth from the optic flow (a) when showing a stationary physical or virtual object to observers who moved their head at a normal or slower speed, and (b) when simulating the same optic flow on a computer and presenting it to stationary observers. Our results show that perceived surface slant is systematically distorted, for both the active and the passive viewing of physical or virtual surfaces. These distortions are modulated by head translation speed, with perceived slant increasing directly with the local velocity gradient of the optic flow. This empirical result allows us to determine the relative merits of two alternative approaches aimed at explaining perceived surface slant in active vision: an “inverse optics” model that takes head motion information into account, and a probabilistic model that ignores extra-retinal signals. We compare these two approaches within the framework of the Bayesian theory. The “inverse optics” Bayesian model produces veridical slant estimates if the optic flow and the head translation velocity are measured with no error; because of the influence of a “prior” for flatness, the slant estimates become systematically biased as the measurement errors increase. The Bayesian model, which ignores the observer's motion, always produces distorted estimates of surface slant. Interestingly, the predictions of this second model, not those of the first one, are consistent with our empirical findings. The present results suggest that (a) in active vision perceived surface slant may be the product of probabilistic processes which do not guarantee the correct solution, and (b) extra-retinal signals may be mainly used for a better measurement of retinal information. PMID:21533197

A Bayesian connectivity-based approach to constructing probabilistic gene regulatory networks.

PubMed

Zhou, Xiaobo; Wang, Xiaodong; Pal, Ranadip; Ivanov, Ivan; Bittner, Michael; Dougherty, Edward R

2004-11-22

We have hypothesized that the construction of transcriptional regulatory networks using a method that optimizes connectivity would lead to regulation consistent with biological expectations. A key expectation is that the hypothetical networks should produce a few, very strong attractors, highly similar to the original observations, mimicking biological state stability and determinism. Another central expectation is that, since it is expected that the biological control is distributed and mutually reinforcing, interpretation of the observations should lead to a very small number of connection schemes. We propose a fully Bayesian approach to constructing probabilistic gene regulatory networks (PGRNs) that emphasizes network topology. The method computes the possible parent sets of each gene, the corresponding predictors and the associated probabilities based on a nonlinear perceptron model, using a reversible jump Markov chain Monte Carlo (MCMC) technique, and an MCMC method is employed to search the network configurations to find those with the highest Bayesian scores to construct the PGRN. The Bayesian method has been used to construct a PGRN based on the observed behavior of a set of genes whose expression patterns vary across a set of melanoma samples exhibiting two very different phenotypes with respect to cell motility and invasiveness. Key biological features have been faithfully reflected in the model. Its steady-state distribution contains attractors that are either identical or very similar to the states observed in the data, and many of the attractors are singletons, which mimics the biological propensity to stably occupy a given state. Most interestingly, the connectivity rules for the most optimal generated networks constituting the PGRN are remarkably similar, as would be expected for a network operating on a distributed basis, with strong interactions between the components.

The Effect of Multispectral Image Fusion Enhancement on Human Efficiency

DTIC Science & Technology

2017-03-20

human visual system by applying a technique commonly used in visual percep- tion research : ideal observer analysis. Using this approach, we establish...applications, analytic tech- niques, and procedural methods used across studies. This paper uses ideal observer analysis to establish a frame- work that allows...augmented similarly to incorpo- rate research involving more complex stimulus content. Additionally, the ideal observer can be adapted for a number of

Bayesian network learning for natural hazard assessments

NASA Astrophysics Data System (ADS)

Vogel, Kristin

2016-04-01

Even though quite different in occurrence and consequences, from a modelling perspective many natural hazards share similar properties and challenges. Their complex nature as well as lacking knowledge about their driving forces and potential effects make their analysis demanding. On top of the uncertainty about the modelling framework, inaccurate or incomplete event observations and the intrinsic randomness of the natural phenomenon add up to different interacting layers of uncertainty, which require a careful handling. Thus, for reliable natural hazard assessments it is crucial not only to capture and quantify involved uncertainties, but also to express and communicate uncertainties in an intuitive way. Decision-makers, who often find it difficult to deal with uncertainties, might otherwise return to familiar (mostly deterministic) proceedings. In the scope of the DFG research training group „NatRiskChange" we apply the probabilistic framework of Bayesian networks for diverse natural hazard and vulnerability studies. The great potential of Bayesian networks was already shown in previous natural hazard assessments. Treating each model component as random variable, Bayesian networks aim at capturing the joint distribution of all considered variables. Hence, each conditional distribution of interest (e.g. the effect of precautionary measures on damage reduction) can be inferred. The (in-)dependencies between the considered variables can be learned purely data driven or be given by experts. Even a combination of both is possible. By translating the (in-)dependences into a graph structure, Bayesian networks provide direct insights into the workings of the system and allow to learn about the underlying processes. Besides numerous studies on the topic, learning Bayesian networks from real-world data remains challenging. In previous studies, e.g. on earthquake induced ground motion and flood damage assessments, we tackled the problems arising with continuous variables and incomplete observations. Further studies rise the challenge of relying on very small data sets. Since parameter estimates for complex models based on few observations are unreliable, it is necessary to focus on simplified, yet still meaningful models. A so called Markov Blanket approach is developed to identify the most relevant model components and to construct a simple Bayesian network based on those findings. Since the proceeding is completely data driven, it can easily be transferred to various applications in natural hazard domains. This study is funded by the Deutsche Forschungsgemeinschaft (DFG) within the research training programme GRK 2043/1 "NatRiskChange - Natural hazards and risks in a changing world" at Potsdam University.

Reducing uncertainties in decadal variability of the global carbon budget with multiple datasets

PubMed Central

Li, Wei; Ciais, Philippe; Wang, Yilong; Peng, Shushi; Broquet, Grégoire; Ballantyne, Ashley P.; Canadell, Josep G.; Cooper, Leila; Friedlingstein, Pierre; Le Quéré, Corinne; Myneni, Ranga B.; Peters, Glen P.; Piao, Shilong; Pongratz, Julia

2016-01-01

Conventional calculations of the global carbon budget infer the land sink as a residual between emissions, atmospheric accumulation, and the ocean sink. Thus, the land sink accumulates the errors from the other flux terms and bears the largest uncertainty. Here, we present a Bayesian fusion approach that combines multiple observations in different carbon reservoirs to optimize the land (B) and ocean (O) carbon sinks, land use change emissions (L), and indirectly fossil fuel emissions (F) from 1980 to 2014. Compared with the conventional approach, Bayesian optimization decreases the uncertainties in B by 41% and in O by 46%. The L uncertainty decreases by 47%, whereas F uncertainty is marginally improved through the knowledge of natural fluxes. Both ocean and net land uptake (B + L) rates have positive trends of 29 ± 8 and 37 ± 17 Tg C⋅y−2 since 1980, respectively. Our Bayesian fusion of multiple observations reduces uncertainties, thereby allowing us to isolate important variability in global carbon cycle processes. PMID:27799533

Bayesian modeling of cue interaction: bistability in stereoscopic slant perception.

PubMed

van Ee, Raymond; Adams, Wendy J; Mamassian, Pascal

2003-07-01

Our two eyes receive different views of a visual scene, and the resulting binocular disparities enable us to reconstruct its three-dimensional layout. However, the visual environment is also rich in monocular depth cues. We examined the resulting percept when observers view a scene in which there are large conflicts between the surface slant signaled by binocular disparities and the slant signaled by monocular perspective. For a range of disparity-perspective cue conflicts, many observers experience bistability: They are able to perceive two distinct slants and to flip between the two percepts in a controlled way. We present a Bayesian model that describes the quantitative aspects of perceived slant on the basis of the likelihoods of both perspective and disparity slant information combined with prior assumptions about the shape and orientation of objects in the scene. Our Bayesian approach can be regarded as an overarching framework that allows researchers to study all cue integration aspects-including perceptual decisions--in a unified manner.

Hydrologic Model Selection using Markov chain Monte Carlo methods

NASA Astrophysics Data System (ADS)

Marshall, L.; Sharma, A.; Nott, D.

2002-12-01

Estimation of parameter uncertainty (and in turn model uncertainty) allows assessment of the risk in likely applications of hydrological models. Bayesian statistical inference provides an ideal means of assessing parameter uncertainty whereby prior knowledge about the parameter is combined with information from the available data to produce a probability distribution (the posterior distribution) that describes uncertainty about the parameter and serves as a basis for selecting appropriate values for use in modelling applications. Widespread use of Bayesian techniques in hydrology has been hindered by difficulties in summarizing and exploring the posterior distribution. These difficulties have been largely overcome by recent advances in Markov chain Monte Carlo (MCMC) methods that involve random sampling of the posterior distribution. This study presents an adaptive MCMC sampling algorithm which has characteristics that are well suited to model parameters with a high degree of correlation and interdependence, as is often evident in hydrological models. The MCMC sampling technique is used to compare six alternative configurations of a commonly used conceptual rainfall-runoff model, the Australian Water Balance Model (AWBM), using 11 years of daily rainfall runoff data from the Bass river catchment in Australia. The alternative configurations considered fall into two classes - those that consider model errors to be independent of prior values, and those that model the errors as an autoregressive process. Each such class consists of three formulations that represent increasing levels of complexity (and parameterisation) of the original model structure. The results from this study point both to the importance of using Bayesian approaches in evaluating model performance, as well as the simplicity of the MCMC sampling framework that has the ability to bring such approaches within the reach of the applied hydrological community.

Improving timing sensitivity in the microhertz frequency regime: limits from PSR J1713+0747 on gravitational waves produced by supermassive black hole binaries

NASA Astrophysics Data System (ADS)

Perera, B. B. P.; Stappers, B. W.; Babak, S.; Keith, M. J.; Antoniadis, J.; Bassa, C. G.; Caballero, R. N.; Champion, D. J.; Cognard, I.; Desvignes, G.; Graikou, E.; Guillemot, L.; Janssen, G. H.; Karuppusamy, R.; Kramer, M.; Lazarus, P.; Lentati, L.; Liu, K.; Lyne, A. G.; McKee, J. W.; Osłowski, S.; Perrodin, D.; Sanidas, S. A.; Sesana, A.; Shaifullah, G.; Theureau, G.; Verbiest, J. P. W.; Taylor, S. R.

2018-07-01

We search for continuous gravitational waves (CGWs) produced by individual supermassive black hole binaries in circular orbits using high-cadence timing observations of PSR J1713+0747. We observe this millisecond pulsar using the telescopes in the European Pulsar Timing Array with an average cadence of approximately 1.6 d over the period between 2011 April and 2015 July, including an approximately daily average between 2013 February and 2014 April. The high-cadence observations are used to improve the pulsar timing sensitivity across the gravitational wave frequency range of 0.008-5μHz. We use two algorithms in the analysis, including a spectral fitting method and a Bayesian approach. For an independent comparison, we also use a previously published Bayesian algorithm. We find that the Bayesian approaches provide optimal results and the timing observations of the pulsar place a 95 per cent upper limit on the sky-averaged strain amplitude of CGWs to be ≲3.5 × 10-13 at a reference frequency of 1 μHz. We also find a 95 per cent upper limit on the sky-averaged strain amplitude of low-frequency CGWs to be ≲1.4 × 10-14 at a reference frequency of 20 nHz.

Improving timing sensitivity in the microhertz frequency regime: limits from PSR J1713+0747 on gravitational waves produced by super-massive black-hole binaries

NASA Astrophysics Data System (ADS)

Perera, B. B. P.; Stappers, B. W.; Babak, S.; Keith, M. J.; Antoniadis, J.; Bassa, C. G.; Caballero, R. N.; Champion, D. J.; Cognard, I.; Desvignes, G.; Graikou, E.; Guillemot, L.; Janssen, G. H.; Karuppusamy, R.; Kramer, M.; Lazarus, P.; Lentati, L.; Liu, K.; Lyne, A. G.; McKee, J. W.; Osłowski, S.; Perrodin, D.; Sanidas, S. A.; Sesana, A.; Shaifullah, G.; Theureau, G.; Verbiest, J. P. W.; Taylor, S. R.

2018-05-01

We search for continuous gravitational waves (CGWs) produced by individual super-massive black-hole binaries (SMBHBs) in circular orbits using high-cadence timing observations of PSR J1713+0747. We observe this millisecond pulsar using the telescopes in the European Pulsar Timing Array (EPTA) with an average cadence of approximately 1.6 days over the period between April 2011 and July 2015, including an approximately daily average between February 2013 and April 2014. The high-cadence observations are used to improve the pulsar timing sensitivity across the GW frequency range of 0.008 - 5 μHz. We use two algorithms in the analysis, including a spectral fitting method and a Bayesian approach. For an independent comparison, we also use a previously published Bayesian algorithm. We find that the Bayesian approaches provide optimal results and the timing observations of the pulsar place a 95 per cent upper limit on the sky-averaged strain amplitude of CGWs to be ≲ 3.5 × 10-13 at a reference frequency of 1 μHz. We also find a 95 per cent upper limit on the sky-averaged strain amplitude of low-frequency CGWs to be ≲ 1.4 × 10-14 at a reference frequency of 20 nHz.

Bayesian networks in neuroscience: a survey.

PubMed

Bielza, Concha; Larrañaga, Pedro

2014-01-01

Bayesian networks are a type of probabilistic graphical models lie at the intersection between statistics and machine learning. They have been shown to be powerful tools to encode dependence relationships among the variables of a domain under uncertainty. Thanks to their generality, Bayesian networks can accommodate continuous and discrete variables, as well as temporal processes. In this paper we review Bayesian networks and how they can be learned automatically from data by means of structure learning algorithms. Also, we examine how a user can take advantage of these networks for reasoning by exact or approximate inference algorithms that propagate the given evidence through the graphical structure. Despite their applicability in many fields, they have been little used in neuroscience, where they have focused on specific problems, like functional connectivity analysis from neuroimaging data. Here we survey key research in neuroscience where Bayesian networks have been used with different aims: discover associations between variables, perform probabilistic reasoning over the model, and classify new observations with and without supervision. The networks are learned from data of any kind-morphological, electrophysiological, -omics and neuroimaging-, thereby broadening the scope-molecular, cellular, structural, functional, cognitive and medical- of the brain aspects to be studied.

Bayesian networks in neuroscience: a survey

PubMed Central

Bielza, Concha; Larrañaga, Pedro

2014-01-01

Bayesian networks are a type of probabilistic graphical models lie at the intersection between statistics and machine learning. They have been shown to be powerful tools to encode dependence relationships among the variables of a domain under uncertainty. Thanks to their generality, Bayesian networks can accommodate continuous and discrete variables, as well as temporal processes. In this paper we review Bayesian networks and how they can be learned automatically from data by means of structure learning algorithms. Also, we examine how a user can take advantage of these networks for reasoning by exact or approximate inference algorithms that propagate the given evidence through the graphical structure. Despite their applicability in many fields, they have been little used in neuroscience, where they have focused on specific problems, like functional connectivity analysis from neuroimaging data. Here we survey key research in neuroscience where Bayesian networks have been used with different aims: discover associations between variables, perform probabilistic reasoning over the model, and classify new observations with and without supervision. The networks are learned from data of any kind–morphological, electrophysiological, -omics and neuroimaging–, thereby broadening the scope–molecular, cellular, structural, functional, cognitive and medical– of the brain aspects to be studied. PMID:25360109

Application of Bayesian Networks to hindcast barrier island morphodynamics

USGS Publications Warehouse

Wilson, Kathleen E.; Adams, Peter N.; Hapke, Cheryl J.; Lentz, Erika E.; Brenner, Owen T.

2015-01-01

We refine a preliminary Bayesian Network by 1) increasing model experience through additional observations, 2) including anthropogenic modification history, and 3) replacing parameterized wave impact values with maximum run-up elevation. Further, we develop and train a pair of generalized models with an additional dataset encompassing a different storm event, which expands the observations beyond our hindcast objective. We compare the skill of the generalized models against the Nor'Ida specific model formulation, balancing the reduced skill with an expectation of increased transferability. Results of Nor'Ida hindcasts ranged in skill from 0.37 to 0.51 and accuracy of 65.0 to 81.9%.

Partitioning Ocean Wave Spectra Obtained from Radar Observations

NASA Astrophysics Data System (ADS)

Delaye, Lauriane; Vergely, Jean-Luc; Hauser, Daniele; Guitton, Gilles; Mouche, Alexis; Tison, Celine

2016-08-01

2D wave spectra of ocean waves can be partitioned into several wave components to better characterize the scene. We present here two methods of component detection: one based on watershed algorithm and the other based on a Bayesian approach. We tested both methods on a set of simulated SWIM data, the Ku-band real aperture radar embarked on the CFOSAT (China- France Oceanography Satellite) mission which launch is planned mid-2018. We present the results and the limits of both approaches and show that Bayesian method can also be applied to other kind of wave spectra observations as those obtained with the radar KuROS, an airborne radar wave spectrometer.

Spatially explicit inference for open populations: estimating demographic parameters from camera-trap studies

USGS Publications Warehouse

Gardner, Beth; Reppucci, Juan; Lucherini, Mauro; Royle, J. Andrew

2010-01-01

We develop a hierarchical capture–recapture model for demographically open populations when auxiliary spatial information about location of capture is obtained. Such spatial capture–recapture data arise from studies based on camera trapping, DNA sampling, and other situations in which a spatial array of devices records encounters of unique individuals. We integrate an individual-based formulation of a Jolly-Seber type model with recently developed spatially explicit capture–recapture models to estimate density and demographic parameters for survival and recruitment. We adopt a Bayesian framework for inference under this model using the method of data augmentation which is implemented in the software program WinBUGS. The model was motivated by a camera trapping study of Pampas cats Leopardus colocolo from Argentina, which we present as an illustration of the model in this paper. We provide estimates of density and the first quantitative assessment of vital rates for the Pampas cat in the High Andes. The precision of these estimates is poor due likely to the sparse data set. Unlike conventional inference methods which usually rely on asymptotic arguments, Bayesian inferences are valid in arbitrary sample sizes, and thus the method is ideal for the study of rare or endangered species for which small data sets are typical.

Spatially explicit inference for open populations: estimating demographic parameters from camera-trap studies.

PubMed

Gardner, Beth; Reppucci, Juan; Lucherini, Mauro; Royle, J Andrew

2010-11-01

We develop a hierarchical capture-recapture model for demographically open populations when auxiliary spatial information about location of capture is obtained. Such spatial capture-recapture data arise from studies based on camera trapping, DNA sampling, and other situations in which a spatial array of devices records encounters of unique individuals. We integrate an individual-based formulation of a Jolly-Seber type model with recently developed spatially explicit capture-recapture models to estimate density and demographic parameters for survival and recruitment. We adopt a Bayesian framework for inference under this model using the method of data augmentation which is implemented in the software program WinBUGS. The model was motivated by a camera trapping study of Pampas cats Leopardus colocolo from Argentina, which we present as an illustration of the model in this paper. We provide estimates of density and the first quantitative assessment of vital rates for the Pampas cat in the High Andes. The precision of these estimates is poor due likely to the sparse data set. Unlike conventional inference methods which usually rely on asymptotic arguments, Bayesian inferences are valid in arbitrary sample sizes, and thus the method is ideal for the study of rare or endangered species for which small data sets are typical.

Classic Maximum Entropy Recovery of the Average Joint Distribution of Apparent FRET Efficiency and Fluorescence Photons for Single-molecule Burst Measurements

PubMed Central

DeVore, Matthew S.; Gull, Stephen F.; Johnson, Carey K.

2012-01-01

We describe a method for analysis of single-molecule Förster resonance energy transfer (FRET) burst measurements using classic maximum entropy. Classic maximum entropy determines the Bayesian inference for the joint probability describing the total fluorescence photons and the apparent FRET efficiency. The method was tested with simulated data and then with DNA labeled with fluorescent dyes. The most probable joint distribution can be marginalized to obtain both the overall distribution of fluorescence photons and the apparent FRET efficiency distribution. This method proves to be ideal for determining the distance distribution of FRET-labeled biomolecules, and it successfully predicts the shape of the recovered distributions. PMID:22338694

Assessing Vermont's stream health and biological integrity using artificial neural networks and Bayesian methods

NASA Astrophysics Data System (ADS)

Rizzo, D. M.; Fytilis, N.; Stevens, L.

2012-12-01

Environmental managers are increasingly required to monitor and forecast long-term effects and vulnerability of biophysical systems to human-generated stresses. Ideally, a study involving both physical and biological assessments conducted concurrently (in space and time) could provide a better understanding of the mechanisms and complex relationships. However, costs and resources associated with monitoring the complex linkages between the physical, geomorphic and habitat conditions and the biological integrity of stream reaches are prohibitive. Researchers have used classification techniques to place individual streams and rivers into a broader spatial context (hydrologic or health condition). Such efforts require environmental managers to gather multiple forms of information - quantitative, qualitative and subjective. We research and develop a novel classification tool that combines self-organizing maps with a Naïve Bayesian classifier to direct resources to stream reaches most in need. The Vermont Agency of Natural Resources has developed and adopted protocols for physical stream geomorphic and habitat assessments throughout the state of Vermont. Separate from these assessments, the Vermont Department of Environmental Conservation monitors the biological communities and the water quality in streams. Our initial hypothesis is that the geomorphic reach assessments and water quality data may be leveraged to reduce error and uncertainty associated with predictions of biological integrity and stream health. We test our hypothesis using over 2500 Vermont stream reaches (~1371 stream miles) assessed by the two agencies. In the development of this work, we combine a Naïve Bayesian classifier with a modified Kohonen Self-Organizing Map (SOM). The SOM is an unsupervised artificial neural network that autonomously analyzes inherent dataset properties using input data only. It is typically used to cluster data into similar categories when a priori classes do not exist. The incorporation of a Bayesian classifier allows one to explicitly incorporate existing knowledge and expert opinion into the data analysis. Since classification plays a leading role in the future development of data-enabled science and engineering, such a computational tool is applicable to a variety of proactive adaptive watershed management applications.

Evaluating Variability and Uncertainty of Geological Strength Index at a Specific Site

NASA Astrophysics Data System (ADS)

Wang, Yu; Aladejare, Adeyemi Emman

2016-09-01

Geological Strength Index (GSI) is an important parameter for estimating rock mass properties. GSI can be estimated from quantitative GSI chart, as an alternative to the direct observational method which requires vast geological experience of rock. GSI chart was developed from past observations and engineering experience, with either empiricism or some theoretical simplifications. The GSI chart thereby contains model uncertainty which arises from its development. The presence of such model uncertainty affects the GSI estimated from GSI chart at a specific site; it is, therefore, imperative to quantify and incorporate the model uncertainty during GSI estimation from the GSI chart. A major challenge for quantifying the GSI chart model uncertainty is a lack of the original datasets that have been used to develop the GSI chart, since the GSI chart was developed from past experience without referring to specific datasets. This paper intends to tackle this problem by developing a Bayesian approach for quantifying the model uncertainty in GSI chart when using it to estimate GSI at a specific site. The model uncertainty in the GSI chart and the inherent spatial variability in GSI are modeled explicitly in the Bayesian approach. The Bayesian approach generates equivalent samples of GSI from the integrated knowledge of GSI chart, prior knowledge and observation data available from site investigation. Equations are derived for the Bayesian approach, and the proposed approach is illustrated using data from a drill and blast tunnel project. The proposed approach effectively tackles the problem of how to quantify the model uncertainty that arises from using GSI chart for characterization of site-specific GSI in a transparent manner.

A Bayesian CUSUM plot: Diagnosing quality of treatment.

PubMed

Rosthøj, Steen; Jacobsen, Rikke-Line

2017-12-01

To present a CUSUM plot based on Bayesian diagnostic reasoning displaying evidence in favour of "healthy" rather than "sick" quality of treatment (QOT), and to demonstrate a technique using Kaplan-Meier survival curves permitting application to case series with ongoing follow-up. For a case series with known final outcomes: Consider each case a diagnostic test of good versus poor QOT (expected vs. increased failure rates), determine the likelihood ratio (LR) of the observed outcome, convert LR to weight taking log to base 2, and add up weights sequentially in a plot showing how many times odds in favour of good QOT have been doubled. For a series with observed survival times and an expected survival curve: Divide the curve into time intervals, determine "healthy" and specify "sick" risks of failure in each interval, construct a "sick" survival curve, determine the LR of survival or failure at the given observation times, convert to weights, and add up. The Bayesian plot was applied retrospectively to 39 children with acute lymphoblastic leukaemia with completed follow-up, using Nordic collaborative results as reference, showing equal odds between good and poor QOT. In the ongoing treatment trial, with 22 of 37 children still at risk for event, QOT has been monitored with average survival curves as reference, odds so far favoring good QOT 2:1. QOT in small patient series can be assessed with a Bayesian CUSUM plot, retrospectively when all treatment outcomes are known, but also in ongoing series with unfinished follow-up. © 2017 John Wiley & Sons, Ltd.

Whose statistical reasoning is facilitated by a causal structure intervention?

PubMed

McNair, Simon; Feeney, Aidan

2015-02-01

People often struggle when making Bayesian probabilistic estimates on the basis of competing sources of statistical evidence. Recently, Krynski and Tenenbaum (Journal of Experimental Psychology: General, 136, 430-450, 2007) proposed that a causal Bayesian framework accounts for peoples' errors in Bayesian reasoning and showed that, by clarifying the causal relations among the pieces of evidence, judgments on a classic statistical reasoning problem could be significantly improved. We aimed to understand whose statistical reasoning is facilitated by the causal structure intervention. In Experiment 1, although we observed causal facilitation effects overall, the effect was confined to participants high in numeracy. We did not find an overall facilitation effect in Experiment 2 but did replicate the earlier interaction between numerical ability and the presence or absence of causal content. This effect held when we controlled for general cognitive ability and thinking disposition. Our results suggest that clarifying causal structure facilitates Bayesian judgments, but only for participants with sufficient understanding of basic concepts in probability and statistics.

Bayesian-information-gap decision theory with an application to CO 2 sequestration

DOE PAGES

O'Malley, D.; Vesselinov, V. V.

2015-09-04

Decisions related to subsurface engineering problems such as groundwater management, fossil fuel production, and geologic carbon sequestration are frequently challenging because of an overabundance of uncertainties (related to conceptualizations, parameters, observations, etc.). Because of the importance of these problems to agriculture, energy, and the climate (respectively), good decisions that are scientifically defensible must be made despite the uncertainties. We describe a general approach to making decisions for challenging problems such as these in the presence of severe uncertainties that combines probabilistic and non-probabilistic methods. The approach uses Bayesian sampling to assess parametric uncertainty and Information-Gap Decision Theory (IGDT) to addressmore » model inadequacy. The combined approach also resolves an issue that frequently arises when applying Bayesian methods to real-world engineering problems related to the enumeration of possible outcomes. In the case of zero non-probabilistic uncertainty, the method reduces to a Bayesian method. Lastly, to illustrate the approach, we apply it to a site-selection decision for geologic CO 2 sequestration.« less

Bayesian Analysis of the Association between Family-Level Factors and Siblings' Dental Caries.

PubMed

Wen, A; Weyant, R J; McNeil, D W; Crout, R J; Neiswanger, K; Marazita, M L; Foxman, B

2017-07-01

We conducted a Bayesian analysis of the association between family-level socioeconomic status and smoking and the prevalence of dental caries among siblings (children from infant to 14 y) among children living in rural and urban Northern Appalachia using data from the Center for Oral Health Research in Appalachia (COHRA). The observed proportion of siblings sharing caries was significantly different from predicted assuming siblings' caries status was independent. Using a Bayesian hierarchical model, we found the inclusion of a household factor significantly improved the goodness of fit. Other findings showed an inverse association between parental education and siblings' caries and a positive association between households with smokers and siblings' caries. Our study strengthens existing evidence suggesting that increased parental education and decreased parental cigarette smoking are associated with reduced childhood caries in the household. Our results also demonstrate the value of a Bayesian approach, which allows us to include household as a random effect, thereby providing more accurate estimates than obtained using generalized linear mixed models.

A Bayesian Approach to More Stable Estimates of Group-Level Effects in Contextual Studies.

PubMed

Zitzmann, Steffen; Lüdtke, Oliver; Robitzsch, Alexander

2015-01-01

Multilevel analyses are often used to estimate the effects of group-level constructs. However, when using aggregated individual data (e.g., student ratings) to assess a group-level construct (e.g., classroom climate), the observed group mean might not provide a reliable measure of the unobserved latent group mean. In the present article, we propose a Bayesian approach that can be used to estimate a multilevel latent covariate model, which corrects for the unreliable assessment of the latent group mean when estimating the group-level effect. A simulation study was conducted to evaluate the choice of different priors for the group-level variance of the predictor variable and to compare the Bayesian approach with the maximum likelihood approach implemented in the software Mplus. Results showed that, under problematic conditions (i.e., small number of groups, predictor variable with a small ICC), the Bayesian approach produced more accurate estimates of the group-level effect than the maximum likelihood approach did.

BANYAN_Sigma: Bayesian classifier for members of young stellar associations

NASA Astrophysics Data System (ADS)

Gagné, Jonathan; Mamajek, Eric E.; Malo, Lison; Riedel, Adric; Rodriguez, David; Lafrenière, David; Faherty, Jacqueline K.; Roy-Loubier, Olivier; Pueyo, Laurent; Robin, Annie C.; Doyon, René

2018-01-01

BANYAN_Sigma calculates the membership probability that a given astrophysical object belongs to one of the currently known 27 young associations within 150 pc of the Sun, using Bayesian inference. This tool uses the sky position and proper motion measurements of an object, with optional radial velocity (RV) and distance (D) measurements, to derive a Bayesian membership probability. By default, the priors are adjusted such that a probability threshold of 90% will recover 50%, 68%, 82% or 90% of true association members depending on what observables are input (only sky position and proper motion, with RV, with D, with both RV and D, respectively). The algorithm is implemented in a Python package, in IDL, and is also implemented as an interactive web page.

Mean Field Variational Bayesian Data Assimilation

NASA Astrophysics Data System (ADS)

Vrettas, M.; Cornford, D.; Opper, M.

2012-04-01

Current data assimilation schemes propose a range of approximate solutions to the classical data assimilation problem, particularly state estimation. Broadly there are three main active research areas: ensemble Kalman filter methods which rely on statistical linearization of the model evolution equations, particle filters which provide a discrete point representation of the posterior filtering or smoothing distribution and 4DVAR methods which seek the most likely posterior smoothing solution. In this paper we present a recent extension to our variational Bayesian algorithm which seeks the most probably posterior distribution over the states, within the family of non-stationary Gaussian processes. Our original work on variational Bayesian approaches to data assimilation sought the best approximating time varying Gaussian process to the posterior smoothing distribution for stochastic dynamical systems. This approach was based on minimising the Kullback-Leibler divergence between the true posterior over paths, and our Gaussian process approximation. So long as the observation density was sufficiently high to bring the posterior smoothing density close to Gaussian the algorithm proved very effective, on lower dimensional systems. However for higher dimensional systems, the algorithm was computationally very demanding. We have been developing a mean field version of the algorithm which treats the state variables at a given time as being independent in the posterior approximation, but still accounts for their relationships between each other in the mean solution arising from the original dynamical system. In this work we present the new mean field variational Bayesian approach, illustrating its performance on a range of classical data assimilation problems. We discuss the potential and limitations of the new approach. We emphasise that the variational Bayesian approach we adopt, in contrast to other variational approaches, provides a bound on the marginal likelihood of the observations given parameters in the model which also allows inference of parameters such as observation errors, and parameters in the model and model error representation, particularly if this is written as a deterministic form with small additive noise. We stress that our approach can address very long time window and weak constraint settings. However like traditional variational approaches our Bayesian variational method has the benefit of being posed as an optimisation problem. We finish with a sketch of the future directions for our approach.

Improving the ideal and human observer consistency: a demonstration of principles

NASA Astrophysics Data System (ADS)

He, Xin

2017-03-01

In addition to being rigorous and realistic, the usefulness of the ideal observer computational tools may also depend on whether they serve the empirical purpose for which they are created, e.g. to identify desirable imaging systems to be used by human observers. In SPIE 10136-35, I have shown that the ideal and the human observers do not necessarily prefer the same system as the optimal or better one due to their different objectives in both hardware and software optimization. In this work, I attempt to identify a necessary but insufficient condition under which the human and the ideal observer may rank systems consistently. If corroborated, such a condition allows a numerical test on the ideal/human consistency without routine human observer studies. I reproduced data from Abbey et al. JOSA 2001 to verify the proposed condition (i.e., not a rigorous falsification study due to the lack of specificity in the proposed conjecture. A roadmap for more falsifiable conditions is proposed). Via this work, I would like to emphasize the reality of practical decision making in addition to the realism in mathematical modeling. (Disclaimer: the views expressed in this work do not necessarily represent those of the FDA.)

Reasoning and choice in the Monty Hall Dilemma (MHD): implications for improving Bayesian reasoning

PubMed Central

Tubau, Elisabet; Aguilar-Lleyda, David; Johnson, Eric D.

2015-01-01

The Monty Hall Dilemma (MHD) is a two-step decision problem involving counterintuitive conditional probabilities. The first choice is made among three equally probable options, whereas the second choice takes place after the elimination of one of the non-selected options which does not hide the prize. Differing from most Bayesian problems, statistical information in the MHD has to be inferred, either by learning outcome probabilities or by reasoning from the presented sequence of events. This often leads to suboptimal decisions and erroneous probability judgments. Specifically, decision makers commonly develop a wrong intuition that final probabilities are equally distributed, together with a preference for their first choice. Several studies have shown that repeated practice enhances sensitivity to the different reward probabilities, but does not facilitate correct Bayesian reasoning. However, modest improvements in probability judgments have been observed after guided explanations. To explain these dissociations, the present review focuses on two types of causes producing the observed biases: Emotional-based choice biases and cognitive limitations in understanding probabilistic information. Among the latter, we identify a crucial cause for the universal difficulty in overcoming the equiprobability illusion: Incomplete representation of prior and conditional probabilities. We conclude that repeated practice and/or high incentives can be effective for overcoming choice biases, but promoting an adequate partitioning of possibilities seems to be necessary for overcoming cognitive illusions and improving Bayesian reasoning. PMID:25873906

Bayesian power spectrum inference with foreground and target contamination treatment

NASA Astrophysics Data System (ADS)

Jasche, J.; Lavaux, G.

2017-10-01

This work presents a joint and self-consistent Bayesian treatment of various foreground and target contaminations when inferring cosmological power spectra and three-dimensional density fields from galaxy redshift surveys. This is achieved by introducing additional block-sampling procedures for unknown coefficients of foreground and target contamination templates to the previously presented ARES framework for Bayesian large-scale structure analyses. As a result, the method infers jointly and fully self-consistently three-dimensional density fields, cosmological power spectra, luminosity-dependent galaxy biases, noise levels of the respective galaxy distributions, and coefficients for a set of a priori specified foreground templates. In addition, this fully Bayesian approach permits detailed quantification of correlated uncertainties amongst all inferred quantities and correctly marginalizes over observational systematic effects. We demonstrate the validity and efficiency of our approach in obtaining unbiased estimates of power spectra via applications to realistic mock galaxy observations that are subject to stellar contamination and dust extinction. While simultaneously accounting for galaxy biases and unknown noise levels, our method reliably and robustly infers three-dimensional density fields and corresponding cosmological power spectra from deep galaxy surveys. Furthermore, our approach correctly accounts for joint and correlated uncertainties between unknown coefficients of foreground templates and the amplitudes of the power spectrum. This effect amounts to correlations and anti-correlations of up to 10 per cent across wide ranges in Fourier space.

Evaluating Observational Learning in a Competitive Two-Sided Crowdsourcing Market: A Bayesian Inferential Approach

ERIC Educational Resources Information Center

Ayaburi, Emmanuel Wusuhon Yanibo

2017-01-01

This dissertation investigates the effect of observational learning in crowdsourcing markets as a lens to identify appropriate mechanism(s) for sustaining this increasingly popular business model. Observational learning occurs when crowdsourcing participating agents obtain knowledge from signals they observe in the marketplace and incorporate such…

Bayesian model selection: Evidence estimation based on DREAM simulation and bridge sampling

NASA Astrophysics Data System (ADS)

Volpi, Elena; Schoups, Gerrit; Firmani, Giovanni; Vrugt, Jasper A.

2017-04-01

Bayesian inference has found widespread application in Earth and Environmental Systems Modeling, providing an effective tool for prediction, data assimilation, parameter estimation, uncertainty analysis and hypothesis testing. Under multiple competing hypotheses, the Bayesian approach also provides an attractive alternative to traditional information criteria (e.g. AIC, BIC) for model selection. The key variable for Bayesian model selection is the evidence (or marginal likelihood) that is the normalizing constant in the denominator of Bayes theorem; while it is fundamental for model selection, the evidence is not required for Bayesian inference. It is computed for each hypothesis (model) by averaging the likelihood function over the prior parameter distribution, rather than maximizing it as by information criteria; the larger a model evidence the more support it receives among a collection of hypothesis as the simulated values assign relatively high probability density to the observed data. Hence, the evidence naturally acts as an Occam's razor, preferring simpler and more constrained models against the selection of over-fitted ones by information criteria that incorporate only the likelihood maximum. Since it is not particularly easy to estimate the evidence in practice, Bayesian model selection via the marginal likelihood has not yet found mainstream use. We illustrate here the properties of a new estimator of the Bayesian model evidence, which provides robust and unbiased estimates of the marginal likelihood; the method is coined Gaussian Mixture Importance Sampling (GMIS). GMIS uses multidimensional numerical integration of the posterior parameter distribution via bridge sampling (a generalization of importance sampling) of a mixture distribution fitted to samples of the posterior distribution derived from the DREAM algorithm (Vrugt et al., 2008; 2009). Some illustrative examples are presented to show the robustness and superiority of the GMIS estimator with respect to other commonly used approaches in the literature.

A Bayesian hierarchical model for mortality data from cluster-sampling household surveys in humanitarian crises.

PubMed

Heudtlass, Peter; Guha-Sapir, Debarati; Speybroeck, Niko

2018-05-31

The crude death rate (CDR) is one of the defining indicators of humanitarian emergencies. When data from vital registration systems are not available, it is common practice to estimate the CDR from household surveys with cluster-sampling design. However, sample sizes are often too small to compare mortality estimates to emergency thresholds, at least in a frequentist framework. Several authors have proposed Bayesian methods for health surveys in humanitarian crises. Here, we develop an approach specifically for mortality data and cluster-sampling surveys. We describe a Bayesian hierarchical Poisson-Gamma mixture model with generic (weakly informative) priors that could be used as default in absence of any specific prior knowledge, and compare Bayesian and frequentist CDR estimates using five different mortality datasets. We provide an interpretation of the Bayesian estimates in the context of an emergency threshold and demonstrate how to interpret parameters at the cluster level and ways in which informative priors can be introduced. With the same set of weakly informative priors, Bayesian CDR estimates are equivalent to frequentist estimates, for all practical purposes. The probability that the CDR surpasses the emergency threshold can be derived directly from the posterior of the mean of the mixing distribution. All observation in the datasets contribute to the estimation of cluster-level estimates, through the hierarchical structure of the model. In a context of sparse data, Bayesian mortality assessments have advantages over frequentist ones already when using only weakly informative priors. More informative priors offer a formal and transparent way of combining new data with existing data and expert knowledge and can help to improve decision-making in humanitarian crises by complementing frequentist estimates.

Evaluation of Flagging Criteria of United States Kidney Transplant Center Performance: How to Best Define Outliers?

PubMed

Schold, Jesse D; Miller, Charles M; Henry, Mitchell L; Buccini, Laura D; Flechner, Stuart M; Goldfarb, David A; Poggio, Emilio D; Andreoni, Kenneth A

2017-06-01

Scientific Registry of Transplant Recipients report cards of US organ transplant center performance are publicly available and used for quality oversight. Low center performance (LP) evaluations are associated with changes in practice including reduced transplant rates and increased waitlist removals. In 2014, Scientific Registry of Transplant Recipients implemented new Bayesian methodology to evaluate performance which was not adopted by Center for Medicare and Medicaid Services (CMS). In May 2016, CMS altered their performance criteria, reducing the likelihood of LP evaluations. Our aims were to evaluate incidence, survival rates, and volume of LP centers with Bayesian, historical (old-CMS) and new-CMS criteria using 6 consecutive program-specific reports (PSR), January 2013 to July 2015 among adult kidney transplant centers. Bayesian, old-CMS and new-CMS criteria identified 13.4%, 8.3%, and 6.1% LP PSRs, respectively. Over the 3-year period, 31.9% (Bayesian), 23.4% (old-CMS), and 19.8% (new-CMS) of centers had 1 or more LP evaluation. For small centers (<83 transplants/PSR), there were 4-fold additional LP evaluations (52 vs 13 PSRs) for 1-year mortality with Bayesian versus new-CMS criteria. For large centers (>183 transplants/PSR), there were 3-fold additional LP evaluations for 1-year mortality with Bayesian versus new-CMS criteria with median differences in observed and expected patient survival of -1.6% and -2.2%, respectively. A significant proportion of kidney transplant centers are identified as low performing with relatively small survival differences compared with expected. Bayesian criteria have significantly higher flagging rates and new-CMS criteria modestly reduce flagging. Critical appraisal of performance criteria is needed to assess whether quality oversight is meeting intended goals and whether further modifications could reduce risk aversion, more efficiently allocate resources, and increase transplant opportunities.

Fully Bayesian inference for structural MRI: application to segmentation and statistical analysis of T2-hypointensities.

PubMed

Schmidt, Paul; Schmid, Volker J; Gaser, Christian; Buck, Dorothea; Bührlen, Susanne; Förschler, Annette; Mühlau, Mark

2013-01-01

Aiming at iron-related T2-hypointensity, which is related to normal aging and neurodegenerative processes, we here present two practicable approaches, based on Bayesian inference, for preprocessing and statistical analysis of a complex set of structural MRI data. In particular, Markov Chain Monte Carlo methods were used to simulate posterior distributions. First, we rendered a segmentation algorithm that uses outlier detection based on model checking techniques within a Bayesian mixture model. Second, we rendered an analytical tool comprising a Bayesian regression model with smoothness priors (in the form of Gaussian Markov random fields) mitigating the necessity to smooth data prior to statistical analysis. For validation, we used simulated data and MRI data of 27 healthy controls (age: [Formula: see text]; range, [Formula: see text]). We first observed robust segmentation of both simulated T2-hypointensities and gray-matter regions known to be T2-hypointense. Second, simulated data and images of segmented T2-hypointensity were analyzed. We found not only robust identification of simulated effects but also a biologically plausible age-related increase of T2-hypointensity primarily within the dentate nucleus but also within the globus pallidus, substantia nigra, and red nucleus. Our results indicate that fully Bayesian inference can successfully be applied for preprocessing and statistical analysis of structural MRI data.

Bayesian propensity scores for high-dimensional causal inference: A comparison of drug-eluting to bare-metal coronary stents.

PubMed

Spertus, Jacob V; Normand, Sharon-Lise T

2018-04-23

High-dimensional data provide many potential confounders that may bolster the plausibility of the ignorability assumption in causal inference problems. Propensity score methods are powerful causal inference tools, which are popular in health care research and are particularly useful for high-dimensional data. Recent interest has surrounded a Bayesian treatment of propensity scores in order to flexibly model the treatment assignment mechanism and summarize posterior quantities while incorporating variance from the treatment model. We discuss methods for Bayesian propensity score analysis of binary treatments, focusing on modern methods for high-dimensional Bayesian regression and the propagation of uncertainty. We introduce a novel and simple estimator for the average treatment effect that capitalizes on conjugacy of the beta and binomial distributions. Through simulations, we show the utility of horseshoe priors and Bayesian additive regression trees paired with our new estimator, while demonstrating the importance of including variance from the treatment regression model. An application to cardiac stent data with almost 500 confounders and 9000 patients illustrates approaches and facilitates comparison with existing alternatives. As measured by a falsifiability endpoint, we improved confounder adjustment compared with past observational research of the same problem. © 2018 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Clinical Outcome Prediction in Aneurysmal Subarachnoid Hemorrhage Using Bayesian Neural Networks with Fuzzy Logic Inferences

PubMed Central

Lo, Benjamin W. Y.; Macdonald, R. Loch; Baker, Andrew; Levine, Mitchell A. H.

2013-01-01

Objective. The novel clinical prediction approach of Bayesian neural networks with fuzzy logic inferences is created and applied to derive prognostic decision rules in cerebral aneurysmal subarachnoid hemorrhage (aSAH). Methods. The approach of Bayesian neural networks with fuzzy logic inferences was applied to data from five trials of Tirilazad for aneurysmal subarachnoid hemorrhage (3551 patients). Results. Bayesian meta-analyses of observational studies on aSAH prognostic factors gave generalizable posterior distributions of population mean log odd ratios (ORs). Similar trends were noted in Bayesian and linear regression ORs. Significant outcome predictors include normal motor response, cerebral infarction, history of myocardial infarction, cerebral edema, history of diabetes mellitus, fever on day 8, prior subarachnoid hemorrhage, admission angiographic vasospasm, neurological grade, intraventricular hemorrhage, ruptured aneurysm size, history of hypertension, vasospasm day, age and mean arterial pressure. Heteroscedasticity was present in the nontransformed dataset. Artificial neural networks found nonlinear relationships with 11 hidden variables in 1 layer, using the multilayer perceptron model. Fuzzy logic decision rules (centroid defuzzification technique) denoted cut-off points for poor prognosis at greater than 2.5 clusters. Discussion. This aSAH prognostic system makes use of existing knowledge, recognizes unknown areas, incorporates one's clinical reasoning, and compensates for uncertainty in prognostication. PMID:23690884

Bayesian approach for counting experiment statistics applied to a neutrino point source analysis

NASA Astrophysics Data System (ADS)

Bose, D.; Brayeur, L.; Casier, M.; de Vries, K. D.; Golup, G.; van Eijndhoven, N.

2013-12-01

In this paper we present a model independent analysis method following Bayesian statistics to analyse data from a generic counting experiment and apply it to the search for neutrinos from point sources. We discuss a test statistic defined following a Bayesian framework that will be used in the search for a signal. In case no signal is found, we derive an upper limit without the introduction of approximations. The Bayesian approach allows us to obtain the full probability density function for both the background and the signal rate. As such, we have direct access to any signal upper limit. The upper limit derivation directly compares with a frequentist approach and is robust in the case of low-counting observations. Furthermore, it allows also to account for previous upper limits obtained by other analyses via the concept of prior information without the need of the ad hoc application of trial factors. To investigate the validity of the presented Bayesian approach, we have applied this method to the public IceCube 40-string configuration data for 10 nearby blazars and we have obtained a flux upper limit, which is in agreement with the upper limits determined via a frequentist approach. Furthermore, the upper limit obtained compares well with the previously published result of IceCube, using the same data set.

Bayesian Sensitivity Analysis of Statistical Models with Missing Data

PubMed Central

ZHU, HONGTU; IBRAHIM, JOSEPH G.; TANG, NIANSHENG

2013-01-01

Methods for handling missing data depend strongly on the mechanism that generated the missing values, such as missing completely at random (MCAR) or missing at random (MAR), as well as other distributional and modeling assumptions at various stages. It is well known that the resulting estimates and tests may be sensitive to these assumptions as well as to outlying observations. In this paper, we introduce various perturbations to modeling assumptions and individual observations, and then develop a formal sensitivity analysis to assess these perturbations in the Bayesian analysis of statistical models with missing data. We develop a geometric framework, called the Bayesian perturbation manifold, to characterize the intrinsic structure of these perturbations. We propose several intrinsic influence measures to perform sensitivity analysis and quantify the effect of various perturbations to statistical models. We use the proposed sensitivity analysis procedure to systematically investigate the tenability of the non-ignorable missing at random (NMAR) assumption. Simulation studies are conducted to evaluate our methods, and a dataset is analyzed to illustrate the use of our diagnostic measures. PMID:24753718

Bayesian coronal seismology

NASA Astrophysics Data System (ADS)

Arregui, Iñigo

2018-01-01

In contrast to the situation in a laboratory, the study of the solar atmosphere has to be pursued without direct access to the physical conditions of interest. Information is therefore incomplete and uncertain and inference methods need to be employed to diagnose the physical conditions and processes. One of such methods, solar atmospheric seismology, makes use of observed and theoretically predicted properties of waves to infer plasma and magnetic field properties. A recent development in solar atmospheric seismology consists in the use of inversion and model comparison methods based on Bayesian analysis. In this paper, the philosophy and methodology of Bayesian analysis are first explained. Then, we provide an account of what has been achieved so far from the application of these techniques to solar atmospheric seismology and a prospect of possible future extensions.

Bayesian approach to non-Gaussian field statistics for diffusive broadband terahertz pulses.

PubMed

Pearce, Jeremy; Jian, Zhongping; Mittleman, Daniel M

2005-11-01

We develop a closed-form expression for the probability distribution function for the field components of a diffusive broadband wave propagating through a random medium. We consider each spectral component to provide an individual observation of a random variable, the configurationally averaged spectral intensity. Since the intensity determines the variance of the field distribution at each frequency, this random variable serves as the Bayesian prior that determines the form of the non-Gaussian field statistics. This model agrees well with experimental results.

Exploiting Cross-sensitivity by Bayesian Decoding of Mixed Potential Sensor Arrays

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kreller, Cortney

LANL mixed-potential electrochemical sensor (MPES) device arrays were coupled with advanced Bayesian inference treatment of the physical model of relevant sensor-analyte interactions. We demonstrated that our approach could be used to uniquely discriminate the composition of ternary gas sensors with three discreet MPES sensors with an average error of less than 2%. We also observed that the MPES exhibited excellent stability over a year of operation at elevated temperatures in the presence of test gases.

A new prior for bayesian anomaly detection: application to biosurveillance.

PubMed

Shen, Y; Cooper, G F

2010-01-01

Bayesian anomaly detection computes posterior probabilities of anomalous events by combining prior beliefs and evidence from data. However, the specification of prior probabilities can be challenging. This paper describes a Bayesian prior in the context of disease outbreak detection. The goal is to provide a meaningful, easy-to-use prior that yields a posterior probability of an outbreak that performs at least as well as a standard frequentist approach. If this goal is achieved, the resulting posterior could be usefully incorporated into a decision analysis about how to act in light of a possible disease outbreak. This paper describes a Bayesian method for anomaly detection that combines learning from data with a semi-informative prior probability over patterns of anomalous events. A univariate version of the algorithm is presented here for ease of illustration of the essential ideas. The paper describes the algorithm in the context of disease-outbreak detection, but it is general and can be used in other anomaly detection applications. For this application, the semi-informative prior specifies that an increased count over baseline is expected for the variable being monitored, such as the number of respiratory chief complaints per day at a given emergency department. The semi-informative prior is derived based on the baseline prior, which is estimated from using historical data. The evaluation reported here used semi-synthetic data to evaluate the detection performance of the proposed Bayesian method and a control chart method, which is a standard frequentist algorithm that is closest to the Bayesian method in terms of the type of data it uses. The disease-outbreak detection performance of the Bayesian method was statistically significantly better than that of the control chart method when proper baseline periods were used to estimate the baseline behavior to avoid seasonal effects. When using longer baseline periods, the Bayesian method performed as well as the control chart method. The time complexity of the Bayesian algorithm is linear in the number of the observed events being monitored, due to a novel, closed-form derivation that is introduced in the paper. This paper introduces a novel prior probability for Bayesian outbreak detection that is expressive, easy-to-apply, computationally efficient, and performs as well or better than a standard frequentist method.

Studies of regional-scale climate variability and change. Hidden Markov models and coupled ocean-atmosphere modes

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ghil, M.; Kravtsov, S.; Robertson, A. W.

2008-10-14

This project was a continuation of previous work under DOE CCPP funding, in which we had developed a twin approach of probabilistic network (PN) models (sometimes called dynamic Bayesian networks) and intermediate-complexity coupled ocean-atmosphere models (ICMs) to identify the predictable modes of climate variability and to investigate their impacts on the regional scale. We had developed a family of PNs (similar to Hidden Markov Models) to simulate historical records of daily rainfall, and used them to downscale GCM seasonal predictions. Using an idealized atmospheric model, we had established a novel mechanism through which ocean-induced sea-surface temperature (SST) anomalies might influencemore » large-scale atmospheric circulation patterns on interannual and longer time scales; we had found similar patterns in a hybrid coupled ocean-atmosphere-sea-ice model. The goal of the this continuation project was to build on these ICM results and PN model development to address prediction of rainfall and temperature statistics at the local scale, associated with global climate variability and change, and to investigate the impact of the latter on coupled ocean-atmosphere modes. Our main results from the grant consist of extensive further development of the hidden Markov models for rainfall simulation and downscaling together with the development of associated software; new intermediate coupled models; a new methodology of inverse modeling for linking ICMs with observations and GCM results; and, observational studies of decadal and multi-decadal natural climate results, informed by ICM results.« less

SELFI: an object-based, Bayesian method for faint emission line source detection in MUSE deep field data cubes

NASA Astrophysics Data System (ADS)

Meillier, Céline; Chatelain, Florent; Michel, Olivier; Bacon, Roland; Piqueras, Laure; Bacher, Raphael; Ayasso, Hacheme

2016-04-01

We present SELFI, the Source Emission Line FInder, a new Bayesian method optimized for detection of faint galaxies in Multi Unit Spectroscopic Explorer (MUSE) deep fields. MUSE is the new panoramic integral field spectrograph at the Very Large Telescope (VLT) that has unique capabilities for spectroscopic investigation of the deep sky. It has provided data cubes with 324 million voxels over a single 1 arcmin2 field of view. To address the challenge of faint-galaxy detection in these large data cubes, we developed a new method that processes 3D data either for modeling or for estimation and extraction of source configurations. This object-based approach yields a natural sparse representation of the sources in massive data fields, such as MUSE data cubes. In the Bayesian framework, the parameters that describe the observed sources are considered random variables. The Bayesian model leads to a general and robust algorithm where the parameters are estimated in a fully data-driven way. This detection algorithm was applied to the MUSE observation of Hubble Deep Field-South. With 27 h total integration time, these observations provide a catalog of 189 sources of various categories and with secured redshift. The algorithm retrieved 91% of the galaxies with only 9% false detection. This method also allowed the discovery of three new Lyα emitters and one [OII] emitter, all without any Hubble Space Telescope counterpart. We analyzed the reasons for failure for some targets, and found that the most important limitation of the method is when faint sources are located in the vicinity of bright spatially resolved galaxies that cannot be approximated by the Sérsic elliptical profile. The software and its documentation are available on the MUSE science web service (muse-vlt.eu/science).

Assessment of CT image quality using a Bayesian approach

NASA Astrophysics Data System (ADS)

Reginatto, M.; Anton, M.; Elster, C.

2017-08-01

One of the most promising approaches for evaluating CT image quality is task-specific quality assessment. This involves a simplified version of a clinical task, e.g. deciding whether an image belongs to the class of images that contain the signature of a lesion or not. Task-specific quality assessment can be done by model observers, which are mathematical procedures that carry out the classification task. The most widely used figure of merit for CT image quality is the area under the ROC curve (AUC), a quantity which characterizes the performance of a given model observer. In order to estimate AUC from a finite sample of images, different approaches from classical statistics have been suggested. The goal of this paper is to introduce task-specific quality assessment of CT images to metrology and to propose a novel Bayesian estimation of AUC for the channelized Hotelling observer (CHO) applied to the task of detecting a lesion at a known image location. It is assumed that signal-present and signal-absent images follow multivariate normal distributions with the same covariance matrix. The Bayesian approach results in a posterior distribution for the AUC of the CHO which provides in addition a complete characterization of the uncertainty of this figure of merit. The approach is illustrated by its application to both simulated and experimental data.

Predicting uncertainty in future marine ice sheet volume using Bayesian statistical methods

NASA Astrophysics Data System (ADS)

Davis, A. D.

2015-12-01

The marine ice instability can trigger rapid retreat of marine ice streams. Recent observations suggest that marine ice systems in West Antarctica have begun retreating. However, unknown ice dynamics, computationally intensive mathematical models, and uncertain parameters in these models make predicting retreat rate and ice volume difficult. In this work, we fuse current observational data with ice stream/shelf models to develop probabilistic predictions of future grounded ice sheet volume. Given observational data (e.g., thickness, surface elevation, and velocity) and a forward model that relates uncertain parameters (e.g., basal friction and basal topography) to these observations, we use a Bayesian framework to define a posterior distribution over the parameters. A stochastic predictive model then propagates uncertainties in these parameters to uncertainty in a particular quantity of interest (QoI)---here, the volume of grounded ice at a specified future time. While the Bayesian approach can in principle characterize the posterior predictive distribution of the QoI, the computational cost of both the forward and predictive models makes this effort prohibitively expensive. To tackle this challenge, we introduce a new Markov chain Monte Carlo method that constructs convergent approximations of the QoI target density in an online fashion, yielding accurate characterizations of future ice sheet volume at significantly reduced computational cost.Our second goal is to attribute uncertainty in these Bayesian predictions to uncertainties in particular parameters. Doing so can help target data collection, for the purpose of constraining the parameters that contribute most strongly to uncertainty in the future volume of grounded ice. For instance, smaller uncertainties in parameters to which the QoI is highly sensitive may account for more variability in the prediction than larger uncertainties in parameters to which the QoI is less sensitive. We use global sensitivity analysis to help answer this question, and make the computation of sensitivity indices computationally tractable using a combination of polynomial chaos and Monte Carlo techniques.

Estimability and simple dynamical analyses of range (range-rate range-difference) observations to artificial satellites. [laser range observations to LAGEOS using non-Bayesian statistics

NASA Technical Reports Server (NTRS)

Vangelder, B. H. W.

1978-01-01

Non-Bayesian statistics were used in simulation studies centered around laser range observations to LAGEOS. The capabilities of satellite laser ranging especially in connection with relative station positioning are evaluated. The satellite measurement system under investigation may fall short in precise determinations of the earth's orientation (precession and nutation) and earth's rotation as opposed to systems as very long baseline interferometry (VLBI) and lunar laser ranging (LLR). Relative station positioning, determination of (differential) polar motion, positioning of stations with respect to the earth's center of mass and determination of the earth's gravity field should be easily realized by satellite laser ranging (SLR). The last two features should be considered as best (or solely) determinable by SLR in contrast to VLBI and LLR.

Constraints on Average Radial Anisotropy in the Lower Mantle

NASA Astrophysics Data System (ADS)

Trampert, J.; De Wit, R. W. L.; Kaeufl, P.; Valentine, A. P.

2014-12-01

Quantifying uncertainties in seismological models is challenging, yet ideally quality assessment is an integral part of the inverse method. We invert centre frequencies for spheroidal and toroidal modes for three parameters of average radial anisotropy, density and P- and S-wave velocities in the lower mantle. We adopt a Bayesian machine learning approach to extract the information on the earth model that is available in the normal mode data. The method is flexible and allows us to infer probability density functions (pdfs), which provide a quantitative description of our knowledge of the individual earth model parameters. The parameters describing shear- and P-wave anisotropy show little deviations from isotropy, but the intermediate parameter η carries robust information on negative anisotropy of ~1% below 1900 km depth. The mass density in the deep mantle (below 1900 km) shows clear positive deviations from existing models. Other parameters (P- and shear-wave velocities) are close to PREM. Our results require that the average mantle is about 150K colder than commonly assumed adiabats and consist of a mixture of about 60% perovskite and 40% ferropericlase containing 10-15% iron. The anisotropy favours a specific orientation of the two minerals. This observation has important consequences for the nature of mantle flow.

Gender in facial representations: a contrast-based study of adaptation within and between the sexes.

PubMed

Oruç, Ipek; Guo, Xiaoyue M; Barton, Jason J S

2011-01-18

Face aftereffects are proving to be an effective means of examining the properties of face-specific processes in the human visual system. We examined the role of gender in the neural representation of faces using a contrast-based adaptation method. If faces of different genders share the same representational face space, then adaptation to a face of one gender should affect both same- and different-gender faces. Further, if these aftereffects differ in magnitude, this may indicate distinct gender-related factors in the organization of this face space. To control for a potential confound between physical similarity and gender, we used a Bayesian ideal observer and human discrimination data to construct a stimulus set in which pairs of different-gender faces were equally dissimilar as same-gender pairs. We found that the recognition of both same-gender and different-gender faces was suppressed following a brief exposure of 100 ms. Moreover, recognition was more suppressed for test faces of a different-gender than those of the same-gender as the adaptor, despite the equivalence in physical and psychophysical similarity. Our results suggest that male and female faces likely occupy the same face space, allowing transfer of aftereffects between the genders, but that there are special properties that emerge along gender-defining dimensions of this space.

Calibrating the Planck cluster mass scale with CLASH

NASA Astrophysics Data System (ADS)

Penna-Lima, M.; Bartlett, J. G.; Rozo, E.; Melin, J.-B.; Merten, J.; Evrard, A. E.; Postman, M.; Rykoff, E.

2017-08-01

We determine the mass scale of Planck galaxy clusters using gravitational lensing mass measurements from the Cluster Lensing And Supernova survey with Hubble (CLASH). We have compared the lensing masses to the Planck Sunyaev-Zeldovich (SZ) mass proxy for 21 clusters in common, employing a Bayesian analysis to simultaneously fit an idealized CLASH selection function and the distribution between the measured observables and true cluster mass. We used a tiered analysis strategy to explicitly demonstrate the importance of priors on weak lensing mass accuracy. In the case of an assumed constant bias, bSZ, between true cluster mass, M500, and the Planck mass proxy, MPL, our analysis constrains 1-bSZ = 0.73 ± 0.10 when moderate priors on weak lensing accuracy are used, including a zero-mean Gaussian with standard deviation of 8% to account for possible bias in lensing mass estimations. Our analysis explicitly accounts for possible selection bias effects in this calibration sourced by the CLASH selection function. Our constraint on the cluster mass scale is consistent with recent results from the Weighing the Giants program and the Canadian Cluster Comparison Project. It is also consistent, at 1.34σ, with the value needed to reconcile the Planck SZ cluster counts with Planck's base ΛCDM model fit to the primary cosmic microwave background anisotropies.

A Bayesian Hybrid Adaptive Randomisation Design for Clinical Trials with Survival Outcomes.

PubMed

Moatti, M; Chevret, S; Zohar, S; Rosenberger, W F

2016-01-01

Response-adaptive randomisation designs have been proposed to improve the efficiency of phase III randomised clinical trials and improve the outcomes of the clinical trial population. In the setting of failure time outcomes, Zhang and Rosenberger (2007) developed a response-adaptive randomisation approach that targets an optimal allocation, based on a fixed sample size. The aim of this research is to propose a response-adaptive randomisation procedure for survival trials with an interim monitoring plan, based on the following optimal criterion: for fixed variance of the estimated log hazard ratio, what allocation minimizes the expected hazard of failure? We demonstrate the utility of the design by redesigning a clinical trial on multiple myeloma. To handle continuous monitoring of data, we propose a Bayesian response-adaptive randomisation procedure, where the log hazard ratio is the effect measure of interest. Combining the prior with the normal likelihood, the mean posterior estimate of the log hazard ratio allows derivation of the optimal target allocation. We perform a simulation study to assess and compare the performance of this proposed Bayesian hybrid adaptive design to those of fixed, sequential or adaptive - either frequentist or fully Bayesian - designs. Non informative normal priors of the log hazard ratio were used, as well as mixture of enthusiastic and skeptical priors. Stopping rules based on the posterior distribution of the log hazard ratio were computed. The method is then illustrated by redesigning a phase III randomised clinical trial of chemotherapy in patients with multiple myeloma, with mixture of normal priors elicited from experts. As expected, there was a reduction in the proportion of observed deaths in the adaptive vs. non-adaptive designs; this reduction was maximized using a Bayes mixture prior, with no clear-cut improvement by using a fully Bayesian procedure. The use of stopping rules allows a slight decrease in the observed proportion of deaths under the alternate hypothesis compared with the adaptive designs with no stopping rules. Such Bayesian hybrid adaptive survival trials may be promising alternatives to traditional designs, reducing the duration of survival trials, as well as optimizing the ethical concerns for patients enrolled in the trial.

Posterior Predictive Bayesian Phylogenetic Model Selection

PubMed Central

Lewis, Paul O.; Xie, Wangang; Chen, Ming-Hui; Fan, Yu; Kuo, Lynn

2014-01-01

We present two distinctly different posterior predictive approaches to Bayesian phylogenetic model selection and illustrate these methods using examples from green algal protein-coding cpDNA sequences and flowering plant rDNA sequences. The Gelfand–Ghosh (GG) approach allows dissection of an overall measure of model fit into components due to posterior predictive variance (GGp) and goodness-of-fit (GGg), which distinguishes this method from the posterior predictive P-value approach. The conditional predictive ordinate (CPO) method provides a site-specific measure of model fit useful for exploratory analyses and can be combined over sites yielding the log pseudomarginal likelihood (LPML) which is useful as an overall measure of model fit. CPO provides a useful cross-validation approach that is computationally efficient, requiring only a sample from the posterior distribution (no additional simulation is required). Both GG and CPO add new perspectives to Bayesian phylogenetic model selection based on the predictive abilities of models and complement the perspective provided by the marginal likelihood (including Bayes Factor comparisons) based solely on the fit of competing models to observed data. [Bayesian; conditional predictive ordinate; CPO; L-measure; LPML; model selection; phylogenetics; posterior predictive.] PMID:24193892

Adoption of American Heart Association 2020 ideal healthy diet recommendations prevents weight gain in young adults.

PubMed

Forget, Geneviève; Doyon, Myriam; Lacerte, Guillaume; Labonté, Mélissa; Brown, Christine; Carpentier, André C; Langlois, Marie-France; Hivert, Marie-France

2013-11-01

In 2010, the American Heart Association established the concept of ideal cardiovascular health. Nationally representative data estimated that <1% of Americans meet the seven health metrics required for achieving ideal cardiovascular health, with the main challenge residing in meeting the criteria for an ideal Healthy Diet Score. In a cohort of young adults (N=196), we aimed to investigate the prevalence of ideal cardiovascular health and ideal Healthy Diet Score and its association to weight gain over a 4-year follow-up period. Anthropometric measures, blood pressure, and blood samples were taken according to standardized procedures. Dietary intake was measured by a 3-day food diary and verified by a registered dietitian. We observed that only 0.5% of our sample met the criteria for ideal cardiovascular health and only 4.1% met the criteria for an ideal Healthy Diet Score. The components of the Healthy Diet Score with the lowest observance were consumption of fruits and vegetables (9.7%) and whole grains (14.8%). Meeting zero or one out of five of the Healthy Diet Score components was associated with increased risk of weight gain over 4 years compared with meeting at least two components (P=0.03). With the exception of dietary criteria, prevalence was high for achieving ideal levels of the remaining six cardiovascular health metrics. In conclusion, in this sample of young adults, a very low prevalence of ideal overall cardiovascular health was observed, mainly driven by poor dietary habits, and a poor Healthy Diet Score was associated with increased weight gain. Copyright © 2013 Academy of Nutrition and Dietetics. Published by Elsevier Inc. All rights reserved.

How People Use Social Information to Find out What to Want in the Paradigmatic Case of Inter-temporal Preferences

PubMed Central

Dolan, Raymond J.

2016-01-01

The weight with which a specific outcome feature contributes to preference quantifies a person’s ‘taste’ for that feature. However, far from being fixed personality characteristics, tastes are plastic. They tend to align, for example, with those of others even if such conformity is not rewarded. We hypothesised that people can be uncertain about their tastes. Personal tastes are therefore uncertain beliefs. People can thus learn about them by considering evidence, such as the preferences of relevant others, and then performing Bayesian updating. If a person’s choice variability reflects uncertainty, as in random-preference models, then a signature of Bayesian updating is that the degree of taste change should correlate with that person’s choice variability. Temporal discounting coefficients are an important example of taste–for patience. These coefficients quantify impulsivity, have good psychometric properties and can change upon observing others’ choices. We examined discounting preferences in a novel, large community study of 14–24 year olds. We assessed discounting behaviour, including decision variability, before and after participants observed another person’s choices. We found good evidence for taste uncertainty and for Bayesian taste updating. First, participants displayed decision variability which was better accounted for by a random-taste than by a response-noise model. Second, apparent taste shifts were well described by a Bayesian model taking into account taste uncertainty and the relevance of social information. Our findings have important neuroscientific, clinical and developmental significance. PMID:27447491

A Fault Diagnosis Methodology for Gear Pump Based on EEMD and Bayesian Network

PubMed Central

Liu, Zengkai; Liu, Yonghong; Shan, Hongkai; Cai, Baoping; Huang, Qing

2015-01-01

This paper proposes a fault diagnosis methodology for a gear pump based on the ensemble empirical mode decomposition (EEMD) method and the Bayesian network. Essentially, the presented scheme is a multi-source information fusion based methodology. Compared with the conventional fault diagnosis with only EEMD, the proposed method is able to take advantage of all useful information besides sensor signals. The presented diagnostic Bayesian network consists of a fault layer, a fault feature layer and a multi-source information layer. Vibration signals from sensor measurement are decomposed by the EEMD method and the energy of intrinsic mode functions (IMFs) are calculated as fault features. These features are added into the fault feature layer in the Bayesian network. The other sources of useful information are added to the information layer. The generalized three-layer Bayesian network can be developed by fully incorporating faults and fault symptoms as well as other useful information such as naked eye inspection and maintenance records. Therefore, diagnostic accuracy and capacity can be improved. The proposed methodology is applied to the fault diagnosis of a gear pump and the structure and parameters of the Bayesian network is established. Compared with artificial neural network and support vector machine classification algorithms, the proposed model has the best diagnostic performance when sensor data is used only. A case study has demonstrated that some information from human observation or system repair records is very helpful to the fault diagnosis. It is effective and efficient in diagnosing faults based on uncertain, incomplete information. PMID:25938760

A Fault Diagnosis Methodology for Gear Pump Based on EEMD and Bayesian Network.

PubMed

Liu, Zengkai; Liu, Yonghong; Shan, Hongkai; Cai, Baoping; Huang, Qing

2015-01-01

This paper proposes a fault diagnosis methodology for a gear pump based on the ensemble empirical mode decomposition (EEMD) method and the Bayesian network. Essentially, the presented scheme is a multi-source information fusion based methodology. Compared with the conventional fault diagnosis with only EEMD, the proposed method is able to take advantage of all useful information besides sensor signals. The presented diagnostic Bayesian network consists of a fault layer, a fault feature layer and a multi-source information layer. Vibration signals from sensor measurement are decomposed by the EEMD method and the energy of intrinsic mode functions (IMFs) are calculated as fault features. These features are added into the fault feature layer in the Bayesian network. The other sources of useful information are added to the information layer. The generalized three-layer Bayesian network can be developed by fully incorporating faults and fault symptoms as well as other useful information such as naked eye inspection and maintenance records. Therefore, diagnostic accuracy and capacity can be improved. The proposed methodology is applied to the fault diagnosis of a gear pump and the structure and parameters of the Bayesian network is established. Compared with artificial neural network and support vector machine classification algorithms, the proposed model has the best diagnostic performance when sensor data is used only. A case study has demonstrated that some information from human observation or system repair records is very helpful to the fault diagnosis. It is effective and efficient in diagnosing faults based on uncertain, incomplete information.

Bayesian Mass Estimates of the Milky Way: Including Measurement Uncertainties with Hierarchical Bayes

NASA Astrophysics Data System (ADS)

Eadie, Gwendolyn M.; Springford, Aaron; Harris, William E.

2017-02-01

We present a hierarchical Bayesian method for estimating the total mass and mass profile of the Milky Way Galaxy. The new hierarchical Bayesian approach further improves the framework presented by Eadie et al. and Eadie and Harris and builds upon the preliminary reports by Eadie et al. The method uses a distribution function f({ E },L) to model the Galaxy and kinematic data from satellite objects, such as globular clusters (GCs), to trace the Galaxy’s gravitational potential. A major advantage of the method is that it not only includes complete and incomplete data simultaneously in the analysis, but also incorporates measurement uncertainties in a coherent and meaningful way. We first test the hierarchical Bayesian framework, which includes measurement uncertainties, using the same data and power-law model assumed in Eadie and Harris and find the results are similar but more strongly constrained. Next, we take advantage of the new statistical framework and incorporate all possible GC data, finding a cumulative mass profile with Bayesian credible regions. This profile implies a mass within 125 kpc of 4.8× {10}11{M}⊙ with a 95% Bayesian credible region of (4.0{--}5.8)× {10}11{M}⊙ . Our results also provide estimates of the true specific energies of all the GCs. By comparing these estimated energies to the measured energies of GCs with complete velocity measurements, we observe that (the few) remote tracers with complete measurements may play a large role in determining a total mass estimate of the Galaxy. Thus, our study stresses the need for more remote tracers with complete velocity measurements.

Application of bayesian networks to real-time flood risk estimation

NASA Astrophysics Data System (ADS)

Garrote, L.; Molina, M.; Blasco, G.

2003-04-01

This paper presents the application of a computational paradigm taken from the field of artificial intelligence - the bayesian network - to model the behaviour of hydrologic basins during floods. The final goal of this research is to develop representation techniques for hydrologic simulation models in order to define, develop and validate a mechanism, supported by a software environment, oriented to build decision models for the prediction and management of river floods in real time. The emphasis is placed on providing decision makers with tools to incorporate their knowledge of basin behaviour, usually formulated in terms of rainfall-runoff models, in the process of real-time decision making during floods. A rainfall-runoff model is only a step in the process of decision making. If a reliable rainfall forecast is available and the rainfall-runoff model is well calibrated, decisions can be based mainly on model results. However, in most practical situations, uncertainties in rainfall forecasts or model performance have to be incorporated in the decision process. The computation paradigm adopted for the simulation of hydrologic processes is the bayesian network. A bayesian network is a directed acyclic graph that represents causal influences between linked variables. Under this representation, uncertain qualitative variables are related through causal relations quantified with conditional probabilities. The solution algorithm allows the computation of the expected probability distribution of unknown variables conditioned to the observations. An approach to represent hydrologic processes by bayesian networks with temporal and spatial extensions is presented in this paper, together with a methodology for the development of bayesian models using results produced by deterministic hydrologic simulation models

Bayesian-based estimation of acoustic surface impedance: Finite difference frequency domain approach.

PubMed

Bockman, Alexander; Fackler, Cameron; Xiang, Ning

2015-04-01

Acoustic performance for an interior requires an accurate description of the boundary materials' surface acoustic impedance. Analytical methods may be applied to a small class of test geometries, but inverse numerical methods provide greater flexibility. The parameter estimation problem requires minimizing prediction vice observed acoustic field pressure. The Bayesian-network sampling approach presented here mitigates other methods' susceptibility to noise inherent to the experiment, model, and numerics. A geometry agnostic method is developed here and its parameter estimation performance is demonstrated for an air-backed micro-perforated panel in an impedance tube. Good agreement is found with predictions from the ISO standard two-microphone, impedance-tube method, and a theoretical model for the material. Data by-products exclusive to a Bayesian approach are analyzed to assess sensitivity of the method to nuisance parameters.

Evaluation of Oceanic Transport Statistics By Use of Transient Tracers and Bayesian Methods

NASA Astrophysics Data System (ADS)

Trossman, D. S.; Thompson, L.; Mecking, S.; Bryan, F.; Peacock, S.

2013-12-01

Key variables that quantify the time scales over which atmospheric signals penetrate into the oceanic interior and their uncertainties are computed using Bayesian methods and transient tracers from both models and observations. First, the mean residence times, subduction rates, and formation rates of Subtropical Mode Water (STMW) and Subpolar Mode Water (SPMW) in the North Atlantic and Subantarctic Mode Water (SAMW) in the Southern Ocean are estimated by combining a model and observations of chlorofluorocarbon-11 (CFC-11) via Bayesian Model Averaging (BMA), statistical technique that weights model estimates according to how close they agree with observations. Second, a Bayesian method is presented to find two oceanic transport parameters associated with the age distribution of ocean waters, the transit-time distribution (TTD), by combining an eddying global ocean model's estimate of the TTD with hydrographic observations of CFC-11, temperature, and salinity. Uncertainties associated with objectively mapping irregularly spaced bottle data are quantified by making use of a thin-plate spline and then propagated via the two Bayesian techniques. It is found that the subduction of STMW, SPMW, and SAMW is mostly an advective process, but up to about one-third of STMW subduction likely owes to non-advective processes. Also, while the formation of STMW is mostly due to subduction, the formation of SPMW is mostly due to other processes. About half of the formation of SAMW is due to subduction and half is due to other processes. A combination of air-sea flux, acting on relatively short time scales, and turbulent mixing, acting on a wide range of time scales, is likely the dominant SPMW erosion mechanism. Air-sea flux is likely responsible for most STMW erosion, and turbulent mixing is likely responsible for most SAMW erosion. Two oceanic transport parameters, the mean age of a water parcel and the half-variance associated with the TTD, estimated using the model's tracers as data (BayesPOP) and those estimated using tracer observations as data (BayesObs) provide information about the sources of model biases, and give a more nuanced picture than can be found by comparing the simulated CFC-11 concentrations with observed CFC-11 concentrations. Using the differences between the two oceanic transport parameters from BayesObs and those from BayesPOP with and without a constant Peclet number assumption along each of the hydrographic cross-sections considered here, it is found that the model's diffusivity tensor biases lead to larger model errors than the model's mean advection time biases. However, it is also found that mean advection time biases in the model are statistically significant at the 95% level where mode water is found.

When global structure "Explains Away" local grammar: a Bayesian account of rule-induction in tone sequences.

PubMed

Dawson, Colin; Gerken, Louann

2011-09-01

While many constraints on learning must be relatively experience-independent, past experience provides a rich source of guidance for subsequent learning. Discovering structure in some domain can inform a learner's future hypotheses about that domain. If a general property accounts for particular sub-patterns, a rational learner should not stipulate separate explanations for each detail without additional evidence, as the general structure has "explained away" the original evidence. In a grammar-learning experiment using tone sequences, manipulating learners' prior exposure to a tone environment affects their sensitivity to the grammar-defining feature, in this case consecutive repeated tones. Grammar-learning performance is worse if context melodies are "smooth" -- when small intervals occur more than large ones -- as Smoothness is a general property accounting for a high rate of repetition. We present an idealized Bayesian model as a "best case" benchmark for learning repetition grammars. When context melodies are Smooth, the model places greater weight on the small-interval constraint, and does not learn the repetition rule as well as when context melodies are not Smooth, paralleling the human learners. These findings support an account of abstract grammar-induction in which learners rationally assess the statistical evidence for underlying structure based on a generative model of the environment. Copyright © 2010 Elsevier B.V. All rights reserved.

Bayes and empirical Bayes estimators of abundance and density from spatial capture-recapture data

USGS Publications Warehouse

Dorazio, Robert M.

2013-01-01

In capture-recapture and mark-resight surveys, movements of individuals both within and between sampling periods can alter the susceptibility of individuals to detection over the region of sampling. In these circumstances spatially explicit capture-recapture (SECR) models, which incorporate the observed locations of individuals, allow population density and abundance to be estimated while accounting for differences in detectability of individuals. In this paper I propose two Bayesian SECR models, one for the analysis of recaptures observed in trapping arrays and another for the analysis of recaptures observed in area searches. In formulating these models I used distinct submodels to specify the distribution of individual home-range centers and the observable recaptures associated with these individuals. This separation of ecological and observational processes allowed me to derive a formal connection between Bayes and empirical Bayes estimators of population abundance that has not been established previously. I showed that this connection applies to every Poisson point-process model of SECR data and provides theoretical support for a previously proposed estimator of abundance based on recaptures in trapping arrays. To illustrate results of both classical and Bayesian methods of analysis, I compared Bayes and empirical Bayes esimates of abundance and density using recaptures from simulated and real populations of animals. Real populations included two iconic datasets: recaptures of tigers detected in camera-trap surveys and recaptures of lizards detected in area-search surveys. In the datasets I analyzed, classical and Bayesian methods provided similar – and often identical – inferences, which is not surprising given the sample sizes and the noninformative priors used in the analyses.

Bayes and empirical Bayes estimators of abundance and density from spatial capture-recapture data.

PubMed

Dorazio, Robert M

2013-01-01

In capture-recapture and mark-resight surveys, movements of individuals both within and between sampling periods can alter the susceptibility of individuals to detection over the region of sampling. In these circumstances spatially explicit capture-recapture (SECR) models, which incorporate the observed locations of individuals, allow population density and abundance to be estimated while accounting for differences in detectability of individuals. In this paper I propose two Bayesian SECR models, one for the analysis of recaptures observed in trapping arrays and another for the analysis of recaptures observed in area searches. In formulating these models I used distinct submodels to specify the distribution of individual home-range centers and the observable recaptures associated with these individuals. This separation of ecological and observational processes allowed me to derive a formal connection between Bayes and empirical Bayes estimators of population abundance that has not been established previously. I showed that this connection applies to every Poisson point-process model of SECR data and provides theoretical support for a previously proposed estimator of abundance based on recaptures in trapping arrays. To illustrate results of both classical and Bayesian methods of analysis, I compared Bayes and empirical Bayes esimates of abundance and density using recaptures from simulated and real populations of animals. Real populations included two iconic datasets: recaptures of tigers detected in camera-trap surveys and recaptures of lizards detected in area-search surveys. In the datasets I analyzed, classical and Bayesian methods provided similar - and often identical - inferences, which is not surprising given the sample sizes and the noninformative priors used in the analyses.

A surrogate-based sensitivity quantification and Bayesian inversion of a regional groundwater flow model

NASA Astrophysics Data System (ADS)

Chen, Mingjie; Izady, Azizallah; Abdalla, Osman A.; Amerjeed, Mansoor

2018-02-01

Bayesian inference using Markov Chain Monte Carlo (MCMC) provides an explicit framework for stochastic calibration of hydrogeologic models accounting for uncertainties; however, the MCMC sampling entails a large number of model calls, and could easily become computationally unwieldy if the high-fidelity hydrogeologic model simulation is time consuming. This study proposes a surrogate-based Bayesian framework to address this notorious issue, and illustrates the methodology by inverse modeling a regional MODFLOW model. The high-fidelity groundwater model is approximated by a fast statistical model using Bagging Multivariate Adaptive Regression Spline (BMARS) algorithm, and hence the MCMC sampling can be efficiently performed. In this study, the MODFLOW model is developed to simulate the groundwater flow in an arid region of Oman consisting of mountain-coast aquifers, and used to run representative simulations to generate training dataset for BMARS model construction. A BMARS-based Sobol' method is also employed to efficiently calculate input parameter sensitivities, which are used to evaluate and rank their importance for the groundwater flow model system. According to sensitivity analysis, insensitive parameters are screened out of Bayesian inversion of the MODFLOW model, further saving computing efforts. The posterior probability distribution of input parameters is efficiently inferred from the prescribed prior distribution using observed head data, demonstrating that the presented BMARS-based Bayesian framework is an efficient tool to reduce parameter uncertainties of a groundwater system.

Past and present cosmic structure in the SDSS DR7 main sample

DOE Office of Scientific and Technical Information (OSTI.GOV)

Jasche, J.; Leclercq, F.; Wandelt, B.D., E-mail: jasche@iap.fr, E-mail: florent.leclercq@polytechnique.org, E-mail: wandelt@iap.fr

2015-01-01

We present a chrono-cosmography project, aiming at the inference of the four dimensional formation history of the observed large scale structure from its origin to the present epoch. To do so, we perform a full-scale Bayesian analysis of the northern galactic cap of the Sloan Digital Sky Survey (SDSS) Data Release 7 main galaxy sample, relying on a fully probabilistic, physical model of the non-linearly evolved density field. Besides inferring initial conditions from observations, our methodology naturally and accurately reconstructs non-linear features at the present epoch, such as walls and filaments, corresponding to high-order correlation functions generated by late-time structuremore » formation. Our inference framework self-consistently accounts for typical observational systematic and statistical uncertainties such as noise, survey geometry and selection effects. We further account for luminosity dependent galaxy biases and automatic noise calibration within a fully Bayesian approach. As a result, this analysis provides highly-detailed and accurate reconstructions of the present density field on scales larger than ∼ 3 Mpc/h, constrained by SDSS observations. This approach also leads to the first quantitative inference of plausible formation histories of the dynamic large scale structure underlying the observed galaxy distribution. The results described in this work constitute the first full Bayesian non-linear analysis of the cosmic large scale structure with the demonstrated capability of uncertainty quantification. Some of these results will be made publicly available along with this work. The level of detail of inferred results and the high degree of control on observational uncertainties pave the path towards high precision chrono-cosmography, the subject of simultaneously studying the dynamics and the morphology of the inhomogeneous Universe.« less

Uncertainty Analysis and Parameter Estimation For Nearshore Hydrodynamic Models

NASA Astrophysics Data System (ADS)

Ardani, S.; Kaihatu, J. M.

2012-12-01

Numerical models represent deterministic approaches used for the relevant physical processes in the nearshore. Complexity of the physics of the model and uncertainty involved in the model inputs compel us to apply a stochastic approach to analyze the robustness of the model. The Bayesian inverse problem is one powerful way to estimate the important input model parameters (determined by apriori sensitivity analysis) and can be used for uncertainty analysis of the outputs. Bayesian techniques can be used to find the range of most probable parameters based on the probability of the observed data and the residual errors. In this study, the effect of input data involving lateral (Neumann) boundary conditions, bathymetry and off-shore wave conditions on nearshore numerical models are considered. Monte Carlo simulation is applied to a deterministic numerical model (the Delft3D modeling suite for coupled waves and flow) for the resulting uncertainty analysis of the outputs (wave height, flow velocity, mean sea level and etc.). Uncertainty analysis of outputs is performed by random sampling from the input probability distribution functions and running the model as required until convergence to the consistent results is achieved. The case study used in this analysis is the Duck94 experiment, which was conducted at the U.S. Army Field Research Facility at Duck, North Carolina, USA in the fall of 1994. The joint probability of model parameters relevant for the Duck94 experiments will be found using the Bayesian approach. We will further show that, by using Bayesian techniques to estimate the optimized model parameters as inputs and applying them for uncertainty analysis, we can obtain more consistent results than using the prior information for input data which means that the variation of the uncertain parameter will be decreased and the probability of the observed data will improve as well. Keywords: Monte Carlo Simulation, Delft3D, uncertainty analysis, Bayesian techniques, MCMC

Allometric Convergence in Savanna Trees and Implications for the Use of Plant Scaling Models in Variable Ecosystems

PubMed Central

Tredennick, Andrew T.; Bentley, Lisa Patrick; Hanan, Niall P.

2013-01-01

Theoretical models of allometric scaling provide frameworks for understanding and predicting how and why the morphology and function of organisms vary with scale. It remains unclear, however, if the predictions of ‘universal’ scaling models for vascular plants hold across diverse species in variable environments. Phenomena such as competition and disturbance may drive allometric scaling relationships away from theoretical predictions based on an optimized tree. Here, we use a hierarchical Bayesian approach to calculate tree-specific, species-specific, and ‘global’ (i.e. interspecific) scaling exponents for several allometric relationships using tree- and branch-level data harvested from three savanna sites across a rainfall gradient in Mali, West Africa. We use these exponents to provide a rigorous test of three plant scaling models (Metabolic Scaling Theory (MST), Geometric Similarity, and Stress Similarity) in savanna systems. For the allometric relationships we evaluated (diameter vs. length, aboveground mass, stem mass, and leaf mass) the empirically calculated exponents broadly overlapped among species from diverse environments, except for the scaling exponents for length, which increased with tree cover and density. When we compare empirical scaling exponents to the theoretical predictions from the three models we find MST predictions are most consistent with our observed allometries. In those situations where observations are inconsistent with MST we find that departure from theory corresponds with expected tradeoffs related to disturbance and competitive interactions. We hypothesize savanna trees have greater length-scaling exponents than predicted by MST due to an evolutionary tradeoff between fire escape and optimization of mechanical stability and internal resource transport. Future research on the drivers of systematic allometric variation could reconcile the differences between observed scaling relationships in variable ecosystems and those predicted by ideal models such as MST. PMID:23484003

Bayesian analysis of U.S. hurricane climate

USGS Publications Warehouse

Elsner, James B.; Bossak, Brian H.

2001-01-01

Predictive climate distributions of U.S. landfalling hurricanes are estimated from observational records over the period 1851–2000. The approach is Bayesian, combining the reliable records of hurricane activity during the twentieth century with the less precise accounts of activity during the nineteenth century to produce a best estimate of the posterior distribution on the annual rates. The methodology provides a predictive distribution of future activity that serves as a climatological benchmark. Results are presented for the entire coast as well as for the Gulf Coast, Florida, and the East Coast. Statistics on the observed annual counts of U.S. hurricanes, both for the entire coast and by region, are similar within each of the three consecutive 50-yr periods beginning in 1851. However, evidence indicates that the records during the nineteenth century are less precise. Bayesian theory provides a rational approach for defining hurricane climate that uses all available information and that makes no assumption about whether the 150-yr record of hurricanes has been adequately or uniformly monitored. The analysis shows that the number of major hurricanes expected to reach the U.S. coast over the next 30 yr is 18 and the number of hurricanes expected to hit Florida is 20.

Bayesian Estimation of the Spatially Varying Completeness Magnitude of Earthquake Catalogs

NASA Astrophysics Data System (ADS)

Mignan, A.; Werner, M.; Wiemer, S.; Chen, C.; Wu, Y.

2010-12-01

Assessing the completeness magnitude Mc of earthquake catalogs is an essential prerequisite for any seismicity analysis. We employ a simple model to compute Mc in space, based on the proximity to seismic stations in a network. We show that a relationship of the form Mcpred(d) = ad^b+c, with d the distance to the 5th nearest seismic station, fits the observations well. We then propose a new Mc mapping approach, the Bayesian Magnitude of Completeness (BMC) method, based on a 2-step procedure: (1) a spatial resolution optimization to minimize spatial heterogeneities and uncertainties in Mc estimates and (2) a Bayesian approach that merges prior information about Mc based on the proximity to seismic stations with locally observed values weighted by their respective uncertainties. This new methodology eliminates most weaknesses associated with current Mc mapping procedures: the radius that defines which earthquakes to include in the local magnitude distribution is chosen according to an objective criterion and there are no gaps in the spatial estimation of Mc. The method solely requires the coordinates of seismic stations. Here, we investigate the Taiwan Central Weather Bureau (CWB) earthquake catalog by computing a Mc map for the period 1994-2010.

Bayesian Atmospheric Radiative Transfer (BART) Code and Application to WASP-43b

NASA Astrophysics Data System (ADS)

Blecic, Jasmina; Harrington, Joseph; Cubillos, Patricio; Bowman, Oliver; Rojo, Patricio; Stemm, Madison; Lust, Nathaniel B.; Challener, Ryan; Foster, Austin James; Foster, Andrew S.; Blumenthal, Sarah D.; Bruce, Dylan

2016-01-01

We present a new open-source Bayesian radiative-transfer framework, Bayesian Atmospheric Radiative Transfer (BART, https://github.com/exosports/BART), and its application to WASP-43b. BART initializes a model for the atmospheric retrieval calculation, generates thousands of theoretical model spectra using parametrized pressure and temperature profiles and line-by-line radiative-transfer calculation, and employs a statistical package to compare the models with the observations. It consists of three self-sufficient modules available to the community under the reproducible-research license, the Thermochemical Equilibrium Abundances module (TEA, https://github.com/dzesmin/TEA, Blecic et al. 2015}, the radiative-transfer module (Transit, https://github.com/exosports/transit), and the Multi-core Markov-chain Monte Carlo statistical module (MCcubed, https://github.com/pcubillos/MCcubed, Cubillos et al. 2015). We applied BART on all available WASP-43b secondary eclipse data from the space- and ground-based observations constraining the temperature-pressure profile and molecular abundances of the dayside atmosphere of WASP-43b. This work was supported by NASA Planetary Atmospheres grant NNX12AI69G and NASA Astrophysics Data Analysis Program grant NNX13AF38G. JB holds a NASA Earth and Space Science Fellowship.

Uncertainty Quantification of Hypothesis Testing for the Integrated Knowledge Engine

DOE Office of Scientific and Technical Information (OSTI.GOV)

Cuellar, Leticia

2012-05-31

The Integrated Knowledge Engine (IKE) is a tool of Bayesian analysis, based on Bayesian Belief Networks or Bayesian networks for short. A Bayesian network is a graphical model (directed acyclic graph) that allows representing the probabilistic structure of many variables assuming a localized type of dependency called the Markov property. The Markov property in this instance makes any node or random variable to be independent of any non-descendant node given information about its parent. A direct consequence of this property is that it is relatively easy to incorporate new evidence and derive the appropriate consequences, which in general is notmore » an easy or feasible task. Typically we use Bayesian networks as predictive models for a small subset of the variables, either the leave nodes or the root nodes. In IKE, since most applications deal with diagnostics, we are interested in predicting the likelihood of the root nodes given new observations on any of the children nodes. The root nodes represent the various possible outcomes of the analysis, and an important problem is to determine when we have gathered enough evidence to lean toward one of these particular outcomes. This document presents criteria to decide when the evidence gathered is sufficient to draw a particular conclusion or decide in favor of a particular outcome by quantifying the uncertainty in the conclusions that are drawn from the data. The material in this document is organized as follows: Section 2 presents briefly a forensics Bayesian network, and we explore evaluating the information provided by new evidence by looking first at the posterior distribution of the nodes of interest, and then at the corresponding posterior odds ratios. Section 3 presents a third alternative: Bayes Factors. In section 4 we finalize by showing the relation between the posterior odds ratios and Bayes factors and showing examples these cases, and in section 5 we conclude by providing clear guidelines of how to use these for the type of Bayesian networks used in IKE.« less

Forecasting neutrino masses from combining KATRIN and the CMB observations: Frequentist and Bayesian analyses

DOE Office of Scientific and Technical Information (OSTI.GOV)

Host, Ole; Lahav, Ofer; Abdalla, Filipe B.

We present a showcase for deriving bounds on the neutrino masses from laboratory experiments and cosmological observations. We compare the frequentist and Bayesian bounds on the effective electron neutrino mass m{sub {beta}} which the KATRIN neutrino mass experiment is expected to obtain, using both an analytical likelihood function and Monte Carlo simulations of KATRIN. Assuming a uniform prior in m{sub {beta}}, we find that a null result yields an upper bound of about 0.17 eV at 90% confidence in the Bayesian analysis, to be compared with the frequentist KATRIN reference value of 0.20 eV. This is a significant difference whenmore » judged relative to the systematic and statistical uncertainties of the experiment. On the other hand, an input m{sub {beta}}=0.35 eV, which is the KATRIN 5{sigma} detection threshold, would be detected at virtually the same level. Finally, we combine the simulated KATRIN results with cosmological data in the form of present (post-WMAP) and future (simulated Planck) observations. If an input of m{sub {beta}}=0.2 eV is assumed in our simulations, KATRIN alone excludes a zero neutrino mass at 2.2{sigma}. Adding Planck data increases the probability of detection to a median 2.7{sigma}. The analysis highlights the importance of combining cosmological and laboratory data on an equal footing.« less

Mixed linear-non-linear inversion of crustal deformation data: Bayesian inference of model, weighting and regularization parameters

NASA Astrophysics Data System (ADS)

Fukuda, Jun'ichi; Johnson, Kaj M.

2010-06-01

We present a unified theoretical framework and solution method for probabilistic, Bayesian inversions of crustal deformation data. The inversions involve multiple data sets with unknown relative weights, model parameters that are related linearly or non-linearly through theoretic models to observations, prior information on model parameters and regularization priors to stabilize underdetermined problems. To efficiently handle non-linear inversions in which some of the model parameters are linearly related to the observations, this method combines both analytical least-squares solutions and a Monte Carlo sampling technique. In this method, model parameters that are linearly and non-linearly related to observations, relative weights of multiple data sets and relative weights of prior information and regularization priors are determined in a unified Bayesian framework. In this paper, we define the mixed linear-non-linear inverse problem, outline the theoretical basis for the method, provide a step-by-step algorithm for the inversion, validate the inversion method using synthetic data and apply the method to two real data sets. We apply the method to inversions of multiple geodetic data sets with unknown relative data weights for interseismic fault slip and locking depth. We also apply the method to the problem of estimating the spatial distribution of coseismic slip on faults with unknown fault geometry, relative data weights and smoothing regularization weight.

Using simple artificial intelligence methods for predicting amyloidogenesis in antibodies

PubMed Central

2010-01-01

Background All polypeptide backbones have the potential to form amyloid fibrils, which are associated with a number of degenerative disorders. However, the likelihood that amyloidosis would actually occur under physiological conditions depends largely on the amino acid composition of a protein. We explore using a naive Bayesian classifier and a weighted decision tree for predicting the amyloidogenicity of immunoglobulin sequences. Results The average accuracy based on leave-one-out (LOO) cross validation of a Bayesian classifier generated from 143 amyloidogenic sequences is 60.84%. This is consistent with the average accuracy of 61.15% for a holdout test set comprised of 103 AM and 28 non-amyloidogenic sequences. The LOO cross validation accuracy increases to 81.08% when the training set is augmented by the holdout test set. In comparison, the average classification accuracy for the holdout test set obtained using a decision tree is 78.64%. Non-amyloidogenic sequences are predicted with average LOO cross validation accuracies between 74.05% and 77.24% using the Bayesian classifier, depending on the training set size. The accuracy for the holdout test set was 89%. For the decision tree, the non-amyloidogenic prediction accuracy is 75.00%. Conclusions This exploratory study indicates that both classification methods may be promising in providing straightforward predictions on the amyloidogenicity of a sequence. Nevertheless, the number of available sequences that satisfy the premises of this study are limited, and are consequently smaller than the ideal training set size. Increasing the size of the training set clearly increases the accuracy, and the expansion of the training set to include not only more derivatives, but more alignments, would make the method more sound. The accuracy of the classifiers may also be improved when additional factors, such as structural and physico-chemical data, are considered. The development of this type of classifier has significant applications in evaluating engineered antibodies, and may be adapted for evaluating engineered proteins in general. PMID:20144194

Using simple artificial intelligence methods for predicting amyloidogenesis in antibodies.

PubMed

David, Maria Pamela C; Concepcion, Gisela P; Padlan, Eduardo A

2010-02-08

All polypeptide backbones have the potential to form amyloid fibrils, which are associated with a number of degenerative disorders. However, the likelihood that amyloidosis would actually occur under physiological conditions depends largely on the amino acid composition of a protein. We explore using a naive Bayesian classifier and a weighted decision tree for predicting the amyloidogenicity of immunoglobulin sequences. The average accuracy based on leave-one-out (LOO) cross validation of a Bayesian classifier generated from 143 amyloidogenic sequences is 60.84%. This is consistent with the average accuracy of 61.15% for a holdout test set comprised of 103 AM and 28 non-amyloidogenic sequences. The LOO cross validation accuracy increases to 81.08% when the training set is augmented by the holdout test set. In comparison, the average classification accuracy for the holdout test set obtained using a decision tree is 78.64%. Non-amyloidogenic sequences are predicted with average LOO cross validation accuracies between 74.05% and 77.24% using the Bayesian classifier, depending on the training set size. The accuracy for the holdout test set was 89%. For the decision tree, the non-amyloidogenic prediction accuracy is 75.00%. This exploratory study indicates that both classification methods may be promising in providing straightforward predictions on the amyloidogenicity of a sequence. Nevertheless, the number of available sequences that satisfy the premises of this study are limited, and are consequently smaller than the ideal training set size. Increasing the size of the training set clearly increases the accuracy, and the expansion of the training set to include not only more derivatives, but more alignments, would make the method more sound. The accuracy of the classifiers may also be improved when additional factors, such as structural and physico-chemical data, are considered. The development of this type of classifier has significant applications in evaluating engineered antibodies, and may be adapted for evaluating engineered proteins in general.

Complementary construction of ideal nonimaging concentrators and its applications.

PubMed

Gordon, J M

1996-10-01

A construction principle for ideal nonimaging concentrators based on the complementary edge rays outside the nominal field of view is presented, with illustrations for the trumpet, compound parabolic concentrator, and compound hyperbolic concentrator. A simple string construction for the trumpet concentrator is shown to follow from this observation-the trumpet having been the one ideal concentrator for which no string-construction method had previously been noted. An application of these observations for solar concentrator design when nonisothermal receivers are advantageous is also presented.

Nonparametric Bayesian Segmentation of a Multivariate Inhomogeneous Space-Time Poisson Process.

PubMed

Ding, Mingtao; He, Lihan; Dunson, David; Carin, Lawrence

2012-12-01

A nonparametric Bayesian model is proposed for segmenting time-evolving multivariate spatial point process data. An inhomogeneous Poisson process is assumed, with a logistic stick-breaking process (LSBP) used to encourage piecewise-constant spatial Poisson intensities. The LSBP explicitly favors spatially contiguous segments, and infers the number of segments based on the observed data. The temporal dynamics of the segmentation and of the Poisson intensities are modeled with exponential correlation in time, implemented in the form of a first-order autoregressive model for uniformly sampled discrete data, and via a Gaussian process with an exponential kernel for general temporal sampling. We consider and compare two different inference techniques: a Markov chain Monte Carlo sampler, which has relatively high computational complexity; and an approximate and efficient variational Bayesian analysis. The model is demonstrated with a simulated example and a real example of space-time crime events in Cincinnati, Ohio, USA.

The NIFTy way of Bayesian signal inference

NASA Astrophysics Data System (ADS)

Selig, Marco

2014-12-01

We introduce NIFTy, "Numerical Information Field Theory", a software package for the development of Bayesian signal inference algorithms that operate independently from any underlying spatial grid and its resolution. A large number of Bayesian and Maximum Entropy methods for 1D signal reconstruction, 2D imaging, as well as 3D tomography, appear formally similar, but one often finds individualized implementations that are neither flexible nor easily transferable. Signal inference in the framework of NIFTy can be done in an abstract way, such that algorithms, prototyped in 1D, can be applied to real world problems in higher-dimensional settings. NIFTy as a versatile library is applicable and already has been applied in 1D, 2D, 3D and spherical settings. A recent application is the D3PO algorithm targeting the non-trivial task of denoising, deconvolving, and decomposing photon observations in high energy astronomy.

Bayesian component separation: The Planck experience

NASA Astrophysics Data System (ADS)

Wehus, Ingunn Kathrine; Eriksen, Hans Kristian

2018-05-01

Bayesian component separation techniques have played a central role in the data reduction process of Planck. The most important strength of this approach is its global nature, in which a parametric and physical model is fitted to the data. Such physical modeling allows the user to constrain very general data models, and jointly probe cosmological, astrophysical and instrumental parameters. This approach also supports statistically robust goodness-of-fit tests in terms of data-minus-model residual maps, which are essential for identifying residual systematic effects in the data. The main challenges are high code complexity and computational cost. Whether or not these costs are justified for a given experiment depends on its final uncertainty budget. We therefore predict that the importance of Bayesian component separation techniques is likely to increase with time for intensity mapping experiments, similar to what has happened in the CMB field, as observational techniques mature, and their overall sensitivity improves.

Bayesian state space models for dynamic genetic network construction across multiple tissues.

PubMed

Liang, Yulan; Kelemen, Arpad

2016-08-01

Construction of gene-gene interaction networks and potential pathways is a challenging and important problem in genomic research for complex diseases while estimating the dynamic changes of the temporal correlations and non-stationarity are the keys in this process. In this paper, we develop dynamic state space models with hierarchical Bayesian settings to tackle this challenge for inferring the dynamic profiles and genetic networks associated with disease treatments. We treat both the stochastic transition matrix and the observation matrix time-variant and include temporal correlation structures in the covariance matrix estimations in the multivariate Bayesian state space models. The unevenly spaced short time courses with unseen time points are treated as hidden state variables. Hierarchical Bayesian approaches with various prior and hyper-prior models with Monte Carlo Markov Chain and Gibbs sampling algorithms are used to estimate the model parameters and the hidden state variables. We apply the proposed Hierarchical Bayesian state space models to multiple tissues (liver, skeletal muscle, and kidney) Affymetrix time course data sets following corticosteroid (CS) drug administration. Both simulation and real data analysis results show that the genomic changes over time and gene-gene interaction in response to CS treatment can be well captured by the proposed models. The proposed dynamic Hierarchical Bayesian state space modeling approaches could be expanded and applied to other large scale genomic data, such as next generation sequence (NGS) combined with real time and time varying electronic health record (EHR) for more comprehensive and robust systematic and network based analysis in order to transform big biomedical data into predictions and diagnostics for precision medicine and personalized healthcare with better decision making and patient outcomes.

Bayesian Redshift Classification of Emission-line Galaxies with Photometric Equivalent Widths

NASA Astrophysics Data System (ADS)

Leung, Andrew S.; Acquaviva, Viviana; Gawiser, Eric; Ciardullo, Robin; Komatsu, Eiichiro; Malz, A. I.; Zeimann, Gregory R.; Bridge, Joanna S.; Drory, Niv; Feldmeier, John J.; Finkelstein, Steven L.; Gebhardt, Karl; Gronwall, Caryl; Hagen, Alex; Hill, Gary J.; Schneider, Donald P.

2017-07-01

We present a Bayesian approach to the redshift classification of emission-line galaxies when only a single emission line is detected spectroscopically. We consider the case of surveys for high-redshift Lyα-emitting galaxies (LAEs), which have traditionally been classified via an inferred rest-frame equivalent width (EW {W}{Lyα }) greater than 20 Å. Our Bayesian method relies on known prior probabilities in measured emission-line luminosity functions and EW distributions for the galaxy populations, and returns the probability that an object in question is an LAE given the characteristics observed. This approach will be directly relevant for the Hobby-Eberly Telescope Dark Energy Experiment (HETDEX), which seeks to classify ˜106 emission-line galaxies into LAEs and low-redshift [{{O}} {{II}}] emitters. For a simulated HETDEX catalog with realistic measurement noise, our Bayesian method recovers 86% of LAEs missed by the traditional {W}{Lyα } > 20 Å cutoff over 2 < z < 3, outperforming the EW cut in both contamination and incompleteness. This is due to the method’s ability to trade off between the two types of binary classification error by adjusting the stringency of the probability requirement for classifying an observed object as an LAE. In our simulations of HETDEX, this method reduces the uncertainty in cosmological distance measurements by 14% with respect to the EW cut, equivalent to recovering 29% more cosmological information. Rather than using binary object labels, this method enables the use of classification probabilities in large-scale structure analyses. It can be applied to narrowband emission-line surveys as well as upcoming large spectroscopic surveys including Euclid and WFIRST.

Evidence cross-validation and Bayesian inference of MAST plasma equilibria

DOE Office of Scientific and Technical Information (OSTI.GOV)

Nessi, G. T. von; Hole, M. J.; Svensson, J.

2012-01-15

In this paper, current profiles for plasma discharges on the mega-ampere spherical tokamak are directly calculated from pickup coil, flux loop, and motional-Stark effect observations via methods based in the statistical theory of Bayesian analysis. By representing toroidal plasma current as a series of axisymmetric current beams with rectangular cross-section and inferring the current for each one of these beams, flux-surface geometry and q-profiles are subsequently calculated by elementary application of Biot-Savart's law. The use of this plasma model in the context of Bayesian analysis was pioneered by Svensson and Werner on the joint-European tokamak [Svensson and Werner,Plasma Phys. Controlledmore » Fusion 50(8), 085002 (2008)]. In this framework, linear forward models are used to generate diagnostic predictions, and the probability distribution for the currents in the collection of plasma beams was subsequently calculated directly via application of Bayes' formula. In this work, we introduce a new diagnostic technique to identify and remove outlier observations associated with diagnostics falling out of calibration or suffering from an unidentified malfunction. These modifications enable a good agreement between Bayesian inference of the last-closed flux-surface with other corroborating data, such as that from force balance considerations using EFIT++[Appel et al., ''A unified approach to equilibrium reconstruction'' Proceedings of the 33rd EPS Conference on Plasma Physics (Rome, Italy, 2006)]. In addition, this analysis also yields errors on the plasma current profile and flux-surface geometry as well as directly predicting the Shafranov shift of the plasma core.« less

DOE Office of Scientific and Technical Information (OSTI.GOV)

La Russa, D

Purpose: The purpose of this project is to develop a robust method of parameter estimation for a Poisson-based TCP model using Bayesian inference. Methods: Bayesian inference was performed using the PyMC3 probabilistic programming framework written in Python. A Poisson-based TCP regression model that accounts for clonogen proliferation was fit to observed rates of local relapse as a function of equivalent dose in 2 Gy fractions for a population of 623 stage-I non-small-cell lung cancer patients. The Slice Markov Chain Monte Carlo sampling algorithm was used to sample the posterior distributions, and was initiated using the maximum of the posterior distributionsmore » found by optimization. The calculation of TCP with each sample step required integration over the free parameter α, which was performed using an adaptive 24-point Gauss-Legendre quadrature. Convergence was verified via inspection of the trace plot and posterior distribution for each of the fit parameters, as well as with comparisons of the most probable parameter values with their respective maximum likelihood estimates. Results: Posterior distributions for α, the standard deviation of α (σ), the average tumour cell-doubling time (Td), and the repopulation delay time (Tk), were generated assuming α/β = 10 Gy, and a fixed clonogen density of 10{sup 7} cm−{sup 3}. Posterior predictive plots generated from samples from these posterior distributions are in excellent agreement with the observed rates of local relapse used in the Bayesian inference. The most probable values of the model parameters also agree well with maximum likelihood estimates. Conclusion: A robust method of performing Bayesian inference of TCP data using a complex TCP model has been established.« less

Bayesian random-effect model for predicting outcome fraught with heterogeneity--an illustration with episodes of 44 patients with intractable epilepsy.

PubMed

Yen, A M-F; Liou, H-H; Lin, H-L; Chen, T H-H

2006-01-01

The study aimed to develop a predictive model to deal with data fraught with heterogeneity that cannot be explained by sampling variation or measured covariates. The random-effect Poisson regression model was first proposed to deal with over-dispersion for data fraught with heterogeneity after making allowance for measured covariates. Bayesian acyclic graphic model in conjunction with Markov Chain Monte Carlo (MCMC) technique was then applied to estimate the parameters of both relevant covariates and random effect. Predictive distribution was then generated to compare the predicted with the observed for the Bayesian model with and without random effect. Data from repeated measurement of episodes among 44 patients with intractable epilepsy were used as an illustration. The application of Poisson regression without taking heterogeneity into account to epilepsy data yielded a large value of heterogeneity (heterogeneity factor = 17.90, deviance = 1485, degree of freedom (df) = 83). After taking the random effect into account, the value of heterogeneity factor was greatly reduced (heterogeneity factor = 0.52, deviance = 42.5, df = 81). The Pearson chi2 for the comparison between the expected seizure frequencies and the observed ones at two and three months of the model with and without random effect were 34.27 (p = 1.00) and 1799.90 (p < 0.0001), respectively. The Bayesian acyclic model using the MCMC method was demonstrated to have great potential for disease prediction while data show over-dispersion attributed either to correlated property or to subject-to-subject variability.

Trending in Probability of Collision Measurements via a Bayesian Zero-Inflated Beta Mixed Model

NASA Technical Reports Server (NTRS)

Vallejo, Jonathon; Hejduk, Matt; Stamey, James

2015-01-01

We investigate the performance of a generalized linear mixed model in predicting the Probabilities of Collision (Pc) for conjunction events. Specifically, we apply this model to the log(sub 10) transformation of these probabilities and argue that this transformation yields values that can be considered bounded in practice. Additionally, this bounded random variable, after scaling, is zero-inflated. Consequently, we model these values using the zero-inflated Beta distribution, and utilize the Bayesian paradigm and the mixed model framework to borrow information from past and current events. This provides a natural way to model the data and provides a basis for answering questions of interest, such as what is the likelihood of observing a probability of collision equal to the effective value of zero on a subsequent observation.

ESS++: a C++ objected-oriented algorithm for Bayesian stochastic search model exploration

PubMed Central

Bottolo, Leonardo; Langley, Sarah R.; Petretto, Enrico; Tiret, Laurence; Tregouet, David; Richardson, Sylvia

2011-01-01

Summary: ESS++ is a C++ implementation of a fully Bayesian variable selection approach for single and multiple response linear regression. ESS++ works well both when the number of observations is larger than the number of predictors and in the ‘large p, small n’ case. In the current version, ESS++ can handle several hundred observations, thousands of predictors and a few responses simultaneously. The core engine of ESS++ for the selection of relevant predictors is based on Evolutionary Monte Carlo. Our implementation is open source, allowing community-based alterations and improvements. Availability: C++ source code and documentation including compilation instructions are available under GNU licence at http://bgx.org.uk/software/ESS.html. Contact: l.bottolo@imperial.ac.uk Supplementary information: Supplementary data are available at Bioinformatics online. PMID:21233165

Application of Bayesian a Priori Distributions for Vehicles' Video Tracking Systems

NASA Astrophysics Data System (ADS)

Mazurek, Przemysław; Okarma, Krzysztof

Intelligent Transportation Systems (ITS) helps to improve the quality and quantity of many car traffic parameters. The use of the ITS is possible when the adequate measuring infrastructure is available. Video systems allow for its implementation with relatively low cost due to the possibility of simultaneous video recording of a few lanes of the road at a considerable distance from the camera. The process of tracking can be realized through different algorithms, the most attractive algorithms are Bayesian, because they use the a priori information derived from previous observations or known limitations. Use of this information is crucial for improving the quality of tracking especially for difficult observability conditions, which occur in the video systems under the influence of: smog, fog, rain, snow and poor lighting conditions.

Understanding Short-Term Nonmigrating Tidal Variability in the Ionospheric Dynamo Region from SABER Using Information Theory and Bayesian Statistics

NASA Astrophysics Data System (ADS)

Kumari, K.; Oberheide, J.

2017-12-01

Nonmigrating tidal diagnostics of SABER temperature observations in the ionospheric dynamo region reveal a large amount of variability on time-scales of a few days to weeks. In this paper, we discuss the physical reasons for the observed short-term tidal variability using a novel approach based on Information theory and Bayesian statistics. We diagnose short-term tidal variability as a function of season, QBO, ENSO, and solar cycle and other drivers using time dependent probability density functions, Shannon entropy and Kullback-Leibler divergence. The statistical significance of the approach and its predictive capability is exemplified using SABER tidal diagnostics with emphasis on the responses to the QBO and solar cycle. Implications for F-region plasma density will be discussed.

Bayesian Inference of High-Dimensional Dynamical Ocean Models

NASA Astrophysics Data System (ADS)

Lin, J.; Lermusiaux, P. F. J.; Lolla, S. V. T.; Gupta, A.; Haley, P. J., Jr.

2015-12-01

This presentation addresses a holistic set of challenges in high-dimension ocean Bayesian nonlinear estimation: i) predict the probability distribution functions (pdfs) of large nonlinear dynamical systems using stochastic partial differential equations (PDEs); ii) assimilate data using Bayes' law with these pdfs; iii) predict the future data that optimally reduce uncertainties; and (iv) rank the known and learn the new model formulations themselves. Overall, we allow the joint inference of the state, equations, geometry, boundary conditions and initial conditions of dynamical models. Examples are provided for time-dependent fluid and ocean flows, including cavity, double-gyre and Strait flows with jets and eddies. The Bayesian model inference, based on limited observations, is illustrated first by the estimation of obstacle shapes and positions in fluid flows. Next, the Bayesian inference of biogeochemical reaction equations and of their states and parameters is presented, illustrating how PDE-based machine learning can rigorously guide the selection and discovery of complex ecosystem models. Finally, the inference of multiscale bottom gravity current dynamics is illustrated, motivated in part by classic overflows and dense water formation sites and their relevance to climate monitoring and dynamics. This is joint work with our MSEAS group at MIT.

A general framework for updating belief distributions.

PubMed

Bissiri, P G; Holmes, C C; Walker, S G

2016-11-01

We propose a framework for general Bayesian inference. We argue that a valid update of a prior belief distribution to a posterior can be made for parameters which are connected to observations through a loss function rather than the traditional likelihood function, which is recovered as a special case. Modern application areas make it increasingly challenging for Bayesians to attempt to model the true data-generating mechanism. For instance, when the object of interest is low dimensional, such as a mean or median, it is cumbersome to have to achieve this via a complete model for the whole data distribution. More importantly, there are settings where the parameter of interest does not directly index a family of density functions and thus the Bayesian approach to learning about such parameters is currently regarded as problematic. Our framework uses loss functions to connect information in the data to functionals of interest. The updating of beliefs then follows from a decision theoretic approach involving cumulative loss functions. Importantly, the procedure coincides with Bayesian updating when a true likelihood is known yet provides coherent subjective inference in much more general settings. Connections to other inference frameworks are highlighted.

Bayesian methods for outliers detection in GNSS time series

NASA Astrophysics Data System (ADS)

Qianqian, Zhang; Qingming, Gui

2013-07-01

This article is concerned with the problem of detecting outliers in GNSS time series based on Bayesian statistical theory. Firstly, a new model is proposed to simultaneously detect different types of outliers based on the conception of introducing different types of classification variables corresponding to the different types of outliers; the problem of outlier detection is converted into the computation of the corresponding posterior probabilities, and the algorithm for computing the posterior probabilities based on standard Gibbs sampler is designed. Secondly, we analyze the reasons of masking and swamping about detecting patches of additive outliers intensively; an unmasking Bayesian method for detecting additive outlier patches is proposed based on an adaptive Gibbs sampler. Thirdly, the correctness of the theories and methods proposed above is illustrated by simulated data and then by analyzing real GNSS observations, such as cycle slips detection in carrier phase data. Examples illustrate that the Bayesian methods for outliers detection in GNSS time series proposed by this paper are not only capable of detecting isolated outliers but also capable of detecting additive outlier patches. Furthermore, it can be successfully used to process cycle slips in phase data, which solves the problem of small cycle slips.

Bayesian aggregation versus majority vote in the characterization of non-specific arm pain based on quantitative needle electromyography

PubMed Central

2010-01-01

Background Methods for the calculation and application of quantitative electromyographic (EMG) statistics for the characterization of EMG data detected from forearm muscles of individuals with and without pain associated with repetitive strain injury are presented. Methods A classification procedure using a multi-stage application of Bayesian inference is presented that characterizes a set of motor unit potentials acquired using needle electromyography. The utility of this technique in characterizing EMG data obtained from both normal individuals and those presenting with symptoms of "non-specific arm pain" is explored and validated. The efficacy of the Bayesian technique is compared with simple voting methods. Results The aggregate Bayesian classifier presented is found to perform with accuracy equivalent to that of majority voting on the test data, with an overall accuracy greater than 0.85. Theoretical foundations of the technique are discussed, and are related to the observations found. Conclusions Aggregation of motor unit potential conditional probability distributions estimated using quantitative electromyographic analysis, may be successfully used to perform electrodiagnostic characterization of "non-specific arm pain." It is expected that these techniques will also be able to be applied to other types of electrodiagnostic data. PMID:20156353

Bayesian Computation Emerges in Generic Cortical Microcircuits through Spike-Timing-Dependent Plasticity

PubMed Central

Nessler, Bernhard; Pfeiffer, Michael; Buesing, Lars; Maass, Wolfgang

2013-01-01

The principles by which networks of neurons compute, and how spike-timing dependent plasticity (STDP) of synaptic weights generates and maintains their computational function, are unknown. Preceding work has shown that soft winner-take-all (WTA) circuits, where pyramidal neurons inhibit each other via interneurons, are a common motif of cortical microcircuits. We show through theoretical analysis and computer simulations that Bayesian computation is induced in these network motifs through STDP in combination with activity-dependent changes in the excitability of neurons. The fundamental components of this emergent Bayesian computation are priors that result from adaptation of neuronal excitability and implicit generative models for hidden causes that are created in the synaptic weights through STDP. In fact, a surprising result is that STDP is able to approximate a powerful principle for fitting such implicit generative models to high-dimensional spike inputs: Expectation Maximization. Our results suggest that the experimentally observed spontaneous activity and trial-to-trial variability of cortical neurons are essential features of their information processing capability, since their functional role is to represent probability distributions rather than static neural codes. Furthermore it suggests networks of Bayesian computation modules as a new model for distributed information processing in the cortex. PMID:23633941

Variational Bayesian identification and prediction of stochastic nonlinear dynamic causal models.

PubMed

Daunizeau, J; Friston, K J; Kiebel, S J

2009-11-01

In this paper, we describe a general variational Bayesian approach for approximate inference on nonlinear stochastic dynamic models. This scheme extends established approximate inference on hidden-states to cover: (i) nonlinear evolution and observation functions, (ii) unknown parameters and (precision) hyperparameters and (iii) model comparison and prediction under uncertainty. Model identification or inversion entails the estimation of the marginal likelihood or evidence of a model. This difficult integration problem can be finessed by optimising a free-energy bound on the evidence using results from variational calculus. This yields a deterministic update scheme that optimises an approximation to the posterior density on the unknown model variables. We derive such a variational Bayesian scheme in the context of nonlinear stochastic dynamic hierarchical models, for both model identification and time-series prediction. The computational complexity of the scheme is comparable to that of an extended Kalman filter, which is critical when inverting high dimensional models or long time-series. Using Monte-Carlo simulations, we assess the estimation efficiency of this variational Bayesian approach using three stochastic variants of chaotic dynamic systems. We also demonstrate the model comparison capabilities of the method, its self-consistency and its predictive power.

Bayesian Inference of Physics Parameters in the DIII-D Charge-Exchange Recombination Spectroscopy System

NASA Astrophysics Data System (ADS)

Bowman, C.; Gibson, K. J.; La Haye, R. J.; Groebner, R. J.; Taylor, N. Z.; Grierson, B. A.

2014-10-01

A Bayesian inference framework has been developed for the DIII-D charge-exchange recombination (CER) system, capable of computing probability distribution functions (PDFs) for desired parameters. CER is a key diagnostic system at DIII-D, measuring important physics parameters such as plasma rotation and impurity ion temperature. This work is motivated by a case in which the CER system was used to probe the plasma rotation radial profile around an m/n = 2/1 tearing mode island rotating at ~ 1 kHz. Due to limited resolution in the tearing mode phase and short integration time, it has proven challenging to observe the structure of the rotation profile across the island. We seek to solve this problem by using the Bayesian framework to improve the estimation accuracy of the plasma rotation, helping to reveal details of how it is perturbed in the magnetic island vicinity. Examples of the PDFs obtained through the Bayesian framework will be presented, and compared with results from a conventional least-squares analysis of the CER data. Work supported by the US DOE under DE-FC02-04ER54698 and DE-AC02-09CH11466.

Objectified quantification of uncertainties in Bayesian atmospheric inversions

NASA Astrophysics Data System (ADS)

Berchet, A.; Pison, I.; Chevallier, F.; Bousquet, P.; Bonne, J.-L.; Paris, J.-D.

2015-05-01

Classical Bayesian atmospheric inversions process atmospheric observations and prior emissions, the two being connected by an observation operator picturing mainly the atmospheric transport. These inversions rely on prescribed errors in the observations, the prior emissions and the observation operator. When data pieces are sparse, inversion results are very sensitive to the prescribed error distributions, which are not accurately known. The classical Bayesian framework experiences difficulties in quantifying the impact of mis-specified error distributions on the optimized fluxes. In order to cope with this issue, we rely on recent research results to enhance the classical Bayesian inversion framework through a marginalization on a large set of plausible errors that can be prescribed in the system. The marginalization consists in computing inversions for all possible error distributions weighted by the probability of occurrence of the error distributions. The posterior distribution of the fluxes calculated by the marginalization is not explicitly describable. As a consequence, we carry out a Monte Carlo sampling based on an approximation of the probability of occurrence of the error distributions. This approximation is deduced from the well-tested method of the maximum likelihood estimation. Thus, the marginalized inversion relies on an automatic objectified diagnosis of the error statistics, without any prior knowledge about the matrices. It robustly accounts for the uncertainties on the error distributions, contrary to what is classically done with frozen expert-knowledge error statistics. Some expert knowledge is still used in the method for the choice of an emission aggregation pattern and of a sampling protocol in order to reduce the computation cost. The relevance and the robustness of the method is tested on a case study: the inversion of methane surface fluxes at the mesoscale with virtual observations on a realistic network in Eurasia. Observing system simulation experiments are carried out with different transport patterns, flux distributions and total prior amounts of emitted methane. The method proves to consistently reproduce the known "truth" in most cases, with satisfactory tolerance intervals. Additionally, the method explicitly provides influence scores and posterior correlation matrices. An in-depth interpretation of the inversion results is then possible. The more objective quantification of the influence of the observations on the fluxes proposed here allows us to evaluate the impact of the observation network on the characterization of the surface fluxes. The explicit correlations between emission aggregates reveal the mis-separated regions, hence the typical temporal and spatial scales the inversion can analyse. These scales are consistent with the chosen aggregation patterns.

Analysis of Viking infrared thermal mapping data of Mars. The effects of non-ideal surfaces on the derived thermal properties of Mars

NASA Technical Reports Server (NTRS)

Muhleman, D. O.; Jakosky, B. M.

1979-01-01

The thermal interia of the surface of Mars varies spatially by a factor of eight. This is attributable to changes in the average particle size of the fine material, the surface elevation, the atmospheric opacity due to dust, and the fraction of the surface covered by rocks and fine material. The effects of these non-ideal properties on the surface temperatures and derived thermal inertias are modeled, along with the the effects of slopes, CO2 condensed onto the surface, and layering of fine material upon solid rock. The non-ideal models are capable of producing thermal behavior similar to that observed by the Viking Infrared Thermal Mapper, including a morning delay in the post-dawn temperature rise and an enhanced cooling in the afternoon relative to any ideal, homogeneous model. The enhanced afternoon cooling observed at the Viking-1 landing site is reproduced by the non-ideal models while that atop Arsia Mons volcano is not, but may be attributed to the observing geometry.

Multiple player tracking in sports video: a dual-mode two-way bayesian inference approach with progressive observation modeling.

PubMed

Xing, Junliang; Ai, Haizhou; Liu, Liwei; Lao, Shihong

2011-06-01

Multiple object tracking (MOT) is a very challenging task yet of fundamental importance for many practical applications. In this paper, we focus on the problem of tracking multiple players in sports video which is even more difficult due to the abrupt movements of players and their complex interactions. To handle the difficulties in this problem, we present a new MOT algorithm which contributes both in the observation modeling level and in the tracking strategy level. For the observation modeling, we develop a progressive observation modeling process that is able to provide strong tracking observations and greatly facilitate the tracking task. For the tracking strategy, we propose a dual-mode two-way Bayesian inference approach which dynamically switches between an offline general model and an online dedicated model to deal with single isolated object tracking and multiple occluded object tracking integrally by forward filtering and backward smoothing. Extensive experiments on different kinds of sports videos, including football, basketball, as well as hockey, demonstrate the effectiveness and efficiency of the proposed method.

The three-class ideal observer for univariate normal data: Decision variable and ROC surface properties

PubMed Central

Edwards, Darrin C.; Metz, Charles E.

2012-01-01

Although a fully general extension of ROC analysis to classification tasks with more than two classes has yet to be developed, the potential benefits to be gained from a practical performance evaluation methodology for classification tasks with three classes have motivated a number of research groups to propose methods based on constrained or simplified observer or data models. Here we consider an ideal observer in a task with underlying data drawn from three univariate normal distributions. We investigate the behavior of the resulting ideal observer’s decision variables and ROC surface. In particular, we show that the pair of ideal observer decision variables is constrained to a parametric curve in two-dimensional likelihood ratio space, and that the decision boundary line segments used by the ideal observer can intersect this curve in at most six places. From this, we further show that the resulting ROC surface has at most four degrees of freedom at any point, and not the five that would be required, in general, for a surface in a six-dimensional space to be non-degenerate. In light of the difficulties we have previously pointed out in generalizing the well-known area under the ROC curve performance metric to tasks with three or more classes, the problem of developing a suitable and fully general performance metric for classification tasks with three or more classes remains unsolved. PMID:23162165

Inverse Modeling of Hydrologic Parameters Using Surface Flux and Runoff Observations in the Community Land Model

DOE Office of Scientific and Technical Information (OSTI.GOV)

Sun, Yu; Hou, Zhangshuan; Huang, Maoyi

2013-12-10

This study demonstrates the possibility of inverting hydrologic parameters using surface flux and runoff observations in version 4 of the Community Land Model (CLM4). Previous studies showed that surface flux and runoff calculations are sensitive to major hydrologic parameters in CLM4 over different watersheds, and illustrated the necessity and possibility of parameter calibration. Two inversion strategies, the deterministic least-square fitting and stochastic Markov-Chain Monte-Carlo (MCMC) - Bayesian inversion approaches, are evaluated by applying them to CLM4 at selected sites. The unknowns to be estimated include surface and subsurface runoff generation parameters and vadose zone soil water parameters. We find thatmore » using model parameters calibrated by the least-square fitting provides little improvements in the model simulations but the sampling-based stochastic inversion approaches are consistent - as more information comes in, the predictive intervals of the calibrated parameters become narrower and the misfits between the calculated and observed responses decrease. In general, parameters that are identified to be significant through sensitivity analyses and statistical tests are better calibrated than those with weak or nonlinear impacts on flux or runoff observations. Temporal resolution of observations has larger impacts on the results of inverse modeling using heat flux data than runoff data. Soil and vegetation cover have important impacts on parameter sensitivities, leading to the different patterns of posterior distributions of parameters at different sites. Overall, the MCMC-Bayesian inversion approach effectively and reliably improves the simulation of CLM under different climates and environmental conditions. Bayesian model averaging of the posterior estimates with different reference acceptance probabilities can smooth the posterior distribution and provide more reliable parameter estimates, but at the expense of wider uncertainty bounds.« less

Sequential Ideal-Observer Analysis of Visual Discriminations.

ERIC Educational Resources Information Center

Geisler, Wilson S.

1989-01-01

A new analysis, based on the concept of the ideal observer in signal detection theory, is described. It allows: tracing of the flow of discrimination information through the initial physiological stages of visual processing for arbitrary spatio-chromatic stimuli, and measurement of the information content of said visual stimuli. (TJH)

THE DYNAMICS OF MERGING CLUSTERS: A MONTE CARLO SOLUTION APPLIED TO THE BULLET AND MUSKET BALL CLUSTERS

DOE Office of Scientific and Technical Information (OSTI.GOV)

Dawson, William A., E-mail: wadawson@ucdavis.edu

2013-08-01

Merging galaxy clusters have become one of the most important probes of dark matter, providing evidence for dark matter over modified gravity and even constraints on the dark matter self-interaction cross-section. To properly constrain the dark matter cross-section it is necessary to understand the dynamics of the merger, as the inferred cross-section is a function of both the velocity of the collision and the observed time since collision. While the best understanding of merging system dynamics comes from N-body simulations, these are computationally intensive and often explore only a limited volume of the merger phase space allowed by observed parametermore » uncertainty. Simple analytic models exist but the assumptions of these methods invalidate their results near the collision time, plus error propagation of the highly correlated merger parameters is unfeasible. To address these weaknesses I develop a Monte Carlo method to discern the properties of dissociative mergers and propagate the uncertainty of the measured cluster parameters in an accurate and Bayesian manner. I introduce this method, verify it against an existing hydrodynamic N-body simulation, and apply it to two known dissociative mergers: 1ES 0657-558 (Bullet Cluster) and DLSCL J0916.2+2951 (Musket Ball Cluster). I find that this method surpasses existing analytic models-providing accurate (10% level) dynamic parameter and uncertainty estimates throughout the merger history. This, coupled with minimal required a priori information (subcluster mass, redshift, and projected separation) and relatively fast computation ({approx}6 CPU hours), makes this method ideal for large samples of dissociative merging clusters.« less

Probabilistic estimation of dune retreat on the Gold Coast, Australia

USGS Publications Warehouse

Palmsten, Margaret L.; Splinter, Kristen D.; Plant, Nathaniel G.; Stockdon, Hilary F.

2014-01-01

Sand dunes are an important natural buffer between storm impacts and development backing the beach on the Gold Coast of Queensland, Australia. The ability to forecast dune erosion at a prediction horizon of days to a week would allow efficient and timely response to dune erosion in this highly populated area. Towards this goal, we modified an existing probabilistic dune erosion model for use on the Gold Coast. The original model was trained using observations of dune response from Hurricane Ivan on Santa Rosa Island, Florida, USA (Plant and Stockdon 2012. Probabilistic prediction of barrier-island response to hurricanes, Journal of Geophysical Research, 117(F3), F03015). The model relates dune position change to pre-storm dune elevations, dune widths, and beach widths, along with storm surge and run-up using a Bayesian network. The Bayesian approach captures the uncertainty of inputs and predictions through the conditional probabilities between variables. Three versions of the barrier island response Bayesian network were tested for use on the Gold Coast. One network has the same structure as the original and was trained with the Santa Rosa Island data. The second network has a modified design and was trained using only pre- and post-storm data from 1988-2009 for the Gold Coast. The third version of the network has the same design as the second version of the network and was trained with the combined data from the Gold Coast and Santa Rosa Island. The two networks modified for use on the Gold Coast hindcast dune retreat with equal accuracy. Both networks explained 60% of the observed dune retreat variance, which is comparable to the skill observed by Plant and Stockdon (2012) in the initial Bayesian network application at Santa Rosa Island. The new networks improved predictions relative to application of the original network on the Gold Coast. Dune width was the most important morphologic variable in hindcasting dune retreat, while hydrodynamic variables, surge and run-up elevation, were also important

Systemic antibiotics in the treatment of aggressive periodontitis. A systematic review and a Bayesian Network meta-analysis.

PubMed

Rabelo, Cleverton Correa; Feres, Magda; Gonçalves, Cristiane; Figueiredo, Luciene C; Faveri, Marcelo; Tu, Yu-Kang; Chambrone, Leandro

2015-07-01

The aim of this study was to assess the effect of systemic antibiotic therapy on the treatment of aggressive periodontitis (AgP). This study was conducted and reported in accordance with the PRISMA statement. The MEDLINE, EMBASE and CENTRAL databases were searched up to June 2014 for randomized clinical trials comparing the treatment of subjects with AgP with either scaling and root planing (SRP) alone or associated with systemic antibiotics. Bayesian network meta-analysis was prepared using the Bayesian random-effects hierarchical models and the outcomes reported at 6-month post-treatment. Out of 350 papers identified, 14 studies were eligible. Greater gain in clinical attachment (CA) (mean difference [MD]: 1.08 mm; p < 0.0001) and reduction in probing depth (PD) (MD: 1.05 mm; p < 0.00001) were observed for SRP + metronidazole (Mtz), and for SRP + Mtz + amoxicillin (Amx) (MD: 0.45 mm, MD: 0.53 mm, respectively; p < 0.00001) than SRP alone/placebo. Bayesian network meta-analysis showed additional benefits in CA gain and PD reduction when SRP was associated with systemic antibiotics. SRP plus systemic antibiotics led to an additional clinical effect compared with SRP alone in the treatment of AgP. Of the antibiotic protocols available for inclusion into the Bayesian network meta-analysis, Mtz and Mtz/Amx provided to the most beneficial outcomes. © 2015 John Wiley & Sons A/S. Published by John Wiley & Sons Ltd.

Statistical analysis of modal parameters of a suspension bridge based on Bayesian spectral density approach and SHM data

NASA Astrophysics Data System (ADS)

Li, Zhijun; Feng, Maria Q.; Luo, Longxi; Feng, Dongming; Xu, Xiuli

2018-01-01

Uncertainty of modal parameters estimation appear in structural health monitoring (SHM) practice of civil engineering to quite some significant extent due to environmental influences and modeling errors. Reasonable methodologies are needed for processing the uncertainty. Bayesian inference can provide a promising and feasible identification solution for the purpose of SHM. However, there are relatively few researches on the application of Bayesian spectral method in the modal identification using SHM data sets. To extract modal parameters from large data sets collected by SHM system, the Bayesian spectral density algorithm was applied to address the uncertainty of mode extraction from output-only response of a long-span suspension bridge. The posterior most possible values of modal parameters and their uncertainties were estimated through Bayesian inference. A long-term variation and statistical analysis was performed using the sensor data sets collected from the SHM system of the suspension bridge over a one-year period. The t location-scale distribution was shown to be a better candidate function for frequencies of lower modes. On the other hand, the burr distribution provided the best fitting to the higher modes which are sensitive to the temperature. In addition, wind-induced variation of modal parameters was also investigated. It was observed that both the damping ratios and modal forces increased during the period of typhoon excitations. Meanwhile, the modal damping ratios exhibit significant correlation with the spectral intensities of the corresponding modal forces.

Sensitivity of Global Methane Bayesian Inversion to Surface Observation Data Sets and Chemical-Transport Model Resolution

NASA Astrophysics Data System (ADS)

Lew, E. J.; Butenhoff, C. L.; Karmakar, S.; Rice, A. L.; Khalil, A. K.

2017-12-01

Methane is the second most important greenhouse gas after carbon dioxide. In efforts to control emissions, a careful examination of the methane budget and source strengths is required. To determine methane surface fluxes, Bayesian methods are often used to provide top-down constraints. Inverse modeling derives unknown fluxes using observed methane concentrations, a chemical transport model (CTM) and prior information. The Bayesian inversion reduces prior flux uncertainties by exploiting information content in the data. While the Bayesian formalism produces internal error estimates of source fluxes, systematic or external errors that arise from user choices in the inversion scheme are often much larger. Here we examine model sensitivity and uncertainty of our inversion under different observation data sets and CTM grid resolution. We compare posterior surface fluxes using the data product GLOBALVIEW-CH4 against the event-level molar mixing ratio data available from NOAA. GLOBALVIEW-CH4 is a collection of CH4 concentration estimates from 221 sites, collected by 12 laboratories, that have been interpolated and extracted to provide weekly records from 1984-2008. Differently, the event-level NOAA data records methane mixing ratios field measurements from 102 sites, containing sampling frequency irregularities and gaps in time. Furthermore, the sampling platform types used by the data sets may influence the posterior flux estimates, namely fixed surface, tower, ship and aircraft sites. To explore the sensitivity of the posterior surface fluxes to the observation network geometry, inversions composed of all sites, only aircraft, only ship, only tower and only fixed surface sites, are performed and compared. Also, we investigate the sensitivity of the error reduction associated with the resolution of the GEOS-Chem simulation (4°×5° vs 2°×2.5°) used to calculate the response matrix. Using a higher resolution grid decreased the model-data error at most sites, thereby increasing the information at that site. These different inversions—event-level and interpolated data, higher and lower resolutions—are compared using an ensemble of descriptive and comparative statistics. Analyzing the sensitivity of the inverse model leads to more accurate estimates of the methane source category uncertainty.

A Bayesian approach for convex combination of two Gumbel-Barnett copulas

NASA Astrophysics Data System (ADS)

Fernández, M.; González-López, V. A.

2013-10-01

In this paper it was applied a new Bayesian approach to model the dependence between two variables of interest in public policy: "Gonorrhea Rates per 100,000 Population" and "400% Federal Poverty Level and over" with a small number of paired observations (one pair for each U.S. state). We use a mixture of Gumbel-Barnett copulas suitable to represent situations with weak and negative dependence, which is the case treated here. The methodology allows even making a prediction of the dependence between the variables from one year to another, showing whether there was any alteration in the dependence.

Probability, statistics, and computational science.

PubMed

Beerenwinkel, Niko; Siebourg, Juliane

2012-01-01

In this chapter, we review basic concepts from probability theory and computational statistics that are fundamental to evolutionary genomics. We provide a very basic introduction to statistical modeling and discuss general principles, including maximum likelihood and Bayesian inference. Markov chains, hidden Markov models, and Bayesian network models are introduced in more detail as they occur frequently and in many variations in genomics applications. In particular, we discuss efficient inference algorithms and methods for learning these models from partially observed data. Several simple examples are given throughout the text, some of which point to models that are discussed in more detail in subsequent chapters.

Annealed Importance Sampling Reversible Jump MCMC algorithms

DOE Office of Scientific and Technical Information (OSTI.GOV)

Karagiannis, Georgios; Andrieu, Christophe

2013-03-20

It will soon be 20 years since reversible jump Markov chain Monte Carlo (RJ-MCMC) algorithms have been proposed. They have significantly extended the scope of Markov chain Monte Carlo simulation methods, offering the promise to be able to routinely tackle transdimensional sampling problems, as encountered in Bayesian model selection problems for example, in a principled and flexible fashion. Their practical efficient implementation, however, still remains a challenge. A particular difficulty encountered in practice is in the choice of the dimension matching variables (both their nature and their distribution) and the reversible transformations which allow one to define the one-to-one mappingsmore » underpinning the design of these algorithms. Indeed, even seemingly sensible choices can lead to algorithms with very poor performance. The focus of this paper is the development and performance evaluation of a method, annealed importance sampling RJ-MCMC (aisRJ), which addresses this problem by mitigating the sensitivity of RJ-MCMC algorithms to the aforementioned poor design. As we shall see the algorithm can be understood as being an “exact approximation” of an idealized MCMC algorithm that would sample from the model probabilities directly in a model selection set-up. Such an idealized algorithm may have good theoretical convergence properties, but typically cannot be implemented, and our algorithms can approximate the performance of such idealized algorithms to an arbitrary degree while not introducing any bias for any degree of approximation. Our approach combines the dimension matching ideas of RJ-MCMC with annealed importance sampling and its Markov chain Monte Carlo implementation. We illustrate the performance of the algorithm with numerical simulations which indicate that, although the approach may at first appear computationally involved, it is in fact competitive.« less

Bayesian data analysis for newcomers.

PubMed

Kruschke, John K; Liddell, Torrin M

2018-02-01

This article explains the foundational concepts of Bayesian data analysis using virtually no mathematical notation. Bayesian ideas already match your intuitions from everyday reasoning and from traditional data analysis. Simple examples of Bayesian data analysis are presented that illustrate how the information delivered by a Bayesian analysis can be directly interpreted. Bayesian approaches to null-value assessment are discussed. The article clarifies misconceptions about Bayesian methods that newcomers might have acquired elsewhere. We discuss prior distributions and explain how they are not a liability but an important asset. We discuss the relation of Bayesian data analysis to Bayesian models of mind, and we briefly discuss what methodological problems Bayesian data analysis is not meant to solve. After you have read this article, you should have a clear sense of how Bayesian data analysis works and the sort of information it delivers, and why that information is so intuitive and useful for drawing conclusions from data.

Reynolds number scaling of the influence of boundary layers on the global behavior of laboratory quasi-Keplerian flows

DOE Office of Scientific and Technical Information (OSTI.GOV)

Edlund, E. M.; Ji, H.

2015-10-06

Here, we present fluid velocity measurements in a modified Taylor-Couette device operated in the quasi-Keplerian regime, where it is observed that nearly ideal flows exhibit self-similarity under scaling of the Reynolds number. In contrast, nonideal flows show progressive departure from ideal Couette as the Reynolds number is increased. We present a model that describes the observed departures from ideal Couette rotation as a function of the fluxes of angular momentum across the boundaries, capturing the dependence on Reynolds number and boundary conditions.

Reynolds number scaling of the influence of boundary layers on the global behavior of laboratory quasi-Keplerian flows.

PubMed

Edlund, E M; Ji, H

2015-10-01

We present fluid velocity measurements in a modified Taylor-Couette device operated in the quasi-Keplerian regime, where it is observed that nearly ideal flows exhibit self-similarity under scaling of the Reynolds number. In contrast, nonideal flows show progressive departure from ideal Couette as the Reynolds number is increased. We present a model that describes the observed departures from ideal Couette rotation as a function of the fluxes of angular momentum across the boundaries, capturing the dependence on Reynolds number and boundary conditions.

Dealing with missing standard deviation and mean values in meta-analysis of continuous outcomes: a systematic review.

PubMed

Weir, Christopher J; Butcher, Isabella; Assi, Valentina; Lewis, Stephanie C; Murray, Gordon D; Langhorne, Peter; Brady, Marian C

2018-03-07

Rigorous, informative meta-analyses rely on availability of appropriate summary statistics or individual participant data. For continuous outcomes, especially those with naturally skewed distributions, summary information on the mean or variability often goes unreported. While full reporting of original trial data is the ideal, we sought to identify methods for handling unreported mean or variability summary statistics in meta-analysis. We undertook two systematic literature reviews to identify methodological approaches used to deal with missing mean or variability summary statistics. Five electronic databases were searched, in addition to the Cochrane Colloquium abstract books and the Cochrane Statistics Methods Group mailing list archive. We also conducted cited reference searching and emailed topic experts to identify recent methodological developments. Details recorded included the description of the method, the information required to implement the method, any underlying assumptions and whether the method could be readily applied in standard statistical software. We provided a summary description of the methods identified, illustrating selected methods in example meta-analysis scenarios. For missing standard deviations (SDs), following screening of 503 articles, fifteen methods were identified in addition to those reported in a previous review. These included Bayesian hierarchical modelling at the meta-analysis level; summary statistic level imputation based on observed SD values from other trials in the meta-analysis; a practical approximation based on the range; and algebraic estimation of the SD based on other summary statistics. Following screening of 1124 articles for methods estimating the mean, one approximate Bayesian computation approach and three papers based on alternative summary statistics were identified. Illustrative meta-analyses showed that when replacing a missing SD the approximation using the range minimised loss of precision and generally performed better than omitting trials. When estimating missing means, a formula using the median, lower quartile and upper quartile performed best in preserving the precision of the meta-analysis findings, although in some scenarios, omitting trials gave superior results. Methods based on summary statistics (minimum, maximum, lower quartile, upper quartile, median) reported in the literature facilitate more comprehensive inclusion of randomised controlled trials with missing mean or variability summary statistics within meta-analyses.

The Role of Idealization in Science and Its Implications for Science Education

NASA Astrophysics Data System (ADS)

Niaz, Mansoor

1999-06-01

The main objective of this article is to study the role of empirical evidence in the interpretation of psychological and epistemological aspects of Piagetian theory. According to Galilean methodology, after having asked the right question, a scientist could experimentally vary one impediment, and observe what happens to the dependent variable, as it approaches the ideal limiting case. Following Galileo's idealization, scientific laws being epistemological constructions do not describe the behavior of actual bodies. It is plausible to suggest that just as Galileo's ideal law can be observed only when all the impediment variables approach zero, similarly individuals in the real world have various `impediments' and it is only when these impediments are gradually removed by experimental manipulation that the real performance of individuals can approximate the competence of Piaget's epistemic subject (ideal knower). Finally, evidence is presented to the effect that by experimentally manipulating the impediment variables (e.g., Pascual-Leone's M-demand and Witkin's perceptual field effect of a task), performance of the real subjects approximates the competence of the ideal epistemic subject, which leads to the construction of a neo-Piagetian epistemological theory.

An Ideal Observer Analysis of Visual Working Memory

ERIC Educational Resources Information Center

Sims, Chris R.; Jacobs, Robert A.; Knill, David C.

2012-01-01

Limits in visual working memory (VWM) strongly constrain human performance across many tasks. However, the nature of these limits is not well understood. In this article we develop an ideal observer analysis of human VWM by deriving the expected behavior of an optimally performing but limited-capacity memory system. This analysis is framed around…

Improvement of Storm Forecasts Using Gridded Bayesian Linear Regression for Northeast United States

NASA Astrophysics Data System (ADS)

Yang, J.; Astitha, M.; Schwartz, C. S.

2017-12-01

Bayesian linear regression (BLR) is a post-processing technique in which regression coefficients are derived and used to correct raw forecasts based on pairs of observation-model values. This study presents the development and application of a gridded Bayesian linear regression (GBLR) as a new post-processing technique to improve numerical weather prediction (NWP) of rain and wind storm forecasts over northeast United States. Ten controlled variables produced from ten ensemble members of the National Center for Atmospheric Research (NCAR) real-time prediction system are used for a GBLR model. In the GBLR framework, leave-one-storm-out cross-validation is utilized to study the performances of the post-processing technique in a database composed of 92 storms. To estimate the regression coefficients of the GBLR, optimization procedures that minimize the systematic and random error of predicted atmospheric variables (wind speed, precipitation, etc.) are implemented for the modeled-observed pairs of training storms. The regression coefficients calculated for meteorological stations of the National Weather Service are interpolated back to the model domain. An analysis of forecast improvements based on error reductions during the storms will demonstrate the value of GBLR approach. This presentation will also illustrate how the variances are optimized for the training partition in GBLR and discuss the verification strategy for grid points where no observations are available. The new post-processing technique is successful in improving wind speed and precipitation storm forecasts using past event-based data and has the potential to be implemented in real-time.

Nonlinear dynamical modes of climate variability: from curves to manifolds

NASA Astrophysics Data System (ADS)

Gavrilov, Andrey; Mukhin, Dmitry; Loskutov, Evgeny; Feigin, Alexander

2016-04-01

The necessity of efficient dimensionality reduction methods capturing dynamical properties of the system from observed data is evident. Recent study shows that nonlinear dynamical mode (NDM) expansion is able to solve this problem and provide adequate phase variables in climate data analysis [1]. A single NDM is logical extension of linear spatio-temporal structure (like empirical orthogonal function pattern): it is constructed as nonlinear transformation of hidden scalar time series to the space of observed variables, i. e. projection of observed dataset onto a nonlinear curve. Both the hidden time series and the parameters of the curve are learned simultaneously using Bayesian approach. The only prior information about the hidden signal is the assumption of its smoothness. The optimal nonlinearity degree and smoothness are found using Bayesian evidence technique. In this work we do further extension and look for vector hidden signals instead of scalar with the same smoothness restriction. As a result we resolve multidimensional manifolds instead of sum of curves. The dimension of the hidden manifold is optimized using also Bayesian evidence. The efficiency of the extension is demonstrated on model examples. Results of application to climate data are demonstrated and discussed. The study is supported by Government of Russian Federation (agreement #14.Z50.31.0033 with the Institute of Applied Physics of RAS). 1. Mukhin, D., Gavrilov, A., Feigin, A., Loskutov, E., & Kurths, J. (2015). Principal nonlinear dynamical modes of climate variability. Scientific Reports, 5, 15510. http://doi.org/10.1038/srep15510

Approximate Bayesian Computation in the estimation of the parameters of the Forbush decrease model

NASA Astrophysics Data System (ADS)

Wawrzynczak, A.; Kopka, P.

2017-12-01

Realistic modeling of the complicated phenomena as Forbush decrease of the galactic cosmic ray intensity is a quite challenging task. One aspect is a numerical solution of the Fokker-Planck equation in five-dimensional space (three spatial variables, the time and particles energy). The second difficulty arises from a lack of detailed knowledge about the spatial and time profiles of the parameters responsible for the creation of the Forbush decrease. Among these parameters, the central role plays a diffusion coefficient. Assessment of the correctness of the proposed model can be done only by comparison of the model output with the experimental observations of the galactic cosmic ray intensity. We apply the Approximate Bayesian Computation (ABC) methodology to match the Forbush decrease model to experimental data. The ABC method is becoming increasing exploited for dynamic complex problems in which the likelihood function is costly to compute. The main idea of all ABC methods is to accept samples as an approximate posterior draw if its associated modeled data are close enough to the observed one. In this paper, we present application of the Sequential Monte Carlo Approximate Bayesian Computation algorithm scanning the space of the diffusion coefficient parameters. The proposed algorithm is adopted to create the model of the Forbush decrease observed by the neutron monitors at the Earth in March 2002. The model of the Forbush decrease is based on the stochastic approach to the solution of the Fokker-Planck equation.

Assessment study of lichenometric methods for dating surfaces

NASA Astrophysics Data System (ADS)

Jomelli, Vincent; Grancher, Delphine; Naveau, Philippe; Cooley, Daniel; Brunstein, Daniel

2007-04-01

In this paper, we discuss the advantages and drawbacks of the most classical approaches used in lichenometry. In particular, we perform a detailed comparison among methods based on the statistical analysis of either the largest lichen diameters recorded on geomorphic features or the frequency of all lichens. To assess the performance of each method, a careful comparison design with well-defined criteria is proposed and applied to two distinct data sets. First, we study 350 tombstones. This represents an ideal test bed because tombstone dates are known and, therefore, the quality of the estimated lichen growth curve can be easily tested for the different techniques. Secondly, 37 moraines from two tropical glaciers are investigated. This analysis corresponds to our real case study. For both data sets, we apply our list of criteria that reflects precision, error measurements and their theoretical foundations when proposing estimated ages and their associated confidence intervals. From this comparison, it clearly appears that two methods, the mean of the n largest lichen diameters and the recent Bayesian method based on extreme value theory, offer the most reliable estimates of moraine and tombstones dates. Concerning the spread of the error, the latter approach provides the smallest uncertainty and it is the only one that takes advantage of the statistical nature of the observations by fitting an extreme value distribution to the largest diameters.

Gender in Facial Representations: A Contrast-Based Study of Adaptation within and between the Sexes

PubMed Central

Oruç, Ipek; Guo, Xiaoyue M.; Barton, Jason J. S.

2011-01-01

Face aftereffects are proving to be an effective means of examining the properties of face-specific processes in the human visual system. We examined the role of gender in the neural representation of faces using a contrast-based adaptation method. If faces of different genders share the same representational face space, then adaptation to a face of one gender should affect both same- and different-gender faces. Further, if these aftereffects differ in magnitude, this may indicate distinct gender-related factors in the organization of this face space. To control for a potential confound between physical similarity and gender, we used a Bayesian ideal observer and human discrimination data to construct a stimulus set in which pairs of different-gender faces were equally dissimilar as same-gender pairs. We found that the recognition of both same-gender and different-gender faces was suppressed following a brief exposure of 100ms. Moreover, recognition was more suppressed for test faces of a different-gender than those of the same-gender as the adaptor, despite the equivalence in physical and psychophysical similarity. Our results suggest that male and female faces likely occupy the same face space, allowing transfer of aftereffects between the genders, but that there are special properties that emerge along gender-defining dimensions of this space. PMID:21267414

EVOLUTION OF THE VELOCITY-DISPERSION FUNCTION OF LUMINOUS RED GALAXIES: A HIERARCHICAL BAYESIAN MEASUREMENT

DOE Office of Scientific and Technical Information (OSTI.GOV)

Shu Yiping; Bolton, Adam S.; Dawson, Kyle S.

2012-04-15

We present a hierarchical Bayesian determination of the velocity-dispersion function of approximately 430,000 massive luminous red galaxies observed at relatively low spectroscopic signal-to-noise ratio (S/N {approx} 3-5 per 69 km s{sup -1}) by the Baryon Oscillation Spectroscopic Survey (BOSS) of the Sloan Digital Sky Survey III. We marginalize over spectroscopic redshift errors, and use the full velocity-dispersion likelihood function for each galaxy to make a self-consistent determination of the velocity-dispersion distribution parameters as a function of absolute magnitude and redshift, correcting as well for the effects of broadband magnitude errors on our binning. Parameterizing the distribution at each point inmore » the luminosity-redshift plane with a log-normal form, we detect significant evolution in the width of the distribution toward higher intrinsic scatter at higher redshifts. Using a subset of deep re-observations of BOSS galaxies, we demonstrate that our distribution-parameter estimates are unbiased regardless of spectroscopic S/N. We also show through simulation that our method introduces no systematic parameter bias with redshift. We highlight the advantage of the hierarchical Bayesian method over frequentist 'stacking' of spectra, and illustrate how our measured distribution parameters can be adopted as informative priors for velocity-dispersion measurements from individual noisy spectra.« less

Bayesian Monte Carlo and Maximum Likelihood Approach for ...

EPA Pesticide Factsheets

Model uncertainty estimation and risk assessment is essential to environmental management and informed decision making on pollution mitigation strategies. In this study, we apply a probabilistic methodology, which combines Bayesian Monte Carlo simulation and Maximum Likelihood estimation (BMCML) to calibrate a lake oxygen recovery model. We first derive an analytical solution of the differential equation governing lake-averaged oxygen dynamics as a function of time-variable wind speed. Statistical inferences on model parameters and predictive uncertainty are then drawn by Bayesian conditioning of the analytical solution on observed daily wind speed and oxygen concentration data obtained from an earlier study during two recovery periods on a eutrophic lake in upper state New York. The model is calibrated using oxygen recovery data for one year and statistical inferences were validated using recovery data for another year. Compared with essentially two-step, regression and optimization approach, the BMCML results are more comprehensive and performed relatively better in predicting the observed temporal dissolved oxygen levels (DO) in the lake. BMCML also produced comparable calibration and validation results with those obtained using popular Markov Chain Monte Carlo technique (MCMC) and is computationally simpler and easier to implement than the MCMC. Next, using the calibrated model, we derive an optimal relationship between liquid film-transfer coefficien

A Bayesian blind survey for cold molecular gas in the Universe

NASA Astrophysics Data System (ADS)

Lentati, L.; Carilli, C.; Alexander, P.; Walter, F.; Decarli, R.

2014-10-01

A new Bayesian method for performing an image domain search for line-emitting galaxies is presented. The method uses both spatial and spectral information to robustly determine the source properties, employing either simple Gaussian, or other physically motivated models whilst using the evidence to determine the probability that the source is real. In this paper, we describe the method, and its application to both a simulated data set, and a blind survey for cold molecular gas using observations of the Hubble Deep Field-North taken with the Plateau de Bure Interferometer. We make a total of six robust detections in the survey, five of which have counterparts in other observing bands. We identify the most secure detections found in a previous investigation, while finding one new probable line source with an optical ID not seen in the previous analysis. This study acts as a pilot application of Bayesian statistics to future searches to be carried out both for low-J CO transitions of high-redshift galaxies using the Jansky Very Large Array (JVLA), and at millimetre wavelengths with Atacama Large Millimeter/submillimeter Array (ALMA), enabling the inference of robust scientific conclusions about the history of the molecular gas properties of star-forming galaxies in the Universe through cosmic time.

Assessing Local Model Adequacy in Bayesian Hierarchical Models Using the Partitioned Deviance Information Criterion

PubMed Central

Wheeler, David C.; Hickson, DeMarc A.; Waller, Lance A.

2010-01-01

Many diagnostic tools and goodness-of-fit measures, such as the Akaike information criterion (AIC) and the Bayesian deviance information criterion (DIC), are available to evaluate the overall adequacy of linear regression models. In addition, visually assessing adequacy in models has become an essential part of any regression analysis. In this paper, we focus on a spatial consideration of the local DIC measure for model selection and goodness-of-fit evaluation. We use a partitioning of the DIC into the local DIC, leverage, and deviance residuals to assess local model fit and influence for both individual observations and groups of observations in a Bayesian framework. We use visualization of the local DIC and differences in local DIC between models to assist in model selection and to visualize the global and local impacts of adding covariates or model parameters. We demonstrate the utility of the local DIC in assessing model adequacy using HIV prevalence data from pregnant women in the Butare province of Rwanda during 1989-1993 using a range of linear model specifications, from global effects only to spatially varying coefficient models, and a set of covariates related to sexual behavior. Results of applying the diagnostic visualization approach include more refined model selection and greater understanding of the models as applied to the data. PMID:21243121

Bridging groundwater models and decision support with a Bayesian network

USGS Publications Warehouse

Fienen, Michael N.; Masterson, John P.; Plant, Nathaniel G.; Gutierrez, Benjamin T.; Thieler, E. Robert

2013-01-01

Resource managers need to make decisions to plan for future environmental conditions, particularly sea level rise, in the face of substantial uncertainty. Many interacting processes factor in to the decisions they face. Advances in process models and the quantification of uncertainty have made models a valuable tool for this purpose. Long-simulation runtimes and, often, numerical instability make linking process models impractical in many cases. A method for emulating the important connections between model input and forecasts, while propagating uncertainty, has the potential to provide a bridge between complicated numerical process models and the efficiency and stability needed for decision making. We explore this using a Bayesian network (BN) to emulate a groundwater flow model. We expand on previous approaches to validating a BN by calculating forecasting skill using cross validation of a groundwater model of Assateague Island in Virginia and Maryland, USA. This BN emulation was shown to capture the important groundwater-flow characteristics and uncertainty of the groundwater system because of its connection to island morphology and sea level. Forecast power metrics associated with the validation of multiple alternative BN designs guided the selection of an optimal level of BN complexity. Assateague island is an ideal test case for exploring a forecasting tool based on current conditions because the unique hydrogeomorphological variability of the island includes a range of settings indicative of past, current, and future conditions. The resulting BN is a valuable tool for exploring the response of groundwater conditions to sea level rise in decision support.

Elastic Properties of Novel Co- and CoNi-Based Superalloys Determined through Bayesian Inference and Resonant Ultrasound Spectroscopy

NASA Astrophysics Data System (ADS)

Goodlet, Brent R.; Mills, Leah; Bales, Ben; Charpagne, Marie-Agathe; Murray, Sean P.; Lenthe, William C.; Petzold, Linda; Pollock, Tresa M.

2018-06-01

Bayesian inference is employed to precisely evaluate single crystal elastic properties of novel γ -γ ' Co- and CoNi-based superalloys from simple and non-destructive resonant ultrasound spectroscopy (RUS) measurements. Nine alloys from three Co-, CoNi-, and Ni-based alloy classes were evaluated in the fully aged condition, with one alloy per class also evaluated in the solution heat-treated condition. Comparisons are made between the elastic properties of the three alloy classes and among the alloys of a single class, with the following trends observed. A monotonic rise in the c_{44} (shear) elastic constant by a total of 12 pct is observed between the three alloy classes as Co is substituted for Ni. Elastic anisotropy ( A) is also increased, with a large majority of the nearly 13 pct increase occurring after Co becomes the dominant constituent. Together the five CoNi alloys, with Co:Ni ratios from 1:1 to 1.5:1, exhibited remarkably similar properties with an average A 1.8 pct greater than the Ni-based alloy CMSX-4. Custom code demonstrating a substantial advance over previously reported methods for RUS inversion is also reported here for the first time. CmdStan-RUS is built upon the open-source probabilistic programing language of Stan and formulates the inverse problem using Bayesian methods. Bayesian posterior distributions are efficiently computed with Hamiltonian Monte Carlo (HMC), while initial parameterization is randomly generated from weakly informative prior distributions. Remarkably robust convergence behavior is demonstrated across multiple independent HMC chains in spite of initial parameterization often very far from actual parameter values. Experimental procedures are substantially simplified by allowing any arbitrary misorientation between the specimen and crystal axes, as elastic properties and misorientation are estimated simultaneously.

An approach based on Hierarchical Bayesian Graphical Models for measurement interpretation under uncertainty

NASA Astrophysics Data System (ADS)

Skataric, Maja; Bose, Sandip; Zeroug, Smaine; Tilke, Peter

2017-02-01

It is not uncommon in the field of non-destructive evaluation that multiple measurements encompassing a variety of modalities are available for analysis and interpretation for determining the underlying states of nature of the materials or parts being tested. Despite and sometimes due to the richness of data, significant challenges arise in the interpretation manifested as ambiguities and inconsistencies due to various uncertain factors in the physical properties (inputs), environment, measurement device properties, human errors, and the measurement data (outputs). Most of these uncertainties cannot be described by any rigorous mathematical means, and modeling of all possibilities is usually infeasible for many real time applications. In this work, we will discuss an approach based on Hierarchical Bayesian Graphical Models (HBGM) for the improved interpretation of complex (multi-dimensional) problems with parametric uncertainties that lack usable physical models. In this setting, the input space of the physical properties is specified through prior distributions based on domain knowledge and expertise, which are represented as Gaussian mixtures to model the various possible scenarios of interest for non-destructive testing applications. Forward models are then used offline to generate the expected distribution of the proposed measurements which are used to train a hierarchical Bayesian network. In Bayesian analysis, all model parameters are treated as random variables, and inference of the parameters is made on the basis of posterior distribution given the observed data. Learned parameters of the posterior distribution obtained after the training can therefore be used to build an efficient classifier for differentiating new observed data in real time on the basis of pre-trained models. We will illustrate the implementation of the HBGM approach to ultrasonic measurements used for cement evaluation of cased wells in the oil industry.

Potential of SNP markers for the characterization of Brazilian cassava germplasm.

PubMed

de Oliveira, Eder Jorge; Ferreira, Cláudia Fortes; da Silva Santos, Vanderlei; de Jesus, Onildo Nunes; Oliveira, Gilmara Alvarenga Fachardo; da Silva, Maiane Suzarte

2014-06-01

High-throughput markers, such as SNPs, along with different methodologies were used to evaluate the applicability of the Bayesian approach and the multivariate analysis in structuring the genetic diversity in cassavas. The objective of the present work was to evaluate the diversity and genetic structure of the largest cassava germplasm bank in Brazil. Complementary methodological approaches such as discriminant analysis of principal components (DAPC), Bayesian analysis and molecular analysis of variance (AMOVA) were used to understand the structure and diversity of 1,280 accessions genotyped using 402 single nucleotide polymorphism markers. The genetic diversity (0.327) and the average observed heterozygosity (0.322) were high considering the bi-allelic markers. In terms of population, the presence of a complex genetic structure was observed indicating the formation of 30 clusters by DAPC and 34 clusters by Bayesian analysis. Both methodologies presented difficulties and controversies in terms of the allocation of some accessions to specific clusters. However, the clusters suggested by the DAPC analysis seemed to be more consistent for presenting higher probability of allocation of the accessions within the clusters. Prior information related to breeding patterns and geographic origins of the accessions were not sufficient for providing clear differentiation between the clusters according to the AMOVA analysis. In contrast, the F ST was maximized when considering the clusters suggested by the Bayesian and DAPC analyses. The high frequency of germplasm exchange between producers and the subsequent alteration of the name of the same material may be one of the causes of the low association between genetic diversity and geographic origin. The results of this study may benefit cassava germplasm conservation programs, and contribute to the maximization of genetic gains in breeding programs.

A Bayesian Hierarchical Modeling Scheme for Estimating Erosion Rates Under Current Climate Conditions

NASA Astrophysics Data System (ADS)

Lowman, L.; Barros, A. P.

2014-12-01

Computational modeling of surface erosion processes is inherently difficult because of the four-dimensional nature of the problem and the multiple temporal and spatial scales that govern individual mechanisms. Landscapes are modified via surface and fluvial erosion and exhumation, each of which takes place over a range of time scales. Traditional field measurements of erosion/exhumation rates are scale dependent, often valid for a single point-wise location or averaging over large aerial extents and periods with intense and mild erosion. We present a method of remotely estimating erosion rates using a Bayesian hierarchical model based upon the stream power erosion law (SPEL). A Bayesian approach allows for estimating erosion rates using the deterministic relationship given by the SPEL and data on channel slopes and precipitation at the basin and sub-basin scale. The spatial scale associated with this framework is the elevation class, where each class is characterized by distinct morphologic behavior observed through different modes in the distribution of basin outlet elevations. Interestingly, the distributions of first-order outlets are similar in shape and extent to the distribution of precipitation events (i.e. individual storms) over a 14-year period between 1998-2011. We demonstrate an application of the Bayesian hierarchical modeling framework for five basins and one intermontane basin located in the central Andes between 5S and 20S. Using remotely sensed data of current annual precipitation rates from the Tropical Rainfall Measuring Mission (TRMM) and topography from a high resolution (3 arc-seconds) digital elevation map (DEM), our erosion rate estimates are consistent with decadal-scale estimates based on landslide mapping and sediment flux observations and 1-2 orders of magnitude larger than most millennial and million year timescale estimates from thermochronology and cosmogenic nuclides.

Parameter estimation for an immortal model of colonic stem cell division using approximate Bayesian computation.

PubMed

Walters, Kevin

2012-08-07

In this paper we use approximate Bayesian computation to estimate the parameters in an immortal model of colonic stem cell division. We base the inferences on the observed DNA methylation patterns of cells sampled from the human colon. Utilising DNA methylation patterns as a form of molecular clock is an emerging area of research and has been used in several studies investigating colonic stem cell turnover. There is much debate concerning the two competing models of stem cell turnover: the symmetric (immortal) and asymmetric models. Early simulation studies concluded that the observed methylation data were not consistent with the immortal model. A later modified version of the immortal model that included preferential strand segregation was subsequently shown to be consistent with the same methylation data. Most of this earlier work assumes site independent methylation models that do not take account of the known processivity of methyltransferases whilst other work does not take into account the methylation errors that occur in differentiated cells. This paper addresses both of these issues for the immortal model and demonstrates that approximate Bayesian computation provides accurate estimates of the parameters in this neighbour-dependent model of methylation error rates. The results indicate that if colonic stem cells divide asymmetrically then colon stem cell niches are maintained by more than 8 stem cells. Results also indicate the possibility of preferential strand segregation and provide clear evidence against a site-independent model for methylation errors. In addition, algebraic expressions for some of the summary statistics used in the approximate Bayesian computation (that allow for the additional variation arising from cell division in differentiated cells) are derived and their utility discussed. Copyright © 2012 Elsevier Ltd. All rights reserved.

Variational Bayesian Learning for Wavelet Independent Component Analysis

NASA Astrophysics Data System (ADS)

Roussos, E.; Roberts, S.; Daubechies, I.

2005-11-01

In an exploratory approach to data analysis, it is often useful to consider the observations as generated from a set of latent generators or "sources" via a generally unknown mapping. For the noisy overcomplete case, where we have more sources than observations, the problem becomes extremely ill-posed. Solutions to such inverse problems can, in many cases, be achieved by incorporating prior knowledge about the problem, captured in the form of constraints. This setting is a natural candidate for the application of the Bayesian methodology, allowing us to incorporate "soft" constraints in a natural manner. The work described in this paper is mainly driven by problems in functional magnetic resonance imaging of the brain, for the neuro-scientific goal of extracting relevant "maps" from the data. This can be stated as a `blind' source separation problem. Recent experiments in the field of neuroscience show that these maps are sparse, in some appropriate sense. The separation problem can be solved by independent component analysis (ICA), viewed as a technique for seeking sparse components, assuming appropriate distributions for the sources. We derive a hybrid wavelet-ICA model, transforming the signals into a domain where the modeling assumption of sparsity of the coefficients with respect to a dictionary is natural. We follow a graphical modeling formalism, viewing ICA as a probabilistic generative model. We use hierarchical source and mixing models and apply Bayesian inference to the problem. This allows us to perform model selection in order to infer the complexity of the representation, as well as automatic denoising. Since exact inference and learning in such a model is intractable, we follow a variational Bayesian mean-field approach in the conjugate-exponential family of distributions, for efficient unsupervised learning in multi-dimensional settings. The performance of the proposed algorithm is demonstrated on some representative experiments.

Charge-Trapping-Induced Non-Ideal Behaviors in Organic Field-Effect Transistors.

PubMed

Un, Hio-Ieng; Cheng, Peng; Lei, Ting; Yang, Chi-Yuan; Wang, Jie-Yu; Pei, Jian

2018-05-01

Organic field-effect transistors (OFETs) with impressively high hole mobilities over 10 cm 2 V -1 s -1 and electron mobilities over 1 cm 2 V -1 s -1 have been reported in the past few years. However, significant non-ideal electrical characteristics, e.g., voltage-dependent mobilities, have been widely observed in both small-molecule and polymer systems. This issue makes the accurate evaluation of the electrical performance impossible and also limits the practical applications of OFETs. Here, a semiconductor-unrelated, charge-trapping-induced non-ideality in OFETs is reported, and a revised model for the non-ideal transfer characteristics is provided. The trapping process can be directly observed using scanning Kelvin probe microscopy. It is found that such trapping-induced non-ideality exists in OFETs with different types of charge carriers (p-type or n-type), different types of dielectric materials (inorganic and organic) that contain different functional groups (OH, NH 2 , COOH, etc.). As fas as it is known, this is the first report for the non-ideal transport behaviors in OFETs caused by semiconductor-independent charge trapping. This work reveals the significant role of dielectric charge trapping in the non-ideal transistor characteristics and also provides guidelines for device engineering toward ideal OFETs. © 2018 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Bayesian inversion analysis of nonlinear dynamics in surface heterogeneous reactions.

PubMed

Omori, Toshiaki; Kuwatani, Tatsu; Okamoto, Atsushi; Hukushima, Koji

2016-09-01

It is essential to extract nonlinear dynamics from time-series data as an inverse problem in natural sciences. We propose a Bayesian statistical framework for extracting nonlinear dynamics of surface heterogeneous reactions from sparse and noisy observable data. Surface heterogeneous reactions are chemical reactions with conjugation of multiple phases, and they have the intrinsic nonlinearity of their dynamics caused by the effect of surface-area between different phases. We adapt a belief propagation method and an expectation-maximization (EM) algorithm to partial observation problem, in order to simultaneously estimate the time course of hidden variables and the kinetic parameters underlying dynamics. The proposed belief propagation method is performed by using sequential Monte Carlo algorithm in order to estimate nonlinear dynamical system. Using our proposed method, we show that the rate constants of dissolution and precipitation reactions, which are typical examples of surface heterogeneous reactions, as well as the temporal changes of solid reactants and products, were successfully estimated only from the observable temporal changes in the concentration of the dissolved intermediate product.

Bayesian Estimates of Autocorrelations in Single-Case Designs

ERIC Educational Resources Information Center

Shadish, William R.; Rindskopf, David M.; Hedges, Larry V.; Sullivan, Kristynn J.

2012-01-01

Researchers in the single-case design tradition have debated the size and importance of the observed autocorrelations in those designs. All of the past estimates of the autocorrelation in that literature have taken the observed autocorrelation estimates as the data to be used in the debate. However, estimates of the autocorrelation are subject to…

The Development of Bayesian Theory and Its Applications in Business and Bioinformatics

NASA Astrophysics Data System (ADS)

Zhang, Yifei

2018-03-01

Bayesian Theory originated from an Essay of a British mathematician named Thomas Bayes in 1763, and after its development in 20th century, Bayesian Statistics has been taking a significant part in statistical study of all fields. Due to the recent breakthrough of high-dimensional integral, Bayesian Statistics has been improved and perfected, and now it can be used to solve problems that Classical Statistics failed to solve. This paper summarizes Bayesian Statistics’ history, concepts and applications, which are illustrated in five parts: the history of Bayesian Statistics, the weakness of Classical Statistics, Bayesian Theory and its development and applications. The first two parts make a comparison between Bayesian Statistics and Classical Statistics in a macroscopic aspect. And the last three parts focus on Bayesian Theory in specific -- from introducing some particular Bayesian Statistics’ concepts to listing their development and finally their applications.

Bayesian demography 250 years after Bayes

PubMed Central

Bijak, Jakub; Bryant, John

2016-01-01

Bayesian statistics offers an alternative to classical (frequentist) statistics. It is distinguished by its use of probability distributions to describe uncertain quantities, which leads to elegant solutions to many difficult statistical problems. Although Bayesian demography, like Bayesian statistics more generally, is around 250 years old, only recently has it begun to flourish. The aim of this paper is to review the achievements of Bayesian demography, address some misconceptions, and make the case for wider use of Bayesian methods in population studies. We focus on three applications: demographic forecasts, limited data, and highly structured or complex models. The key advantages of Bayesian methods are the ability to integrate information from multiple sources and to describe uncertainty coherently. Bayesian methods also allow for including additional (prior) information next to the data sample. As such, Bayesian approaches are complementary to many traditional methods, which can be productively re-expressed in Bayesian terms. PMID:26902889

A Bayesian framework for knowledge attribution: evidence from semantic integration.

PubMed

Powell, Derek; Horne, Zachary; Pinillos, N Ángel; Holyoak, Keith J

2015-06-01

We propose a Bayesian framework for the attribution of knowledge, and apply this framework to generate novel predictions about knowledge attribution for different types of "Gettier cases", in which an agent is led to a justified true belief yet has made erroneous assumptions. We tested these predictions using a paradigm based on semantic integration. We coded the frequencies with which participants falsely recalled the word "thought" as "knew" (or a near synonym), yielding an implicit measure of conceptual activation. Our experiments confirmed the predictions of our Bayesian account of knowledge attribution across three experiments. We found that Gettier cases due to counterfeit objects were not treated as knowledge (Experiment 1), but those due to intentionally-replaced evidence were (Experiment 2). Our findings are not well explained by an alternative account focused only on luck, because accidentally-replaced evidence activated the knowledge concept more strongly than did similar false belief cases (Experiment 3). We observed a consistent pattern of results across a number of different vignettes that varied the quality and type of evidence available to agents, the relative stakes involved, and surface details of content. Accordingly, the present findings establish basic phenomena surrounding people's knowledge attributions in Gettier cases, and provide explanations of these phenomena within a Bayesian framework. Copyright © 2015 Elsevier B.V. All rights reserved.

Simultaneous Force Regression and Movement Classification of Fingers via Surface EMG within a Unified Bayesian Framework.

PubMed

Baldacchino, Tara; Jacobs, William R; Anderson, Sean R; Worden, Keith; Rowson, Jennifer

2018-01-01

This contribution presents a novel methodology for myolectric-based control using surface electromyographic (sEMG) signals recorded during finger movements. A multivariate Bayesian mixture of experts (MoE) model is introduced which provides a powerful method for modeling force regression at the fingertips, while also performing finger movement classification as a by-product of the modeling algorithm. Bayesian inference of the model allows uncertainties to be naturally incorporated into the model structure. This method is tested using data from the publicly released NinaPro database which consists of sEMG recordings for 6 degree-of-freedom force activations for 40 intact subjects. The results demonstrate that the MoE model achieves similar performance compared to the benchmark set by the authors of NinaPro for finger force regression. Additionally, inherent to the Bayesian framework is the inclusion of uncertainty in the model parameters, naturally providing confidence bounds on the force regression predictions. Furthermore, the integrated clustering step allows a detailed investigation into classification of the finger movements, without incurring any extra computational effort. Subsequently, a systematic approach to assessing the importance of the number of electrodes needed for accurate control is performed via sensitivity analysis techniques. A slight degradation in regression performance is observed for a reduced number of electrodes, while classification performance is unaffected.

A Bayesian joint probability modeling approach for seasonal forecasting of streamflows at multiple sites

NASA Astrophysics Data System (ADS)

Wang, Q. J.; Robertson, D. E.; Chiew, F. H. S.

2009-05-01

Seasonal forecasting of streamflows can be highly valuable for water resources management. In this paper, a Bayesian joint probability (BJP) modeling approach for seasonal forecasting of streamflows at multiple sites is presented. A Box-Cox transformed multivariate normal distribution is proposed to model the joint distribution of future streamflows and their predictors such as antecedent streamflows and El Niño-Southern Oscillation indices and other climate indicators. Bayesian inference of model parameters and uncertainties is implemented using Markov chain Monte Carlo sampling, leading to joint probabilistic forecasts of streamflows at multiple sites. The model provides a parametric structure for quantifying relationships between variables, including intersite correlations. The Box-Cox transformed multivariate normal distribution has considerable flexibility for modeling a wide range of predictors and predictands. The Bayesian inference formulated allows the use of data that contain nonconcurrent and missing records. The model flexibility and data-handling ability means that the BJP modeling approach is potentially of wide practical application. The paper also presents a number of statistical measures and graphical methods for verification of probabilistic forecasts of continuous variables. Results for streamflows at three river gauges in the Murrumbidgee River catchment in southeast Australia show that the BJP modeling approach has good forecast quality and that the fitted model is consistent with observed data.

Stoffenmanager exposure model: company-specific exposure assessments using a Bayesian methodology.

PubMed

van de Ven, Peter; Fransman, Wouter; Schinkel, Jody; Rubingh, Carina; Warren, Nicholas; Tielemans, Erik

2010-04-01

The web-based tool "Stoffenmanager" was initially developed to assist small- and medium-sized enterprises in the Netherlands to make qualitative risk assessments and to provide advice on control at the workplace. The tool uses a mechanistic model to arrive at a "Stoffenmanager score" for exposure. In a recent study it was shown that variability in exposure measurements given a certain Stoffenmanager score is still substantial. This article discusses an extension to the tool that uses a Bayesian methodology for quantitative workplace/scenario-specific exposure assessment. This methodology allows for real exposure data observed in the company of interest to be combined with the prior estimate (based on the Stoffenmanager model). The output of the tool is a company-specific assessment of exposure levels for a scenario for which data is available. The Bayesian approach provides a transparent way of synthesizing different types of information and is especially preferred in situations where available data is sparse, as is often the case in small- and medium sized-enterprises. Real-world examples as well as simulation studies were used to assess how different parameters such as sample size, difference between prior and data, uncertainty in prior, and variance in the data affect the eventual posterior distribution of a Bayesian exposure assessment.

Development of reversible jump Markov Chain Monte Carlo algorithm in the Bayesian mixture modeling for microarray data in Indonesia

NASA Astrophysics Data System (ADS)

Astuti, Ani Budi; Iriawan, Nur; Irhamah, Kuswanto, Heri

2017-12-01

In the Bayesian mixture modeling requires stages the identification number of the most appropriate mixture components thus obtained mixture models fit the data through data driven concept. Reversible Jump Markov Chain Monte Carlo (RJMCMC) is a combination of the reversible jump (RJ) concept and the Markov Chain Monte Carlo (MCMC) concept used by some researchers to solve the problem of identifying the number of mixture components which are not known with certainty number. In its application, RJMCMC using the concept of the birth/death and the split-merge with six types of movement, that are w updating, θ updating, z updating, hyperparameter β updating, split-merge for components and birth/death from blank components. The development of the RJMCMC algorithm needs to be done according to the observed case. The purpose of this study is to know the performance of RJMCMC algorithm development in identifying the number of mixture components which are not known with certainty number in the Bayesian mixture modeling for microarray data in Indonesia. The results of this study represent that the concept RJMCMC algorithm development able to properly identify the number of mixture components in the Bayesian normal mixture model wherein the component mixture in the case of microarray data in Indonesia is not known for certain number.

Relating memory to functional performance in normal aging to dementia using hierarchical Bayesian cognitive processing models.

PubMed

Shankle, William R; Pooley, James P; Steyvers, Mark; Hara, Junko; Mangrola, Tushar; Reisberg, Barry; Lee, Michael D

2013-01-01

Determining how cognition affects functional abilities is important in Alzheimer disease and related disorders. A total of 280 patients (normal or Alzheimer disease and related disorders) received a total of 1514 assessments using the functional assessment staging test (FAST) procedure and the MCI Screen. A hierarchical Bayesian cognitive processing model was created by embedding a signal detection theory model of the MCI Screen-delayed recognition memory task into a hierarchical Bayesian framework. The signal detection theory model used latent parameters of discriminability (memory process) and response bias (executive function) to predict, simultaneously, recognition memory performance for each patient and each FAST severity group. The observed recognition memory data did not distinguish the 6 FAST severity stages, but the latent parameters completely separated them. The latent parameters were also used successfully to transform the ordinal FAST measure into a continuous measure reflecting the underlying continuum of functional severity. Hierarchical Bayesian cognitive processing models applied to recognition memory data from clinical practice settings accurately translated a latent measure of cognition into a continuous measure of functional severity for both individuals and FAST groups. Such a translation links 2 levels of brain information processing and may enable more accurate correlations with other levels, such as those characterized by biomarkers.

Optimal speech motor control and token-to-token variability: a Bayesian modeling approach.

PubMed

Patri, Jean-François; Diard, Julien; Perrier, Pascal

2015-12-01

The remarkable capacity of the speech motor system to adapt to various speech conditions is due to an excess of degrees of freedom, which enables producing similar acoustical properties with different sets of control strategies. To explain how the central nervous system selects one of the possible strategies, a common approach, in line with optimal motor control theories, is to model speech motor planning as the solution of an optimality problem based on cost functions. Despite the success of this approach, one of its drawbacks is the intrinsic contradiction between the concept of optimality and the observed experimental intra-speaker token-to-token variability. The present paper proposes an alternative approach by formulating feedforward optimal control in a probabilistic Bayesian modeling framework. This is illustrated by controlling a biomechanical model of the vocal tract for speech production and by comparing it with an existing optimal control model (GEPPETO). The essential elements of this optimal control model are presented first. From them the Bayesian model is constructed in a progressive way. Performance of the Bayesian model is evaluated based on computer simulations and compared to the optimal control model. This approach is shown to be appropriate for solving the speech planning problem while accounting for variability in a principled way.

Bayesian Inversion of 2D Models from Airborne Transient EM Data

NASA Astrophysics Data System (ADS)

Blatter, D. B.; Key, K.; Ray, A.

2016-12-01

The inherent non-uniqueness in most geophysical inverse problems leads to an infinite number of Earth models that fit observed data to within an adequate tolerance. To resolve this ambiguity, traditional inversion methods based on optimization techniques such as the Gauss-Newton and conjugate gradient methods rely on an additional regularization constraint on the properties that an acceptable model can possess, such as having minimal roughness. While allowing such an inversion scheme to converge on a solution, regularization makes it difficult to estimate the uncertainty associated with the model parameters. This is because regularization biases the inversion process toward certain models that satisfy the regularization constraint and away from others that don't, even when both may suitably fit the data. By contrast, a Bayesian inversion framework aims to produce not a single `most acceptable' model but an estimate of the posterior likelihood of the model parameters, given the observed data. In this work, we develop a 2D Bayesian framework for the inversion of transient electromagnetic (TEM) data. Our method relies on a reversible-jump Markov Chain Monte Carlo (RJ-MCMC) Bayesian inverse method with parallel tempering. Previous gradient-based inversion work in this area used a spatially constrained scheme wherein individual (1D) soundings were inverted together and non-uniqueness was tackled by using lateral and vertical smoothness constraints. By contrast, our work uses a 2D model space of Voronoi cells whose parameterization (including number of cells) is fully data-driven. To make the problem work practically, we approximate the forward solution for each TEM sounding using a local 1D approximation where the model is obtained from the 2D model by retrieving a vertical profile through the Voronoi cells. The implicit parsimony of the Bayesian inversion process leads to the simplest models that adequately explain the data, obviating the need for explicit smoothness constraints. In addition, credible intervals in model space are directly obtained, resolving some of the uncertainty introduced by regularization. An example application shows how the method can be used to quantify the uncertainty in airborne EM soundings for imaging subglacial brine channels and groundwater systems.

Bayesian classification for the selection of in vitro human embryos using morphological and clinical data.

PubMed

Morales, Dinora Araceli; Bengoetxea, Endika; Larrañaga, Pedro; García, Miguel; Franco, Yosu; Fresnada, Mónica; Merino, Marisa

2008-05-01

In vitro fertilization (IVF) is a medically assisted reproduction technique that enables infertile couples to achieve successful pregnancy. Given the uncertainty of the treatment, we propose an intelligent decision support system based on supervised classification by Bayesian classifiers to aid to the selection of the most promising embryos that will form the batch to be transferred to the woman's uterus. The aim of the supervised classification system is to improve overall success rate of each IVF treatment in which a batch of embryos is transferred each time, where the success is achieved when implantation (i.e. pregnancy) is obtained. Due to ethical reasons, different legislative restrictions apply in every country on this technique. In Spain, legislation allows a maximum of three embryos to form each transfer batch. As a result, clinicians prefer to select the embryos by non-invasive embryo examination based on simple methods and observation focused on morphology and dynamics of embryo development after fertilization. This paper proposes the application of Bayesian classifiers to this embryo selection problem in order to provide a decision support system that allows a more accurate selection than with the actual procedures which fully rely on the expertise and experience of embryologists. For this, we propose to take into consideration a reduced subset of feature variables related to embryo morphology and clinical data of patients, and from this data to induce Bayesian classification models. Results obtained applying a filter technique to choose the subset of variables, and the performance of Bayesian classifiers using them, are presented.

Tipping point analysis of atmospheric oxygen concentration

DOE Office of Scientific and Technical Information (OSTI.GOV)

Livina, V. N.; Forbes, A. B.; Vaz Martins, T. M.

2015-03-15

We apply tipping point analysis to nine observational oxygen concentration records around the globe, analyse their dynamics and perform projections under possible future scenarios, leading to oxygen deficiency in the atmosphere. The analysis is based on statistical physics framework with stochastic modelling, where we represent the observed data as a composition of deterministic and stochastic components estimated from the observed data using Bayesian and wavelet techniques.

Predicting ICU mortality: a comparison of stationary and nonstationary temporal models.

PubMed Central

Kayaalp, M.; Cooper, G. F.; Clermont, G.

2000-01-01

OBJECTIVE: This study evaluates the effectiveness of the stationarity assumption in predicting the mortality of intensive care unit (ICU) patients at the ICU discharge. DESIGN: This is a comparative study. A stationary temporal Bayesian network learned from data was compared to a set of (33) nonstationary temporal Bayesian networks learned from data. A process observed as a sequence of events is stationary if its stochastic properties stay the same when the sequence is shifted in a positive or negative direction by a constant time parameter. The temporal Bayesian networks forecast mortalities of patients, where each patient has one record per day. The predictive performance of the stationary model is compared with nonstationary models using the area under the receiver operating characteristics (ROC) curves. RESULTS: The stationary model usually performed best. However, one nonstationary model using large data sets performed significantly better than the stationary model. CONCLUSION: Results suggest that using a combination of stationary and nonstationary models may predict better than using either alone. PMID:11079917

Information-Based Analysis of Data Assimilation (Invited)

NASA Astrophysics Data System (ADS)

Nearing, G. S.; Gupta, H. V.; Crow, W. T.; Gong, W.

2013-12-01

Data assimilation is defined as the Bayesian conditioning of uncertain model simulations on observations for the purpose of reducing uncertainty about model states. Practical data assimilation methods make the application of Bayes' law tractable either by employing assumptions about the prior, posterior and likelihood distributions (e.g., the Kalman family of filters) or by using resampling methods (e.g., bootstrap filter). We propose to quantify the efficiency of these approximations in an OSSE setting using information theory and, in an OSSE or real-world validation setting, to measure the amount - and more importantly, the quality - of information extracted from observations during data assimilation. To analyze DA assumptions, uncertainty is quantified as the Shannon-type entropy of a discretized probability distribution. The maximum amount of information that can be extracted from observations about model states is the mutual information between states and observations, which is equal to the reduction in entropy in our estimate of the state due to Bayesian filtering. The difference between this potential and the actual reduction in entropy due to Kalman (or other type of) filtering measures the inefficiency of the filter assumptions. Residual uncertainty in DA posterior state estimates can be attributed to three sources: (i) non-injectivity of the observation operator, (ii) noise in the observations, and (iii) filter approximations. The contribution of each of these sources is measurable in an OSSE setting. The amount of information extracted from observations by data assimilation (or system identification, including parameter estimation) can also be measured by Shannon's theory. Since practical filters are approximations of Bayes' law, it is important to know whether the information that is extracted form observations by a filter is reliable. We define information as either good or bad, and propose to measure these two types of information using partial Kullback-Leibler divergences. Defined this way, good and bad information sum to total information. This segregation of information into good and bad components requires a validation target distribution; in a DA OSSE setting, this can be the true Bayesian posterior, but in a real-world setting the validation target might be determined by a set of in situ observations.

An algorithm that improves speech intelligibility in noise for normal-hearing listeners.

PubMed

Kim, Gibak; Lu, Yang; Hu, Yi; Loizou, Philipos C

2009-09-01

Traditional noise-suppression algorithms have been shown to improve speech quality, but not speech intelligibility. Motivated by prior intelligibility studies of speech synthesized using the ideal binary mask, an algorithm is proposed that decomposes the input signal into time-frequency (T-F) units and makes binary decisions, based on a Bayesian classifier, as to whether each T-F unit is dominated by the target or the masker. Speech corrupted at low signal-to-noise ratio (SNR) levels (-5 and 0 dB) using different types of maskers is synthesized by this algorithm and presented to normal-hearing listeners for identification. Results indicated substantial improvements in intelligibility (over 60% points in -5 dB babble) over that attained by human listeners with unprocessed stimuli. The findings from this study suggest that algorithms that can estimate reliably the SNR in each T-F unit can improve speech intelligibility.

Cognitive diagnosis modelling incorporating item response times.

PubMed

Zhan, Peida; Jiao, Hong; Liao, Dandan

2018-05-01

To provide more refined diagnostic feedback with collateral information in item response times (RTs), this study proposed joint modelling of attributes and response speed using item responses and RTs simultaneously for cognitive diagnosis. For illustration, an extended deterministic input, noisy 'and' gate (DINA) model was proposed for joint modelling of responses and RTs. Model parameter estimation was explored using the Bayesian Markov chain Monte Carlo (MCMC) method. The PISA 2012 computer-based mathematics data were analysed first. These real data estimates were treated as true values in a subsequent simulation study. A follow-up simulation study with ideal testing conditions was conducted as well to further evaluate model parameter recovery. The results indicated that model parameters could be well recovered using the MCMC approach. Further, incorporating RTs into the DINA model would improve attribute and profile correct classification rates and result in more accurate and precise estimation of the model parameters. © 2017 The British Psychological Society.

Stepwise and stagewise approaches for spatial cluster detection

PubMed Central

Xu, Jiale

2016-01-01

Spatial cluster detection is an important tool in many areas such as sociology, botany and public health. Previous work has mostly taken either hypothesis testing framework or Bayesian framework. In this paper, we propose a few approaches under a frequentist variable selection framework for spatial cluster detection. The forward stepwise methods search for multiple clusters by iteratively adding currently most likely cluster while adjusting for the effects of previously identified clusters. The stagewise methods also consist of a series of steps, but with tiny step size in each iteration. We study the features and performances of our proposed methods using simulations on idealized grids or real geographic area. From the simulations, we compare the performance of the proposed methods in terms of estimation accuracy and power of detections. These methods are applied to the the well-known New York leukemia data as well as Indiana poverty data. PMID:27246273

Stepwise and stagewise approaches for spatial cluster detection.

PubMed

Xu, Jiale; Gangnon, Ronald E

2016-05-01

Spatial cluster detection is an important tool in many areas such as sociology, botany and public health. Previous work has mostly taken either a hypothesis testing framework or a Bayesian framework. In this paper, we propose a few approaches under a frequentist variable selection framework for spatial cluster detection. The forward stepwise methods search for multiple clusters by iteratively adding currently most likely cluster while adjusting for the effects of previously identified clusters. The stagewise methods also consist of a series of steps, but with a tiny step size in each iteration. We study the features and performances of our proposed methods using simulations on idealized grids or real geographic areas. From the simulations, we compare the performance of the proposed methods in terms of estimation accuracy and power. These methods are applied to the the well-known New York leukemia data as well as Indiana poverty data. Copyright © 2016 Elsevier Ltd. All rights reserved.

Extracting Prior Distributions from a Large Dataset of In-Situ Measurements to Support SWOT-based Estimation of River Discharge

NASA Astrophysics Data System (ADS)

Hagemann, M.; Gleason, C. J.

2017-12-01

The upcoming (2021) Surface Water and Ocean Topography (SWOT) NASA satellite mission aims, in part, to estimate discharge on major rivers worldwide using reach-scale measurements of stream width, slope, and height. Current formalizations of channel and floodplain hydraulics are insufficient to fully constrain this problem mathematically, resulting in an infinitely large solution set for any set of satellite observations. Recent work has reformulated this problem in a Bayesian statistical setting, in which the likelihood distributions derive directly from hydraulic flow-law equations. When coupled with prior distributions on unknown flow-law parameters, this formulation probabilistically constrains the parameter space, and results in a computationally tractable description of discharge. Using a curated dataset of over 200,000 in-situ acoustic Doppler current profiler (ADCP) discharge measurements from over 10,000 USGS gaging stations throughout the United States, we developed empirical prior distributions for flow-law parameters that are not observable by SWOT, but that are required in order to estimate discharge. This analysis quantified prior uncertainties on quantities including cross-sectional area, at-a-station hydraulic geometry width exponent, and discharge variability, that are dependent on SWOT-observable variables including reach-scale statistics of width and height. When compared against discharge estimation approaches that do not use this prior information, the Bayesian approach using ADCP-derived priors demonstrated consistently improved performance across a range of performance metrics. This Bayesian approach formally transfers information from in-situ gaging stations to remote-sensed estimation of discharge, in which the desired quantities are not directly observable. Further investigation using large in-situ datasets is therefore a promising way forward in improving satellite-based estimates of river discharge.

Inverse modeling of hydrologic parameters using surface flux and runoff observations in the Community Land Model

NASA Astrophysics Data System (ADS)

Sun, Y.; Hou, Z.; Huang, M.; Tian, F.; Leung, L. Ruby

2013-12-01

This study demonstrates the possibility of inverting hydrologic parameters using surface flux and runoff observations in version 4 of the Community Land Model (CLM4). Previous studies showed that surface flux and runoff calculations are sensitive to major hydrologic parameters in CLM4 over different watersheds, and illustrated the necessity and possibility of parameter calibration. Both deterministic least-square fitting and stochastic Markov-chain Monte Carlo (MCMC)-Bayesian inversion approaches are evaluated by applying them to CLM4 at selected sites with different climate and soil conditions. The unknowns to be estimated include surface and subsurface runoff generation parameters and vadose zone soil water parameters. We find that using model parameters calibrated by the sampling-based stochastic inversion approaches provides significant improvements in the model simulations compared to using default CLM4 parameter values, and that as more information comes in, the predictive intervals (ranges of posterior distributions) of the calibrated parameters become narrower. In general, parameters that are identified to be significant through sensitivity analyses and statistical tests are better calibrated than those with weak or nonlinear impacts on flux or runoff observations. Temporal resolution of observations has larger impacts on the results of inverse modeling using heat flux data than runoff data. Soil and vegetation cover have important impacts on parameter sensitivities, leading to different patterns of posterior distributions of parameters at different sites. Overall, the MCMC-Bayesian inversion approach effectively and reliably improves the simulation of CLM under different climates and environmental conditions. Bayesian model averaging of the posterior estimates with different reference acceptance probabilities can smooth the posterior distribution and provide more reliable parameter estimates, but at the expense of wider uncertainty bounds.

Sparsely sampling the sky: a Bayesian experimental design approach

NASA Astrophysics Data System (ADS)

Paykari, P.; Jaffe, A. H.

2013-08-01

The next generation of galaxy surveys will observe millions of galaxies over large volumes of the Universe. These surveys are expensive both in time and cost, raising questions regarding the optimal investment of this time and money. In this work, we investigate criteria for selecting amongst observing strategies for constraining the galaxy power spectrum and a set of cosmological parameters. Depending on the parameters of interest, it may be more efficient to observe a larger, but sparsely sampled, area of sky instead of a smaller contiguous area. In this work, by making use of the principles of Bayesian experimental design, we will investigate the advantages and disadvantages of the sparse sampling of the sky and discuss the circumstances in which a sparse survey is indeed the most efficient strategy. For the Dark Energy Survey (DES), we find that by sparsely observing the same area in a smaller amount of time, we only increase the errors on the parameters by a maximum of 0.45 per cent. Conversely, investing the same amount of time as the original DES to observe a sparser but larger area of sky, we can in fact constrain the parameters with errors reduced by 28 per cent.

A Bayesian Approach to Evaluating Consistency between Climate Model Output and Observations

NASA Astrophysics Data System (ADS)

Braverman, A. J.; Cressie, N.; Teixeira, J.

2010-12-01

Like other scientific and engineering problems that involve physical modeling of complex systems, climate models can be evaluated and diagnosed by comparing their output to observations of similar quantities. Though the global remote sensing data record is relatively short by climate research standards, these data offer opportunities to evaluate model predictions in new ways. For example, remote sensing data are spatially and temporally dense enough to provide distributional information that goes beyond simple moments to allow quantification of temporal and spatial dependence structures. In this talk, we propose a new method for exploiting these rich data sets using a Bayesian paradigm. For a collection of climate models, we calculate posterior probabilities its members best represent the physical system each seeks to reproduce. The posterior probability is based on the likelihood that a chosen summary statistic, computed from observations, would be obtained when the model's output is considered as a realization from a stochastic process. By exploring how posterior probabilities change with different statistics, we may paint a more quantitative and complete picture of the strengths and weaknesses of the models relative to the observations. We demonstrate our method using model output from the CMIP archive, and observations from NASA's Atmospheric Infrared Sounder.

Adaptive selection and validation of models of complex systems in the presence of uncertainty

DOE Office of Scientific and Technical Information (OSTI.GOV)

Farrell-Maupin, Kathryn; Oden, J. T.

This study describes versions of OPAL, the Occam-Plausibility Algorithm in which the use of Bayesian model plausibilities is replaced with information theoretic methods, such as the Akaike Information Criterion and the Bayes Information Criterion. Applications to complex systems of coarse-grained molecular models approximating atomistic models of polyethylene materials are described. All of these model selection methods take into account uncertainties in the model, the observational data, the model parameters, and the predicted quantities of interest. A comparison of the models chosen by Bayesian model selection criteria and those chosen by the information-theoretic criteria is given.

Spectral Analysis of B Stars: An Application of Bayesian Statistics

NASA Astrophysics Data System (ADS)

Mugnes, J.-M.; Robert, C.

2012-12-01

To better understand the processes involved in stellar physics, it is necessary to obtain accurate stellar parameters (effective temperature, surface gravity, abundances…). Spectral analysis is a powerful tool for investigating stars, but it is also vital to reduce uncertainties at a decent computational cost. Here we present a spectral analysis method based on a combination of Bayesian statistics and grids of synthetic spectra obtained with TLUSTY. This method simultaneously constrains the stellar parameters by using all the lines accessible in observed spectra and thus greatly reduces uncertainties and improves the overall spectrum fitting. Preliminary results are shown using spectra from the Observatoire du Mont-Mégantic.

Bayesian model for matching the radiometric measurements of aerospace and field ocean color sensors.

PubMed

Salama, Mhd Suhyb; Su, Zhongbo

2010-01-01

A Bayesian model is developed to match aerospace ocean color observation to field measurements and derive the spatial variability of match-up sites. The performance of the model is tested against populations of synthesized spectra and full and reduced resolutions of MERIS data. The model derived the scale difference between synthesized satellite pixel and point measurements with R(2) > 0.88 and relative error < 21% in the spectral range from 400 nm to 695 nm. The sub-pixel variabilities of reduced resolution MERIS image are derived with less than 12% of relative errors in heterogeneous region. The method is generic and applicable to different sensors.

Adaptive selection and validation of models of complex systems in the presence of uncertainty

DOE PAGES

Farrell-Maupin, Kathryn; Oden, J. T.

2017-08-01

This study describes versions of OPAL, the Occam-Plausibility Algorithm in which the use of Bayesian model plausibilities is replaced with information theoretic methods, such as the Akaike Information Criterion and the Bayes Information Criterion. Applications to complex systems of coarse-grained molecular models approximating atomistic models of polyethylene materials are described. All of these model selection methods take into account uncertainties in the model, the observational data, the model parameters, and the predicted quantities of interest. A comparison of the models chosen by Bayesian model selection criteria and those chosen by the information-theoretic criteria is given.

From bridewealth to dowry? : A bayesian estimation of ancestral states of marriage transfers in Indo-European groups.

PubMed

Fortunato, Laura; Holden, Clare; Mace, Ruth

2006-12-01

Significant amounts of wealth have been exchanged as part of marriage settlements throughout history. Although various models have been proposed for interpreting these practices, their development over time has not been investigated systematically. In this paper we use a Bayesian MCMC phylogenetic comparative approach to reconstruct the evolution of two forms of wealth transfers at marriage, dowry and bridewealth, for 51 Indo-European cultural groups. Results indicate that dowry is more likely to have been the ancestral practice, and that a minimum of four changes to bridewealth is necessary to explain the observed distribution of the two states across the cultural groups.

IMAGINE: Interstellar MAGnetic field INference Engine

NASA Astrophysics Data System (ADS)

Steininger, Theo

2018-03-01

IMAGINE (Interstellar MAGnetic field INference Engine) performs inference on generic parametric models of the Galaxy. The modular open source framework uses highly optimized tools and technology such as the MultiNest sampler (ascl:1109.006) and the information field theory framework NIFTy (ascl:1302.013) to create an instance of the Milky Way based on a set of parameters for physical observables, using Bayesian statistics to judge the mismatch between measured data and model prediction. The flexibility of the IMAGINE framework allows for simple refitting for newly available data sets and makes state-of-the-art Bayesian methods easily accessible particularly for random components of the Galactic magnetic field.

The equivalence of a human observer and an ideal observer in binary diagnostic tasks

NASA Astrophysics Data System (ADS)

He, Xin; Samuelson, Frank; Gallas, Brandon D.; Sahiner, Berkman; Myers, Kyle

2013-03-01

The Ideal Observer (IO) is "ideal" for given data populations. In the image perception process, as the raw images are degraded by factors such as display and eye optics, there is an equivalent IO (EIO). The EIO uses the statistical information that exits the perception/cognitive degradations as the data. We assume a human observer who received sufficient training, e.g., radiologists, and hypothesize that such a human observer can be modeled as if he is an EIO. To measure the likelihood ratio (LR) distributions of an EIO, we formalize experimental design principles that encourage rationality based on von Neumann and Morgenstern's (vNM) axioms. We present examples to show that many observer study design refinements, although motivated by empirical principles explicitly, implicitly encourage rationality. Our hypothesis is supported by a recent review paper on ROC curve convexity by Pesce, Metz, and Berbaum. We also provide additional evidence based on a collection of observer studies in medical imaging. EIO theory shows that the "sub-optimal" performance of a human observer can be mathematically formalized in the form of an IO, and measured through rationality encouragement.

A menu-driven software package of Bayesian nonparametric (and parametric) mixed models for regression analysis and density estimation.

PubMed

Karabatsos, George

2017-02-01

Most of applied statistics involves regression analysis of data. In practice, it is important to specify a regression model that has minimal assumptions which are not violated by data, to ensure that statistical inferences from the model are informative and not misleading. This paper presents a stand-alone and menu-driven software package, Bayesian Regression: Nonparametric and Parametric Models, constructed from MATLAB Compiler. Currently, this package gives the user a choice from 83 Bayesian models for data analysis. They include 47 Bayesian nonparametric (BNP) infinite-mixture regression models; 5 BNP infinite-mixture models for density estimation; and 31 normal random effects models (HLMs), including normal linear models. Each of the 78 regression models handles either a continuous, binary, or ordinal dependent variable, and can handle multi-level (grouped) data. All 83 Bayesian models can handle the analysis of weighted observations (e.g., for meta-analysis), and the analysis of left-censored, right-censored, and/or interval-censored data. Each BNP infinite-mixture model has a mixture distribution assigned one of various BNP prior distributions, including priors defined by either the Dirichlet process, Pitman-Yor process (including the normalized stable process), beta (two-parameter) process, normalized inverse-Gaussian process, geometric weights prior, dependent Dirichlet process, or the dependent infinite-probits prior. The software user can mouse-click to select a Bayesian model and perform data analysis via Markov chain Monte Carlo (MCMC) sampling. After the sampling completes, the software automatically opens text output that reports MCMC-based estimates of the model's posterior distribution and model predictive fit to the data. Additional text and/or graphical output can be generated by mouse-clicking other menu options. This includes output of MCMC convergence analyses, and estimates of the model's posterior predictive distribution, for selected functionals and values of covariates. The software is illustrated through the BNP regression analysis of real data.

Do the Particles of an Ideal Gas Collide?

ERIC Educational Resources Information Center

Lesk, Arthur M.

1974-01-01

Describes the collisional properties as a logically essential component of the ideal gas model since an actual intraparticle process cannot support observable anisotropic velocity distributions without collisions taken into account. (CC)

UNITY: Confronting Supernova Cosmology's Statistical and Systematic Uncertainties in a Unified Bayesian Framework

NASA Astrophysics Data System (ADS)

Rubin, D.; Aldering, G.; Barbary, K.; Boone, K.; Chappell, G.; Currie, M.; Deustua, S.; Fagrelius, P.; Fruchter, A.; Hayden, B.; Lidman, C.; Nordin, J.; Perlmutter, S.; Saunders, C.; Sofiatti, C.; Supernova Cosmology Project, The

2015-11-01

While recent supernova (SN) cosmology research has benefited from improved measurements, current analysis approaches are not statistically optimal and will prove insufficient for future surveys. This paper discusses the limitations of current SN cosmological analyses in treating outliers, selection effects, shape- and color-standardization relations, unexplained dispersion, and heterogeneous observations. We present a new Bayesian framework, called UNITY (Unified Nonlinear Inference for Type-Ia cosmologY), that incorporates significant improvements in our ability to confront these effects. We apply the framework to real SN observations and demonstrate smaller statistical and systematic uncertainties. We verify earlier results that SNe Ia require nonlinear shape and color standardizations, but we now include these nonlinear relations in a statistically well-justified way. This analysis was primarily performed blinded, in that the basic framework was first validated on simulated data before transitioning to real data. We also discuss possible extensions of the method.

Sensitivity analyses for sparse-data problems-using weakly informative bayesian priors.

PubMed

Hamra, Ghassan B; MacLehose, Richard F; Cole, Stephen R

2013-03-01

Sparse-data problems are common, and approaches are needed to evaluate the sensitivity of parameter estimates based on sparse data. We propose a Bayesian approach that uses weakly informative priors to quantify sensitivity of parameters to sparse data. The weakly informative prior is based on accumulated evidence regarding the expected magnitude of relationships using relative measures of disease association. We illustrate the use of weakly informative priors with an example of the association of lifetime alcohol consumption and head and neck cancer. When data are sparse and the observed information is weak, a weakly informative prior will shrink parameter estimates toward the prior mean. Additionally, the example shows that when data are not sparse and the observed information is not weak, a weakly informative prior is not influential. Advancements in implementation of Markov Chain Monte Carlo simulation make this sensitivity analysis easily accessible to the practicing epidemiologist.

Sensitivity Analyses for Sparse-Data Problems—Using Weakly Informative Bayesian Priors

PubMed Central

Hamra, Ghassan B.; MacLehose, Richard F.; Cole, Stephen R.

2013-01-01

Sparse-data problems are common, and approaches are needed to evaluate the sensitivity of parameter estimates based on sparse data. We propose a Bayesian approach that uses weakly informative priors to quantify sensitivity of parameters to sparse data. The weakly informative prior is based on accumulated evidence regarding the expected magnitude of relationships using relative measures of disease association. We illustrate the use of weakly informative priors with an example of the association of lifetime alcohol consumption and head and neck cancer. When data are sparse and the observed information is weak, a weakly informative prior will shrink parameter estimates toward the prior mean. Additionally, the example shows that when data are not sparse and the observed information is not weak, a weakly informative prior is not influential. Advancements in implementation of Markov Chain Monte Carlo simulation make this sensitivity analysis easily accessible to the practicing epidemiologist. PMID:23337241

Implementation of a Bayesian design in a dose-escalation study of an experimental agent in healthy volunteers.

PubMed

Zhou, Yinghui; Whitehead, John; Korhonen, Pasi; Mustonen, Mika

2008-03-01

Bayesian decision procedures have recently been developed for dose escalation in phase I clinical trials concerning pharmacokinetic responses observed in healthy volunteers. This article describes how that general methodology was extended and evaluated for implementation in a specific phase I trial of a novel compound. At the time of writing, the study is ongoing, and it will be some time before the sponsor will wish to put the results into the public domain. This article is an account of how the study was designed in a way that should prove to be safe, accurate, and efficient whatever the true nature of the compound. The study involves the observation of two pharmacokinetic endpoints relating to the plasma concentration of the compound itself and of a metabolite as well as a safety endpoint relating to the occurrence of adverse events. Construction of the design and its evaluation via simulation are presented.

Optical+Near-IR Bayesian Classification of Quasars

NASA Astrophysics Data System (ADS)

Mehta, Sajjan S.; Richards, G. T.; Myers, A. D.

2011-05-01

We describe the details of an optimal Bayesian classification of quasars with combined optical+near-IR photometry from the SDSS and UKIDSS LAS surveys. Using only deep co-added SDSS photometry from the "Stripe 82" region and requiring full four-band UKIDSS detections, we reliably identify 2665 quasar candidates with a computed efficiency in excess of 99%. Relaxing the data constraints to combinations of two-band detections yields up to 6424 candidates with minimal trade-off in completeness and efficiency. The completeness and efficiency of the sample are investigated with existing spectra from the SDSS, 2SLAQ, and AUS surveys in addition to recent single-slit observations from Palomar Observatory, which revealed 22 quasars from a subsample of 29 high-z candidates. SDSS-III/BOSS observations will allow further exploration of the completeness/efficiency of the sample over 2.2

Combination of dynamic Bayesian network classifiers for the recognition of degraded characters

NASA Astrophysics Data System (ADS)

Likforman-Sulem, Laurence; Sigelle, Marc

2009-01-01

We investigate in this paper the combination of DBN (Dynamic Bayesian Network) classifiers, either independent or coupled, for the recognition of degraded characters. The independent classifiers are a vertical HMM and a horizontal HMM whose observable outputs are the image columns and the image rows respectively. The coupled classifiers, presented in a previous study, associate the vertical and horizontal observation streams into single DBNs. The scores of the independent and coupled classifiers are then combined linearly at the decision level. We compare the different classifiers -independent, coupled or linearly combined- on two tasks: the recognition of artificially degraded handwritten digits and the recognition of real degraded old printed characters. Our results show that coupled DBNs perform better on degraded characters than the linear combination of independent HMM scores. Our results also show that the best classifier is obtained by linearly combining the scores of the best coupled DBN and the best independent HMM.

Determining open cluster membership. A Bayesian framework for quantitative member classification

NASA Astrophysics Data System (ADS)

Stott, Jonathan J.

2018-01-01

Aims: My goal is to develop a quantitative algorithm for assessing open cluster membership probabilities. The algorithm is designed to work with single-epoch observations. In its simplest form, only one set of program images and one set of reference images are required. Methods: The algorithm is based on a two-stage joint astrometric and photometric assessment of cluster membership probabilities. The probabilities were computed within a Bayesian framework using any available prior information. Where possible, the algorithm emphasizes simplicity over mathematical sophistication. Results: The algorithm was implemented and tested against three observational fields using published survey data. M 67 and NGC 654 were selected as cluster examples while a third, cluster-free, field was used for the final test data set. The algorithm shows good quantitative agreement with the existing surveys and has a false-positive rate significantly lower than the astrometric or photometric methods used individually.

The development of a probabilistic approach to forecast coastal change

USGS Publications Warehouse

Lentz, Erika E.; Hapke, Cheryl J.; Rosati, Julie D.; Wang, Ping; Roberts, Tiffany M.

2011-01-01

This study demonstrates the applicability of a Bayesian probabilistic model as an effective tool in predicting post-storm beach changes along sandy coastlines. Volume change and net shoreline movement are modeled for two study sites at Fire Island, New York in response to two extratropical storms in 2007 and 2009. Both study areas include modified areas adjacent to unmodified areas in morphologically different segments of coast. Predicted outcomes are evaluated against observed changes to test model accuracy and uncertainty along 163 cross-shore transects. Results show strong agreement in the cross validation of predictions vs. observations, with 70-82% accuracies reported. Although no consistent spatial pattern in inaccurate predictions could be determined, the highest prediction uncertainties appeared in locations that had been recently replenished. Further testing and model refinement are needed; however, these initial results show that Bayesian networks have the potential to serve as important decision-support tools in forecasting coastal change.

A dust spectral energy distribution model with hierarchical Bayesian inference - I. Formalism and benchmarking

NASA Astrophysics Data System (ADS)

Galliano, Frédéric

2018-05-01

This article presents a new dust spectral energy distribution (SED) model, named HerBIE, aimed at eliminating the noise-induced correlations and large scatter obtained when performing least-squares fits. The originality of this code is to apply the hierarchical Bayesian approach to full dust models, including realistic optical properties, stochastic heating, and the mixing of physical conditions in the observed regions. We test the performances of our model by applying it to synthetic observations. We explore the impact on the recovered parameters of several effects: signal-to-noise ratio, SED shape, sample size, the presence of intrinsic correlations, the wavelength coverage, and the use of different SED model components. We show that this method is very efficient: the recovered parameters are consistently distributed around their true values. We do not find any clear bias, even for the most degenerate parameters, or with extreme signal-to-noise ratios.

Fermi's paradox, extraterrestrial life and the future of humanity: a Bayesian analysis

NASA Astrophysics Data System (ADS)

Verendel, Vilhelm; Häggström, Olle

2017-01-01

The Great Filter interpretation of Fermi's great silence asserts that Npq is not a very large number, where N is the number of potentially life-supporting planets in the observable universe, p is the probability that a randomly chosen such planet develops intelligent life to the level of present-day human civilization, and q is the conditional probability that it then goes on to develop a technological supercivilization visible all over the observable universe. Evidence suggests that N is huge, which implies that pq is very small. Hanson (1998) and Bostrom (2008) have argued that the discovery of extraterrestrial life would point towards p not being small and therefore a very small q, which can be seen as bad news for humanity's prospects of colonizing the universe. Here we investigate whether a Bayesian analysis supports their argument, and the answer turns out to depend critically on the choice of prior distribution.

Context Effects in Multi-Alternative Decision Making: Empirical Data and a Bayesian Model

ERIC Educational Resources Information Center

Hawkins, Guy; Brown, Scott D.; Steyvers, Mark; Wagenmakers, Eric-Jan

2012-01-01

For decisions between many alternatives, the benchmark result is Hick's Law: that response time increases log-linearly with the number of choice alternatives. Even when Hick's Law is observed for response times, divergent results have been observed for error rates--sometimes error rates increase with the number of choice alternatives, and…

A simple parametric model observer for quality assurance in computer tomography

NASA Astrophysics Data System (ADS)

Anton, M.; Khanin, A.; Kretz, T.; Reginatto, M.; Elster, C.

2018-04-01

Model observers are mathematical classifiers that are used for the quality assessment of imaging systems such as computer tomography. The quality of the imaging system is quantified by means of the performance of a selected model observer. For binary classification tasks, the performance of the model observer is defined by the area under its ROC curve (AUC). Typically, the AUC is estimated by applying the model observer to a large set of training and test data. However, the recording of these large data sets is not always practical for routine quality assurance. In this paper we propose as an alternative a parametric model observer that is based on a simple phantom, and we provide a Bayesian estimation of its AUC. It is shown that a limited number of repeatedly recorded images (10–15) is already sufficient to obtain results suitable for the quality assessment of an imaging system. A MATLAB® function is provided for the calculation of the results. The performance of the proposed model observer is compared to that of the established channelized Hotelling observer and the nonprewhitening matched filter for simulated images as well as for images obtained from a low-contrast phantom on an x-ray tomography scanner. The results suggest that the proposed parametric model observer, along with its Bayesian treatment, can provide an efficient, practical alternative for the quality assessment of CT imaging systems.

Model Diagnostics for Bayesian Networks

ERIC Educational Resources Information Center

Sinharay, Sandip

2006-01-01

Bayesian networks are frequently used in educational assessments primarily for learning about students' knowledge and skills. There is a lack of works on assessing fit of Bayesian networks. This article employs the posterior predictive model checking method, a popular Bayesian model checking tool, to assess fit of simple Bayesian networks. A…

A Gentle Introduction to Bayesian Analysis: Applications to Developmental Research

PubMed Central

van de Schoot, Rens; Kaplan, David; Denissen, Jaap; Asendorpf, Jens B; Neyer, Franz J; van Aken, Marcel AG

2014-01-01

Bayesian statistical methods are becoming ever more popular in applied and fundamental research. In this study a gentle introduction to Bayesian analysis is provided. It is shown under what circumstances it is attractive to use Bayesian estimation, and how to interpret properly the results. First, the ingredients underlying Bayesian methods are introduced using a simplified example. Thereafter, the advantages and pitfalls of the specification of prior knowledge are discussed. To illustrate Bayesian methods explained in this study, in a second example a series of studies that examine the theoretical framework of dynamic interactionism are considered. In the Discussion the advantages and disadvantages of using Bayesian statistics are reviewed, and guidelines on how to report on Bayesian statistics are provided. PMID:24116396

On the predictive information criteria for model determination in seismic hazard analysis

NASA Astrophysics Data System (ADS)

Varini, Elisa; Rotondi, Renata

2016-04-01

Many statistical tools have been developed for evaluating, understanding, and comparing models, from both frequentist and Bayesian perspectives. In particular, the problem of model selection can be addressed according to whether the primary goal is explanation or, alternatively, prediction. In the former case, the criteria for model selection are defined over the parameter space whose physical interpretation can be difficult; in the latter case, they are defined over the space of the observations, which has a more direct physical meaning. In the frequentist approaches, model selection is generally based on an asymptotic approximation which may be poor for small data sets (e.g. the F-test, the Kolmogorov-Smirnov test, etc.); moreover, these methods often apply under specific assumptions on models (e.g. models have to be nested in the likelihood ratio test). In the Bayesian context, among the criteria for explanation, the ratio of the observed marginal densities for two competing models, named Bayes Factor (BF), is commonly used for both model choice and model averaging (Kass and Raftery, J. Am. Stat. Ass., 1995). But BF does not apply to improper priors and, even when the prior is proper, it is not robust to the specification of the prior. These limitations can be extended to two famous penalized likelihood methods as the Akaike Information Criterion (AIC) and the Bayesian Information Criterion (BIC), since they are proved to be approximations of -2log BF . In the perspective that a model is as good as its predictions, the predictive information criteria aim at evaluating the predictive accuracy of Bayesian models or, in other words, at estimating expected out-of-sample prediction error using a bias-correction adjustment of within-sample error (Gelman et al., Stat. Comput., 2014). In particular, the Watanabe criterion is fully Bayesian because it averages the predictive distribution over the posterior distribution of parameters rather than conditioning on a point estimate, but it is hardly applicable to data which are not independent given parameters (Watanabe, J. Mach. Learn. Res., 2010). A solution is given by Ando and Tsay criterion where the joint density may be decomposed into the product of the conditional densities (Ando and Tsay, Int. J. Forecast., 2010). The above mentioned criteria are global summary measures of model performance, but more detailed analysis could be required to discover the reasons for poor global performance. In this latter case, a retrospective predictive analysis is performed on each individual observation. In this study we performed the Bayesian analysis of Italian data sets by four versions of a long-term hazard model known as the stress release model (Vere-Jones, J. Physics Earth, 1978; Bebbington and Harte, Geophys. J. Int., 2003; Varini and Rotondi, Environ. Ecol. Stat., 2015). Then we illustrate the results on their performance evaluated by Bayes Factor, predictive information criteria and retrospective predictive analysis.

Toward improved prediction of the bedrock depth underneath hillslopes: Bayesian inference of the bottom-up control hypothesis using high-resolution topographic data

NASA Astrophysics Data System (ADS)

Gomes, Guilherme J. C.; Vrugt, Jasper A.; Vargas, Eurípedes A.

2016-04-01

The depth to bedrock controls a myriad of processes by influencing subsurface flow paths, erosion rates, soil moisture, and water uptake by plant roots. As hillslope interiors are very difficult and costly to illuminate and access, the topography of the bedrock surface is largely unknown. This essay is concerned with the prediction of spatial patterns in the depth to bedrock (DTB) using high-resolution topographic data, numerical modeling, and Bayesian analysis. Our DTB model builds on the bottom-up control on fresh-bedrock topography hypothesis of Rempe and Dietrich (2014) and includes a mass movement and bedrock-valley morphology term to extent the usefulness and general applicability of the model. We reconcile the DTB model with field observations using Bayesian analysis with the DREAM algorithm. We investigate explicitly the benefits of using spatially distributed parameter values to account implicitly, and in a relatively simple way, for rock mass heterogeneities that are very difficult, if not impossible, to characterize adequately in the field. We illustrate our method using an artificial data set of bedrock depth observations and then evaluate our DTB model with real-world data collected at the Papagaio river basin in Rio de Janeiro, Brazil. Our results demonstrate that the DTB model predicts accurately the observed bedrock depth data. The posterior mean DTB simulation is shown to be in good agreement with the measured data. The posterior prediction uncertainty of the DTB model can be propagated forward through hydromechanical models to derive probabilistic estimates of factors of safety.

Observations of density fluctuations in an elongated Bose gas: ideal gas and quasicondensate regimes.

PubMed

Esteve, J; Trebbia, J-B; Schumm, T; Aspect, A; Westbrook, C I; Bouchoule, I

2006-04-07

We report in situ measurements of density fluctuations in a quasi-one-dimensional 87Rb Bose gas at thermal equilibrium in an elongated harmonic trap. We observe an excess of fluctuations compared to the shot-noise level expected for uncorrelated atoms. At low atomic density, the measured excess is in good agreement with the expected "bunching" for an ideal Bose gas. At high density, the measured fluctuations are strongly reduced compared to the ideal gas case. We attribute this reduction to repulsive interatomic interactions. The data are compared with a calculation for an interacting Bose gas in the quasicondensate regime.

A Gentle Introduction to Bayesian Analysis: Applications to Developmental Research

ERIC Educational Resources Information Center

van de Schoot, Rens; Kaplan, David; Denissen, Jaap; Asendorpf, Jens B.; Neyer, Franz J.; van Aken, Marcel A. G.

2014-01-01

Bayesian statistical methods are becoming ever more popular in applied and fundamental research. In this study a gentle introduction to Bayesian analysis is provided. It is shown under what circumstances it is attractive to use Bayesian estimation, and how to interpret properly the results. First, the ingredients underlying Bayesian methods are…

Bayesian correction for covariate measurement error: A frequentist evaluation and comparison with regression calibration.

PubMed

Bartlett, Jonathan W; Keogh, Ruth H

2018-06-01

Bayesian approaches for handling covariate measurement error are well established and yet arguably are still relatively little used by researchers. For some this is likely due to unfamiliarity or disagreement with the Bayesian inferential paradigm. For others a contributory factor is the inability of standard statistical packages to perform such Bayesian analyses. In this paper, we first give an overview of the Bayesian approach to handling covariate measurement error, and contrast it with regression calibration, arguably the most commonly adopted approach. We then argue why the Bayesian approach has a number of statistical advantages compared to regression calibration and demonstrate that implementing the Bayesian approach is usually quite feasible for the analyst. Next, we describe the closely related maximum likelihood and multiple imputation approaches and explain why we believe the Bayesian approach to generally be preferable. We then empirically compare the frequentist properties of regression calibration and the Bayesian approach through simulation studies. The flexibility of the Bayesian approach to handle both measurement error and missing data is then illustrated through an analysis of data from the Third National Health and Nutrition Examination Survey.

On parametrized cold dense matter equation-of-state inference

NASA Astrophysics Data System (ADS)

Riley, Thomas E.; Raaijmakers, Geert; Watts, Anna L.

2018-07-01

Constraining the equation of state of cold dense matter in compact stars is a major science goal for observing programmes being conducted using X-ray, radio, and gravitational wave telescopes. We discuss Bayesian hierarchical inference of parametrized dense matter equations of state. In particular, we generalize and examine two inference paradigms from the literature: (i) direct posterior equation-of-state parameter estimation, conditioned on observations of a set of rotating compact stars; and (ii) indirect parameter estimation, via transformation of an intermediary joint posterior distribution of exterior spacetime parameters (such as gravitational masses and coordinate equatorial radii). We conclude that the former paradigm is not only tractable for large-scale analyses, but is principled and flexible from a Bayesian perspective while the latter paradigm is not. The thematic problem of Bayesian prior definition emerges as the crux of the difference between these paradigms. The second paradigm should in general only be considered as an ill-defined approach to the problem of utilizing archival posterior constraints on exterior spacetime parameters; we advocate for an alternative approach whereby such information is repurposed as an approximative likelihood function. We also discuss why conditioning on a piecewise-polytropic equation-of-state model - currently standard in the field of dense matter study - can easily violate conditions required for transformation of a probability density distribution between spaces of exterior (spacetime) and interior (source matter) parameters.

Efficiency of nuclear and mitochondrial markers recovering and supporting known amniote groups.

PubMed

Lambret-Frotté, Julia; Perini, Fernando Araújo; de Moraes Russo, Claudia Augusta

2012-01-01

We have analysed the efficiency of all mitochondrial protein coding genes and six nuclear markers (Adora3, Adrb2, Bdnf, Irbp, Rag2 and Vwf) in reconstructing and statistically supporting known amniote groups (murines, rodents, primates, eutherians, metatherians, therians). The efficiencies of maximum likelihood, Bayesian inference, maximum parsimony, neighbor-joining and UPGMA were also evaluated, by assessing the number of correct and incorrect recovered groupings. In addition, we have compared support values using the conservative bootstrap test and the Bayesian posterior probabilities. First, no correlation was observed between gene size and marker efficiency in recovering or supporting correct nodes. As expected, tree-building methods performed similarly, even UPGMA that, in some cases, outperformed other most extensively used methods. Bayesian posterior probabilities tend to show much higher support values than the conservative bootstrap test, for correct and incorrect nodes. Our results also suggest that nuclear markers do not necessarily show a better performance than mitochondrial genes. The so-called dependency among mitochondrial markers was not observed comparing genome performances. Finally, the amniote groups with lowest recovery rates were therians and rodents, despite the morphological support for their monophyletic status. We suggest that, regardless of the tree-building method, a few carefully selected genes are able to unfold a detailed and robust scenario of phylogenetic hypotheses, particularly if taxon sampling is increased.

On parametrised cold dense matter equation of state inference

NASA Astrophysics Data System (ADS)

Riley, Thomas E.; Raaijmakers, Geert; Watts, Anna L.

2018-04-01

Constraining the equation of state of cold dense matter in compact stars is a major science goal for observing programmes being conducted using X-ray, radio, and gravitational wave telescopes. We discuss Bayesian hierarchical inference of parametrised dense matter equations of state. In particular we generalise and examine two inference paradigms from the literature: (i) direct posterior equation of state parameter estimation, conditioned on observations of a set of rotating compact stars; and (ii) indirect parameter estimation, via transformation of an intermediary joint posterior distribution of exterior spacetime parameters (such as gravitational masses and coordinate equatorial radii). We conclude that the former paradigm is not only tractable for large-scale analyses, but is principled and flexible from a Bayesian perspective whilst the latter paradigm is not. The thematic problem of Bayesian prior definition emerges as the crux of the difference between these paradigms. The second paradigm should in general only be considered as an ill-defined approach to the problem of utilising archival posterior constraints on exterior spacetime parameters; we advocate for an alternative approach whereby such information is repurposed as an approximative likelihood function. We also discuss why conditioning on a piecewise-polytropic equation of state model - currently standard in the field of dense matter study - can easily violate conditions required for transformation of a probability density distribution between spaces of exterior (spacetime) and interior (source matter) parameters.

Sensitivity of a Bayesian atmospheric-transport inversion model to spatio-temporal sensor resolution applied to the 2006 North Korean nuclear test

NASA Astrophysics Data System (ADS)

Lundquist, K. A.; Jensen, D. D.; Lucas, D. D.

2017-12-01

Atmospheric source reconstruction allows for the probabilistic estimate of source characteristics of an atmospheric release using observations of the release. Performance of the inversion depends partially on the temporal frequency and spatial scale of the observations. The objective of this study is to quantify the sensitivity of the source reconstruction method to sparse spatial and temporal observations. To this end, simulations of atmospheric transport of noble gasses are created for the 2006 nuclear test at the Punggye-ri nuclear test site. Synthetic observations are collected from the simulation, and are taken as "ground truth". Data denial techniques are used to progressively coarsen the temporal and spatial resolution of the synthetic observations, while the source reconstruction model seeks to recover the true input parameters from the synthetic observations. Reconstructed parameters considered here are source location, source timing and source quantity. Reconstruction is achieved by running an ensemble of thousands of dispersion model runs that sample from a uniform distribution of the input parameters. Machine learning is used to train a computationally-efficient surrogate model from the ensemble simulations. Monte Carlo sampling and Bayesian inversion are then used in conjunction with the surrogate model to quantify the posterior probability density functions of source input parameters. This research seeks to inform decision makers of the tradeoffs between more expensive, high frequency observations and less expensive, low frequency observations.

Potential Use of a Bayesian Network for Discriminating Flash Type from Future GOES-R Geostationary Lightning Mapper (GLM) data

NASA Technical Reports Server (NTRS)

Solakiewiz, Richard; Koshak, William

2008-01-01

Continuous monitoring of the ratio of cloud flashes to ground flashes may provide a better understanding of thunderstorm dynamics, intensification, and evolution, and it may be useful in severe weather warning. The National Lighting Detection Network TM (NLDN) senses ground flashes with exceptional detection efficiency and accuracy over most of the continental United States. A proposed Geostationary Lightning Mapper (GLM) aboard the Geostationary Operational Environmental Satellite (GOES-R) will look at the western hemisphere, and among the lightning data products to be made available will be the fundamental optical flash parameters for both cloud and ground flashes: radiance, area, duration, number of optical groups, and number of optical events. Previous studies have demonstrated that the optical flash parameter statistics of ground and cloud lightning, which are observable from space, are significantly different. This study investigates a Bayesian network methodology for discriminating lightning flash type (ground or cloud) using the lightning optical data and ancillary GOES-R data. A Directed Acyclic Graph (DAG) is set up with lightning as a "root" and data observed by GLM as the "leaves." This allows for a direct calculation of the joint probability distribution function for the lighting type and radiance, area, etc. Initially, the conditional probabilities that will be required can be estimated from the Lightning Imaging Sensor (LIS) and the Optical Transient Detector (OTD) together with NLDN data. Directly manipulating the joint distribution will yield the conditional probability that a lightning flash is a ground flash given the evidence, which consists of the observed lightning optical data [and possibly cloud data retrieved from the GOES-R Advanced Baseline Imager (ABI) in a more mature Bayesian network configuration]. Later, actual GLM and NLDN data can be used to refine the estimates of the conditional probabilities used in the model; i.e., the Bayesian network is a learning network. Methods for efficient calculation of the conditional probabilities (e.g., an algorithm using junction trees), finding data conflicts, goodness of fit, and dealing with missing data will also be addressed.

Technical Note: Approximate Bayesian parameterization of a process-based tropical forest model

NASA Astrophysics Data System (ADS)

Hartig, F.; Dislich, C.; Wiegand, T.; Huth, A.

2014-02-01

Inverse parameter estimation of process-based models is a long-standing problem in many scientific disciplines. A key question for inverse parameter estimation is how to define the metric that quantifies how well model predictions fit to the data. This metric can be expressed by general cost or objective functions, but statistical inversion methods require a particular metric, the probability of observing the data given the model parameters, known as the likelihood. For technical and computational reasons, likelihoods for process-based stochastic models are usually based on general assumptions about variability in the observed data, and not on the stochasticity generated by the model. Only in recent years have new methods become available that allow the generation of likelihoods directly from stochastic simulations. Previous applications of these approximate Bayesian methods have concentrated on relatively simple models. Here, we report on the application of a simulation-based likelihood approximation for FORMIND, a parameter-rich individual-based model of tropical forest dynamics. We show that approximate Bayesian inference, based on a parametric likelihood approximation placed in a conventional Markov chain Monte Carlo (MCMC) sampler, performs well in retrieving known parameter values from virtual inventory data generated by the forest model. We analyze the results of the parameter estimation, examine its sensitivity to the choice and aggregation of model outputs and observed data (summary statistics), and demonstrate the application of this method by fitting the FORMIND model to field data from an Ecuadorian tropical forest. Finally, we discuss how this approach differs from approximate Bayesian computation (ABC), another method commonly used to generate simulation-based likelihood approximations. Our results demonstrate that simulation-based inference, which offers considerable conceptual advantages over more traditional methods for inverse parameter estimation, can be successfully applied to process-based models of high complexity. The methodology is particularly suitable for heterogeneous and complex data structures and can easily be adjusted to other model types, including most stochastic population and individual-based models. Our study therefore provides a blueprint for a fairly general approach to parameter estimation of stochastic process-based models.

Technical Note: Approximate Bayesian parameterization of a complex tropical forest model

NASA Astrophysics Data System (ADS)

Hartig, F.; Dislich, C.; Wiegand, T.; Huth, A.

2013-08-01

Inverse parameter estimation of process-based models is a long-standing problem in ecology and evolution. A key problem of inverse parameter estimation is to define a metric that quantifies how well model predictions fit to the data. Such a metric can be expressed by general cost or objective functions, but statistical inversion approaches are based on a particular metric, the probability of observing the data given the model, known as the likelihood. Deriving likelihoods for dynamic models requires making assumptions about the probability for observations to deviate from mean model predictions. For technical reasons, these assumptions are usually derived without explicit consideration of the processes in the simulation. Only in recent years have new methods become available that allow generating likelihoods directly from stochastic simulations. Previous applications of these approximate Bayesian methods have concentrated on relatively simple models. Here, we report on the application of a simulation-based likelihood approximation for FORMIND, a parameter-rich individual-based model of tropical forest dynamics. We show that approximate Bayesian inference, based on a parametric likelihood approximation placed in a conventional MCMC, performs well in retrieving known parameter values from virtual field data generated by the forest model. We analyze the results of the parameter estimation, examine the sensitivity towards the choice and aggregation of model outputs and observed data (summary statistics), and show results from using this method to fit the FORMIND model to field data from an Ecuadorian tropical forest. Finally, we discuss differences of this approach to Approximate Bayesian Computing (ABC), another commonly used method to generate simulation-based likelihood approximations. Our results demonstrate that simulation-based inference, which offers considerable conceptual advantages over more traditional methods for inverse parameter estimation, can successfully be applied to process-based models of high complexity. The methodology is particularly suited to heterogeneous and complex data structures and can easily be adjusted to other model types, including most stochastic population and individual-based models. Our study therefore provides a blueprint for a fairly general approach to parameter estimation of stochastic process-based models in ecology and evolution.

Earth system responses to cumulative carbon emissions

NASA Astrophysics Data System (ADS)

Steinacher, M.; Joos, F.

2015-07-01

Information on the relationship between cumulative fossil carbon emissions and multiple climate targets are essential to design emission mitigation and climate adaptation strategies. In this study, the transient responses in different climate variables are quantified for a large set of multi-forcing scenarios extended to year 2300 towards stabilization and in idealized experiments using the Bern3D-LPJ carbon-climate model. The model outcomes are constrained by 26 physical and biogeochemical observational data sets in a Bayesian, Monte-Carlo type framework. Cumulative fossil emissions of 1000 Gt C result in a global mean surface air temperature change of 1.88 °C (68 % confidence interval (c.i.): 1.28 to 2.69 °C), a decrease in surface ocean pH of 0.19 (0.18 to 0.22), and in steric sea level rise of 20 cm (13 to 27 cm until 2300). Linearity between cumulative emissions and transient response is high for pH and reasonably high for surface air and sea surface temperatures, but less pronounced for changes in Atlantic Meridional Overturning, Southern Ocean and tropical surface water saturation with respect to biogenic structures of calcium carbonate, and carbon stocks in soils. The slopes of the relationships change when CO2 is stabilized. The Transient Climate Response is constrained, primarily by long-term ocean heat observations, to 1.7 °C (68 % c.i.: 1.3 to 2.2 °C) and the Equilibrium Climate Sensitivity to 2.9 °C (2.0 to 4.2 °C). This is consistent with results by CMIP5 models, but inconsistent with recent studies that relied on short-term air temperature data affected by natural climate variability.

Extreme-Scale Bayesian Inference for Uncertainty Quantification of Complex Simulations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Biros, George

Uncertainty quantification (UQ)—that is, quantifying uncertainties in complex mathematical models and their large-scale computational implementations—is widely viewed as one of the outstanding challenges facing the field of CS&E over the coming decade. The EUREKA project set to address the most difficult class of UQ problems: those for which both the underlying PDE model as well as the uncertain parameters are of extreme scale. In the project we worked on these extreme-scale challenges in the following four areas: 1. Scalable parallel algorithms for sampling and characterizing the posterior distribution that exploit the structure of the underlying PDEs and parameter-to-observable map. Thesemore » include structure-exploiting versions of the randomized maximum likelihood method, which aims to overcome the intractability of employing conventional MCMC methods for solving extreme-scale Bayesian inversion problems by appealing to and adapting ideas from large-scale PDE-constrained optimization, which have been very successful at exploring high-dimensional spaces. 2. Scalable parallel algorithms for construction of prior and likelihood functions based on learning methods and non-parametric density estimation. Constructing problem-specific priors remains a critical challenge in Bayesian inference, and more so in high dimensions. Another challenge is construction of likelihood functions that capture unmodeled couplings between observations and parameters. We will create parallel algorithms for non-parametric density estimation using high dimensional N-body methods and combine them with supervised learning techniques for the construction of priors and likelihood functions. 3. Bayesian inadequacy models, which augment physics models with stochastic models that represent their imperfections. The success of the Bayesian inference framework depends on the ability to represent the uncertainty due to imperfections of the mathematical model of the phenomena of interest. This is a central challenge in UQ, especially for large-scale models. We propose to develop the mathematical tools to address these challenges in the context of extreme-scale problems. 4. Parallel scalable algorithms for Bayesian optimal experimental design (OED). Bayesian inversion yields quantified uncertainties in the model parameters, which can be propagated forward through the model to yield uncertainty in outputs of interest. This opens the way for designing new experiments to reduce the uncertainties in the model parameters and model predictions. Such experimental design problems have been intractable for large-scale problems using conventional methods; we will create OED algorithms that exploit the structure of the PDE model and the parameter-to-output map to overcome these challenges. Parallel algorithms for these four problems were created, analyzed, prototyped, implemented, tuned, and scaled up for leading-edge supercomputers, including UT-Austin’s own 10 petaflops Stampede system, ANL’s Mira system, and ORNL’s Titan system. While our focus is on fundamental mathematical/computational methods and algorithms, we will assess our methods on model problems derived from several DOE mission applications, including multiscale mechanics and ice sheet dynamics.« less

Missing Link: Bayesian detection and measurement of intermediate-mass black-hole binaries

NASA Astrophysics Data System (ADS)

Graff, Philip B.; Buonanno, Alessandra; Sathyaprakash, B. S.

2015-07-01

We perform Bayesian analysis of gravitational-wave signals from nonspinning, intermediate-mass black-hole binaries (IMBHBs) with observed total mass, Mobs, from 50 M⊙ to 500 M⊙ and mass ratio 1-4 using advanced LIGO and Virgo detectors. We employ inspiral-merger-ringdown waveform models based on the effective-one-body formalism and include subleading modes of radiation beyond the leading (2,2) mode. The presence of subleading modes increases signal power for inclined binaries and allows for improved accuracy and precision in measurements of the masses as well as breaking of degeneracies in distance, orientation and polarization. For low total masses, Mobs≲50 M⊙ , for which the inspiral signal dominates, the observed chirp mass Mobs=Mobsη3 /5 (η being the symmetric mass ratio) is better measured. In contrast, as increasing power comes from merger and ringdown, we find that the total mass Mobs has better relative precision than Mobs. Indeed, at high Mobs (≥300 M⊙ ), the signal resembles a burst and the measurement thus extracts the dominant frequency of the signal that depends on Mobs. Depending on the binary's inclination, at signal-to-noise ratio (SNR) of 12, uncertainties in Mobs can be as large as ˜20 - 25 % while uncertainties in Mobs are ˜50 - 60 % in binaries with unequal masses (those numbers become ˜17 % vs. ˜22 % in more symmetric mass-ratio binaries). Although large, those uncertainties in Mobs will establish the existence of IMBHs. We find that effective-one-body waveforms with subleading modes are essential to confirm a signal's presence in the data, with calculated Bayesian evidences yielding a false alarm probability below 10-5 for SNR ≳9 in Gaussian noise. Our results show that gravitational-wave observations can offer a unique tool to observe and understand the formation, evolution and demographics of IMBHs, which are difficult to observe in the electromagnetic window.

Quantifying structural uncertainty on fault networks using a marked point process within a Bayesian framework

NASA Astrophysics Data System (ADS)

Aydin, Orhun; Caers, Jef Karel

2017-08-01

Faults are one of the building-blocks for subsurface modeling studies. Incomplete observations of subsurface fault networks lead to uncertainty pertaining to location, geometry and existence of faults. In practice, gaps in incomplete fault network observations are filled based on tectonic knowledge and interpreter's intuition pertaining to fault relationships. Modeling fault network uncertainty with realistic models that represent tectonic knowledge is still a challenge. Although methods that address specific sources of fault network uncertainty and complexities of fault modeling exists, a unifying framework is still lacking. In this paper, we propose a rigorous approach to quantify fault network uncertainty. Fault pattern and intensity information are expressed by means of a marked point process, marked Strauss point process. Fault network information is constrained to fault surface observations (complete or partial) within a Bayesian framework. A structural prior model is defined to quantitatively express fault patterns, geometries and relationships within the Bayesian framework. Structural relationships between faults, in particular fault abutting relations, are represented with a level-set based approach. A Markov Chain Monte Carlo sampler is used to sample posterior fault network realizations that reflect tectonic knowledge and honor fault observations. We apply the methodology to a field study from Nankai Trough & Kumano Basin. The target for uncertainty quantification is a deep site with attenuated seismic data with only partially visible faults and many faults missing from the survey or interpretation. A structural prior model is built from shallow analog sites that are believed to have undergone similar tectonics compared to the site of study. Fault network uncertainty for the field is quantified with fault network realizations that are conditioned to structural rules, tectonic information and partially observed fault surfaces. We show the proposed methodology generates realistic fault network models conditioned to data and a conceptual model of the underlying tectonics.

"The part of me that you bring out": ideal similarity and the Michelangelo phenomenon.

PubMed

Rusbult, Caryl E; Kumashiro, Madoka; Kubacka, Kaska E; Finkel, Eli J

2009-01-01

This work examines the Michelangelo phenomenon, an interpersonal model of the means by which people move closer to (vs. further from) their ideal selves. The authors propose that partner similarity--similarity to the ideal self, in particular--plays an important role in this process. Across 4 studies employing diverse designs and measurement techniques, they observed consistent evidence that when partners possess key elements of one another's ideal selves, each person affirms the other by eliciting important aspects of the other's ideals, each person moves closer to his or her ideal self, and couple well-being is enhanced. Partner similarity to the actual self also accounts for unique variance in key elements of this model. The associations of ideal similarity and actual similarity with couple well-being are fully attributable to the Michelangelo process, to partner affirmation and target movement toward the ideal self. The authors also performed auxiliary analyses to rule out several alternative interpretations of these findings.

Faithful Pointer for Qubit Measurement

NASA Astrophysics Data System (ADS)

Kumari, Asmita; Pan, A. K.

2018-02-01

In the context of von Neumann projective measurement scenario for a qubit system, it is widely believed that the mutual orthogonality between the post-interaction pointer states is the sufficient condition for achieving the ideal measurement situation. However, for experimentally verifying the observable probabilities, the real space distinction between the pointer distributions corresponding to post-interaction pointer states play crucial role. It is implicitly assumed that mutual orthogonality ensures the support between the post-interaction pointer distributions to be disjoint. We point out that mutual orthogonality (formal idealness) does not necessarily imply the real space distinguishability (operational idealness), but converse is true. In fact, for the commonly referred Gaussian wavefunction, it is possible to obtain a measurement situation which is formally ideal but fully nonideal operationally. In this paper, we derive a class of pointer states, that we call faithful pointers, for which the degree of formal (non)idealness is equal to the operational (non)idealness. In other words, for the faithful pointers, if a measurement situation is formally ideal then it is operationally ideal and vice versa.

SOMBI: Bayesian identification of parameter relations in unstructured cosmological data

NASA Astrophysics Data System (ADS)

Frank, Philipp; Jasche, Jens; Enßlin, Torsten A.

2016-11-01

This work describes the implementation and application of a correlation determination method based on self organizing maps and Bayesian inference (SOMBI). SOMBI aims to automatically identify relations between different observed parameters in unstructured cosmological or astrophysical surveys by automatically identifying data clusters in high-dimensional datasets via the self organizing map neural network algorithm. Parameter relations are then revealed by means of a Bayesian inference within respective identified data clusters. Specifically such relations are assumed to be parametrized as a polynomial of unknown order. The Bayesian approach results in a posterior probability distribution function for respective polynomial coefficients. To decide which polynomial order suffices to describe correlation structures in data, we include a method for model selection, the Bayesian information criterion, to the analysis. The performance of the SOMBI algorithm is tested with mock data. As illustration we also provide applications of our method to cosmological data. In particular, we present results of a correlation analysis between galaxy and active galactic nucleus (AGN) properties provided by the SDSS catalog with the cosmic large-scale-structure (LSS). The results indicate that the combined galaxy and LSS dataset indeed is clustered into several sub-samples of data with different average properties (for example different stellar masses or web-type classifications). The majority of data clusters appear to have a similar correlation structure between galaxy properties and the LSS. In particular we revealed a positive and linear dependency between the stellar mass, the absolute magnitude and the color of a galaxy with the corresponding cosmic density field. A remaining subset of data shows inverted correlations, which might be an artifact of non-linear redshift distortions.

Bayesian inference of the number of factors in gene-expression analysis: application to human virus challenge studies.

PubMed

Chen, Bo; Chen, Minhua; Paisley, John; Zaas, Aimee; Woods, Christopher; Ginsburg, Geoffrey S; Hero, Alfred; Lucas, Joseph; Dunson, David; Carin, Lawrence

2010-11-09

Nonparametric Bayesian techniques have been developed recently to extend the sophistication of factor models, allowing one to infer the number of appropriate factors from the observed data. We consider such techniques for sparse factor analysis, with application to gene-expression data from three virus challenge studies. Particular attention is placed on employing the Beta Process (BP), the Indian Buffet Process (IBP), and related sparseness-promoting techniques to infer a proper number of factors. The posterior density function on the model parameters is computed using Gibbs sampling and variational Bayesian (VB) analysis. Time-evolving gene-expression data are considered for respiratory syncytial virus (RSV), Rhino virus, and influenza, using blood samples from healthy human subjects. These data were acquired in three challenge studies, each executed after receiving institutional review board (IRB) approval from Duke University. Comparisons are made between several alternative means of per-forming nonparametric factor analysis on these data, with comparisons as well to sparse-PCA and Penalized Matrix Decomposition (PMD), closely related non-Bayesian approaches. Applying the Beta Process to the factor scores, or to the singular values of a pseudo-SVD construction, the proposed algorithms infer the number of factors in gene-expression data. For real data the "true" number of factors is unknown; in our simulations we consider a range of noise variances, and the proposed Bayesian models inferred the number of factors accurately relative to other methods in the literature, such as sparse-PCA and PMD. We have also identified a "pan-viral" factor of importance for each of the three viruses considered in this study. We have identified a set of genes associated with this pan-viral factor, of interest for early detection of such viruses based upon the host response, as quantified via gene-expression data.

Bayesian LASSO, scale space and decision making in association genetics.

PubMed

Pasanen, Leena; Holmström, Lasse; Sillanpää, Mikko J

2015-01-01

LASSO is a penalized regression method that facilitates model fitting in situations where there are as many, or even more explanatory variables than observations, and only a few variables are relevant in explaining the data. We focus on the Bayesian version of LASSO and consider four problems that need special attention: (i) controlling false positives, (ii) multiple comparisons, (iii) collinearity among explanatory variables, and (iv) the choice of the tuning parameter that controls the amount of shrinkage and the sparsity of the estimates. The particular application considered is association genetics, where LASSO regression can be used to find links between chromosome locations and phenotypic traits in a biological organism. However, the proposed techniques are relevant also in other contexts where LASSO is used for variable selection. We separate the true associations from false positives using the posterior distribution of the effects (regression coefficients) provided by Bayesian LASSO. We propose to solve the multiple comparisons problem by using simultaneous inference based on the joint posterior distribution of the effects. Bayesian LASSO also tends to distribute an effect among collinear variables, making detection of an association difficult. We propose to solve this problem by considering not only individual effects but also their functionals (i.e. sums and differences). Finally, whereas in Bayesian LASSO the tuning parameter is often regarded as a random variable, we adopt a scale space view and consider a whole range of fixed tuning parameters, instead. The effect estimates and the associated inference are considered for all tuning parameters in the selected range and the results are visualized with color maps that provide useful insights into data and the association problem considered. The methods are illustrated using two sets of artificial data and one real data set, all representing typical settings in association genetics.

Differentiating Wheat Genotypes by Bayesian Hierarchical Nonlinear Mixed Modeling of Wheat Root Density.

PubMed

Wasson, Anton P; Chiu, Grace S; Zwart, Alexander B; Binns, Timothy R

2017-01-01

Ensuring future food security for a growing population while climate change and urban sprawl put pressure on agricultural land will require sustainable intensification of current farming practices. For the crop breeder this means producing higher crop yields with less resources due to greater environmental stresses. While easy gains in crop yield have been made mostly "above ground," little progress has been made "below ground"; and yet it is these root system traits that can improve productivity and resistance to drought stress. Wheat pre-breeders use soil coring and core-break counts to phenotype root architecture traits, with data collected on rooting density for hundreds of genotypes in small increments of depth. The measured densities are both large datasets and highly variable even within the same genotype, hence, any rigorous, comprehensive statistical analysis of such complex field data would be technically challenging. Traditionally, most attributes of the field data are therefore discarded in favor of simple numerical summary descriptors which retain much of the high variability exhibited by the raw data. This poses practical challenges: although plant scientists have established that root traits do drive resource capture in crops, traits that are more randomly (rather than genetically) determined are difficult to breed for. In this paper we develop a hierarchical nonlinear mixed modeling approach that utilizes the complete field data for wheat genotypes to fit, under the Bayesian paradigm, an "idealized" relative intensity function for the root distribution over depth. Our approach was used to determine heritability : how much of the variation between field samples was purely random vs. being mechanistically driven by the plant genetics? Based on the genotypic intensity functions, the overall heritability estimate was 0.62 (95% Bayesian confidence interval was 0.52 to 0.71). Despite root count profiles that were statistically very noisy, our approach led to denoised profiles which exhibited rigorously discernible phenotypic traits. Profile-specific traits could be representative of a genotype, and thus, used as a quantitative tool to associate phenotypic traits with specific genotypes. This would allow breeders to select for whole root system distributions appropriate for sustainable intensification, and inform policy for mitigating crop yield risk and food insecurity.

Bayesian network interface for assisting radiology interpretation and education

NASA Astrophysics Data System (ADS)

Duda, Jeffrey; Botzolakis, Emmanuel; Chen, Po-Hao; Mohan, Suyash; Nasrallah, Ilya; Rauschecker, Andreas; Rudie, Jeffrey; Bryan, R. Nick; Gee, James; Cook, Tessa

2018-03-01

In this work, we present the use of Bayesian networks for radiologist decision support during clinical interpretation. This computational approach has the advantage of avoiding incorrect diagnoses that result from known human cognitive biases such as anchoring bias, framing effect, availability bias, and premature closure. To integrate Bayesian networks into clinical practice, we developed an open-source web application that provides diagnostic support for a variety of radiology disease entities (e.g., basal ganglia diseases, bone lesions). The Clinical tool presents the user with a set of buttons representing clinical and imaging features of interest. These buttons are used to set the value for each observed feature. As features are identified, the conditional probabilities for each possible diagnosis are updated in real time. Additionally, using sensitivity analysis, the interface may be set to inform the user which remaining imaging features provide maximum discriminatory information to choose the most likely diagnosis. The Case Submission tools allow the user to submit a validated case and the associated imaging features to a database, which can then be used for future tuning/testing of the Bayesian networks. These submitted cases are then reviewed by an assigned expert using the provided QC tool. The Research tool presents users with cases with previously labeled features and a chosen diagnosis, for the purpose of performance evaluation. Similarly, the Education page presents cases with known features, but provides real time feedback on feature selection.

Conventional, Bayesian, and Modified Prony's methods for characterizing fast and slow waves in equine cancellous bone

PubMed Central

Groopman, Amber M.; Katz, Jonathan I.; Holland, Mark R.; Fujita, Fuminori; Matsukawa, Mami; Mizuno, Katsunori; Wear, Keith A.; Miller, James G.

2015-01-01

Conventional, Bayesian, and the modified least-squares Prony's plus curve-fitting (MLSP + CF) methods were applied to data acquired using 1 MHz center frequency, broadband transducers on a single equine cancellous bone specimen that was systematically shortened from 11.8 mm down to 0.5 mm for a total of 24 sample thicknesses. Due to overlapping fast and slow waves, conventional analysis methods were restricted to data from sample thicknesses ranging from 11.8 mm to 6.0 mm. In contrast, Bayesian and MLSP + CF methods successfully separated fast and slow waves and provided reliable estimates of the ultrasonic properties of fast and slow waves for sample thicknesses ranging from 11.8 mm down to 3.5 mm. Comparisons of the three methods were carried out for phase velocity at the center frequency and the slope of the attenuation coefficient for the fast and slow waves. Good agreement among the three methods was also observed for average signal loss at the center frequency. The Bayesian and MLSP + CF approaches were able to separate the fast and slow waves and provide good estimates of the fast and slow wave properties even when the two wave modes overlapped in both time and frequency domains making conventional analysis methods unreliable. PMID:26328678

The current state of Bayesian methods in medical product development: survey results and recommendations from the DIA Bayesian Scientific Working Group.

PubMed

Natanegara, Fanni; Neuenschwander, Beat; Seaman, John W; Kinnersley, Nelson; Heilmann, Cory R; Ohlssen, David; Rochester, George

2014-01-01

Bayesian applications in medical product development have recently gained popularity. Despite many advances in Bayesian methodology and computations, increase in application across the various areas of medical product development has been modest. The DIA Bayesian Scientific Working Group (BSWG), which includes representatives from industry, regulatory agencies, and academia, has adopted the vision to ensure Bayesian methods are well understood, accepted more broadly, and appropriately utilized to improve decision making and enhance patient outcomes. As Bayesian applications in medical product development are wide ranging, several sub-teams were formed to focus on various topics such as patient safety, non-inferiority, prior specification, comparative effectiveness, joint modeling, program-wide decision making, analytical tools, and education. The focus of this paper is on the recent effort of the BSWG Education sub-team to administer a Bayesian survey to statisticians across 17 organizations involved in medical product development. We summarize results of this survey, from which we provide recommendations on how to accelerate progress in Bayesian applications throughout medical product development. The survey results support findings from the literature and provide additional insight on regulatory acceptance of Bayesian methods and information on the need for a Bayesian infrastructure within an organization. The survey findings support the claim that only modest progress in areas of education and implementation has been made recently, despite substantial progress in Bayesian statistical research and software availability. Copyright © 2013 John Wiley & Sons, Ltd.

On the Adequacy of Bayesian Evaluations of Categorization Models: Reply to Vanpaemel and Lee (2012)

ERIC Educational Resources Information Center

Wills, Andy J.; Pothos, Emmanuel M.

2012-01-01

Vanpaemel and Lee (2012) argued, and we agree, that the comparison of formal models can be facilitated by Bayesian methods. However, Bayesian methods neither precede nor supplant our proposals (Wills & Pothos, 2012), as Bayesian methods can be applied both to our proposals and to their polar opposites. Furthermore, the use of Bayesian methods to…

Moving beyond qualitative evaluations of Bayesian models of cognition.

PubMed

Hemmer, Pernille; Tauber, Sean; Steyvers, Mark

2015-06-01

Bayesian models of cognition provide a powerful way to understand the behavior and goals of individuals from a computational point of view. Much of the focus in the Bayesian cognitive modeling approach has been on qualitative model evaluations, where predictions from the models are compared to data that is often averaged over individuals. In many cognitive tasks, however, there are pervasive individual differences. We introduce an approach to directly infer individual differences related to subjective mental representations within the framework of Bayesian models of cognition. In this approach, Bayesian data analysis methods are used to estimate cognitive parameters and motivate the inference process within a Bayesian cognitive model. We illustrate this integrative Bayesian approach on a model of memory. We apply the model to behavioral data from a memory experiment involving the recall of heights of people. A cross-validation analysis shows that the Bayesian memory model with inferred subjective priors predicts withheld data better than a Bayesian model where the priors are based on environmental statistics. In addition, the model with inferred priors at the individual subject level led to the best overall generalization performance, suggesting that individual differences are important to consider in Bayesian models of cognition.

cosmoabc: Likelihood-free inference for cosmology

NASA Astrophysics Data System (ADS)

Ishida, Emille E. O.; Vitenti, Sandro D. P.; Penna-Lima, Mariana; Trindade, Arlindo M.; Cisewski, Jessi; M.; de Souza, Rafael; Cameron, Ewan; Busti, Vinicius C.

2015-05-01

Approximate Bayesian Computation (ABC) enables parameter inference for complex physical systems in cases where the true likelihood function is unknown, unavailable, or computationally too expensive. It relies on the forward simulation of mock data and comparison between observed and synthetic catalogs. cosmoabc is a Python Approximate Bayesian Computation (ABC) sampler featuring a Population Monte Carlo variation of the original ABC algorithm, which uses an adaptive importance sampling scheme. The code can be coupled to an external simulator to allow incorporation of arbitrary distance and prior functions. When coupled with the numcosmo library, it has been used to estimate posterior probability distributions over cosmological parameters based on measurements of galaxy clusters number counts without computing the likelihood function.

Bayesian Model for Matching the Radiometric Measurements of Aerospace and Field Ocean Color Sensors

PubMed Central

Salama, Mhd. Suhyb; Su, Zhongbo

2010-01-01

A Bayesian model is developed to match aerospace ocean color observation to field measurements and derive the spatial variability of match-up sites. The performance of the model is tested against populations of synthesized spectra and full and reduced resolutions of MERIS data. The model derived the scale difference between synthesized satellite pixel and point measurements with R2 > 0.88 and relative error < 21% in the spectral range from 400 nm to 695 nm. The sub-pixel variabilities of reduced resolution MERIS image are derived with less than 12% of relative errors in heterogeneous region. The method is generic and applicable to different sensors. PMID:22163615

Accuracy of latent-variable estimation in Bayesian semi-supervised learning.

PubMed

Yamazaki, Keisuke

2015-09-01

Hierarchical probabilistic models, such as Gaussian mixture models, are widely used for unsupervised learning tasks. These models consist of observable and latent variables, which represent the observable data and the underlying data-generation process, respectively. Unsupervised learning tasks, such as cluster analysis, are regarded as estimations of latent variables based on the observable ones. The estimation of latent variables in semi-supervised learning, where some labels are observed, will be more precise than that in unsupervised, and one of the concerns is to clarify the effect of the labeled data. However, there has not been sufficient theoretical analysis of the accuracy of the estimation of latent variables. In a previous study, a distribution-based error function was formulated, and its asymptotic form was calculated for unsupervised learning with generative models. It has been shown that, for the estimation of latent variables, the Bayes method is more accurate than the maximum-likelihood method. The present paper reveals the asymptotic forms of the error function in Bayesian semi-supervised learning for both discriminative and generative models. The results show that the generative model, which uses all of the given data, performs better when the model is well specified. Copyright © 2015 Elsevier Ltd. All rights reserved.

Visual and Auditory Components in the Perception of Asynchronous Audiovisual Speech

PubMed Central

Alcalá-Quintana, Rocío

2015-01-01

Research on asynchronous audiovisual speech perception manipulates experimental conditions to observe their effects on synchrony judgments. Probabilistic models establish a link between the sensory and decisional processes underlying such judgments and the observed data, via interpretable parameters that allow testing hypotheses and making inferences about how experimental manipulations affect such processes. Two models of this type have recently been proposed, one based on independent channels and the other using a Bayesian approach. Both models are fitted here to a common data set, with a subsequent analysis of the interpretation they provide about how experimental manipulations affected the processes underlying perceived synchrony. The data consist of synchrony judgments as a function of audiovisual offset in a speech stimulus, under four within-subjects manipulations of the quality of the visual component. The Bayesian model could not accommodate asymmetric data, was rejected by goodness-of-fit statistics for 8/16 observers, and was found to be nonidentifiable, which renders uninterpretable parameter estimates. The independent-channels model captured asymmetric data, was rejected for only 1/16 observers, and identified how sensory and decisional processes mediating asynchronous audiovisual speech perception are affected by manipulations that only alter the quality of the visual component of the speech signal. PMID:27551361

Bayesian Analysis of the Glacial-Interglacial Methane Increase Constrained by Stable Isotopes and Earth System Modeling

NASA Astrophysics Data System (ADS)

Hopcroft, Peter O.; Valdes, Paul J.; Kaplan, Jed O.

2018-04-01

The observed rise in atmospheric methane (CH4) from 375 ppbv during the Last Glacial Maximum (LGM: 21,000 years ago) to 680 ppbv during the late preindustrial era is not well understood. Atmospheric chemistry considerations implicate an increase in CH4 sources, but process-based estimates fail to reproduce the required amplitude. CH4 stable isotopes provide complementary information that can help constrain the underlying causes of the increase. We combine Earth System model simulations of the late preindustrial and LGM CH4 cycles, including process-based estimates of the isotopic discrimination of vegetation, in a box model of atmospheric CH4 and its isotopes. Using a Bayesian approach, we show how model-based constraints and ice core observations may be combined in a consistent probabilistic framework. The resultant posterior distributions point to a strong reduction in wetland and other biogenic CH4 emissions during the LGM, with a modest increase in the geological source, or potentially natural or anthropogenic fires, accounting for the observed enrichment of δ13CH4.

On the Estimation of Disease Prevalence by Latent Class Models for Screening Studies Using Two Screening Tests with Categorical Disease Status Verified in Test Positives Only

PubMed Central

Chu, Haitao; Zhou, Yijie; Cole, Stephen R.; Ibrahim, Joseph G.

2010-01-01

Summary To evaluate the probabilities of a disease state, ideally all subjects in a study should be diagnosed by a definitive diagnostic or gold standard test. However, since definitive diagnostic tests are often invasive and expensive, it is generally unethical to apply them to subjects whose screening tests are negative. In this article, we consider latent class models for screening studies with two imperfect binary diagnostic tests and a definitive categorical disease status measured only for those with at least one positive screening test. Specifically, we discuss a conditional independent and three homogeneous conditional dependent latent class models and assess the impact of misspecification of the dependence structure on the estimation of disease category probabilities using frequentist and Bayesian approaches. Interestingly, the three homogeneous dependent models can provide identical goodness-of-fit but substantively different estimates for a given study. However, the parametric form of the assumed dependence structure itself is not “testable” from the data, and thus the dependence structure modeling considered here can only be viewed as a sensitivity analysis concerning a more complicated non-identifiable model potentially involving heterogeneous dependence structure. Furthermore, we discuss Bayesian model averaging together with its limitations as an alternative way to partially address this particularly challenging problem. The methods are applied to two cancer screening studies, and simulations are conducted to evaluate the performance of these methods. In summary, further research is needed to reduce the impact of model misspecification on the estimation of disease prevalence in such settings. PMID:20191614

Bayesian structural equation modeling in sport and exercise psychology.

PubMed

Stenling, Andreas; Ivarsson, Andreas; Johnson, Urban; Lindwall, Magnus

2015-08-01

Bayesian statistics is on the rise in mainstream psychology, but applications in sport and exercise psychology research are scarce. In this article, the foundations of Bayesian analysis are introduced, and we will illustrate how to apply Bayesian structural equation modeling in a sport and exercise psychology setting. More specifically, we contrasted a confirmatory factor analysis on the Sport Motivation Scale II estimated with the most commonly used estimator, maximum likelihood, and a Bayesian approach with weakly informative priors for cross-loadings and correlated residuals. The results indicated that the model with Bayesian estimation and weakly informative priors provided a good fit to the data, whereas the model estimated with a maximum likelihood estimator did not produce a well-fitting model. The reasons for this discrepancy between maximum likelihood and Bayesian estimation are discussed as well as potential advantages and caveats with the Bayesian approach.

Temperature and the Ideal Gas

ERIC Educational Resources Information Center

Daisley, R. E.

1973-01-01

Presents some organized ideas in thermodynamics which are suitable for use with high school (GCE A level or ONC) students. Emphases are placed upon macroscopic observations and intimate connection of the modern definition of temperature with the concept of ideal gas. (CC)

An ideal observer analysis of visual working memory.

PubMed

Sims, Chris R; Jacobs, Robert A; Knill, David C

2012-10-01

Limits in visual working memory (VWM) strongly constrain human performance across many tasks. However, the nature of these limits is not well understood. In this article we develop an ideal observer analysis of human VWM by deriving the expected behavior of an optimally performing but limited-capacity memory system. This analysis is framed around rate-distortion theory, a branch of information theory that provides optimal bounds on the accuracy of information transmission subject to a fixed information capacity. The result of the ideal observer analysis is a theoretical framework that provides a task-independent and quantitative definition of visual memory capacity and yields novel predictions regarding human performance. These predictions are subsequently evaluated and confirmed in 2 empirical studies. Further, the framework is general enough to allow the specification and testing of alternative models of visual memory (e.g., how capacity is distributed across multiple items). We demonstrate that a simple model developed on the basis of the ideal observer analysis-one that allows variability in the number of stored memory representations but does not assume the presence of a fixed item limit-provides an excellent account of the empirical data and further offers a principled reinterpretation of existing models of VWM. PsycINFO Database Record (c) 2012 APA, all rights reserved.

An Ideal Observer Analysis of Visual Working Memory

PubMed Central

Sims, Chris R.; Jacobs, Robert A.; Knill, David C.

2013-01-01

Limits in visual working memory (VWM) strongly constrain human performance across many tasks. However, the nature of these limits is not well understood. In this paper we develop an ideal observer analysis of human visual working memory, by deriving the expected behavior of an optimally performing, but limited-capacity memory system. This analysis is framed around rate–distortion theory, a branch of information theory that provides optimal bounds on the accuracy of information transmission subject to a fixed information capacity. The result of the ideal observer analysis is a theoretical framework that provides a task-independent and quantitative definition of visual memory capacity and yields novel predictions regarding human performance. These predictions are subsequently evaluated and confirmed in two empirical studies. Further, the framework is general enough to allow the specification and testing of alternative models of visual memory (for example, how capacity is distributed across multiple items). We demonstrate that a simple model developed on the basis of the ideal observer analysis—one which allows variability in the number of stored memory representations, but does not assume the presence of a fixed item limit—provides an excellent account of the empirical data, and further offers a principled re-interpretation of existing models of visual working memory. PMID:22946744

Bayesian Maximum Entropy Integration of Ozone Observations and Model Predictions: A National Application.

PubMed

Xu, Yadong; Serre, Marc L; Reyes, Jeanette; Vizuete, William

2016-04-19

To improve ozone exposure estimates for ambient concentrations at a national scale, we introduce our novel Regionalized Air Quality Model Performance (RAMP) approach to integrate chemical transport model (CTM) predictions with the available ozone observations using the Bayesian Maximum Entropy (BME) framework. The framework models the nonlinear and nonhomoscedastic relation between air pollution observations and CTM predictions and for the first time accounts for variability in CTM model performance. A validation analysis using only noncollocated data outside of a validation radius rv was performed and the R(2) between observations and re-estimated values for two daily metrics, the daily maximum 8-h average (DM8A) and the daily 24-h average (D24A) ozone concentrations, were obtained with the OBS scenario using ozone observations only in contrast with the RAMP and a Constant Air Quality Model Performance (CAMP) scenarios. We show that, by accounting for the spatial and temporal variability in model performance, our novel RAMP approach is able to extract more information in terms of R(2) increase percentage, with over 12 times for the DM8A and over 3.5 times for the D24A ozone concentrations, from CTM predictions than the CAMP approach assuming that model performance does not change across space and time.

Bayesian Inference for Functional Dynamics Exploring in fMRI Data.

PubMed

Guo, Xuan; Liu, Bing; Chen, Le; Chen, Guantao; Pan, Yi; Zhang, Jing

2016-01-01

This paper aims to review state-of-the-art Bayesian-inference-based methods applied to functional magnetic resonance imaging (fMRI) data. Particularly, we focus on one specific long-standing challenge in the computational modeling of fMRI datasets: how to effectively explore typical functional interactions from fMRI time series and the corresponding boundaries of temporal segments. Bayesian inference is a method of statistical inference which has been shown to be a powerful tool to encode dependence relationships among the variables with uncertainty. Here we provide an introduction to a group of Bayesian-inference-based methods for fMRI data analysis, which were designed to detect magnitude or functional connectivity change points and to infer their functional interaction patterns based on corresponding temporal boundaries. We also provide a comparison of three popular Bayesian models, that is, Bayesian Magnitude Change Point Model (BMCPM), Bayesian Connectivity Change Point Model (BCCPM), and Dynamic Bayesian Variable Partition Model (DBVPM), and give a summary of their applications. We envision that more delicate Bayesian inference models will be emerging and play increasingly important roles in modeling brain functions in the years to come.

Credible occurrence probabilities for extreme geophysical events: earthquakes, volcanic eruptions, magnetic storms

USGS Publications Warehouse

Love, Jeffrey J.

2012-01-01

Statistical analysis is made of rare, extreme geophysical events recorded in historical data -- counting the number of events $k$ with sizes that exceed chosen thresholds during specific durations of time $\\tau$. Under transformations that stabilize data and model-parameter variances, the most likely Poisson-event occurrence rate, $k/\\tau$, applies for frequentist inference and, also, for Bayesian inference with a Jeffreys prior that ensures posterior invariance under changes of variables. Frequentist confidence intervals and Bayesian (Jeffreys) credibility intervals are approximately the same and easy to calculate: $(1/\\tau)[(\\sqrt{k} - z/2)^{2},(\\sqrt{k} + z/2)^{2}]$, where $z$ is a parameter that specifies the width, $z=1$ ($z=2$) corresponding to $1\\sigma$, $68.3\\%$ ($2\\sigma$, $95.4\\%$). If only a few events have been observed, as is usually the case for extreme events, then these "error-bar" intervals might be considered to be relatively wide. From historical records, we estimate most likely long-term occurrence rates, 10-yr occurrence probabilities, and intervals of frequentist confidence and Bayesian credibility for large earthquakes, explosive volcanic eruptions, and magnetic storms.

Bayesian Assessment of the Uncertainties of Estimates of a Conceptual Rainfall-Runoff Model Parameters

NASA Astrophysics Data System (ADS)

Silva, F. E. O. E.; Naghettini, M. D. C.; Fernandes, W.

2014-12-01

This paper evaluated the uncertainties associated with the estimation of the parameters of a conceptual rainfall-runoff model, through the use of Bayesian inference techniques by Monte Carlo simulation. The Pará River sub-basin, located in the upper São Francisco river basin, in southeastern Brazil, was selected for developing the studies. In this paper, we used the Rio Grande conceptual hydrologic model (EHR/UFMG, 2001) and the Markov Chain Monte Carlo simulation method named DREAM (VRUGT, 2008a). Two probabilistic models for the residues were analyzed: (i) the classic [Normal likelihood - r ≈ N (0, σ²)]; and (ii) a generalized likelihood (SCHOUPS & VRUGT, 2010), in which it is assumed that the differences between observed and simulated flows are correlated, non-stationary, and distributed as a Skew Exponential Power density. The assumptions made for both models were checked to ensure that the estimation of uncertainties in the parameters was not biased. The results showed that the Bayesian approach proved to be adequate to the proposed objectives, enabling and reinforcing the importance of assessing the uncertainties associated with hydrological modeling.

Improving photoelectron counting and particle identification in scintillation detectors with Bayesian techniques

NASA Astrophysics Data System (ADS)

Akashi-Ronquest, M.; Amaudruz, P.-A.; Batygov, M.; Beltran, B.; Bodmer, M.; Boulay, M. G.; Broerman, B.; Buck, B.; Butcher, A.; Cai, B.; Caldwell, T.; Chen, M.; Chen, Y.; Cleveland, B.; Coakley, K.; Dering, K.; Duncan, F. A.; Formaggio, J. A.; Gagnon, R.; Gastler, D.; Giuliani, F.; Gold, M.; Golovko, V. V.; Gorel, P.; Graham, K.; Grace, E.; Guerrero, N.; Guiseppe, V.; Hallin, A. L.; Harvey, P.; Hearns, C.; Henning, R.; Hime, A.; Hofgartner, J.; Jaditz, S.; Jillings, C. J.; Kachulis, C.; Kearns, E.; Kelsey, J.; Klein, J. R.; Kuźniak, M.; LaTorre, A.; Lawson, I.; Li, O.; Lidgard, J. J.; Liimatainen, P.; Linden, S.; McFarlane, K.; McKinsey, D. N.; MacMullin, S.; Mastbaum, A.; Mathew, R.; McDonald, A. B.; Mei, D.-M.; Monroe, J.; Muir, A.; Nantais, C.; Nicolics, K.; Nikkel, J. A.; Noble, T.; O'Dwyer, E.; Olsen, K.; Orebi Gann, G. D.; Ouellet, C.; Palladino, K.; Pasuthip, P.; Perumpilly, G.; Pollmann, T.; Rau, P.; Retière, F.; Rielage, K.; Schnee, R.; Seibert, S.; Skensved, P.; Sonley, T.; Vázquez-Jáuregui, E.; Veloce, L.; Walding, J.; Wang, B.; Wang, J.; Ward, M.; Zhang, C.

2015-05-01

Many current and future dark matter and neutrino detectors are designed to measure scintillation light with a large array of photomultiplier tubes (PMTs). The energy resolution and particle identification capabilities of these detectors depend in part on the ability to accurately identify individual photoelectrons in PMT waveforms despite large variability in pulse amplitudes and pulse pileup. We describe a Bayesian technique that can identify the times of individual photoelectrons in a sampled PMT waveform without deconvolution, even when pileup is present. To demonstrate the technique, we apply it to the general problem of particle identification in single-phase liquid argon dark matter detectors. Using the output of the Bayesian photoelectron counting algorithm described in this paper, we construct several test statistics for rejection of backgrounds for dark matter searches in argon. Compared to simpler methods based on either observed charge or peak finding, the photoelectron counting technique improves both energy resolution and particle identification of low energy events in calibration data from the DEAP-1 detector and simulation of the larger MiniCLEAN dark matter detector.

Topics in Computational Bayesian Statistics With Applications to Hierarchical Models in Astronomy and Sociology

NASA Astrophysics Data System (ADS)

Sahai, Swupnil

This thesis includes three parts. The overarching theme is how to analyze structured hierarchical data, with applications to astronomy and sociology. The first part discusses how expectation propagation can be used to parallelize the computation when fitting big hierarchical bayesian models. This methodology is then used to fit a novel, nonlinear mixture model to ultraviolet radiation from various regions of the observable universe. The second part discusses how the Stan probabilistic programming language can be used to numerically integrate terms in a hierarchical bayesian model. This technique is demonstrated on supernovae data to significantly speed up convergence to the posterior distribution compared to a previous study that used a Gibbs-type sampler. The third part builds a formal latent kernel representation for aggregate relational data as a way to more robustly estimate the mixing characteristics of agents in a network. In particular, the framework is applied to sociology surveys to estimate, as a function of ego age, the age and sex composition of the personal networks of individuals in the United States.

Evaluating science arguments: evidence, uncertainty, and argument strength.

PubMed

Corner, Adam; Hahn, Ulrike

2009-09-01

Public debates about socioscientific issues are increasingly prevalent, but the public response to messages about, for example, climate change, does not always seem to match the seriousness of the problem identified by scientists. Is there anything unique about appeals based on scientific evidence-do people evaluate science and nonscience arguments differently? In an attempt to apply a systematic framework to people's evaluation of science arguments, the authors draw on the Bayesian approach to informal argumentation. The Bayesian approach permits questions about how people evaluate science arguments to be posed and comparisons to be made between the evaluation of science and nonscience arguments. In an experiment involving three separate argument evaluation tasks, the authors investigated whether people's evaluations of science and nonscience arguments differed in any meaningful way. Although some differences were observed in the relative strength of science and nonscience arguments, the evaluation of science arguments was determined by the same factors as nonscience arguments. Our results suggest that science communicators wishing to construct a successful appeal can make use of the Bayesian framework to distinguish strong and weak arguments. 2009 APA, all rights reserved

Incorporating prior knowledge induced from stochastic differential equations in the classification of stochastic observations.

PubMed

Zollanvari, Amin; Dougherty, Edward R

2016-12-01

In classification, prior knowledge is incorporated in a Bayesian framework by assuming that the feature-label distribution belongs to an uncertainty class of feature-label distributions governed by a prior distribution. A posterior distribution is then derived from the prior and the sample data. An optimal Bayesian classifier (OBC) minimizes the expected misclassification error relative to the posterior distribution. From an application perspective, prior construction is critical. The prior distribution is formed by mapping a set of mathematical relations among the features and labels, the prior knowledge, into a distribution governing the probability mass across the uncertainty class. In this paper, we consider prior knowledge in the form of stochastic differential equations (SDEs). We consider a vector SDE in integral form involving a drift vector and dispersion matrix. Having constructed the prior, we develop the optimal Bayesian classifier between two models and examine, via synthetic experiments, the effects of uncertainty in the drift vector and dispersion matrix. We apply the theory to a set of SDEs for the purpose of differentiating the evolutionary history between two species.

Chiral Crystallization of Ethylenediamine Sulfate

ERIC Educational Resources Information Center

Koby, Lawrence; Ningappa, Jyothi B.; Dakesssian, Maria; Cuccia, Louis A.

2005-01-01

The optimal conditions for the crystallization of achiral ethylenediamine sulfate into large chiral crystals that are ideal for polarimetry studies and observation using Polaroid sheets are presented. This experiment is an ideal undergraduate experiment, which clearly demonstrates the chiral crystallization of an achiral molecule.

An approximately Bayesian delta-rule model explains the dynamics of belief updating in a changing environment.

PubMed

Nassar, Matthew R; Wilson, Robert C; Heasly, Benjamin; Gold, Joshua I

2010-09-15

Maintaining appropriate beliefs about variables needed for effective decision making can be difficult in a dynamic environment. One key issue is the amount of influence that unexpected outcomes should have on existing beliefs. In general, outcomes that are unexpected because of a fundamental change in the environment should carry more influence than outcomes that are unexpected because of persistent environmental stochasticity. Here we use a novel task to characterize how well human subjects follow these principles under a range of conditions. We show that the influence of an outcome depends on both the error made in predicting that outcome and the number of similar outcomes experienced previously. We also show that the exact nature of these tendencies varies considerably across subjects. Finally, we show that these patterns of behavior are consistent with a computationally simple reduction of an ideal-observer model. The model adjusts the influence of newly experienced outcomes according to ongoing estimates of uncertainty and the probability of a fundamental change in the process by which outcomes are generated. A prior that quantifies the expected frequency of such environmental changes accounts for individual variability, including a positive relationship between subjective certainty and the degree to which new information influences existing beliefs. The results suggest that the brain adaptively regulates the influence of decision outcomes on existing beliefs using straightforward updating rules that take into account both recent outcomes and prior expectations about higher-order environmental structure.

AFLP markers provide insights into the evolutionary relationships and diversification of New Caledonian Araucaria species (Araucariaceae).

PubMed

Gaudeul, Myriam; Rouhan, Germinal; Gardner, Martin F; Hollingsworth, Peter M

2012-01-01

Despite its small size, New Caledonia is characterized by a very diverse flora and striking environmental gradients, which make it an ideal setting to study species diversification. Thirteen of the 19 Araucaria species are endemic to the territory and form a monophyletic group, but patterns and processes that lead to such a high species richness are largely unexplored. We used 142 polymorphic AFLP markers and performed analyses based on Bayesian clustering algorithms, genetic distances, and cladistics on 71 samples representing all New Caledonian Araucaria species. We examined correlations between the inferred evolutionary relationships and shared morphological, ecological, or geographic parameters among species, to investigate evolutionary processes that may have driven speciation. We showed that genetic divergence among the present New Caledonian Araucaria species is low, suggesting recent diversification rather than pre-existence on Gondwana. We identified three genetic groups that included small-leaved, large-leaved, and coastal species, but detected no association with soil preference, ecological habitat, or rainfall. The observed patterns suggested that speciation events resulted from both differential adaptation and vicariance. Last, we hypothesize that speciation is ongoing and/or there are cryptic species in some genetically (sometimes also morphologically) divergent populations. Further data are required to provide better resolution and understanding of the diversification of New Caledonian Araucaria species. Nevertheless, our study allowed insights into their evolutionary relationships and provides a framework for future investigations on the evolution of this emblematic group of plants in one of the world's biodiversity hotspots.

Estimating relative risks in multicenter studies with a small number of centers - which methods to use? A simulation study.

PubMed

Pedroza, Claudia; Truong, Van Thi Thanh

2017-11-02

Analyses of multicenter studies often need to account for center clustering to ensure valid inference. For binary outcomes, it is particularly challenging to properly adjust for center when the number of centers or total sample size is small, or when there are few events per center. Our objective was to evaluate the performance of generalized estimating equation (GEE) log-binomial and Poisson models, generalized linear mixed models (GLMMs) assuming binomial and Poisson distributions, and a Bayesian binomial GLMM to account for center effect in these scenarios. We conducted a simulation study with few centers (≤30) and 50 or fewer subjects per center, using both a randomized controlled trial and an observational study design to estimate relative risk. We compared the GEE and GLMM models with a log-binomial model without adjustment for clustering in terms of bias, root mean square error (RMSE), and coverage. For the Bayesian GLMM, we used informative neutral priors that are skeptical of large treatment effects that are almost never observed in studies of medical interventions. All frequentist methods exhibited little bias, and the RMSE was very similar across the models. The binomial GLMM had poor convergence rates, ranging from 27% to 85%, but performed well otherwise. The results show that both GEE models need to use small sample corrections for robust SEs to achieve proper coverage of 95% CIs. The Bayesian GLMM had similar convergence rates but resulted in slightly more biased estimates for the smallest sample sizes. However, it had the smallest RMSE and good coverage across all scenarios. These results were very similar for both study designs. For the analyses of multicenter studies with a binary outcome and few centers, we recommend adjustment for center with either a GEE log-binomial or Poisson model with appropriate small sample corrections or a Bayesian binomial GLMM with informative priors.

Improved Determination of the Myelin Water Fraction in Human Brain using Magnetic Resonance Imaging through Bayesian Analysis of mcDESPOT

PubMed Central

Bouhrara, Mustapha; Spencer, Richard G.

2015-01-01

Myelin water fraction (MWF) mapping with magnetic resonance imaging has led to the ability to directly observe myelination and demyelination in both the developing brain and in disease. Multicomponent driven equilibrium single pulse observation of T1 and T2 (mcDESPOT) has been proposed as a rapid approach for multicomponent relaxometry and has been applied to map MWF in human brain. However, even for the simplest two-pool signal model consisting of MWF and non-myelin-associated water, the dimensionality of the parameter space for obtaining MWF estimates remains high. This renders parameter estimation difficult, especially at low-to-moderate signal-to-noise ratios (SNR), due to the presence of local minima and the flatness of the fit residual energy surface used for parameter determination using conventional nonlinear least squares (NLLS)-based algorithms. In this study, we introduce three Bayesian approaches for analysis of the mcDESPOT signal model to determine MWF. Given the high dimensional nature of mcDESPOT signal model, and, thereby, the high dimensional marginalizations over nuisance parameters needed to derive the posterior probability distribution of MWF parameter, the introduced Bayesian analyses use different approaches to reduce the dimensionality of the parameter space. The first approach uses normalization by average signal amplitude, and assumes that noise can be accurately estimated from signal-free regions of the image. The second approach likewise uses average amplitude normalization, but incorporates a full treatment of noise as an unknown variable through marginalization. The third approach does not use amplitude normalization and incorporates marginalization over both noise and signal amplitude. Through extensive Monte Carlo numerical simulations and analysis of in-vivo human brain datasets exhibiting a range of SNR and spatial resolution, we demonstrated the markedly improved accuracy and precision in the estimation of MWF using these Bayesian methods as compared to the stochastic region contraction (SRC) implementation of NLLS. PMID:26499810

Bayesian multimodel inference of soil microbial respiration models: Theory, application and future prospective

NASA Astrophysics Data System (ADS)

Elshall, A. S.; Ye, M.; Niu, G. Y.; Barron-Gafford, G.

2015-12-01

Models in biogeoscience involve uncertainties in observation data, model inputs, model structure, model processes and modeling scenarios. To accommodate for different sources of uncertainty, multimodal analysis such as model combination, model selection, model elimination or model discrimination are becoming more popular. To illustrate theoretical and practical challenges of multimodal analysis, we use an example about microbial soil respiration modeling. Global soil respiration releases more than ten times more carbon dioxide to the atmosphere than all anthropogenic emissions. Thus, improving our understanding of microbial soil respiration is essential for improving climate change models. This study focuses on a poorly understood phenomena, which is the soil microbial respiration pulses in response to episodic rainfall pulses (the "Birch effect"). We hypothesize that the "Birch effect" is generated by the following three mechanisms. To test our hypothesis, we developed and assessed five evolving microbial-enzyme models against field measurements from a semiarid Savannah that is characterized by pulsed precipitation. These five model evolve step-wise such that the first model includes none of these three mechanism, while the fifth model includes the three mechanisms. The basic component of Bayesian multimodal analysis is the estimation of marginal likelihood to rank the candidate models based on their overall likelihood with respect to observation data. The first part of the study focuses on using this Bayesian scheme to discriminate between these five candidate models. The second part discusses some theoretical and practical challenges, which are mainly the effect of likelihood function selection and the marginal likelihood estimation methods on both model ranking and Bayesian model averaging. The study shows that making valid inference from scientific data is not a trivial task, since we are not only uncertain about the candidate scientific models, but also about the statistical methods that are used to discriminate between these models.

Bayesian uncertainty analysis for complex systems biology models: emulation, global parameter searches and evaluation of gene functions.

PubMed

Vernon, Ian; Liu, Junli; Goldstein, Michael; Rowe, James; Topping, Jen; Lindsey, Keith

2018-01-02

Many mathematical models have now been employed across every area of systems biology. These models increasingly involve large numbers of unknown parameters, have complex structure which can result in substantial evaluation time relative to the needs of the analysis, and need to be compared to observed data of various forms. The correct analysis of such models usually requires a global parameter search, over a high dimensional parameter space, that incorporates and respects the most important sources of uncertainty. This can be an extremely difficult task, but it is essential for any meaningful inference or prediction to be made about any biological system. It hence represents a fundamental challenge for the whole of systems biology. Bayesian statistical methodology for the uncertainty analysis of complex models is introduced, which is designed to address the high dimensional global parameter search problem. Bayesian emulators that mimic the systems biology model but which are extremely fast to evaluate are embeded within an iterative history match: an efficient method to search high dimensional spaces within a more formal statistical setting, while incorporating major sources of uncertainty. The approach is demonstrated via application to a model of hormonal crosstalk in Arabidopsis root development, which has 32 rate parameters, for which we identify the sets of rate parameter values that lead to acceptable matches between model output and observed trend data. The multiple insights into the model's structure that this analysis provides are discussed. The methodology is applied to a second related model, and the biological consequences of the resulting comparison, including the evaluation of gene functions, are described. Bayesian uncertainty analysis for complex models using both emulators and history matching is shown to be a powerful technique that can greatly aid the study of a large class of systems biology models. It both provides insight into model behaviour and identifies the sets of rate parameters of interest.

Approximate Bayesian Computation by Subset Simulation using hierarchical state-space models

NASA Astrophysics Data System (ADS)

Vakilzadeh, Majid K.; Huang, Yong; Beck, James L.; Abrahamsson, Thomas

2017-02-01

A new multi-level Markov Chain Monte Carlo algorithm for Approximate Bayesian Computation, ABC-SubSim, has recently appeared that exploits the Subset Simulation method for efficient rare-event simulation. ABC-SubSim adaptively creates a nested decreasing sequence of data-approximating regions in the output space that correspond to increasingly closer approximations of the observed output vector in this output space. At each level, multiple samples of the model parameter vector are generated by a component-wise Metropolis algorithm so that the predicted output corresponding to each parameter value falls in the current data-approximating region. Theoretically, if continued to the limit, the sequence of data-approximating regions would converge on to the observed output vector and the approximate posterior distributions, which are conditional on the data-approximation region, would become exact, but this is not practically feasible. In this paper we study the performance of the ABC-SubSim algorithm for Bayesian updating of the parameters of dynamical systems using a general hierarchical state-space model. We note that the ABC methodology gives an approximate posterior distribution that actually corresponds to an exact posterior where a uniformly distributed combined measurement and modeling error is added. We also note that ABC algorithms have a problem with learning the uncertain error variances in a stochastic state-space model and so we treat them as nuisance parameters and analytically integrate them out of the posterior distribution. In addition, the statistical efficiency of the original ABC-SubSim algorithm is improved by developing a novel strategy to regulate the proposal variance for the component-wise Metropolis algorithm at each level. We demonstrate that Self-regulated ABC-SubSim is well suited for Bayesian system identification by first applying it successfully to model updating of a two degree-of-freedom linear structure for three cases: globally, locally and un-identifiable model classes, and then to model updating of a two degree-of-freedom nonlinear structure with Duffing nonlinearities in its interstory force-deflection relationship.

Prediction of road accidents: A Bayesian hierarchical approach.

PubMed

Deublein, Markus; Schubert, Matthias; Adey, Bryan T; Köhler, Jochen; Faber, Michael H

2013-03-01

In this paper a novel methodology for the prediction of the occurrence of road accidents is presented. The methodology utilizes a combination of three statistical methods: (1) gamma-updating of the occurrence rates of injury accidents and injured road users, (2) hierarchical multivariate Poisson-lognormal regression analysis taking into account correlations amongst multiple dependent model response variables and effects of discrete accident count data e.g. over-dispersion, and (3) Bayesian inference algorithms, which are applied by means of data mining techniques supported by Bayesian Probabilistic Networks in order to represent non-linearity between risk indicating and model response variables, as well as different types of uncertainties which might be present in the development of the specific models. Prior Bayesian Probabilistic Networks are first established by means of multivariate regression analysis of the observed frequencies of the model response variables, e.g. the occurrence of an accident, and observed values of the risk indicating variables, e.g. degree of road curvature. Subsequently, parameter learning is done using updating algorithms, to determine the posterior predictive probability distributions of the model response variables, conditional on the values of the risk indicating variables. The methodology is illustrated through a case study using data of the Austrian rural motorway network. In the case study, on randomly selected road segments the methodology is used to produce a model to predict the expected number of accidents in which an injury has occurred and the expected number of light, severe and fatally injured road users. Additionally, the methodology is used for geo-referenced identification of road sections with increased occurrence probabilities of injury accident events on a road link between two Austrian cities. It is shown that the proposed methodology can be used to develop models to estimate the occurrence of road accidents for any road network provided that the required data are available. Copyright © 2012 Elsevier Ltd. All rights reserved.

Development and comparison of Bayesian modularization method in uncertainty assessment of hydrological models

NASA Astrophysics Data System (ADS)

Li, L.; Xu, C.-Y.; Engeland, K.

2012-04-01

With respect to model calibration, parameter estimation and analysis of uncertainty sources, different approaches have been used in hydrological models. Bayesian method is one of the most widely used methods for uncertainty assessment of hydrological models, which incorporates different sources of information into a single analysis through Bayesian theorem. However, none of these applications can well treat the uncertainty in extreme flows of hydrological models' simulations. This study proposes a Bayesian modularization method approach in uncertainty assessment of conceptual hydrological models by considering the extreme flows. It includes a comprehensive comparison and evaluation of uncertainty assessments by a new Bayesian modularization method approach and traditional Bayesian models using the Metropolis Hasting (MH) algorithm with the daily hydrological model WASMOD. Three likelihood functions are used in combination with traditional Bayesian: the AR (1) plus Normal and time period independent model (Model 1), the AR (1) plus Normal and time period dependent model (Model 2) and the AR (1) plus multi-normal model (Model 3). The results reveal that (1) the simulations derived from Bayesian modularization method are more accurate with the highest Nash-Sutcliffe efficiency value, and (2) the Bayesian modularization method performs best in uncertainty estimates of entire flows and in terms of the application and computational efficiency. The study thus introduces a new approach for reducing the extreme flow's effect on the discharge uncertainty assessment of hydrological models via Bayesian. Keywords: extreme flow, uncertainty assessment, Bayesian modularization, hydrological model, WASMOD

Assessing methane emission estimation methods based on atmospheric measurements from oil and gas production using LES simulations

NASA Astrophysics Data System (ADS)

Saide, P. E.; Steinhoff, D.; Kosovic, B.; Weil, J.; Smith, N.; Blewitt, D.; Delle Monache, L.

2017-12-01

There are a wide variety of methods that have been proposed and used to estimate methane emissions from oil and gas production by using air composition and meteorology observations in conjunction with dispersion models. Although there has been some verification of these methodologies using controlled releases and concurrent atmospheric measurements, it is difficult to assess the accuracy of these methods for more realistic scenarios considering factors such as terrain, emissions from multiple components within a well pad, and time-varying emissions representative of typical operations. In this work we use a large-eddy simulation (LES) to generate controlled but realistic synthetic observations, which can be used to test multiple source term estimation methods, also known as an Observing System Simulation Experiment (OSSE). The LES is based on idealized simulations of the Weather Research & Forecasting (WRF) model at 10 m horizontal grid-spacing covering an 8 km by 7 km domain with terrain representative of a region located in the Barnett shale. Well pads are setup in the domain following a realistic distribution and emissions are prescribed every second for the components of each well pad (e.g., chemical injection pump, pneumatics, compressor, tanks, and dehydrator) using a simulator driven by oil and gas production volume, composition and realistic operational conditions. The system is setup to allow assessments under different scenarios such as normal operations, during liquids unloading events, or during other prescribed operational upset events. Methane and meteorology model output are sampled following the specifications of the emission estimation methodologies and considering typical instrument uncertainties, resulting in realistic observations (see Figure 1). We will show the evaluation of several emission estimation methods including the EPA Other Test Method 33A and estimates using the EPA AERMOD regulatory model. We will also show source estimation results from advanced methods such as variational inverse modeling, and Bayesian inference and stochastic sampling techniques. Future directions including other types of observations, other hydrocarbons being considered, and assessment of additional emission estimation methods will be discussed.

Coronal loop seismology using damping of standing kink oscillations by mode coupling. II. additional physical effects and Bayesian analysis

NASA Astrophysics Data System (ADS)

Pascoe, D. J.; Anfinogentov, S.; Nisticò, G.; Goddard, C. R.; Nakariakov, V. M.

2017-04-01

Context. The strong damping of kink oscillations of coronal loops can be explained by mode coupling. The damping envelope depends on the transverse density profile of the loop. Observational measurements of the damping envelope have been used to determine the transverse loop structure which is important for understanding other physical processes such as heating. Aims: The general damping envelope describing the mode coupling of kink waves consists of a Gaussian damping regime followed by an exponential damping regime. Recent observational detection of these damping regimes has been employed as a seismological tool. We extend the description of the damping behaviour to account for additional physical effects, namely a time-dependent period of oscillation, the presence of additional longitudinal harmonics, and the decayless regime of standing kink oscillations. Methods: We examine four examples of standing kink oscillations observed by the Atmospheric Imaging Assembly (AIA) onboard the Solar Dynamics Observatory (SDO). We use forward modelling of the loop position and investigate the dependence on the model parameters using Bayesian inference and Markov chain Monte Carlo (MCMC) sampling. Results: Our improvements to the physical model combined with the use of Bayesian inference and MCMC produce improved estimates of model parameters and their uncertainties. Calculation of the Bayes factor also allows us to compare the suitability of different physical models. We also use a new method based on spline interpolation of the zeroes of the oscillation to accurately describe the background trend of the oscillating loop. Conclusions: This powerful and robust method allows for accurate seismology of coronal loops, in particular the transverse density profile, and potentially reveals additional physical effects.

Prevalence of Neuropathic Pain in Cancer Patients: Pooled Estimates From a Systematic Review of Published Literature and Results From a Survey Conducted in 50 Italian Palliative Care Centers.

PubMed

Roberto, Anna; Deandrea, Silvia; Greco, Maria Teresa; Corli, Oscar; Negri, Eva; Pizzuto, Massimo; Ruggeri, Fabrizio

2016-06-01

Because of the increasing body of literature on neuropathic cancer pain (NCP), an accurate estimate of its prevalence requires recurring updates. To provide this estimate using information from a systematic review and a survey. Using MEDLINE, Embase, and a previous review, we searched for studies published up to 2014 reporting data on NCP prevalence in adult cancer populations. Pooled prevalence rates from observational prospective studies were computed. The association between NCP prevalence and possible predictors was investigated for oncology and palliative settings. Prevalence rates were extracted from a questionnaire answered by 137 physicians working in 50 Italian centers of palliative care. Estimates from studies conducted in palliative settings and from the experts were analyzed separately and eventually pooled with an informative Bayesian random-effect model. Twenty-nine observational studies were identified. The overall pooled prevalence was 31.2%, with high heterogeneity; similar figures were observed when oncology and palliative settings were individually considered. A slightly higher prevalence of NCP was detected for hospice/inpatients as compared to outpatients, in both settings. The mean NCP prevalence reported by the survey experts was 44.2%; the pooled Bayesian estimate for the palliative setting corresponded to 43.0% (95% CI: 40.0-46.0). The subgroup with the lowest heterogeneity and where the literature and experts' estimates were closest is hospice/inpatients, with a pooled Bayesian prevalence rate of 34.9% (95% CI: 29.9-41.0). The systematic review and the survey suggest that more than one in three patients with cancer pain also experiences NCP. Copyright © 2016 American Academy of Hospice and Palliative Medicine. Published by Elsevier Inc. All rights reserved.

A Bayesian prediction model between a biomarker and the clinical endpoint for dichotomous variables.

PubMed

Jiang, Zhiwei; Song, Yang; Shou, Qiong; Xia, Jielai; Wang, William

2014-12-20

Early biomarkers are helpful for predicting clinical endpoints and for evaluating efficacy in clinical trials even if the biomarker cannot replace clinical outcome as a surrogate. The building and evaluation of an association model between biomarkers and clinical outcomes are two equally important concerns regarding the prediction of clinical outcome. This paper is to address both issues in a Bayesian framework. A Bayesian meta-analytic approach is proposed to build a prediction model between the biomarker and clinical endpoint for dichotomous variables. Compared with other Bayesian methods, the proposed model only requires trial-level summary data of historical trials in model building. By using extensive simulations, we evaluate the link function and the application condition of the proposed Bayesian model under scenario (i) equal positive predictive value (PPV) and negative predictive value (NPV) and (ii) higher NPV and lower PPV. In the simulations, the patient-level data is generated to evaluate the meta-analytic model. PPV and NPV are employed to describe the patient-level relationship between the biomarker and the clinical outcome. The minimum number of historical trials to be included in building the model is also considered. It is seen from the simulations that the logit link function performs better than the odds and cloglog functions under both scenarios. PPV/NPV ≥0.5 for equal PPV and NPV, and PPV + NPV ≥1 for higher NPV and lower PPV are proposed in order to predict clinical outcome accurately and precisely when the proposed model is considered. Twenty historical trials are required to be included in model building when PPV and NPV are equal. For unequal PPV and NPV, the minimum number of historical trials for model building is proposed to be five. A hypothetical example shows an application of the proposed model in global drug development. The proposed Bayesian model is able to predict well the clinical endpoint from the observed biomarker data for dichotomous variables as long as the conditions are satisfied. It could be applied in drug development. But the practical problems in applications have to be studied in further research.

Bayesian data analysis in population ecology: motivations, methods, and benefits

USGS Publications Warehouse

Dorazio, Robert

2016-01-01

During the 20th century ecologists largely relied on the frequentist system of inference for the analysis of their data. However, in the past few decades ecologists have become increasingly interested in the use of Bayesian methods of data analysis. In this article I provide guidance to ecologists who would like to decide whether Bayesian methods can be used to improve their conclusions and predictions. I begin by providing a concise summary of Bayesian methods of analysis, including a comparison of differences between Bayesian and frequentist approaches to inference when using hierarchical models. Next I provide a list of problems where Bayesian methods of analysis may arguably be preferred over frequentist methods. These problems are usually encountered in analyses based on hierarchical models of data. I describe the essentials required for applying modern methods of Bayesian computation, and I use real-world examples to illustrate these methods. I conclude by summarizing what I perceive to be the main strengths and weaknesses of using Bayesian methods to solve ecological inference problems.

A Bayesian-frequentist two-stage single-arm phase II clinical trial design.

PubMed

Dong, Gaohong; Shih, Weichung Joe; Moore, Dirk; Quan, Hui; Marcella, Stephen

2012-08-30

It is well-known that both frequentist and Bayesian clinical trial designs have their own advantages and disadvantages. To have better properties inherited from these two types of designs, we developed a Bayesian-frequentist two-stage single-arm phase II clinical trial design. This design allows both early acceptance and rejection of the null hypothesis ( H(0) ). The measures (for example probability of trial early termination, expected sample size, etc.) of the design properties under both frequentist and Bayesian settings are derived. Moreover, under the Bayesian setting, the upper and lower boundaries are determined with predictive probability of trial success outcome. Given a beta prior and a sample size for stage I, based on the marginal distribution of the responses at stage I, we derived Bayesian Type I and Type II error rates. By controlling both frequentist and Bayesian error rates, the Bayesian-frequentist two-stage design has special features compared with other two-stage designs. Copyright © 2012 John Wiley & Sons, Ltd.

Using SPM 12’s Second-Level Bayesian Inference Procedure for fMRI Analysis: Practical Guidelines for End Users

PubMed Central

Han, Hyemin; Park, Joonsuk

2018-01-01

Recent debates about the conventional traditional threshold used in the fields of neuroscience and psychology, namely P < 0.05, have spurred researchers to consider alternative ways to analyze fMRI data. A group of methodologists and statisticians have considered Bayesian inference as a candidate methodology. However, few previous studies have attempted to provide end users of fMRI analysis tools, such as SPM 12, with practical guidelines about how to conduct Bayesian inference. In the present study, we aim to demonstrate how to utilize Bayesian inference, Bayesian second-level inference in particular, implemented in SPM 12 by analyzing fMRI data available to public via NeuroVault. In addition, to help end users understand how Bayesian inference actually works in SPM 12, we examine outcomes from Bayesian second-level inference implemented in SPM 12 by comparing them with those from classical second-level inference. Finally, we provide practical guidelines about how to set the parameters for Bayesian inference and how to interpret the results, such as Bayes factors, from the inference. We also discuss the practical and philosophical benefits of Bayesian inference and directions for future research. PMID:29456498

An introduction to Bayesian statistics in health psychology.

PubMed

Depaoli, Sarah; Rus, Holly M; Clifton, James P; van de Schoot, Rens; Tiemensma, Jitske

2017-09-01

The aim of the current article is to provide a brief introduction to Bayesian statistics within the field of health psychology. Bayesian methods are increasing in prevalence in applied fields, and they have been shown in simulation research to improve the estimation accuracy of structural equation models, latent growth curve (and mixture) models, and hierarchical linear models. Likewise, Bayesian methods can be used with small sample sizes since they do not rely on large sample theory. In this article, we discuss several important components of Bayesian statistics as they relate to health-based inquiries. We discuss the incorporation and impact of prior knowledge into the estimation process and the different components of the analysis that should be reported in an article. We present an example implementing Bayesian estimation in the context of blood pressure changes after participants experienced an acute stressor. We conclude with final thoughts on the implementation of Bayesian statistics in health psychology, including suggestions for reviewing Bayesian manuscripts and grant proposals. We have also included an extensive amount of online supplementary material to complement the content presented here, including Bayesian examples using many different software programmes and an extensive sensitivity analysis examining the impact of priors.

Dyadic Interactions in Service Encounter: Bayesian SEM Approach

NASA Astrophysics Data System (ADS)

Sagan, Adam; Kowalska-Musiał, Magdalena

Dyadic interactions are an important aspects in service encounters. They may be observed in B2B distribution channels, professional services, buying centers, family decision making or WOM communications. The networks consist of dyadic bonds that form dense but weak ties among the actors.

Prior approval: the growth of Bayesian methods in psychology.

PubMed

Andrews, Mark; Baguley, Thom

2013-02-01

Within the last few years, Bayesian methods of data analysis in psychology have proliferated. In this paper, we briefly review the history or the Bayesian approach to statistics, and consider the implications that Bayesian methods have for the theory and practice of data analysis in psychology.

Nonlinear, discrete flood event models, 1. Bayesian estimation of parameters

NASA Astrophysics Data System (ADS)

Bates, Bryson C.; Townley, Lloyd R.

1988-05-01

In this paper (Part 1), a Bayesian procedure for parameter estimation is applied to discrete flood event models. The essence of the procedure is the minimisation of a sum of squares function for models in which the computed peak discharge is nonlinear in terms of the parameters. This objective function is dependent on the observed and computed peak discharges for several storms on the catchment, information on the structure of observation error, and prior information on parameter values. The posterior covariance matrix gives a measure of the precision of the estimated parameters. The procedure is demonstrated using rainfall and runoff data from seven Australian catchments. It is concluded that the procedure is a powerful alternative to conventional parameter estimation techniques in situations where a number of floods are available for parameter estimation. Parts 2 and 3 will discuss the application of statistical nonlinearity measures and prediction uncertainty analysis to calibrated flood models. Bates (this volume) and Bates and Townley (this volume).

Non-local gravity and comparison with observational datasets. II. Updated results and Bayesian model comparison with ΛCDM

DOE Office of Scientific and Technical Information (OSTI.GOV)

Dirian, Yves; Foffa, Stefano; Kunz, Martin

We present a comprehensive and updated comparison with cosmological observations of two non-local modifications of gravity previously introduced by our group, the so called RR and RT models. We implement the background evolution and the cosmological perturbations of the models in a modified Boltzmann code, using CLASS. We then test the non-local models against the Planck 2015 TT, TE, EE and Cosmic Microwave Background (CMB) lensing data, isotropic and anisotropic Baryonic Acoustic Oscillations (BAO) data, JLA supernovae, H {sub 0} measurements and growth rate data, and we perform Bayesian parameter estimation. We then compare the RR, RT and ΛCDM models,more » using the Savage-Dickey method. We find that the RT model and ΛCDM perform equally well, while the performance of the RR model with respect to ΛCDM depends on whether or not we include a prior on H {sub 0} based on local measurements.« less

A Bayesian technique for improving the sensitivity of the atmospheric neutrino L/E analysis

DOE Office of Scientific and Technical Information (OSTI.GOV)

Blake, A. S. T.; Chapman, J. D.; Thomson, M. A.

Tmore » his paper outlines a method for improving the precision of atmospheric neutrino oscillation measurements. One experimental signature for these oscillations is an observed deficit in the rate of ν μ charged-current interactions with an oscillatory dependence on L ν / E ν , where L ν is the neutrino propagation distance and E mrow is="true"> ν is the neutrino energy. For contained-vertex atmospheric neutrino interactions, the L ν / E ν resolution varies significantly from event to event. he precision of the oscillation measurement can be improved by incorporating information on L ν / E ν resolution into the oscillation analysis. In the analysis presented here, a Bayesian technique is used to estimate the L ν / E ν resolution of observed atmospheric neutrinos on an event-by-event basis. By separating the events into bins of L ν / E ν resolution in the oscillation analysis, a significant improvement in oscillation sensitivity can be achieved.« less

A local approach for focussed Bayesian fusion

NASA Astrophysics Data System (ADS)

Sander, Jennifer; Heizmann, Michael; Goussev, Igor; Beyerer, Jürgen

2009-04-01

Local Bayesian fusion approaches aim to reduce high storage and computational costs of Bayesian fusion which is separated from fixed modeling assumptions. Using the small world formalism, we argue why this proceeding is conform with Bayesian theory. Then, we concentrate on the realization of local Bayesian fusion by focussing the fusion process solely on local regions that are task relevant with a high probability. The resulting local models correspond then to restricted versions of the original one. In a previous publication, we used bounds for the probability of misleading evidence to show the validity of the pre-evaluation of task specific knowledge and prior information which we perform to build local models. In this paper, we prove the validity of this proceeding using information theoretic arguments. For additional efficiency, local Bayesian fusion can be realized in a distributed manner. Here, several local Bayesian fusion tasks are evaluated and unified after the actual fusion process. For the practical realization of distributed local Bayesian fusion, software agents are predestinated. There is a natural analogy between the resulting agent based architecture and criminal investigations in real life. We show how this analogy can be used to improve the efficiency of distributed local Bayesian fusion additionally. Using a landscape model, we present an experimental study of distributed local Bayesian fusion in the field of reconnaissance, which highlights its high potential.

Opinion Dynamics with Confirmation Bias

PubMed Central

Allahverdyan, Armen E.; Galstyan, Aram

2014-01-01

Background Confirmation bias is the tendency to acquire or evaluate new information in a way that is consistent with one's preexisting beliefs. It is omnipresent in psychology, economics, and even scientific practices. Prior theoretical research of this phenomenon has mainly focused on its economic implications possibly missing its potential connections with broader notions of cognitive science. Methodology/Principal Findings We formulate a (non-Bayesian) model for revising subjective probabilistic opinion of a confirmationally-biased agent in the light of a persuasive opinion. The revision rule ensures that the agent does not react to persuasion that is either far from his current opinion or coincides with it. We demonstrate that the model accounts for the basic phenomenology of the social judgment theory, and allows to study various phenomena such as cognitive dissonance and boomerang effect. The model also displays the order of presentation effect–when consecutively exposed to two opinions, the preference is given to the last opinion (recency) or the first opinion (primacy) –and relates recency to confirmation bias. Finally, we study the model in the case of repeated persuasion and analyze its convergence properties. Conclusions The standard Bayesian approach to probabilistic opinion revision is inadequate for describing the observed phenomenology of persuasion process. The simple non-Bayesian model proposed here does agree with this phenomenology and is capable of reproducing a spectrum of effects observed in psychology: primacy-recency phenomenon, boomerang effect and cognitive dissonance. We point out several limitations of the model that should motivate its future development. PMID:25007078

Approximate Bayesian computation for forward modeling in cosmology

DOE Office of Scientific and Technical Information (OSTI.GOV)

Akeret, Joël; Refregier, Alexandre; Amara, Adam

Bayesian inference is often used in cosmology and astrophysics to derive constraints on model parameters from observations. This approach relies on the ability to compute the likelihood of the data given a choice of model parameters. In many practical situations, the likelihood function may however be unavailable or intractable due to non-gaussian errors, non-linear measurements processes, or complex data formats such as catalogs and maps. In these cases, the simulation of mock data sets can often be made through forward modeling. We discuss how Approximate Bayesian Computation (ABC) can be used in these cases to derive an approximation to themore » posterior constraints using simulated data sets. This technique relies on the sampling of the parameter set, a distance metric to quantify the difference between the observation and the simulations and summary statistics to compress the information in the data. We first review the principles of ABC and discuss its implementation using a Population Monte-Carlo (PMC) algorithm and the Mahalanobis distance metric. We test the performance of the implementation using a Gaussian toy model. We then apply the ABC technique to the practical case of the calibration of image simulations for wide field cosmological surveys. We find that the ABC analysis is able to provide reliable parameter constraints for this problem and is therefore a promising technique for other applications in cosmology and astrophysics. Our implementation of the ABC PMC method is made available via a public code release.« less

Disease Mapping for Stomach Cancer in Libya Based on Besag– York– Mollié (BYM) Model

PubMed

Alhdiri, Maryam Ahmed Salem; Samat, Nor Azah; Mohamed, Zulkifley

2017-06-25

Globally, Cancer is the ever-increasing health problem and most common cause of medical deaths. In Libya, it is an important health concern, especially in the setting of an aging population and limited healthcare facilities. Therefore, the goal of this research is to map of the county’ cancer incidence rate using the Bayesian method and identify the high-risk regions (for the first time in a decade). In the field of disease mapping, very little has been done to address the issue of analyzing sparse cancer diseases in Libya. Standardized Morbidity Ratio or SMR is known as a traditional approach to measure the relative risk of the disease, which is the ratio of observed and expected number of accounts in a region that has the greatest uncertainty if the disease is rare or small geographical region. Therefore, to solve some of SMR’s problems, we used statistical smoothing or Bayesian models to estimate the relative risk for stomach cancer incidence in Libya in 2007 based on the BYM model. This research begins with a short offer of the SMR and Bayesian model with BYM model, which we applied to stomach cancer incidence in Libya. We compared all of the results using maps and tables. We found that BYM model is potentially beneficial, because it gives better relative risk estimates compared to SMR method. As well as, it has can overcome the classical method problem when there is no observed stomach cancer in a region. Creative Commons Attribution License

Estimating mountain basin-mean precipitation from streamflow using Bayesian inference

NASA Astrophysics Data System (ADS)

Henn, Brian; Clark, Martyn P.; Kavetski, Dmitri; Lundquist, Jessica D.

2015-10-01

Estimating basin-mean precipitation in complex terrain is difficult due to uncertainty in the topographical representativeness of precipitation gauges relative to the basin. To address this issue, we use Bayesian methodology coupled with a multimodel framework to infer basin-mean precipitation from streamflow observations, and we apply this approach to snow-dominated basins in the Sierra Nevada of California. Using streamflow observations, forcing data from lower-elevation stations, the Bayesian Total Error Analysis (BATEA) methodology and the Framework for Understanding Structural Errors (FUSE), we infer basin-mean precipitation, and compare it to basin-mean precipitation estimated using topographically informed interpolation from gauges (PRISM, the Parameter-elevation Regression on Independent Slopes Model). The BATEA-inferred spatial patterns of precipitation show agreement with PRISM in terms of the rank of basins from wet to dry but differ in absolute values. In some of the basins, these differences may reflect biases in PRISM, because some implied PRISM runoff ratios may be inconsistent with the regional climate. We also infer annual time series of basin precipitation using a two-step calibration approach. Assessment of the precision and robustness of the BATEA approach suggests that uncertainty in the BATEA-inferred precipitation is primarily related to uncertainties in hydrologic model structure. Despite these limitations, time series of inferred annual precipitation under different model and parameter assumptions are strongly correlated with one another, suggesting that this approach is capable of resolving year-to-year variability in basin-mean precipitation.

Probabilistic prediction of barrier-island response to hurricanes

USGS Publications Warehouse

Plant, Nathaniel G.; Stockdon, Hilary F.

2012-01-01

Prediction of barrier-island response to hurricane attack is important for assessing the vulnerability of communities, infrastructure, habitat, and recreational assets to the impacts of storm surge, waves, and erosion. We have demonstrated that a conceptual model intended to make qualitative predictions of the type of beach response to storms (e.g., beach erosion, dune erosion, dune overwash, inundation) can be reformulated in a Bayesian network to make quantitative predictions of the morphologic response. In an application of this approach at Santa Rosa Island, FL, predicted dune-crest elevation changes in response to Hurricane Ivan explained about 20% to 30% of the observed variance. An extended Bayesian network based on the original conceptual model, which included dune elevations, storm surge, and swash, but with the addition of beach and dune widths as input variables, showed improved skill compared to the original model, explaining 70% of dune elevation change variance and about 60% of dune and shoreline position change variance. This probabilistic approach accurately represented prediction uncertainty (measured with the log likelihood ratio), and it outperformed the baseline prediction (i.e., the prior distribution based on the observations). Finally, sensitivity studies demonstrated that degrading the resolution of the Bayesian network or removing data from the calibration process reduced the skill of the predictions by 30% to 40%. The reduction in skill did not change conclusions regarding the relative importance of the input variables, and the extended model's skill always outperformed the original model.

Capturing changes in flood risk with Bayesian approaches for flood damage assessment

NASA Astrophysics Data System (ADS)

Vogel, Kristin; Schröter, Kai; Kreibich, Heidi; Thieken, Annegret; Müller, Meike; Sieg, Tobias; Laudan, Jonas; Kienzler, Sarah; Weise, Laura; Merz, Bruno; Scherbaum, Frank

2016-04-01

Flood risk is a function of hazard as well as of exposure and vulnerability. All three components are under change over space and time and have to be considered for reliable damage estimations and risk analyses, since this is the basis for an efficient, adaptable risk management. Hitherto, models for estimating flood damage are comparatively simple and cannot sufficiently account for changing conditions. The Bayesian network approach allows for a multivariate modeling of complex systems without relying on expert knowledge about physical constraints. In a Bayesian network each model component is considered to be a random variable. The way of interactions between those variables can be learned from observations or be defined by expert knowledge. Even a combination of both is possible. Moreover, the probabilistic framework captures uncertainties related to the prediction and provides a probability distribution for the damage instead of a point estimate. The graphical representation of Bayesian networks helps to study the change of probabilities for changing circumstances and may thus simplify the communication between scientists and public authorities. In the framework of the DFG-Research Training Group "NatRiskChange" we aim to develop Bayesian networks for flood damage and vulnerability assessments of residential buildings and companies under changing conditions. A Bayesian network learned from data, collected over the last 15 years in flooded regions in the Elbe and Danube catchments (Germany), reveals the impact of many variables like building characteristics, precaution and warning situation on flood damage to residential buildings. While the handling of incomplete and hybrid (discrete mixed with continuous) data are the most challenging issues in the study on residential buildings, a similar study, that focuses on the vulnerability of small to medium sized companies, bears new challenges. Relying on a much smaller data set for the determination of the model parameters, overly complex models should be avoided. A so called Markov Blanket approach aims at the identification of the most relevant factors and constructs a Bayesian network based on those findings. With our approach we want to exploit a major advantage of Bayesian networks which is their ability to consider dependencies not only pairwise, but to capture the joint effects and interactions of driving forces. Hence, the flood damage network does not only show the impact of precaution on the building damage separately, but also reveals the mutual effects of precaution and the quality of warning for a variety of flood settings. Thus, it allows for a consideration of changing conditions and different courses of action and forms a novel and valuable tool for decision support. This study is funded by the Deutsche Forschungsgemeinschaft (DFG) within the research training program GRK 2043/1 "NatRiskChange - Natural hazards and risks in a changing world" at the University of Potsdam.

Recognition of degraded handwritten digits using dynamic Bayesian networks

NASA Astrophysics Data System (ADS)

Likforman-Sulem, Laurence; Sigelle, Marc

2007-01-01

We investigate in this paper the application of dynamic Bayesian networks (DBNs) to the recognition of handwritten digits. The main idea is to couple two separate HMMs into various architectures. First, a vertical HMM and a horizontal HMM are built observing the evolving streams of image columns and image rows respectively. Then, two coupled architectures are proposed to model interactions between these two streams and to capture the 2D nature of character images. Experiments performed on the MNIST handwritten digit database show that coupled architectures yield better recognition performances than non-coupled ones. Additional experiments conducted on artificially degraded (broken) characters demonstrate that coupled architectures better cope with such degradation than non coupled ones and than discriminative methods such as SVMs.

A Community Assessmet of Biosignatures and their Frameworks

NASA Astrophysics Data System (ADS)

Domagal-Goldman, Shawn David; Nexus for Exoplanet Systems Science (NExSS)

2018-01-01

The Nexus for Exoplanet Systems Science (NExSS) organized a workshop to assess the current state of exoplanet biosignature research. Here, we review the products from that workshop. This includes: 1) a review of previously-proposed biosignatures in both the atmosphere and on the sruface of an exoplanet; 2) the need for context in assessing those biosignatures; 3) the potential for a Bayesian framework to formalize and quantify the need for context; 4) the interdisciplinary research required to advance that Bayesian framework; and 5) the missions that would search for biosignatures, including required contextual observations. Here we will revie those findings, the future path for research they suggest, and the implications they have for future missions, including both ground- and space-based missions.

VizieR Online Data Catalog: Giant HII regions BOND abundances (Vale Asari+, 2016)

NASA Astrophysics Data System (ADS)

Vale Asari, N.; Stasinska, G.; Morisset, C.; Cid Fernandes, R.

2017-10-01

BOND determines nitrogen and oxygen gas-phase abundances by using strong and semistrong lines and comparing them to a grid of photoionization models in a Bayesian framework. The code is written in python and its source is publicly available at http://bond.ufsc.br. The grid of models presented here is included in the 3MdB data base (Morisset, Delgado-Inglada & Flores-Fajardo 2015RMxAA..51..103M, see https://sites.google.com/site/mexicanmillionmodels/) under the reference 'BOND'. The Bayesian posterior probability calculated by bond stands on two pillars: our grid of models and our choice of observational constraints (from which we calculate our likelihoods). We discuss each of these in turn. (2 data files).

A full-Bayesian approach to parameter inference from tracer travel time moments and investigation of scale effects at the Cape Cod experimental site

USGS Publications Warehouse

Woodbury, Allan D.; Rubin, Yoram

2000-01-01

A method for inverting the travel time moments of solutes in heterogeneous aquifers is presented and is based on peak concentration arrival times as measured at various samplers in an aquifer. The approach combines a Lagrangian [Rubin and Dagan, 1992] solute transport framework with full‐Bayesian hydrogeological parameter inference. In the full‐Bayesian approach the noise values in the observed data are treated as hyperparameters, and their effects are removed by marginalization. The prior probability density functions (pdfs) for the model parameters (horizontal integral scale, velocity, and log K variance) and noise values are represented by prior pdfs developed from minimum relative entropy considerations. Analysis of the Cape Cod (Massachusetts) field experiment is presented. Inverse results for the hydraulic parameters indicate an expected value for the velocity, variance of log hydraulic conductivity, and horizontal integral scale of 0.42 m/d, 0.26, and 3.0 m, respectively. While these results are consistent with various direct‐field determinations, the importance of the findings is in the reduction of confidence range about the various expected values. On selected control planes we compare observed travel time frequency histograms with the theoretical pdf, conditioned on the observed travel time moments. We observe a positive skew in the travel time pdf which tends to decrease as the travel time distance grows. We also test the hypothesis that there is no scale dependence of the integral scale λ with the scale of the experiment at Cape Cod. We adopt two strategies. The first strategy is to use subsets of the full data set and then to see if the resulting parameter fits are different as we use different data from control planes at expanding distances from the source. The second approach is from the viewpoint of entropy concentration. No increase in integral scale with distance is inferred from either approach over the range of the Cape Cod tracer experiment.

Learning Parsimonious Classification Rules from Gene Expression Data Using Bayesian Networks with Local Structure.

PubMed

Lustgarten, Jonathan Lyle; Balasubramanian, Jeya Balaji; Visweswaran, Shyam; Gopalakrishnan, Vanathi

2017-03-01

The comprehensibility of good predictive models learned from high-dimensional gene expression data is attractive because it can lead to biomarker discovery. Several good classifiers provide comparable predictive performance but differ in their abilities to summarize the observed data. We extend a Bayesian Rule Learning (BRL-GSS) algorithm, previously shown to be a significantly better predictor than other classical approaches in this domain. It searches a space of Bayesian networks using a decision tree representation of its parameters with global constraints, and infers a set of IF-THEN rules. The number of parameters and therefore the number of rules are combinatorial to the number of predictor variables in the model. We relax these global constraints to a more generalizable local structure (BRL-LSS). BRL-LSS entails more parsimonious set of rules because it does not have to generate all combinatorial rules. The search space of local structures is much richer than the space of global structures. We design the BRL-LSS with the same worst-case time-complexity as BRL-GSS while exploring a richer and more complex model space. We measure predictive performance using Area Under the ROC curve (AUC) and Accuracy. We measure model parsimony performance by noting the average number of rules and variables needed to describe the observed data. We evaluate the predictive and parsimony performance of BRL-GSS, BRL-LSS and the state-of-the-art C4.5 decision tree algorithm, across 10-fold cross-validation using ten microarray gene-expression diagnostic datasets. In these experiments, we observe that BRL-LSS is similar to BRL-GSS in terms of predictive performance, while generating a much more parsimonious set of rules to explain the same observed data. BRL-LSS also needs fewer variables than C4.5 to explain the data with similar predictive performance. We also conduct a feasibility study to demonstrate the general applicability of our BRL methods on the newer RNA sequencing gene-expression data.

Adaptive framework to better characterize errors of apriori fluxes and observational residuals in a Bayesian setup for the urban flux inversions.

NASA Astrophysics Data System (ADS)

Ghosh, S.; Lopez-Coto, I.; Prasad, K.; Karion, A.; Mueller, K.; Gourdji, S.; Martin, C.; Whetstone, J. R.

2017-12-01

The National Institute of Standards and Technology (NIST) supports the North-East Corridor Baltimore Washington (NEC-B/W) project and Indianapolis Flux Experiment (INFLUX) aiming to quantify sources of Greenhouse Gas (GHG) emissions as well as their uncertainties. These projects employ different flux estimation methods including top-down inversion approaches. The traditional Bayesian inversion method estimates emission distributions by updating prior information using atmospheric observations of Green House Gases (GHG) coupled to an atmospheric and dispersion model. The magnitude of the update is dependent upon the observed enhancement along with the assumed errors such as those associated with prior information and the atmospheric transport and dispersion model. These errors are specified within the inversion covariance matrices. The assumed structure and magnitude of the specified errors can have large impact on the emission estimates from the inversion. The main objective of this work is to build a data-adaptive model for these covariances matrices. We construct a synthetic data experiment using a Kalman Filter inversion framework (Lopez et al., 2017) employing different configurations of transport and dispersion model and an assumed prior. Unlike previous traditional Bayesian approaches, we estimate posterior emissions using regularized sample covariance matrices associated with prior errors to investigate whether the structure of the matrices help to better recover our hypothetical true emissions. To incorporate transport model error, we use ensemble of transport models combined with space-time analytical covariance to construct a covariance that accounts for errors in space and time. A Kalman Filter is then run using these covariances along with Maximum Likelihood Estimates (MLE) of the involved parameters. Preliminary results indicate that specifying sptio-temporally varying errors in the error covariances can improve the flux estimates and uncertainties. We also demonstrate that differences between the modeled and observed meteorology can be used to predict uncertainties associated with atmospheric transport and dispersion modeling which can help improve the skill of an inversion at urban scales.

A Bayesian Nonparametric Approach to Test Equating

ERIC Educational Resources Information Center

Karabatsos, George; Walker, Stephen G.

2009-01-01

A Bayesian nonparametric model is introduced for score equating. It is applicable to all major equating designs, and has advantages over previous equating models. Unlike the previous models, the Bayesian model accounts for positive dependence between distributions of scores from two tests. The Bayesian model and the previous equating models are…

Bayesian Model Averaging for Propensity Score Analysis

ERIC Educational Resources Information Center

Kaplan, David; Chen, Jianshen

2013-01-01

The purpose of this study is to explore Bayesian model averaging in the propensity score context. Previous research on Bayesian propensity score analysis does not take into account model uncertainty. In this regard, an internally consistent Bayesian framework for model building and estimation must also account for model uncertainty. The…

Bayesian Analysis of Biogeography when the Number of Areas is Large

PubMed Central

Landis, Michael J.; Matzke, Nicholas J.; Moore, Brian R.; Huelsenbeck, John P.

2013-01-01

Historical biogeography is increasingly studied from an explicitly statistical perspective, using stochastic models to describe the evolution of species range as a continuous-time Markov process of dispersal between and extinction within a set of discrete geographic areas. The main constraint of these methods is the computational limit on the number of areas that can be specified. We propose a Bayesian approach for inferring biogeographic history that extends the application of biogeographic models to the analysis of more realistic problems that involve a large number of areas. Our solution is based on a “data-augmentation” approach, in which we first populate the tree with a history of biogeographic events that is consistent with the observed species ranges at the tips of the tree. We then calculate the likelihood of a given history by adopting a mechanistic interpretation of the instantaneous-rate matrix, which specifies both the exponential waiting times between biogeographic events and the relative probabilities of each biogeographic change. We develop this approach in a Bayesian framework, marginalizing over all possible biogeographic histories using Markov chain Monte Carlo (MCMC). Besides dramatically increasing the number of areas that can be accommodated in a biogeographic analysis, our method allows the parameters of a given biogeographic model to be estimated and different biogeographic models to be objectively compared. Our approach is implemented in the program, BayArea. [ancestral area analysis; Bayesian biogeographic inference; data augmentation; historical biogeography; Markov chain Monte Carlo.] PMID:23736102

Bayesian structured additive regression modeling of epidemic data: application to cholera

PubMed Central

2012-01-01

Background A significant interest in spatial epidemiology lies in identifying associated risk factors which enhances the risk of infection. Most studies, however, make no, or limited use of the spatial structure of the data, as well as possible nonlinear effects of the risk factors. Methods We develop a Bayesian Structured Additive Regression model for cholera epidemic data. Model estimation and inference is based on fully Bayesian approach via Markov Chain Monte Carlo (MCMC) simulations. The model is applied to cholera epidemic data in the Kumasi Metropolis, Ghana. Proximity to refuse dumps, density of refuse dumps, and proximity to potential cholera reservoirs were modeled as continuous functions; presence of slum settlers and population density were modeled as fixed effects, whereas spatial references to the communities were modeled as structured and unstructured spatial effects. Results We observe that the risk of cholera is associated with slum settlements and high population density. The risk of cholera is equal and lower for communities with fewer refuse dumps, but variable and higher for communities with more refuse dumps. The risk is also lower for communities distant from refuse dumps and potential cholera reservoirs. The results also indicate distinct spatial variation in the risk of cholera infection. Conclusion The study highlights the usefulness of Bayesian semi-parametric regression model analyzing public health data. These findings could serve as novel information to help health planners and policy makers in making effective decisions to control or prevent cholera epidemics. PMID:22866662

Uncertainty plus prior equals rational bias: an intuitive Bayesian probability weighting function.

PubMed

Fennell, John; Baddeley, Roland

2012-10-01

Empirical research has shown that when making choices based on probabilistic options, people behave as if they overestimate small probabilities, underestimate large probabilities, and treat positive and negative outcomes differently. These distortions have been modeled using a nonlinear probability weighting function, which is found in several nonexpected utility theories, including rank-dependent models and prospect theory; here, we propose a Bayesian approach to the probability weighting function and, with it, a psychological rationale. In the real world, uncertainty is ubiquitous and, accordingly, the optimal strategy is to combine probability statements with prior information using Bayes' rule. First, we show that any reasonable prior on probabilities leads to 2 of the observed effects; overweighting of low probabilities and underweighting of high probabilities. We then investigate 2 plausible kinds of priors: informative priors based on previous experience and uninformative priors of ignorance. Individually, these priors potentially lead to large problems of bias and inefficiency, respectively; however, when combined using Bayesian model comparison methods, both forms of prior can be applied adaptively, gaining the efficiency of empirical priors and the robustness of ignorance priors. We illustrate this for the simple case of generic good and bad options, using Internet blogs to estimate the relevant priors of inference. Given this combined ignorant/informative prior, the Bayesian probability weighting function is not only robust and efficient but also matches all of the major characteristics of the distortions found in empirical research. PsycINFO Database Record (c) 2012 APA, all rights reserved.

Evaluation of Bayesian approaches to identify DDT source contributions to soils in Southeast China.

PubMed

Zeng, Faming; Yang, Dan; Xing, Xinli; Qi, Shihua

2017-06-01

Dicofol application may be an important source to elevate the dichlorodiphenyltrichloroethane (DDT) residues to soils in Fujian, Southeast China, after the technical DDT was banned, which left DDT residues from the historical application. The DDT residues varied geographically, corresponding to the varied potential sources of DDT. In this study, a novel approach based on the Bayesian method (BM) was developed to identify the source contributions of DDT to soils, composed with both historical DDT and dicofol. The Naive Bayesian classifier was used basing on the subset of the samples, which were determined by chemical analysis independent of the Bayesian approach. The results show that BM (95%) was higher than that using the ratio of o, p'-/p, p'-DDT (84%) to identify DDT source contributions. High detection rate (97%) of dicofol (p, p'-OH-DDT) was observed in the subset, showing dicofol application influenced the DDX levels in soils in Fujian. However, the contribution from historical technical DDT source was greater than that from dicofol in Fujian, indicating historical technical DDT was still an important pollution source to soils. In addition, both the DDX (DDT isomers and derivatives) level and dicofol contribution in non-agricultural soils were higher than other agricultural land uses, especially in hilly regions, the potential cause may be the atmospheric transport of dicofol type DDT, after spraying during daytime, or regional difference on production and application. Copyright © 2017 Elsevier Ltd. All rights reserved.

A Bayesian Analysis of the Post-seismic Deformation of the Great 11 March 2011 Tohoku-Oki (Mw 9.0) Earthquake: Implications for Future Earthquake Occurrence

NASA Astrophysics Data System (ADS)

Ortega Culaciati, F. H.; Simons, M.; Minson, S. E.; Owen, S. E.; Moore, A. W.; Hetland, E. A.

2011-12-01

We aim to quantify the spatial distribution of after-slip following the Great 11 March 2011 Tohoku-Oki (Mw 9.0) earthquake and its implications for the occurrence of a future Great Earthquake, particularly in the Ibaraki region of Japan. We use a Bayesian approach (CATMIP algorithm), constrained by on-land Geonet GPS time series, to infer models of after-slip to date in the Japan megathrust. Unlike traditional inverse methods, in which a single optimum model is found, the Bayesian approach allows a complete characterization of the model parameter space by searching a-posteriori estimates of the range of plausible models. We use the Kullback-Liebler information divergence as a metric of the information gain on each subsurface slip patch, to quantify the extent to which land-based geodetic observations can constrain the upper parts of the megathrust, where the Great Tohoku-Oki earthquake took place. We aim to understand the relationships of spatial distribution of fault slip behavior in the different stages of the seismic cycle. We compare our post-seismic slip distributions to inter- and co-seismic slip distributions obtained through a Bayesian methodology as well as through traditional (optimization) inverse estimates in the published literature. We discuss implications of these analyses for the occurrence of a large earthquake in the Japan megathrust regions adjacent to the Great Tohoku-Oki earthquake.

Quantifying uncertainties in streamflow predictions through signature based inference of hydrological model parameters

NASA Astrophysics Data System (ADS)

Fenicia, Fabrizio; Reichert, Peter; Kavetski, Dmitri; Albert, Calro

2016-04-01

The calibration of hydrological models based on signatures (e.g. Flow Duration Curves - FDCs) is often advocated as an alternative to model calibration based on the full time series of system responses (e.g. hydrographs). Signature based calibration is motivated by various arguments. From a conceptual perspective, calibration on signatures is a way to filter out errors that are difficult to represent when calibrating on the full time series. Such errors may for example occur when observed and simulated hydrographs are shifted, either on the "time" axis (i.e. left or right), or on the "streamflow" axis (i.e. above or below). These shifts may be due to errors in the precipitation input (time or amount), and if not properly accounted in the likelihood function, may cause biased parameter estimates (e.g. estimated model parameters that do not reproduce the recession characteristics of a hydrograph). From a practical perspective, signature based calibration is seen as a possible solution for making predictions in ungauged basins. Where streamflow data are not available, it may in fact be possible to reliably estimate streamflow signatures. Previous research has for example shown how FDCs can be reliably estimated at ungauged locations based on climatic and physiographic influence factors. Typically, the goal of signature based calibration is not the prediction of the signatures themselves, but the prediction of the system responses. Ideally, the prediction of system responses should be accompanied by a reliable quantification of the associated uncertainties. Previous approaches for signature based calibration, however, do not allow reliable estimates of streamflow predictive distributions. Here, we illustrate how the Bayesian approach can be employed to obtain reliable streamflow predictive distributions based on signatures. A case study is presented, where a hydrological model is calibrated on FDCs and additional signatures. We propose an approach where the likelihood function for the signatures is derived from the likelihood for streamflow (rather than using an "ad-hoc" likelihood for the signatures as done in previous approaches). This likelihood is not easily tractable analytically and we therefore cannot apply "simple" MCMC methods. This numerical problem is solved using Approximate Bayesian Computation (ABC). Our result indicate that the proposed approach is suitable for producing reliable streamflow predictive distributions based on calibration to signature data. Moreover, our results provide indications on which signatures are more appropriate to represent the information content of the hydrograph.

The developmental effects of media-ideal internalization and self-objectification processes on adolescents' negative body-feelings, dietary restraint, and binge eating.

PubMed

Dakanalis, Antonios; Carrà, Giuseppe; Calogero, Rachel; Fida, Roberta; Clerici, Massimo; Zanetti, Maria Assunta; Riva, Giuseppe

2015-08-01

Despite accumulated experimental evidence of the negative effects of exposure to media-idealized images, the degree to which body image, and eating related disturbances are caused by media portrayals of gendered beauty ideals remains controversial. On the basis of the most up-to-date meta-analysis of experimental studies indicating that media-idealized images have the most harmful and substantial impact on vulnerable individuals regardless of gender (i.e., "internalizers" and "self-objectifiers"), the current longitudinal study examined the direct and mediated links posited in objectification theory among media-ideal internalization, self-objectification, shame and anxiety surrounding the body and appearance, dietary restraint, and binge eating. Data collected from 685 adolescents aged between 14 and 15 at baseline (47 % males), who were interviewed and completed standardized measures annually over a 3-year period, were analyzed using a structural equation modeling approach. Results indicated that media-ideal internalization predicted later thinking and scrutinizing of one's body from an external observer's standpoint (or self-objectification), which then predicted later negative emotional experiences related to one's body and appearance. In turn, these negative emotional experiences predicted subsequent dietary restraint and binge eating, and each of these core features of eating disorders influenced each other. Differences in the strength of these associations across gender were not observed, and all indirect effects were significant. The study provides valuable information about how the cultural values embodied by gendered beauty ideals negatively influence adolescents' feelings, thoughts and behaviors regarding their own body, and on the complex processes involved in disordered eating. Practical implications are discussed.

Quantized vortices in the ideal bose gas: a physical realization of random polynomials.

PubMed

Castin, Yvan; Hadzibabic, Zoran; Stock, Sabine; Dalibard, Jean; Stringari, Sandro

2006-02-03

We propose a physical system allowing one to experimentally observe the distribution of the complex zeros of a random polynomial. We consider a degenerate, rotating, quasi-ideal atomic Bose gas prepared in the lowest Landau level. Thermal fluctuations provide the randomness of the bosonic field and of the locations of the vortex cores. These vortices can be mapped to zeros of random polynomials, and observed in the density profile of the gas.

Bayesian Regression with Network Prior: Optimal Bayesian Filtering Perspective

PubMed Central

Qian, Xiaoning; Dougherty, Edward R.

2017-01-01

The recently introduced intrinsically Bayesian robust filter (IBRF) provides fully optimal filtering relative to a prior distribution over an uncertainty class ofjoint random process models, whereas formerly the theory was limited to model-constrained Bayesian robust filters, for which optimization was limited to the filters that are optimal for models in the uncertainty class. This paper extends the IBRF theory to the situation where there are both a prior on the uncertainty class and sample data. The result is optimal Bayesian filtering (OBF), where optimality is relative to the posterior distribution derived from the prior and the data. The IBRF theories for effective characteristics and canonical expansions extend to the OBF setting. A salient focus of the present work is to demonstrate the advantages of Bayesian regression within the OBF setting over the classical Bayesian approach in the context otlinear Gaussian models. PMID:28824268

An introduction to using Bayesian linear regression with clinical data.

PubMed

Baldwin, Scott A; Larson, Michael J

2017-11-01

Statistical training psychology focuses on frequentist methods. Bayesian methods are an alternative to standard frequentist methods. This article provides researchers with an introduction to fundamental ideas in Bayesian modeling. We use data from an electroencephalogram (EEG) and anxiety study to illustrate Bayesian models. Specifically, the models examine the relationship between error-related negativity (ERN), a particular event-related potential, and trait anxiety. Methodological topics covered include: how to set up a regression model in a Bayesian framework, specifying priors, examining convergence of the model, visualizing and interpreting posterior distributions, interval estimates, expected and predicted values, and model comparison tools. We also discuss situations where Bayesian methods can outperform frequentist methods as well has how to specify more complicated regression models. Finally, we conclude with recommendations about reporting guidelines for those using Bayesian methods in their own research. We provide data and R code for replicating our analyses. Copyright © 2017 Elsevier Ltd. All rights reserved.

A SAS Interface for Bayesian Analysis with WinBUGS

ERIC Educational Resources Information Center

Zhang, Zhiyong; McArdle, John J.; Wang, Lijuan; Hamagami, Fumiaki

2008-01-01

Bayesian methods are becoming very popular despite some practical difficulties in implementation. To assist in the practical application of Bayesian methods, we show how to implement Bayesian analysis with WinBUGS as part of a standard set of SAS routines. This implementation procedure is first illustrated by fitting a multiple regression model…

BMDS: A Collection of R Functions for Bayesian Multidimensional Scaling

ERIC Educational Resources Information Center

Okada, Kensuke; Shigemasu, Kazuo

2009-01-01

Bayesian multidimensional scaling (MDS) has attracted a great deal of attention because: (1) it provides a better fit than do classical MDS and ALSCAL; (2) it provides estimation errors of the distances; and (3) the Bayesian dimension selection criterion, MDSIC, provides a direct indication of optimal dimensionality. However, Bayesian MDS is not…

A Two-Step Bayesian Approach for Propensity Score Analysis: Simulations and Case Study

ERIC Educational Resources Information Center

Kaplan, David; Chen, Jianshen

2012-01-01

A two-step Bayesian propensity score approach is introduced that incorporates prior information in the propensity score equation and outcome equation without the problems associated with simultaneous Bayesian propensity score approaches. The corresponding variance estimators are also provided. The two-step Bayesian propensity score is provided for…

Bayesian inference for psychology. Part II: Example applications with JASP.

PubMed

Wagenmakers, Eric-Jan; Love, Jonathon; Marsman, Maarten; Jamil, Tahira; Ly, Alexander; Verhagen, Josine; Selker, Ravi; Gronau, Quentin F; Dropmann, Damian; Boutin, Bruno; Meerhoff, Frans; Knight, Patrick; Raj, Akash; van Kesteren, Erik-Jan; van Doorn, Johnny; Šmíra, Martin; Epskamp, Sacha; Etz, Alexander; Matzke, Dora; de Jong, Tim; van den Bergh, Don; Sarafoglou, Alexandra; Steingroever, Helen; Derks, Koen; Rouder, Jeffrey N; Morey, Richard D

2018-02-01

Bayesian hypothesis testing presents an attractive alternative to p value hypothesis testing. Part I of this series outlined several advantages of Bayesian hypothesis testing, including the ability to quantify evidence and the ability to monitor and update this evidence as data come in, without the need to know the intention with which the data were collected. Despite these and other practical advantages, Bayesian hypothesis tests are still reported relatively rarely. An important impediment to the widespread adoption of Bayesian tests is arguably the lack of user-friendly software for the run-of-the-mill statistical problems that confront psychologists for the analysis of almost every experiment: the t-test, ANOVA, correlation, regression, and contingency tables. In Part II of this series we introduce JASP ( http://www.jasp-stats.org ), an open-source, cross-platform, user-friendly graphical software package that allows users to carry out Bayesian hypothesis tests for standard statistical problems. JASP is based in part on the Bayesian analyses implemented in Morey and Rouder's BayesFactor package for R. Armed with JASP, the practical advantages of Bayesian hypothesis testing are only a mouse click away.

Applying Bayesian statistics to the study of psychological trauma: A suggestion for future research.

PubMed

Yalch, Matthew M

2016-03-01

Several contemporary researchers have noted the virtues of Bayesian methods of data analysis. Although debates continue about whether conventional or Bayesian statistics is the "better" approach for researchers in general, there are reasons why Bayesian methods may be well suited to the study of psychological trauma in particular. This article describes how Bayesian statistics offers practical solutions to the problems of data non-normality, small sample size, and missing data common in research on psychological trauma. After a discussion of these problems and the effects they have on trauma research, this article explains the basic philosophical and statistical foundations of Bayesian statistics and how it provides solutions to these problems using an applied example. Results of the literature review and the accompanying example indicates the utility of Bayesian statistics in addressing problems common in trauma research. Bayesian statistics provides a set of methodological tools and a broader philosophical framework that is useful for trauma researchers. Methodological resources are also provided so that interested readers can learn more. (c) 2016 APA, all rights reserved).

Bayesian analyses of time-interval data for environmental radiation monitoring.

PubMed

Luo, Peng; Sharp, Julia L; DeVol, Timothy A

2013-01-01

Time-interval (time difference between two consecutive pulses) analysis based on the principles of Bayesian inference was investigated for online radiation monitoring. Using experimental and simulated data, Bayesian analysis of time-interval data [Bayesian (ti)] was compared with Bayesian and a conventional frequentist analysis of counts in a fixed count time [Bayesian (cnt) and single interval test (SIT), respectively]. The performances of the three methods were compared in terms of average run length (ARL) and detection probability for several simulated detection scenarios. Experimental data were acquired with a DGF-4C system in list mode. Simulated data were obtained using Monte Carlo techniques to obtain a random sampling of the Poisson distribution. All statistical algorithms were developed using the R Project for statistical computing. Bayesian analysis of time-interval information provided a similar detection probability as Bayesian analysis of count information, but the authors were able to make a decision with fewer pulses at relatively higher radiation levels. In addition, for the cases with very short presence of the source (< count time), time-interval information is more sensitive to detect a change than count information since the source data is averaged by the background data over the entire count time. The relationships of the source time, change points, and modifications to the Bayesian approach for increasing detection probability are presented.

Embedding the results of focussed Bayesian fusion into a global context

NASA Astrophysics Data System (ADS)

Sander, Jennifer; Heizmann, Michael

2014-05-01

Bayesian statistics offers a well-founded and powerful fusion methodology also for the fusion of heterogeneous information sources. However, except in special cases, the needed posterior distribution is not analytically derivable. As consequence, Bayesian fusion may cause unacceptably high computational and storage costs in practice. Local Bayesian fusion approaches aim at reducing the complexity of the Bayesian fusion methodology significantly. This is done by concentrating the actual Bayesian fusion on the potentially most task relevant parts of the domain of the Properties of Interest. Our research on these approaches is motivated by an analogy to criminal investigations where criminalists pursue clues also only locally. This publication follows previous publications on a special local Bayesian fusion technique called focussed Bayesian fusion. Here, the actual calculation of the posterior distribution gets completely restricted to a suitably chosen local context. By this, the global posterior distribution is not completely determined. Strategies for using the results of a focussed Bayesian analysis appropriately are needed. In this publication, we primarily contrast different ways of embedding the results of focussed Bayesian fusion explicitly into a global context. To obtain a unique global posterior distribution, we analyze the application of the Maximum Entropy Principle that has been shown to be successfully applicable in metrology and in different other areas. To address the special need for making further decisions subsequently to the actual fusion task, we further analyze criteria for decision making under partial information.

Recent global methane trends: an investigation using hierarchical Bayesian methods

NASA Astrophysics Data System (ADS)

Rigby, M. L.; Stavert, A.; Ganesan, A.; Lunt, M. F.

2014-12-01

Following a decade with little growth, methane concentrations began to increase across the globe in 2007, and have continued to rise ever since. The reasons for this renewed growth are currently the subject of much debate. Here, we discuss the recent observed trends, and highlight some of the strengths and weaknesses in current "inverse" methods for quantifying fluxes using observations. In particular, we focus on the outstanding problems of accurately quantifying uncertainties in inverse frameworks. We examine to what extent the recent methane changes can be explained by the current generation of flux models and inventories. We examine the major modes of variability in wetland models along with the Global Fire Emissions Database (GFED) and the Emissions Database for Global Atmospheric Research (EDGAR). Using the Model for Ozone and Related Tracers (MOZART), we determine whether the spatial and temporal atmospheric trends predicted using these emissions can be brought into consistency with in situ atmospheric observations. We use a novel hierarchical Bayesian methodology in which scaling factors applied to the principal components of the flux fields are estimated simultaneously with the uncertainties associated with the a priori fluxes and with model representations of the observations. Using this method, we examine the predictive power of methane flux models for explaining recent fluctuations.

Multitime correlators in continuous measurement of qubit observables

NASA Astrophysics Data System (ADS)

Atalaya, Juan; Hacohen-Gourgy, Shay; Martin, Leigh S.; Siddiqi, Irfan; Korotkov, Alexander N.

2018-02-01

We consider multitime correlators for output signals from linear detectors, continuously measuring several qubit observables at the same time. Using the quantum Bayesian formalism, we show that for unital (symmetric) evolution in the absence of phase backaction, an N -time correlator can be expressed as a product of two-time correlators when N is even. For odd N , there is a similar factorization, which also includes a single-time average. Theoretical predictions agree well with experimental results for two detectors, which simultaneously measure noncommuting qubit observables.

The effectiveness of 28S and 16S molecular regions in resolving phylogeny of Malaysian microgastrinae (Hymenoptera: Braconidae)

NASA Astrophysics Data System (ADS)

Zuki, Ameyra Aman; Mohammed, Muhamad Azmi; Md-Zain, Badrul Munir; Yaakop, Salmah

2018-04-01

The phylogenetic relationships of Microgastrinae remains unclear though some studies have been conducted to resolve it. The function of Microgastrinae as endoparasitoids of Lepidopteran larvae makes this subfamily an ideal and potential species to be applied as biological control agent of infesting crops. In this study, a total of 13 microgastrine samples under 13 genera were collected from nine localities throughout Peninsular Malaysia. Two molecular regions, 28S nuclear marker and 16S mitochondrial marker were utilized in this study to examine the effectiveness of those regions in resolving the relationships within Microgastrinae. Total of 36 sequences were implemented in the analyses of NJ, MP and Bayesian for both markers. Results obtained from this study were supported by morphological and biological characters. Henceforth, the outcome from this study provides a proof of effectiveness of 28S and 16S molecular markers in studying the phylogenetic relationships of Microgastrinae from Malaysia exclusively and Oriental generally.

Idealism and materialism in perception.

PubMed

Rose, David; Brown, Dora

2015-01-01

Koenderink (2014, Perception, 43, 1-6) has said most Perception readers are deluded, because they believe an 'All Seeing Eye' observes an objective reality. We trace the source of Koenderink's assertion to his metaphysical idealism, and point to two major weaknesses in his position-namely, its dualism and foundationalism. We counter with arguments from modern philosophy of science for the existence of an objective material reality, contrast Koenderink's enactivism to his idealism, and point to ways in which phenomenology and cognitive science are complementary and not mutually exclusive.

Quantifying and reducing model-form uncertainties in Reynolds-averaged Navier–Stokes simulations: A data-driven, physics-informed Bayesian approach

DOE Office of Scientific and Technical Information (OSTI.GOV)

Xiao, H., E-mail: hengxiao@vt.edu; Wu, J.-L.; Wang, J.-X.

Despite their well-known limitations, Reynolds-Averaged Navier–Stokes (RANS) models are still the workhorse tools for turbulent flow simulations in today's engineering analysis, design and optimization. While the predictive capability of RANS models depends on many factors, for many practical flows the turbulence models are by far the largest source of uncertainty. As RANS models are used in the design and safety evaluation of many mission-critical systems such as airplanes and nuclear power plants, quantifying their model-form uncertainties has significant implications in enabling risk-informed decision-making. In this work we develop a data-driven, physics-informed Bayesian framework for quantifying model-form uncertainties in RANS simulations.more » Uncertainties are introduced directly to the Reynolds stresses and are represented with compact parameterization accounting for empirical prior knowledge and physical constraints (e.g., realizability, smoothness, and symmetry). An iterative ensemble Kalman method is used to assimilate the prior knowledge and observation data in a Bayesian framework, and to propagate them to posterior distributions of velocities and other Quantities of Interest (QoIs). We use two representative cases, the flow over periodic hills and the flow in a square duct, to evaluate the performance of the proposed framework. Both cases are challenging for standard RANS turbulence models. Simulation results suggest that, even with very sparse observations, the obtained posterior mean velocities and other QoIs have significantly better agreement with the benchmark data compared to the baseline results. At most locations the posterior distribution adequately captures the true model error within the developed model form uncertainty bounds. The framework is a major improvement over existing black-box, physics-neutral methods for model-form uncertainty quantification, where prior knowledge and details of the models are not exploited. This approach has potential implications in many fields in which the governing equations are well understood but the model uncertainty comes from unresolved physical processes. - Highlights: • Proposed a physics–informed framework to quantify uncertainty in RANS simulations. • Framework incorporates physical prior knowledge and observation data. • Based on a rigorous Bayesian framework yet fully utilizes physical model. • Applicable for many complex physical systems beyond turbulent flows.« less

Assessing global vegetation activity using spatio-temporal Bayesian modelling

NASA Astrophysics Data System (ADS)

Mulder, Vera L.; van Eck, Christel M.; Friedlingstein, Pierre; Regnier, Pierre A. G.

2016-04-01

This work demonstrates the potential of modelling vegetation activity using a hierarchical Bayesian spatio-temporal model. This approach allows modelling changes in vegetation and climate simultaneous in space and time. Changes of vegetation activity such as phenology are modelled as a dynamic process depending on climate variability in both space and time. Additionally, differences in observed vegetation status can be contributed to other abiotic ecosystem properties, e.g. soil and terrain properties. Although these properties do not change in time, they do change in space and may provide valuable information in addition to the climate dynamics. The spatio-temporal Bayesian models were calibrated at a regional scale because the local trends in space and time can be better captured by the model. The regional subsets were defined according to the SREX segmentation, as defined by the IPCC. Each region is considered being relatively homogeneous in terms of large-scale climate and biomes, still capturing small-scale (grid-cell level) variability. Modelling within these regions is hence expected to be less uncertain due to the absence of these large-scale patterns, compared to a global approach. This overall modelling approach allows the comparison of model behavior for the different regions and may provide insights on the main dynamic processes driving the interaction between vegetation and climate within different regions. The data employed in this study encompasses the global datasets for soil properties (SoilGrids), terrain properties (Global Relief Model based on SRTM DEM and ETOPO), monthly time series of satellite-derived vegetation indices (GIMMS NDVI3g) and climate variables (Princeton Meteorological Forcing Dataset). The findings proved the potential of a spatio-temporal Bayesian modelling approach for assessing vegetation dynamics, at a regional scale. The observed interrelationships of the employed data and the different spatial and temporal trends support our hypothesis. That is, the change of vegetation in space and time may be better understood when modelling vegetation change as both a dynamic and multivariate process. Therefore, future research will focus on a multivariate dynamical spatio-temporal modelling approach. This ongoing research is performed within the context of the project "Global impacts of hydrological and climatic extremes on vegetation" (project acronym: SAT-EX) which is part of the Belgian research programme for Earth Observation Stereo III.

Bayesian inference and assessment for rare-event bycatch in marine fisheries: a drift gillnet fishery case study.

PubMed

Martin, Summer L; Stohs, Stephen M; Moore, Jeffrey E

2015-03-01

Fisheries bycatch is a global threat to marine megafauna. Environmental laws require bycatch assessment for protected species, but this is difficult when bycatch is rare. Low bycatch rates, combined with low observer coverage, may lead to biased, imprecise estimates when using standard ratio estimators. Bayesian model-based approaches incorporate uncertainty, produce less volatile estimates, and enable probabilistic evaluation of estimates relative to management thresholds. Here, we demonstrate a pragmatic decision-making process that uses Bayesian model-based inferences to estimate the probability of exceeding management thresholds for bycatch in fisheries with < 100% observer coverage. Using the California drift gillnet fishery as a case study, we (1) model rates of rare-event bycatch and mortality using Bayesian Markov chain Monte Carlo estimation methods and 20 years of observer data; (2) predict unobserved counts of bycatch and mortality; (3) infer expected annual mortality; (4) determine probabilities of mortality exceeding regulatory thresholds; and (5) classify the fishery as having low, medium, or high bycatch impact using those probabilities. We focused on leatherback sea turtles (Dermochelys coriacea) and humpback whales (Megaptera novaeangliae). Candidate models included Poisson or zero-inflated Poisson likelihood, fishing effort, and a bycatch rate that varied with area, time, or regulatory regime. Regulatory regime had the strongest effect on leatherback bycatch, with the highest levels occurring prior to a regulatory change. Area had the strongest effect on humpback bycatch. Cumulative bycatch estimates for the 20-year period were 104-242 leatherbacks (52-153 deaths) and 6-50 humpbacks (0-21 deaths). The probability of exceeding a regulatory threshold under the U.S. Marine Mammal Protection Act (Potential Biological Removal, PBR) of 0.113 humpback deaths was 0.58, warranting a "medium bycatch impact" classification of the fishery. No PBR thresholds exist for leatherbacks, but the probability of exceeding an anticipated level of two deaths per year, stated as part of a U.S. Endangered Species Act assessment process, was 0.0007. The approach demonstrated here would allow managers to objectively and probabilistically classify fisheries with respect to bycatch impacts on species that have population-relevant mortality reference points, and declare with a stipulated level of certainty that bycatch did or did not exceed estimated upper bounds.

Quantifying the influences of spectral resolution on uncertainty in leaf trait estimates through a Bayesian approach to RTM inversion

DOE PAGES

Shiklomanov, Alexey N.; Dietze, Michael C.; Viskari, Toni; ...

2016-06-09

The remote monitoring of plant canopies is critically needed for understanding of terrestrial ecosystem mechanics and biodiversity as well as capturing the short- to long-term responses of vegetation to disturbance and climate change. A variety of orbital, sub-orbital, and field instruments have been used to retrieve optical spectral signals and to study different vegetation properties such as plant biochemistry, nutrient cycling, physiology, water status, and stress. Radiative transfer models (RTMs) provide a mechanistic link between vegetation properties and observed spectral features, and RTM spectral inversion is a useful framework for estimating these properties from spectral data. However, existing approaches tomore » RTM spectral inversion are typically limited by the inability to characterize uncertainty in parameter estimates. Here, we introduce a Bayesian algorithm for the spectral inversion of the PROSPECT 5 leaf RTM that is distinct from past approaches in two important ways: First, the algorithm only uses reflectance and does not require transmittance observations, which have been plagued by a variety of measurement and equipment challenges. Second, the output is not a point estimate for each parameter but rather the joint probability distribution that includes estimates of parameter uncertainties and covariance structure. We validated our inversion approach using a database of leaf spectra together with measurements of equivalent water thickness (EWT) and leaf dry mass per unit area (LMA). The parameters estimated by our inversion were able to accurately reproduce the observed reflectance (RMSE VIS = 0.0063, RMSE NIR-SWIR = 0.0098) and transmittance (RMSE VIS = 0.0404, RMSE NIR-SWIR = 0.0551) for both broadleaved and conifer species. Inversion estimates of EWT and LMA for broadleaved species agreed well with direct measurements (CV EWT = 18.8%, CV LMA = 24.5%), while estimates for conifer species were less accurate (CV EWT = 53.2%, CV LMA = 63.3%). To examine the influence of spectral resolution on parameter uncertainty, we simulated leaf reflectance as observed by ten common remote sensing platforms with varying spectral configurations and performed a Bayesian inversion on the resulting spectra. We found that full-range hyperspectral platforms were able to retrieve all parameters accurately and precisely, while the parameter estimates of multispectral platforms were much less precise and prone to bias at high and low values. We also observed that variations in the width and location of spectral bands influenced the shape of the covariance structure of parameter estimates. Lastly, our Bayesian spectral inversion provides a powerful and versatile framework for future RTM development and single- and multi-instrumental remote sensing of vegetation.« less

Quantifying the influences of spectral resolution on uncertainty in leaf trait estimates through a Bayesian approach to RTM inversion

DOE Office of Scientific and Technical Information (OSTI.GOV)

Shiklomanov, Alexey N.; Dietze, Michael C.; Viskari, Toni

The remote monitoring of plant canopies is critically needed for understanding of terrestrial ecosystem mechanics and biodiversity as well as capturing the short- to long-term responses of vegetation to disturbance and climate change. A variety of orbital, sub-orbital, and field instruments have been used to retrieve optical spectral signals and to study different vegetation properties such as plant biochemistry, nutrient cycling, physiology, water status, and stress. Radiative transfer models (RTMs) provide a mechanistic link between vegetation properties and observed spectral features, and RTM spectral inversion is a useful framework for estimating these properties from spectral data. However, existing approaches tomore » RTM spectral inversion are typically limited by the inability to characterize uncertainty in parameter estimates. Here, we introduce a Bayesian algorithm for the spectral inversion of the PROSPECT 5 leaf RTM that is distinct from past approaches in two important ways: First, the algorithm only uses reflectance and does not require transmittance observations, which have been plagued by a variety of measurement and equipment challenges. Second, the output is not a point estimate for each parameter but rather the joint probability distribution that includes estimates of parameter uncertainties and covariance structure. We validated our inversion approach using a database of leaf spectra together with measurements of equivalent water thickness (EWT) and leaf dry mass per unit area (LMA). The parameters estimated by our inversion were able to accurately reproduce the observed reflectance (RMSE VIS = 0.0063, RMSE NIR-SWIR = 0.0098) and transmittance (RMSE VIS = 0.0404, RMSE NIR-SWIR = 0.0551) for both broadleaved and conifer species. Inversion estimates of EWT and LMA for broadleaved species agreed well with direct measurements (CV EWT = 18.8%, CV LMA = 24.5%), while estimates for conifer species were less accurate (CV EWT = 53.2%, CV LMA = 63.3%). To examine the influence of spectral resolution on parameter uncertainty, we simulated leaf reflectance as observed by ten common remote sensing platforms with varying spectral configurations and performed a Bayesian inversion on the resulting spectra. We found that full-range hyperspectral platforms were able to retrieve all parameters accurately and precisely, while the parameter estimates of multispectral platforms were much less precise and prone to bias at high and low values. We also observed that variations in the width and location of spectral bands influenced the shape of the covariance structure of parameter estimates. Lastly, our Bayesian spectral inversion provides a powerful and versatile framework for future RTM development and single- and multi-instrumental remote sensing of vegetation.« less

Incorporation of GRACE Data into a Bayesian Model for Groundwater Drought Monitoring

NASA Astrophysics Data System (ADS)

Slinski, K.; Hogue, T. S.; McCray, J. E.; Porter, A.

2015-12-01

Groundwater drought, defined as the sustained occurrence of below average availability of groundwater, is marked by below average water levels in aquifers and reduced flows to groundwater-fed rivers and wetlands. The impact of groundwater drought on ecosystems, agriculture, municipal water supply, and the energy sector is an increasingly important global issue. However, current drought monitors heavily rely on precipitation and vegetative stress indices to characterize the timing, duration, and severity of drought events. The paucity of in situ observations of aquifer levels is a substantial obstacle to the development of systems to monitor groundwater drought in drought-prone areas, particularly in developing countries. Observations from the NASA/German Space Agency's Gravity Recovery and Climate Experiment (GRACE) have been used to estimate changes in groundwater storage over areas with sparse point measurements. This study incorporates GRACE total water storage observations into a Bayesian framework to assess the performance of a probabilistic model for monitoring groundwater drought based on remote sensing data. Overall, it is hoped that these methods will improve global drought preparedness and risk reduction by providing information on groundwater drought necessary to manage its impacts on ecosystems, as well as on the agricultural, municipal, and energy sectors.

Eddington's demon: inferring galaxy mass functions and other distributions from uncertain data

NASA Astrophysics Data System (ADS)

Obreschkow, D.; Murray, S. G.; Robotham, A. S. G.; Westmeier, T.

2018-03-01

We present a general modified maximum likelihood (MML) method for inferring generative distribution functions from uncertain and biased data. The MML estimator is identical to, but easier and many orders of magnitude faster to compute than the solution of the exact Bayesian hierarchical modelling of all measurement errors. As a key application, this method can accurately recover the mass function (MF) of galaxies, while simultaneously dealing with observational uncertainties (Eddington bias), complex selection functions and unknown cosmic large-scale structure. The MML method is free of binning and natively accounts for small number statistics and non-detections. Its fast implementation in the R-package dftools is equally applicable to other objects, such as haloes, groups, and clusters, as well as observables other than mass. The formalism readily extends to multidimensional distribution functions, e.g. a Choloniewski function for the galaxy mass-angular momentum distribution, also handled by dftools. The code provides uncertainties and covariances for the fitted model parameters and approximate Bayesian evidences. We use numerous mock surveys to illustrate and test the MML method, as well as to emphasize the necessity of accounting for observational uncertainties in MFs of modern galaxy surveys.

The Psychology of Bayesian Reasoning

DTIC Science & Technology

2014-10-21

The psychology of Bayesian reasoning David R. Mandel* Socio-Cognitive Systems Section, Defence Research and Development Canada and Department...belief revision, subjective probability, human judgment, psychological methods. Most psychological research on Bayesian reasoning since the 1970s has...attention to some important problems with the conventional approach to studying Bayesian reasoning in psychology that has been dominant since the

Bayesian Just-So Stories in Psychology and Neuroscience

ERIC Educational Resources Information Center

Bowers, Jeffrey S.; Davis, Colin J.

2012-01-01

According to Bayesian theories in psychology and neuroscience, minds and brains are (near) optimal in solving a wide range of tasks. We challenge this view and argue that more traditional, non-Bayesian approaches are more promising. We make 3 main arguments. First, we show that the empirical evidence for Bayesian theories in psychology is weak.…

Teaching Bayesian Statistics in a Health Research Methodology Program

ERIC Educational Resources Information Center

Pullenayegum, Eleanor M.; Thabane, Lehana

2009-01-01

Despite the appeal of Bayesian methods in health research, they are not widely used. This is partly due to a lack of courses in Bayesian methods at an appropriate level for non-statisticians in health research. Teaching such a course can be challenging because most statisticians have been taught Bayesian methods using a mathematical approach, and…

Bayesian inference based on dual generalized order statistics from the exponentiated Weibull model

NASA Astrophysics Data System (ADS)

Al Sobhi, Mashail M.

2015-02-01

Bayesian estimation for the two parameters and the reliability function of the exponentiated Weibull model are obtained based on dual generalized order statistics (DGOS). Also, Bayesian prediction bounds for future DGOS from exponentiated Weibull model are obtained. The symmetric and asymmetric loss functions are considered for Bayesian computations. The Markov chain Monte Carlo (MCMC) methods are used for computing the Bayes estimates and prediction bounds. The results have been specialized to the lower record values. Comparisons are made between Bayesian and maximum likelihood estimators via Monte Carlo simulation.

The Bayesian New Statistics: Hypothesis testing, estimation, meta-analysis, and power analysis from a Bayesian perspective.

PubMed

Kruschke, John K; Liddell, Torrin M

2018-02-01

In the practice of data analysis, there is a conceptual distinction between hypothesis testing, on the one hand, and estimation with quantified uncertainty on the other. Among frequentists in psychology, a shift of emphasis from hypothesis testing to estimation has been dubbed "the New Statistics" (Cumming 2014). A second conceptual distinction is between frequentist methods and Bayesian methods. Our main goal in this article is to explain how Bayesian methods achieve the goals of the New Statistics better than frequentist methods. The article reviews frequentist and Bayesian approaches to hypothesis testing and to estimation with confidence or credible intervals. The article also describes Bayesian approaches to meta-analysis, randomized controlled trials, and power analysis.

Application of Bayesian Approach in Cancer Clinical Trial

PubMed Central

Bhattacharjee, Atanu

2014-01-01

The application of Bayesian approach in clinical trials becomes more useful over classical method. It is beneficial from design to analysis phase. The straight forward statement is possible to obtain through Bayesian about the drug treatment effect. Complex computational problems are simple to handle with Bayesian techniques. The technique is only feasible to performing presence of prior information of the data. The inference is possible to establish through posterior estimates. However, some limitations are present in this method. The objective of this work was to explore the several merits and demerits of Bayesian approach in cancer research. The review of the technique will be helpful for the clinical researcher involved in the oncology to explore the limitation and power of Bayesian techniques. PMID:29147387

BONNSAI: correlated stellar observables in Bayesian methods

NASA Astrophysics Data System (ADS)

Schneider, F. R. N.; Castro, N.; Fossati, L.; Langer, N.; de Koter, A.

2017-02-01

In an era of large spectroscopic surveys of stars and big data, sophisticated statistical methods become more and more important in order to infer fundamental stellar parameters such as mass and age. Bayesian techniques are powerful methods because they can match all available observables simultaneously to stellar models while taking prior knowledge properly into account. However, in most cases it is assumed that observables are uncorrelated which is generally not the case. Here, we include correlations in the Bayesian code Bonnsai by incorporating the covariance matrix in the likelihood function. We derive a parametrisation of the covariance matrix that, in addition to classical uncertainties, only requires the specification of a correlation parameter that describes how observables co-vary. Our correlation parameter depends purely on the method with which observables have been determined and can be analytically derived in some cases. This approach therefore has the advantage that correlations can be accounted for even if information for them are not available in specific cases but are known in general. Because the new likelihood model is a better approximation of the data, the reliability and robustness of the inferred parameters are improved. We find that neglecting correlations biases the most likely values of inferred stellar parameters and affects the precision with which these parameters can be determined. The importance of these biases depends on the strength of the correlations and the uncertainties. For example, we apply our technique to massive OB stars, but emphasise that it is valid for any type of stars. For effective temperatures and surface gravities determined from atmosphere modelling, we find that masses can be underestimated on average by 0.5σ and mass uncertainties overestimated by a factor of about 2 when neglecting correlations. At the same time, the age precisions are underestimated over a wide range of stellar parameters. We conclude that accounting for correlations is essential in order to derive reliable stellar parameters including robust uncertainties and will be vital when entering an era of precision stellar astrophysics thanks to the Gaia satellite.

Bayesian Statistical Inference in Ion-Channel Models with Exact Missed Event Correction.

PubMed

Epstein, Michael; Calderhead, Ben; Girolami, Mark A; Sivilotti, Lucia G

2016-07-26

The stochastic behavior of single ion channels is most often described as an aggregated continuous-time Markov process with discrete states. For ligand-gated channels each state can represent a different conformation of the channel protein or a different number of bound ligands. Single-channel recordings show only whether the channel is open or shut: states of equal conductance are aggregated, so transitions between them have to be inferred indirectly. The requirement to filter noise from the raw signal further complicates the modeling process, as it limits the time resolution of the data. The consequence of the reduced bandwidth is that openings or shuttings that are shorter than the resolution cannot be observed; these are known as missed events. Postulated models fitted using filtered data must therefore explicitly account for missed events to avoid bias in the estimation of rate parameters and therefore assess parameter identifiability accurately. In this article, we present the first, to our knowledge, Bayesian modeling of ion-channels with exact missed events correction. Bayesian analysis represents uncertain knowledge of the true value of model parameters by considering these parameters as random variables. This allows us to gain a full appreciation of parameter identifiability and uncertainty when estimating values for model parameters. However, Bayesian inference is particularly challenging in this context as the correction for missed events increases the computational complexity of the model likelihood. Nonetheless, we successfully implemented a two-step Markov chain Monte Carlo method that we called "BICME", which performs Bayesian inference in models of realistic complexity. The method is demonstrated on synthetic and real single-channel data from muscle nicotinic acetylcholine channels. We show that parameter uncertainty can be characterized more accurately than with maximum-likelihood methods. Our code for performing inference in these ion channel models is publicly available. Copyright © 2016 Biophysical Society. Published by Elsevier Inc. All rights reserved.

Bayesian inference of the number of factors in gene-expression analysis: application to human virus challenge studies

PubMed Central

2010-01-01

Background Nonparametric Bayesian techniques have been developed recently to extend the sophistication of factor models, allowing one to infer the number of appropriate factors from the observed data. We consider such techniques for sparse factor analysis, with application to gene-expression data from three virus challenge studies. Particular attention is placed on employing the Beta Process (BP), the Indian Buffet Process (IBP), and related sparseness-promoting techniques to infer a proper number of factors. The posterior density function on the model parameters is computed using Gibbs sampling and variational Bayesian (VB) analysis. Results Time-evolving gene-expression data are considered for respiratory syncytial virus (RSV), Rhino virus, and influenza, using blood samples from healthy human subjects. These data were acquired in three challenge studies, each executed after receiving institutional review board (IRB) approval from Duke University. Comparisons are made between several alternative means of per-forming nonparametric factor analysis on these data, with comparisons as well to sparse-PCA and Penalized Matrix Decomposition (PMD), closely related non-Bayesian approaches. Conclusions Applying the Beta Process to the factor scores, or to the singular values of a pseudo-SVD construction, the proposed algorithms infer the number of factors in gene-expression data. For real data the "true" number of factors is unknown; in our simulations we consider a range of noise variances, and the proposed Bayesian models inferred the number of factors accurately relative to other methods in the literature, such as sparse-PCA and PMD. We have also identified a "pan-viral" factor of importance for each of the three viruses considered in this study. We have identified a set of genes associated with this pan-viral factor, of interest for early detection of such viruses based upon the host response, as quantified via gene-expression data. PMID:21062443

A fast Bayesian approach to discrete object detection in astronomical data sets - PowellSnakes I

NASA Astrophysics Data System (ADS)

Carvalho, Pedro; Rocha, Graça; Hobson, M. P.

2009-03-01

A new fast Bayesian approach is introduced for the detection of discrete objects immersed in a diffuse background. This new method, called PowellSnakes, speeds up traditional Bayesian techniques by (i) replacing the standard form of the likelihood for the parameters characterizing the discrete objects by an alternative exact form that is much quicker to evaluate; (ii) using a simultaneous multiple minimization code based on Powell's direction set algorithm to locate rapidly the local maxima in the posterior and (iii) deciding whether each located posterior peak corresponds to a real object by performing a Bayesian model selection using an approximate evidence value based on a local Gaussian approximation to the peak. The construction of this Gaussian approximation also provides the covariance matrix of the uncertainties in the derived parameter values for the object in question. This new approach provides a speed up in performance by a factor of `100' as compared to existing Bayesian source extraction methods that use Monte Carlo Markov chain to explore the parameter space, such as that presented by Hobson & McLachlan. The method can be implemented in either real or Fourier space. In the case of objects embedded in a homogeneous random field, working in Fourier space provides a further speed up that takes advantage of the fact that the correlation matrix of the background is circulant. We illustrate the capabilities of the method by applying to some simplified toy models. Furthermore, PowellSnakes has the advantage of consistently defining the threshold for acceptance/rejection based on priors which cannot be said of the frequentist methods. We present here the first implementation of this technique (version I). Further improvements to this implementation are currently under investigation and will be published shortly. The application of the method to realistic simulated Planck observations will be presented in a forthcoming publication.

Genomic prediction using an iterative conditional expectation algorithm for a fast BayesC-like model.

PubMed

Dong, Linsong; Wang, Zhiyong

2018-06-11

Genomic prediction is feasible for estimating genomic breeding values because of dense genome-wide markers and credible statistical methods, such as Genomic Best Linear Unbiased Prediction (GBLUP) and various Bayesian methods. Compared with GBLUP, Bayesian methods propose more flexible assumptions for the distributions of SNP effects. However, most Bayesian methods are performed based on Markov chain Monte Carlo (MCMC) algorithms, leading to computational efficiency challenges. Hence, some fast Bayesian approaches, such as fast BayesB (fBayesB), were proposed to speed up the calculation. This study proposed another fast Bayesian method termed fast BayesC (fBayesC). The prior distribution of fBayesC assumes that a SNP with probability γ has a non-zero effect which comes from a normal density with a common variance. The simulated data from QTLMAS XII workshop and actual data on large yellow croaker were used to compare the predictive results of fBayesB, fBayesC and (MCMC-based) BayesC. The results showed that when γ was set as a small value, such as 0.01 in the simulated data or 0.001 in the actual data, fBayesB and fBayesC yielded lower prediction accuracies (abilities) than BayesC. In the actual data, fBayesC could yield very similar predictive abilities as BayesC when γ ≥ 0.01. When γ = 0.01, fBayesB could also yield similar results as fBayesC and BayesC. However, fBayesB could not yield an explicit result when γ ≥ 0.1, but a similar situation was not observed for fBayesC. Moreover, the computational speed of fBayesC was significantly faster than that of BayesC, making fBayesC a promising method for genomic prediction.

Development of an ideal observer that incorporates nuisance parameters and processes list-mode data

DOE PAGES

MacGahan, Christopher Jonathan; Kupinski, Matthew Alan; Hilton, Nathan R.; ...

2016-02-01

Observer models were developed to process data in list-mode format in order to perform binary discrimination tasks for use in an arms-control-treaty context. Data used in this study was generated using GEANT4 Monte Carlo simulations for photons using custom models of plutonium inspection objects and a radiation imaging system. We evaluated observer model performance and then presented using the area under the receiver operating characteristic curve. Lastly, we studied the ideal observer under both signal-known-exactly conditions and in the presence of unknowns such as object orientation and absolute count-rate variability; when these additional sources of randomness were present, their incorporationmore » into the observer yielded superior performance.« less

Task performance in astronomical adaptive optics

NASA Astrophysics Data System (ADS)

Barrett, Harrison H.; Myers, Kyle J.; Devaney, Nicholas; Dainty, J. C.; Caucci, Luca

2006-06-01

In objective or task-based assessment of image quality, figures of merit are defined by the performance of some specific observer on some task of scientific interest. This methodology is well established in medical imaging but is just beginning to be applied in astronomy. In this paper we survey the theory needed to understand the performance of ideal or ideal-linear (Hotelling) observers on detection tasks with adaptive-optical data. The theory is illustrated by discussing its application to detection of exoplanets from a sequence of short-exposure images.

Analyzing Genome-Wide Association Studies with an FDR Controlling Modification of the Bayesian Information Criterion

PubMed Central

Dolejsi, Erich; Bodenstorfer, Bernhard; Frommlet, Florian

2014-01-01

The prevailing method of analyzing GWAS data is still to test each marker individually, although from a statistical point of view it is quite obvious that in case of complex traits such single marker tests are not ideal. Recently several model selection approaches for GWAS have been suggested, most of them based on LASSO-type procedures. Here we will discuss an alternative model selection approach which is based on a modification of the Bayesian Information Criterion (mBIC2) which was previously shown to have certain asymptotic optimality properties in terms of minimizing the misclassification error. Heuristic search strategies are introduced which attempt to find the model which minimizes mBIC2, and which are efficient enough to allow the analysis of GWAS data. Our approach is implemented in a software package called MOSGWA. Its performance in case control GWAS is compared with the two algorithms HLASSO and d-GWASelect, as well as with single marker tests, where we performed a simulation study based on real SNP data from the POPRES sample. Our results show that MOSGWA performs slightly better than HLASSO, where specifically for more complex models MOSGWA is more powerful with only a slight increase in Type I error. On the other hand according to our simulations GWASelect does not at all control the type I error when used to automatically determine the number of important SNPs. We also reanalyze the GWAS data from the Wellcome Trust Case-Control Consortium and compare the findings of the different procedures, where MOSGWA detects for complex diseases a number of interesting SNPs which are not found by other methods. PMID:25061809

Uncertainty Quantification Techniques for Population Density Estimates Derived from Sparse Open Source Data

DOE Office of Scientific and Technical Information (OSTI.GOV)

Stewart, Robert N; White, Devin A; Urban, Marie L

2013-01-01

The Population Density Tables (PDT) project at the Oak Ridge National Laboratory (www.ornl.gov) is developing population density estimates for specific human activities under normal patterns of life based largely on information available in open source. Currently, activity based density estimates are based on simple summary data statistics such as range and mean. Researchers are interested in improving activity estimation and uncertainty quantification by adopting a Bayesian framework that considers both data and sociocultural knowledge. Under a Bayesian approach knowledge about population density may be encoded through the process of expert elicitation. Due to the scale of the PDT effort whichmore » considers over 250 countries, spans 40 human activity categories, and includes numerous contributors, an elicitation tool is required that can be operationalized within an enterprise data collection and reporting system. Such a method would ideally require that the contributor have minimal statistical knowledge, require minimal input by a statistician or facilitator, consider human difficulties in expressing qualitative knowledge in a quantitative setting, and provide methods by which the contributor can appraise whether their understanding and associated uncertainty was well captured. This paper introduces an algorithm that transforms answers to simple, non-statistical questions into a bivariate Gaussian distribution as the prior for the Beta distribution. Based on geometric properties of the Beta distribution parameter feasibility space and the bivariate Gaussian distribution, an automated method for encoding is developed that responds to these challenging enterprise requirements. Though created within the context of population density, this approach may be applicable to a wide array of problem domains requiring informative priors for the Beta distribution.« less

In vivo social comparison to a thin-ideal peer promotes body dissatisfaction: a randomized experiment.

PubMed

Krones, Pamela G; Stice, Eric; Batres, Carla; Orjada, Kendra

2005-09-01

Although social comparison with media-portrayed thin-ideal images has been found to increase body dissatisfaction and negative affect, research has not yet tested whether social comparison with attractive peers in the real world produces similar effects. We randomly assigned 119 young women to interact either with a confederate who conformed to the thin ideal or one who conformed to the average body dimensions of women, within the context of an ostensive dating study. Exposure to the thin-ideal confederate resulted in an increase in body dissatisfaction but not negative affect or heart rate. Initial thin-ideal internalization, perceived sociocultural pressure, self-esteem, and observer-rated attractiveness did not moderate these effects. Results suggest that social comparative pressure to be thin fosters body dissatisfaction but may not promote negative affect. 2005 by Wiley Periodicals, Inc.

Bayesian models for cost-effectiveness analysis in the presence of structural zero costs

PubMed Central

Baio, Gianluca

2014-01-01

Bayesian modelling for cost-effectiveness data has received much attention in both the health economics and the statistical literature, in recent years. Cost-effectiveness data are characterised by a relatively complex structure of relationships linking a suitable measure of clinical benefit (e.g. quality-adjusted life years) and the associated costs. Simplifying assumptions, such as (bivariate) normality of the underlying distributions, are usually not granted, particularly for the cost variable, which is characterised by markedly skewed distributions. In addition, individual-level data sets are often characterised by the presence of structural zeros in the cost variable. Hurdle models can be used to account for the presence of excess zeros in a distribution and have been applied in the context of cost data. We extend their application to cost-effectiveness data, defining a full Bayesian specification, which consists of a model for the individual probability of null costs, a marginal model for the costs and a conditional model for the measure of effectiveness (given the observed costs). We presented the model using a working example to describe its main features. © 2013 The Authors. Statistics in Medicine published by John Wiley & Sons, Ltd. PMID:24343868

Nuclear charge radii: density functional theory meets Bayesian neural networks

NASA Astrophysics Data System (ADS)

Utama, R.; Chen, Wei-Chia; Piekarewicz, J.

2016-11-01

The distribution of electric charge in atomic nuclei is fundamental to our understanding of the complex nuclear dynamics and a quintessential observable to validate nuclear structure models. The aim of this study is to explore a novel approach that combines sophisticated models of nuclear structure with Bayesian neural networks (BNN) to generate predictions for the charge radii of thousands of nuclei throughout the nuclear chart. A class of relativistic energy density functionals is used to provide robust predictions for nuclear charge radii. In turn, these predictions are refined through Bayesian learning for a neural network that is trained using residuals between theoretical predictions and the experimental data. Although predictions obtained with density functional theory provide a fairly good description of experiment, our results show significant improvement (better than 40%) after BNN refinement. Moreover, these improved results for nuclear charge radii are supplemented with theoretical error bars. We have successfully demonstrated the ability of the BNN approach to significantly increase the accuracy of nuclear models in the predictions of nuclear charge radii. However, as many before us, we failed to uncover the underlying physics behind the intriguing behavior of charge radii along the calcium isotopic chain.

Bayesian models for cost-effectiveness analysis in the presence of structural zero costs.

PubMed

Baio, Gianluca

2014-05-20

Bayesian modelling for cost-effectiveness data has received much attention in both the health economics and the statistical literature, in recent years. Cost-effectiveness data are characterised by a relatively complex structure of relationships linking a suitable measure of clinical benefit (e.g. quality-adjusted life years) and the associated costs. Simplifying assumptions, such as (bivariate) normality of the underlying distributions, are usually not granted, particularly for the cost variable, which is characterised by markedly skewed distributions. In addition, individual-level data sets are often characterised by the presence of structural zeros in the cost variable. Hurdle models can be used to account for the presence of excess zeros in a distribution and have been applied in the context of cost data. We extend their application to cost-effectiveness data, defining a full Bayesian specification, which consists of a model for the individual probability of null costs, a marginal model for the costs and a conditional model for the measure of effectiveness (given the observed costs). We presented the model using a working example to describe its main features. © 2013 The Authors. Statistics in Medicine published by John Wiley & Sons, Ltd.

Uncertainty analysis of depth predictions from seismic reflection data using Bayesian statistics

NASA Astrophysics Data System (ADS)

Michelioudakis, Dimitrios G.; Hobbs, Richard W.; Caiado, Camila C. S.

2018-03-01

Estimating the depths of target horizons from seismic reflection data is an important task in exploration geophysics. To constrain these depths we need a reliable and accurate velocity model. Here, we build an optimum 2D seismic reflection data processing flow focused on pre - stack deghosting filters and velocity model building and apply Bayesian methods, including Gaussian process emulation and Bayesian History Matching (BHM), to estimate the uncertainties of the depths of key horizons near the borehole DSDP-258 located in the Mentelle Basin, south west of Australia, and compare the results with the drilled core from that well. Following this strategy, the tie between the modelled and observed depths from DSDP-258 core was in accordance with the ± 2σ posterior credibility intervals and predictions for depths to key horizons were made for the two new drill sites, adjacent the existing borehole of the area. The probabilistic analysis allowed us to generate multiple realizations of pre-stack depth migrated images, these can be directly used to better constrain interpretation and identify potential risk at drill sites. The method will be applied to constrain the drilling targets for the upcoming International Ocean Discovery Program (IODP), leg 369.

Uncertainty analysis of depth predictions from seismic reflection data using Bayesian statistics

NASA Astrophysics Data System (ADS)

Michelioudakis, Dimitrios G.; Hobbs, Richard W.; Caiado, Camila C. S.

2018-06-01

Estimating the depths of target horizons from seismic reflection data is an important task in exploration geophysics. To constrain these depths we need a reliable and accurate velocity model. Here, we build an optimum 2-D seismic reflection data processing flow focused on pre-stack deghosting filters and velocity model building and apply Bayesian methods, including Gaussian process emulation and Bayesian History Matching, to estimate the uncertainties of the depths of key horizons near the Deep Sea Drilling Project (DSDP) borehole 258 (DSDP-258) located in the Mentelle Basin, southwest of Australia, and compare the results with the drilled core from that well. Following this strategy, the tie between the modelled and observed depths from DSDP-258 core was in accordance with the ±2σ posterior credibility intervals and predictions for depths to key horizons were made for the two new drill sites, adjacent to the existing borehole of the area. The probabilistic analysis allowed us to generate multiple realizations of pre-stack depth migrated images, these can be directly used to better constrain interpretation and identify potential risk at drill sites. The method will be applied to constrain the drilling targets for the upcoming International Ocean Discovery Program, leg 369.

Hybrid-coded 3D structured illumination imaging with Bayesian estimation (Conference Presentation)

NASA Astrophysics Data System (ADS)

Chen, Hsi-Hsun; Luo, Yuan; Singh, Vijay R.

2016-03-01

Light induced fluorescent microscopy has long been developed to observe and understand the object at microscale, such as cellular sample. However, the transfer function of lense-based imaging system limits the resolution so that the fine and detailed structure of sample cannot be identified clearly. The techniques of resolution enhancement are fascinated to break the limit of resolution for objective given. In the past decades, the resolution enhancement imaging has been investigated through variety of strategies, including photoactivated localization microscopy (PALM), stochastic optical reconstruction microscopy (STORM), stimulated emission depletion (STED), and structure illuminated microscopy (SIM). In those methods, only SIM can intrinsically improve the resolution limit for a system without taking the structure properties of object into account. In this paper, we develop a SIM associated with Bayesian estimation, furthermore, with optical sectioning capability rendered from HiLo processing, resulting the high resolution through 3D volume. This 3D SIM can provide the optical sectioning and resolution enhancement performance, and be robust to noise owing to the Data driven Bayesian estimation reconstruction proposed. For validating the 3D SIM, we show our simulation result of algorithm, and the experimental result demonstrating the 3D resolution enhancement.

Bayesian energy landscape tilting: towards concordant models of molecular ensembles.

PubMed

Beauchamp, Kyle A; Pande, Vijay S; Das, Rhiju

2014-03-18

Predicting biological structure has remained challenging for systems such as disordered proteins that take on myriad conformations. Hybrid simulation/experiment strategies have been undermined by difficulties in evaluating errors from computational model inaccuracies and data uncertainties. Building on recent proposals from maximum entropy theory and nonequilibrium thermodynamics, we address these issues through a Bayesian energy landscape tilting (BELT) scheme for computing Bayesian hyperensembles over conformational ensembles. BELT uses Markov chain Monte Carlo to directly sample maximum-entropy conformational ensembles consistent with a set of input experimental observables. To test this framework, we apply BELT to model trialanine, starting from disagreeing simulations with the force fields ff96, ff99, ff99sbnmr-ildn, CHARMM27, and OPLS-AA. BELT incorporation of limited chemical shift and (3)J measurements gives convergent values of the peptide's α, β, and PPII conformational populations in all cases. As a test of predictive power, all five BELT hyperensembles recover set-aside measurements not used in the fitting and report accurate errors, even when starting from highly inaccurate simulations. BELT's principled framework thus enables practical predictions for complex biomolecular systems from discordant simulations and sparse data. Copyright © 2014 Biophysical Society. Published by Elsevier Inc. All rights reserved.

An application of Bayesian statistics to the extragalactic Cepheid distance scale

NASA Astrophysics Data System (ADS)

Barnes, Thomas G., III; Moffett, Thomas J.; Jefferys, W. H.; Forestell, Amy D.

2004-05-01

We have determined quasi-geometric distances to the Magellanic Clouds, M31 and M33. Our analysis uses a Bayesian statistical method to provide mathematically rigorous and objective solutions for individual Cepheids. We combine the individual distances with a hierarchial Bayesian model to determine the galactic distances. We obtain distance moduli 18.87 ± 0.07 mag (LMC, 12 stars), 19.14 ± 0.10 (SMC, 8 stars), 23.83 ± 0.35 mag (M33, 1 star) and 25.2 ± 0.6 mag (M31, 1 star) - all uncorrected for metallicity. The M31 and M33 distances are very preliminary. If the Pl relations of the LMC, SMC, and Galaxy are identical, our results exclude the metallicity effect in the V, (V - R) surface brightness method predicted by Hindsley and Bell (1989) at the 5σ level. Alternately, if Hindsley & Bell's prediction is adopted as true, we find a metallicity effect intrinsic to the Cepheid PL relation requiring a correction Δ(V - Mv) = (0.36 ± 0.07)Δ[A/H] mag. The latter has the opposite sign to other observational estimates of the Cepheid metallicity effect.

Sequential Bayesian Filters for Estimating Time Series of Wrapped and Unwrapped Angles with Hyperparameter Estimation

NASA Astrophysics Data System (ADS)

Umehara, Hiroaki; Okada, Masato; Naruse, Yasushi

2018-03-01

The estimation of angular time series data is a widespread issue relating to various situations involving rotational motion and moving objects. There are two kinds of problem settings: the estimation of wrapped angles, which are principal values in a circular coordinate system (e.g., the direction of an object), and the estimation of unwrapped angles in an unbounded coordinate system such as for the positioning and tracking of moving objects measured by the signal-wave phase. Wrapped angles have been estimated in previous studies by sequential Bayesian filtering; however, the hyperparameters that are to be solved and that control the properties of the estimation model were given a priori. The present study establishes a procedure of hyperparameter estimation from the observation data of angles only, using the framework of Bayesian inference completely as the maximum likelihood estimation. Moreover, the filter model is modified to estimate the unwrapped angles. It is proved that without noise our model reduces to the existing algorithm of Itoh's unwrapping transform. It is numerically confirmed that our model is an extension of unwrapping estimation from Itoh's unwrapping transform to the case with noise.

A cost minimisation and Bayesian inference model predicts startle reflex modulation across species.

PubMed

Bach, Dominik R

2015-04-07

In many species, rapid defensive reflexes are paramount to escaping acute danger. These reflexes are modulated by the state of the environment. This is exemplified in fear-potentiated startle, a more vigorous startle response during conditioned anticipation of an unrelated threatening event. Extant explanations of this phenomenon build on descriptive models of underlying psychological states, or neural processes. Yet, they fail to predict invigorated startle during reward anticipation and instructed attention, and do not explain why startle reflex modulation evolved. Here, we fill this lacuna by developing a normative cost minimisation model based on Bayesian optimality principles. This model predicts the observed pattern of startle modification by rewards, punishments, instructed attention, and several other states. Moreover, the mathematical formalism furnishes predictions that can be tested experimentally. Comparing the model with existing data suggests a specific neural implementation of the underlying computations which yields close approximations to the optimal solution under most circumstances. This analysis puts startle modification into the framework of Bayesian decision theory and predictive coding, and illustrates the importance of an adaptive perspective to interpret defensive behaviour across species. Copyright © 2015 The Author. Published by Elsevier Ltd.. All rights reserved.

A Bayesian analysis of HAT-P-7b using the EXONEST algorithm

DOE Office of Scientific and Technical Information (OSTI.GOV)

Placek, Ben; Knuth, Kevin H.

2015-01-13

The study of exoplanets (planets orbiting other stars) is revolutionizing the way we view our universe. High-precision photometric data provided by the Kepler Space Telescope (Kepler) enables not only the detection of such planets, but also their characterization. This presents a unique opportunity to apply Bayesian methods to better characterize the multitude of previously confirmed exoplanets. This paper focuses on applying the EXONEST algorithm to characterize the transiting short-period-hot-Jupiter, HAT-P-7b (also referred to as Kepler-2b). EXONEST evaluates a suite of exoplanet photometric models by applying Bayesian Model Selection, which is implemented with the MultiNest algorithm. These models take into accountmore » planetary effects, such as reflected light and thermal emissions, as well as the effect of the planetary motion on the host star, such as Doppler beaming, or boosting, of light from the reflex motion of the host star, and photometric variations due to the planet-induced ellipsoidal shape of the host star. By calculating model evidences, one can determine which model best describes the observed data, thus identifying which effects dominate the planetary system. Presented are parameter estimates and model evidences for HAT-P-7b.« less

Bayesian nonparametric regression with varying residual density

PubMed Central

Pati, Debdeep; Dunson, David B.

2013-01-01

We consider the problem of robust Bayesian inference on the mean regression function allowing the residual density to change flexibly with predictors. The proposed class of models is based on a Gaussian process prior for the mean regression function and mixtures of Gaussians for the collection of residual densities indexed by predictors. Initially considering the homoscedastic case, we propose priors for the residual density based on probit stick-breaking (PSB) scale mixtures and symmetrized PSB (sPSB) location-scale mixtures. Both priors restrict the residual density to be symmetric about zero, with the sPSB prior more flexible in allowing multimodal densities. We provide sufficient conditions to ensure strong posterior consistency in estimating the regression function under the sPSB prior, generalizing existing theory focused on parametric residual distributions. The PSB and sPSB priors are generalized to allow residual densities to change nonparametrically with predictors through incorporating Gaussian processes in the stick-breaking components. This leads to a robust Bayesian regression procedure that automatically down-weights outliers and influential observations in a locally-adaptive manner. Posterior computation relies on an efficient data augmentation exact block Gibbs sampler. The methods are illustrated using simulated and real data applications. PMID:24465053