Bayesian Travel Time Inversion adopting Gaussian Process Regression

NASA Astrophysics Data System (ADS)

Mauerberger, S.; Holschneider, M.

2017-12-01

A major application in seismology is the determination of seismic velocity models. Travel time measurements are putting an integral constraint on the velocity between source and receiver. We provide insight into travel time inversion from a correlation-based Bayesian point of view. Therefore, the concept of Gaussian process regression is adopted to estimate a velocity model. The non-linear travel time integral is approximated by a 1st order Taylor expansion. A heuristic covariance describes correlations amongst observations and a priori model. That approach enables us to assess a proxy of the Bayesian posterior distribution at ordinary computational costs. No multi dimensional numeric integration nor excessive sampling is necessary. Instead of stacking the data, we suggest to progressively build the posterior distribution. Incorporating only a single evidence at a time accounts for the deficit of linearization. As a result, the most probable model is given by the posterior mean whereas uncertainties are described by the posterior covariance.As a proof of concept, a synthetic purely 1d model is addressed. Therefore a single source accompanied by multiple receivers is considered on top of a model comprising a discontinuity. We consider travel times of both phases - direct and reflected wave - corrupted by noise. Left and right of the interface are assumed independent where the squared exponential kernel serves as covariance.

Bayesian spatiotemporal analysis of zero-inflated biological population density data by a delta-normal spatiotemporal additive model.

PubMed

Arcuti, Simona; Pollice, Alessio; Ribecco, Nunziata; D'Onghia, Gianfranco

2016-03-01

We evaluate the spatiotemporal changes in the density of a particular species of crustacean known as deep-water rose shrimp, Parapenaeus longirostris, based on biological sample data collected during trawl surveys carried out from 1995 to 2006 as part of the international project MEDITS (MEDiterranean International Trawl Surveys). As is the case for many biological variables, density data are continuous and characterized by unusually large amounts of zeros, accompanied by a skewed distribution of the remaining values. Here we analyze the normalized density data by a Bayesian delta-normal semiparametric additive model including the effects of covariates, using penalized regression with low-rank thin-plate splines for nonlinear spatial and temporal effects. Modeling the zero and nonzero values by two joint processes, as we propose in this work, allows to obtain great flexibility and easily handling of complex likelihood functions, avoiding inaccurate statistical inferences due to misclassification of the high proportion of exact zeros in the model. Bayesian model estimation is obtained by Markov chain Monte Carlo simulations, suitably specifying the complex likelihood function of the zero-inflated density data. The study highlights relevant nonlinear spatial and temporal effects and the influence of the annual Mediterranean oscillations index and of the sea surface temperature on the distribution of the deep-water rose shrimp density. © 2015 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

Nonlinear Bayesian filtering and learning: a neuronal dynamics for perception.

PubMed

Kutschireiter, Anna; Surace, Simone Carlo; Sprekeler, Henning; Pfister, Jean-Pascal

2017-08-18

The robust estimation of dynamical hidden features, such as the position of prey, based on sensory inputs is one of the hallmarks of perception. This dynamical estimation can be rigorously formulated by nonlinear Bayesian filtering theory. Recent experimental and behavioral studies have shown that animals' performance in many tasks is consistent with such a Bayesian statistical interpretation. However, it is presently unclear how a nonlinear Bayesian filter can be efficiently implemented in a network of neurons that satisfies some minimum constraints of biological plausibility. Here, we propose the Neural Particle Filter (NPF), a sampling-based nonlinear Bayesian filter, which does not rely on importance weights. We show that this filter can be interpreted as the neuronal dynamics of a recurrently connected rate-based neural network receiving feed-forward input from sensory neurons. Further, it captures properties of temporal and multi-sensory integration that are crucial for perception, and it allows for online parameter learning with a maximum likelihood approach. The NPF holds the promise to avoid the 'curse of dimensionality', and we demonstrate numerically its capability to outperform weighted particle filters in higher dimensions and when the number of particles is limited.

Nonlinear and non-Gaussian Bayesian based handwriting beautification

NASA Astrophysics Data System (ADS)

Shi, Cao; Xiao, Jianguo; Xu, Canhui; Jia, Wenhua

2013-03-01

A framework is proposed in this paper to effectively and efficiently beautify handwriting by means of a novel nonlinear and non-Gaussian Bayesian algorithm. In the proposed framework, format and size of handwriting image are firstly normalized, and then typeface in computer system is applied to optimize vision effect of handwriting. The Bayesian statistics is exploited to characterize the handwriting beautification process as a Bayesian dynamic model. The model parameters to translate, rotate and scale typeface in computer system are controlled by state equation, and the matching optimization between handwriting and transformed typeface is employed by measurement equation. Finally, the new typeface, which is transformed from the original one and gains the best nonlinear and non-Gaussian optimization, is the beautification result of handwriting. Experimental results demonstrate the proposed framework provides a creative handwriting beautification methodology to improve visual acceptance.

A Bayesian Approach for Nonlinear Structural Equation Models with Dichotomous Variables Using Logit and Probit Links

ERIC Educational Resources Information Center

Lee, Sik-Yum; Song, Xin-Yuan; Cai, Jing-Heng

2010-01-01

Analysis of ordered binary and unordered binary data has received considerable attention in social and psychological research. This article introduces a Bayesian approach, which has several nice features in practical applications, for analyzing nonlinear structural equation models with dichotomous data. We demonstrate how to use the software…

A baker's dozen of new particle flows for nonlinear filters, Bayesian decisions and transport

NASA Astrophysics Data System (ADS)

Daum, Fred; Huang, Jim

2015-05-01

We describe a baker's dozen of new particle flows to compute Bayes' rule for nonlinear filters, Bayesian decisions and learning as well as transport. Several of these new flows were inspired by transport theory, but others were inspired by physics or statistics or Markov chain Monte Carlo methods.

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.

A SEMIPARAMETRIC BAYESIAN MODEL FOR CIRCULAR-LINEAR REGRESSION

EPA Science Inventory

We present a Bayesian approach to regress a circular variable on a linear predictor. The regression coefficients are assumed to have a nonparametric distribution with a Dirichlet process prior. The semiparametric Bayesian approach gives added flexibility to the model and is usefu...

Kernel-imbedded Gaussian processes for disease classification using microarray gene expression data

PubMed Central

Zhao, Xin; Cheung, Leo Wang-Kit

2007-01-01

Background Designing appropriate machine learning methods for identifying genes that have a significant discriminating power for disease outcomes has become more and more important for our understanding of diseases at genomic level. Although many machine learning methods have been developed and applied to the area of microarray gene expression data analysis, the majority of them are based on linear models, which however are not necessarily appropriate for the underlying connection between the target disease and its associated explanatory genes. Linear model based methods usually also bring in false positive significant features more easily. Furthermore, linear model based algorithms often involve calculating the inverse of a matrix that is possibly singular when the number of potentially important genes is relatively large. This leads to problems of numerical instability. To overcome these limitations, a few non-linear methods have recently been introduced to the area. Many of the existing non-linear methods have a couple of critical problems, the model selection problem and the model parameter tuning problem, that remain unsolved or even untouched. In general, a unified framework that allows model parameters of both linear and non-linear models to be easily tuned is always preferred in real-world applications. Kernel-induced learning methods form a class of approaches that show promising potentials to achieve this goal. Results A hierarchical statistical model named kernel-imbedded Gaussian process (KIGP) is developed under a unified Bayesian framework for binary disease classification problems using microarray gene expression data. In particular, based on a probit regression setting, an adaptive algorithm with a cascading structure is designed to find the appropriate kernel, to discover the potentially significant genes, and to make the optimal class prediction accordingly. A Gibbs sampler is built as the core of the algorithm to make Bayesian inferences. Simulation studies showed that, even without any knowledge of the underlying generative model, the KIGP performed very close to the theoretical Bayesian bound not only in the case with a linear Bayesian classifier but also in the case with a very non-linear Bayesian classifier. This sheds light on its broader usability to microarray data analysis problems, especially to those that linear methods work awkwardly. The KIGP was also applied to four published microarray datasets, and the results showed that the KIGP performed better than or at least as well as any of the referred state-of-the-art methods did in all of these cases. Conclusion Mathematically built on the kernel-induced feature space concept under a Bayesian framework, the KIGP method presented in this paper provides a unified machine learning approach to explore both the linear and the possibly non-linear underlying relationship between the target features of a given binary disease classification problem and the related explanatory gene expression data. More importantly, it incorporates the model parameter tuning into the framework. The model selection problem is addressed in the form of selecting a proper kernel type. The KIGP method also gives Bayesian probabilistic predictions for disease classification. These properties and features are beneficial to most real-world applications. The algorithm is naturally robust in numerical computation. The simulation studies and the published data studies demonstrated that the proposed KIGP performs satisfactorily and consistently. PMID:17328811

Bayesian Techniques for Plasma Theory to Bridge the Gap Between Space and Lab Plasmas

NASA Astrophysics Data System (ADS)

Crabtree, Chris; Ganguli, Gurudas; Tejero, Erik

2017-10-01

We will show how Bayesian techniques provide a general data analysis methodology that is better suited to investigate phenomena that require a nonlinear theory for an explanation. We will provide short examples of how Bayesian techniques have been successfully used in the radiation belts to provide precise nonlinear spectral estimates of whistler mode chorus and how these techniques have been verified in laboratory plasmas. We will demonstrate how Bayesian techniques allow for the direct competition of different physical theories with data acting as the necessary arbitrator. This work is supported by the Naval Research Laboratory base program and by the National Aeronautics and Space Administration under Grant No. NNH15AZ90I.

A Bayesian Model for the Estimation of Latent Interaction and Quadratic Effects When Latent Variables Are Non-Normally Distributed

ERIC Educational Resources Information Center

Kelava, Augustin; Nagengast, Benjamin

2012-01-01

Structural equation models with interaction and quadratic effects have become a standard tool for testing nonlinear hypotheses in the social sciences. Most of the current approaches assume normally distributed latent predictor variables. In this article, we present a Bayesian model for the estimation of latent nonlinear effects when the latent…

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.

Regression analysis using dependent Polya trees.

PubMed

Schörgendorfer, Angela; Branscum, Adam J

2013-11-30

Many commonly used models for linear regression analysis force overly simplistic shape and scale constraints on the residual structure of data. We propose a semiparametric Bayesian model for regression analysis that produces data-driven inference by using a new type of dependent Polya tree prior to model arbitrary residual distributions that are allowed to evolve across increasing levels of an ordinal covariate (e.g., time, in repeated measurement studies). By modeling residual distributions at consecutive covariate levels or time points using separate, but dependent Polya tree priors, distributional information is pooled while allowing for broad pliability to accommodate many types of changing residual distributions. We can use the proposed dependent residual structure in a wide range of regression settings, including fixed-effects and mixed-effects linear and nonlinear models for cross-sectional, prospective, and repeated measurement data. A simulation study illustrates the flexibility of our novel semiparametric regression model to accurately capture evolving residual distributions. In an application to immune development data on immunoglobulin G antibodies in children, our new model outperforms several contemporary semiparametric regression models based on a predictive model selection criterion. Copyright © 2013 John Wiley & Sons, Ltd.

Bayesian hierarchical piecewise regression models: a tool to detect trajectory divergence between groups in long-term observational studies.

PubMed

Buscot, Marie-Jeanne; Wotherspoon, Simon S; Magnussen, Costan G; Juonala, Markus; Sabin, Matthew A; Burgner, David P; Lehtimäki, Terho; Viikari, Jorma S A; Hutri-Kähönen, Nina; Raitakari, Olli T; Thomson, Russell J

2017-06-06

Bayesian hierarchical piecewise regression (BHPR) modeling has not been previously formulated to detect and characterise the mechanism of trajectory divergence between groups of participants that have longitudinal responses with distinct developmental phases. These models are useful when participants in a prospective cohort study are grouped according to a distal dichotomous health outcome. Indeed, a refined understanding of how deleterious risk factor profiles develop across the life-course may help inform early-life interventions. Previous techniques to determine between-group differences in risk factors at each age may result in biased estimate of the age at divergence. We demonstrate the use of Bayesian hierarchical piecewise regression (BHPR) to generate a point estimate and credible interval for the age at which trajectories diverge between groups for continuous outcome measures that exhibit non-linear within-person response profiles over time. We illustrate our approach by modeling the divergence in childhood-to-adulthood body mass index (BMI) trajectories between two groups of adults with/without type 2 diabetes mellitus (T2DM) in the Cardiovascular Risk in Young Finns Study (YFS). Using the proposed BHPR approach, we estimated the BMI profiles of participants with T2DM diverged from healthy participants at age 16 years for males (95% credible interval (CI):13.5-18 years) and 21 years for females (95% CI: 19.5-23 years). These data suggest that a critical window for weight management intervention in preventing T2DM might exist before the age when BMI growth rate is naturally expected to decrease. Simulation showed that when using pairwise comparison of least-square means from categorical mixed models, smaller sample sizes tended to conclude a later age of divergence. In contrast, the point estimate of the divergence time is not biased by sample size when using the proposed BHPR method. BHPR is a powerful analytic tool to model long-term non-linear longitudinal outcomes, enabling the identification of the age at which risk factor trajectories diverge between groups of participants. The method is suitable for the analysis of unbalanced longitudinal data, with only a limited number of repeated measures per participants and where the time-related outcome is typically marked by transitional changes or by distinct phases of change over time.

Flexible link functions in nonparametric binary regression with Gaussian process priors.

PubMed

Li, Dan; Wang, Xia; Lin, Lizhen; Dey, Dipak K

2016-09-01

In many scientific fields, it is a common practice to collect a sequence of 0-1 binary responses from a subject across time, space, or a collection of covariates. Researchers are interested in finding out how the expected binary outcome is related to covariates, and aim at better prediction in the future 0-1 outcomes. Gaussian processes have been widely used to model nonlinear systems; in particular to model the latent structure in a binary regression model allowing nonlinear functional relationship between covariates and the expectation of binary outcomes. A critical issue in modeling binary response data is the appropriate choice of link functions. Commonly adopted link functions such as probit or logit links have fixed skewness and lack the flexibility to allow the data to determine the degree of the skewness. To address this limitation, we propose a flexible binary regression model which combines a generalized extreme value link function with a Gaussian process prior on the latent structure. Bayesian computation is employed in model estimation. Posterior consistency of the resulting posterior distribution is demonstrated. The flexibility and gains of the proposed model are illustrated through detailed simulation studies and two real data examples. Empirical results show that the proposed model outperforms a set of alternative models, which only have either a Gaussian process prior on the latent regression function or a Dirichlet prior on the link function. © 2015, The International Biometric Society.

Flexible Link Functions in Nonparametric Binary Regression with Gaussian Process Priors

PubMed Central

Li, Dan; Lin, Lizhen; Dey, Dipak K.

2015-01-01

Summary In many scientific fields, it is a common practice to collect a sequence of 0-1 binary responses from a subject across time, space, or a collection of covariates. Researchers are interested in finding out how the expected binary outcome is related to covariates, and aim at better prediction in the future 0-1 outcomes. Gaussian processes have been widely used to model nonlinear systems; in particular to model the latent structure in a binary regression model allowing nonlinear functional relationship between covariates and the expectation of binary outcomes. A critical issue in modeling binary response data is the appropriate choice of link functions. Commonly adopted link functions such as probit or logit links have fixed skewness and lack the flexibility to allow the data to determine the degree of the skewness. To address this limitation, we propose a flexible binary regression model which combines a generalized extreme value link function with a Gaussian process prior on the latent structure. Bayesian computation is employed in model estimation. Posterior consistency of the resulting posterior distribution is demonstrated. The flexibility and gains of the proposed model are illustrated through detailed simulation studies and two real data examples. Empirical results show that the proposed model outperforms a set of alternative models, which only have either a Gaussian process prior on the latent regression function or a Dirichlet prior on the link function. PMID:26686333

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.

[Evaluation of estimation of prevalence ratio using bayesian log-binomial regression model].

PubMed

Gao, W L; Lin, H; Liu, X N; Ren, X W; Li, J S; Shen, X P; Zhu, S L

2017-03-10

To evaluate the estimation of prevalence ratio ( PR ) by using bayesian log-binomial regression model and its application, we estimated the PR of medical care-seeking prevalence to caregivers' recognition of risk signs of diarrhea in their infants by using bayesian log-binomial regression model in Openbugs software. The results showed that caregivers' recognition of infant' s risk signs of diarrhea was associated significantly with a 13% increase of medical care-seeking. Meanwhile, we compared the differences in PR 's point estimation and its interval estimation of medical care-seeking prevalence to caregivers' recognition of risk signs of diarrhea and convergence of three models (model 1: not adjusting for the covariates; model 2: adjusting for duration of caregivers' education, model 3: adjusting for distance between village and township and child month-age based on model 2) between bayesian log-binomial regression model and conventional log-binomial regression model. The results showed that all three bayesian log-binomial regression models were convergence and the estimated PRs were 1.130(95 %CI : 1.005-1.265), 1.128(95 %CI : 1.001-1.264) and 1.132(95 %CI : 1.004-1.267), respectively. Conventional log-binomial regression model 1 and model 2 were convergence and their PRs were 1.130(95 % CI : 1.055-1.206) and 1.126(95 % CI : 1.051-1.203), respectively, but the model 3 was misconvergence, so COPY method was used to estimate PR , which was 1.125 (95 %CI : 1.051-1.200). In addition, the point estimation and interval estimation of PRs from three bayesian log-binomial regression models differed slightly from those of PRs from conventional log-binomial regression model, but they had a good consistency in estimating PR . Therefore, bayesian log-binomial regression model can effectively estimate PR with less misconvergence and have more advantages in application compared with conventional log-binomial regression model.

Bayesian inference of nonlinear unsteady aerodynamics from aeroelastic limit cycle oscillations

NASA Astrophysics Data System (ADS)

Sandhu, Rimple; Poirel, Dominique; Pettit, Chris; Khalil, Mohammad; Sarkar, Abhijit

2016-07-01

A Bayesian model selection and parameter estimation algorithm is applied to investigate the influence of nonlinear and unsteady aerodynamic loads on the limit cycle oscillation (LCO) of a pitching airfoil in the transitional Reynolds number regime. At small angles of attack, laminar boundary layer trailing edge separation causes negative aerodynamic damping leading to the LCO. The fluid-structure interaction of the rigid, but elastically mounted, airfoil and nonlinear unsteady aerodynamics is represented by two coupled nonlinear stochastic ordinary differential equations containing uncertain parameters and model approximation errors. Several plausible aerodynamic models with increasing complexity are proposed to describe the aeroelastic system leading to LCO. The likelihood in the posterior parameter probability density function (pdf) is available semi-analytically using the extended Kalman filter for the state estimation of the coupled nonlinear structural and unsteady aerodynamic model. The posterior parameter pdf is sampled using a parallel and adaptive Markov Chain Monte Carlo (MCMC) algorithm. The posterior probability of each model is estimated using the Chib-Jeliazkov method that directly uses the posterior MCMC samples for evidence (marginal likelihood) computation. The Bayesian algorithm is validated through a numerical study and then applied to model the nonlinear unsteady aerodynamic loads using wind-tunnel test data at various Reynolds numbers.

Bayesian inference of nonlinear unsteady aerodynamics from aeroelastic limit cycle oscillations

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

Sandhu, Rimple; Poirel, Dominique; Pettit, Chris

2016-07-01

A Bayesian model selection and parameter estimation algorithm is applied to investigate the influence of nonlinear and unsteady aerodynamic loads on the limit cycle oscillation (LCO) of a pitching airfoil in the transitional Reynolds number regime. At small angles of attack, laminar boundary layer trailing edge separation causes negative aerodynamic damping leading to the LCO. The fluid–structure interaction of the rigid, but elastically mounted, airfoil and nonlinear unsteady aerodynamics is represented by two coupled nonlinear stochastic ordinary differential equations containing uncertain parameters and model approximation errors. Several plausible aerodynamic models with increasing complexity are proposed to describe the aeroelastic systemmore » leading to LCO. The likelihood in the posterior parameter probability density function (pdf) is available semi-analytically using the extended Kalman filter for the state estimation of the coupled nonlinear structural and unsteady aerodynamic model. The posterior parameter pdf is sampled using a parallel and adaptive Markov Chain Monte Carlo (MCMC) algorithm. The posterior probability of each model is estimated using the Chib–Jeliazkov method that directly uses the posterior MCMC samples for evidence (marginal likelihood) computation. The Bayesian algorithm is validated through a numerical study and then applied to model the nonlinear unsteady aerodynamic loads using wind-tunnel test data at various Reynolds numbers.« less

Bayesian parameter estimation for nonlinear modelling of biological pathways.

PubMed

Ghasemi, Omid; Lindsey, Merry L; Yang, Tianyi; Nguyen, Nguyen; Huang, Yufei; Jin, Yu-Fang

2011-01-01

The availability of temporal measurements on biological experiments has significantly promoted research areas in systems biology. To gain insight into the interaction and regulation of biological systems, mathematical frameworks such as ordinary differential equations have been widely applied to model biological pathways and interpret the temporal data. Hill equations are the preferred formats to represent the reaction rate in differential equation frameworks, due to their simple structures and their capabilities for easy fitting to saturated experimental measurements. However, Hill equations are highly nonlinearly parameterized functions, and parameters in these functions cannot be measured easily. Additionally, because of its high nonlinearity, adaptive parameter estimation algorithms developed for linear parameterized differential equations cannot be applied. Therefore, parameter estimation in nonlinearly parameterized differential equation models for biological pathways is both challenging and rewarding. In this study, we propose a Bayesian parameter estimation algorithm to estimate parameters in nonlinear mathematical models for biological pathways using time series data. We used the Runge-Kutta method to transform differential equations to difference equations assuming a known structure of the differential equations. This transformation allowed us to generate predictions dependent on previous states and to apply a Bayesian approach, namely, the Markov chain Monte Carlo (MCMC) method. We applied this approach to the biological pathways involved in the left ventricle (LV) response to myocardial infarction (MI) and verified our algorithm by estimating two parameters in a Hill equation embedded in the nonlinear model. We further evaluated our estimation performance with different parameter settings and signal to noise ratios. Our results demonstrated the effectiveness of the algorithm for both linearly and nonlinearly parameterized dynamic systems. Our proposed Bayesian algorithm successfully estimated parameters in nonlinear mathematical models for biological pathways. This method can be further extended to high order systems and thus provides a useful tool to analyze biological dynamics and extract information using temporal data.

Research on Nonlinear Time Series Forecasting of Time-Delay NN Embedded with Bayesian Regularization

NASA Astrophysics Data System (ADS)

Jiang, Weijin; Xu, Yusheng; Xu, Yuhui; Wang, Jianmin

Based on the idea of nonlinear prediction of phase space reconstruction, this paper presented a time delay BP neural network model, whose generalization capability was improved by Bayesian regularization. Furthermore, the model is applied to forecast the imp&exp trades in one industry. The results showed that the improved model has excellent generalization capabilities, which not only learned the historical curve, but efficiently predicted the trend of business. Comparing with common evaluation of forecasts, we put on a conclusion that nonlinear forecast can not only focus on data combination and precision improvement, it also can vividly reflect the nonlinear characteristic of the forecasting system. While analyzing the forecasting precision of the model, we give a model judgment by calculating the nonlinear characteristic value of the combined serial and original serial, proved that the forecasting model can reasonably 'catch' the dynamic characteristic of the nonlinear system which produced the origin serial.

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

Bayesian Unimodal Density Regression for Causal Inference

ERIC Educational Resources Information Center

Karabatsos, George; Walker, Stephen G.

2011-01-01

Karabatsos and Walker (2011) introduced a new Bayesian nonparametric (BNP) regression model. Through analyses of real and simulated data, they showed that the BNP regression model outperforms other parametric and nonparametric regression models of common use, in terms of predictive accuracy of the outcome (dependent) variable. The other,…

Bayesian Asymmetric Regression as a Means to Estimate and Evaluate Oral Reading Fluency Slopes

ERIC Educational Resources Information Center

Solomon, Benjamin G.; Forsberg, Ole J.

2017-01-01

Bayesian techniques have become increasingly present in the social sciences, fueled by advances in computer speed and the development of user-friendly software. In this paper, we forward the use of Bayesian Asymmetric Regression (BAR) to monitor intervention responsiveness when using Curriculum-Based Measurement (CBM) to assess oral reading…

Bayesian multivariate hierarchical transformation models for ROC analysis.

PubMed

O'Malley, A James; Zou, Kelly H

2006-02-15

A Bayesian multivariate hierarchical transformation model (BMHTM) is developed for receiver operating characteristic (ROC) curve analysis based on clustered continuous diagnostic outcome data with covariates. Two special features of this model are that it incorporates non-linear monotone transformations of the outcomes and that multiple correlated outcomes may be analysed. The mean, variance, and transformation components are all modelled parametrically, enabling a wide range of inferences. The general framework is illustrated by focusing on two problems: (1) analysis of the diagnostic accuracy of a covariate-dependent univariate test outcome requiring a Box-Cox transformation within each cluster to map the test outcomes to a common family of distributions; (2) development of an optimal composite diagnostic test using multivariate clustered outcome data. In the second problem, the composite test is estimated using discriminant function analysis and compared to the test derived from logistic regression analysis where the gold standard is a binary outcome. The proposed methodology is illustrated on prostate cancer biopsy data from a multi-centre clinical trial.

Bayesian multivariate hierarchical transformation models for ROC analysis

PubMed Central

O'Malley, A. James; Zou, Kelly H.

2006-01-01

SUMMARY A Bayesian multivariate hierarchical transformation model (BMHTM) is developed for receiver operating characteristic (ROC) curve analysis based on clustered continuous diagnostic outcome data with covariates. Two special features of this model are that it incorporates non-linear monotone transformations of the outcomes and that multiple correlated outcomes may be analysed. The mean, variance, and transformation components are all modelled parametrically, enabling a wide range of inferences. The general framework is illustrated by focusing on two problems: (1) analysis of the diagnostic accuracy of a covariate-dependent univariate test outcome requiring a Box–Cox transformation within each cluster to map the test outcomes to a common family of distributions; (2) development of an optimal composite diagnostic test using multivariate clustered outcome data. In the second problem, the composite test is estimated using discriminant function analysis and compared to the test derived from logistic regression analysis where the gold standard is a binary outcome. The proposed methodology is illustrated on prostate cancer biopsy data from a multi-centre clinical trial. PMID:16217836

Two papers on feed-forward networks

NASA Technical Reports Server (NTRS)

Buntine, Wray L.; Weigend, Andreas S.

1991-01-01

Connectionist feed-forward networks, trained with back-propagation, can be used both for nonlinear regression and for (discrete one-of-C) classification, depending on the form of training. This report contains two papers on feed-forward networks. The papers can be read independently. They are intended for the theoretically-aware practitioner or algorithm-designer; however, they also contain a review and comparison of several learning theories so they provide a perspective for the theoretician. The first paper works through Bayesian methods to complement back-propagation in the training of feed-forward networks. The second paper addresses a problem raised by the first: how to efficiently calculate second derivatives on feed-forward networks.

Meta-regression analysis of the effect of trans fatty acids on low-density lipoprotein cholesterol.

PubMed

Allen, Bruce C; Vincent, Melissa J; Liska, DeAnn; Haber, Lynne T

2016-12-01

We conducted a meta-regression of controlled clinical trial data to investigate quantitatively the relationship between dietary intake of industrial trans fatty acids (iTFA) and increased low-density lipoprotein cholesterol (LDL-C). Previous regression analyses included insufficient data to determine the nature of the dose response in the low-dose region and have nonetheless assumed a linear relationship between iTFA intake and LDL-C levels. This work contributes to the previous work by 1) including additional studies examining low-dose intake (identified using an evidence mapping procedure); 2) investigating a range of curve shapes, including both linear and nonlinear models; and 3) using Bayesian meta-regression to combine results across trials. We found that, contrary to previous assumptions, the linear model does not acceptably fit the data, while the nonlinear, S-shaped Hill model fits the data well. Based on a conservative estimate of the degree of intra-individual variability in LDL-C (0.1 mmoL/L), as an estimate of a change in LDL-C that is not adverse, a change in iTFA intake of 2.2% of energy intake (%en) (corresponding to a total iTFA intake of 2.2-2.9%en) does not cause adverse effects on LDL-C. The iTFA intake associated with this change in LDL-C is substantially higher than the average iTFA intake (0.5%en). Copyright © 2016 The Authors. Published by Elsevier Ltd.. All rights reserved.

An Experimental Study in Determining Energy Expenditure from Treadmill Walking using Hip-Worn Inertial Sensors

PubMed Central

Vathsangam, Harshvardhan; Emken, Adar; Schroeder, E. Todd; Spruijt-Metz, Donna; Sukhatme, Gaurav S.

2011-01-01

This paper describes an experimental study in estimating energy expenditure from treadmill walking using a single hip-mounted triaxial inertial sensor comprised of a triaxial accelerometer and a triaxial gyroscope. Typical physical activity characterization using accelerometer generated counts suffers from two drawbacks - imprecison (due to proprietary counts) and incompleteness (due to incomplete movement description). We address these problems in the context of steady state walking by directly estimating energy expenditure with data from a hip-mounted inertial sensor. We represent the cyclic nature of walking with a Fourier transform of sensor streams and show how one can map this representation to energy expenditure (as measured by V O2 consumption, mL/min) using three regression techniques - Least Squares Regression (LSR), Bayesian Linear Regression (BLR) and Gaussian Process Regression (GPR). We perform a comparative analysis of the accuracy of sensor streams in predicting energy expenditure (measured by RMS prediction accuracy). Triaxial information is more accurate than uniaxial information. LSR based approaches are prone to outlier sensitivity and overfitting. Gyroscopic information showed equivalent if not better prediction accuracy as compared to accelerometers. Combining accelerometer and gyroscopic information provided better accuracy than using either sensor alone. We also analyze the best algorithmic approach among linear and nonlinear methods as measured by RMS prediction accuracy and run time. Nonlinear regression methods showed better prediction accuracy but required an order of magnitude of run time. This paper emphasizes the role of probabilistic techniques in conjunction with joint modeling of triaxial accelerations and rotational rates to improve energy expenditure prediction for steady-state treadmill walking. PMID:21690001

Sparse-grid, reduced-basis Bayesian inversion: Nonaffine-parametric nonlinear equations

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

Chen, Peng, E-mail: peng@ices.utexas.edu; Schwab, Christoph, E-mail: christoph.schwab@sam.math.ethz.ch

2016-07-01

We extend the reduced basis (RB) accelerated Bayesian inversion methods for affine-parametric, linear operator equations which are considered in [16,17] to non-affine, nonlinear parametric operator equations. We generalize the analysis of sparsity of parametric forward solution maps in [20] and of Bayesian inversion in [48,49] to the fully discrete setting, including Petrov–Galerkin high-fidelity (“HiFi”) discretization of the forward maps. We develop adaptive, stochastic collocation based reduction methods for the efficient computation of reduced bases on the parametric solution manifold. The nonaffinity and nonlinearity with respect to (w.r.t.) the distributed, uncertain parameters and the unknown solution is collocated; specifically, by themore » so-called Empirical Interpolation Method (EIM). For the corresponding Bayesian inversion problems, computational efficiency is enhanced in two ways: first, expectations w.r.t. the posterior are computed by adaptive quadratures with dimension-independent convergence rates proposed in [49]; the present work generalizes [49] to account for the impact of the PG discretization in the forward maps on the convergence rates of the Quantities of Interest (QoI for short). Second, we propose to perform the Bayesian estimation only w.r.t. a parsimonious, RB approximation of the posterior density. Based on the approximation results in [49], the infinite-dimensional parametric, deterministic forward map and operator admit N-term RB and EIM approximations which converge at rates which depend only on the sparsity of the parametric forward map. In several numerical experiments, the proposed algorithms exhibit dimension-independent convergence rates which equal, at least, the currently known rate estimates for N-term approximation. We propose to accelerate Bayesian estimation by first offline construction of reduced basis surrogates of the Bayesian posterior density. The parsimonious surrogates can then be employed for online data assimilation and for Bayesian estimation. They also open a perspective for optimal experimental design.« less

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.

A Bayesian approach to identifying structural nonlinearity using free-decay response: Application to damage detection in composites

USGS Publications Warehouse

Nichols, J.M.; Link, W.A.; Murphy, K.D.; Olson, C.C.

2010-01-01

This work discusses a Bayesian approach to approximating the distribution of parameters governing nonlinear structural systems. Specifically, we use a Markov Chain Monte Carlo method for sampling the posterior parameter distributions thus producing both point and interval estimates for parameters. The method is first used to identify both linear and nonlinear parameters in a multiple degree-of-freedom structural systems using free-decay vibrations. The approach is then applied to the problem of identifying the location, size, and depth of delamination in a model composite beam. The influence of additive Gaussian noise on the response data is explored with respect to the quality of the resulting parameter estimates.

Expectation propagation for large scale Bayesian inference of non-linear molecular networks from perturbation data.

PubMed

Narimani, Zahra; Beigy, Hamid; Ahmad, Ashar; Masoudi-Nejad, Ali; Fröhlich, Holger

2017-01-01

Inferring the structure of molecular networks from time series protein or gene expression data provides valuable information about the complex biological processes of the cell. Causal network structure inference has been approached using different methods in the past. Most causal network inference techniques, such as Dynamic Bayesian Networks and ordinary differential equations, are limited by their computational complexity and thus make large scale inference infeasible. This is specifically true if a Bayesian framework is applied in order to deal with the unavoidable uncertainty about the correct model. We devise a novel Bayesian network reverse engineering approach using ordinary differential equations with the ability to include non-linearity. Besides modeling arbitrary, possibly combinatorial and time dependent perturbations with unknown targets, one of our main contributions is the use of Expectation Propagation, an algorithm for approximate Bayesian inference over large scale network structures in short computation time. We further explore the possibility of integrating prior knowledge into network inference. We evaluate the proposed model on DREAM4 and DREAM8 data and find it competitive against several state-of-the-art existing network inference methods.

A review and comparison of Bayesian and likelihood-based inferences in beta regression and zero-or-one-inflated beta regression.

PubMed

Liu, Fang; Eugenio, Evercita C

2018-04-01

Beta regression is an increasingly popular statistical technique in medical research for modeling of outcomes that assume values in (0, 1), such as proportions and patient reported outcomes. When outcomes take values in the intervals [0,1), (0,1], or [0,1], zero-or-one-inflated beta (zoib) regression can be used. We provide a thorough review on beta regression and zoib regression in the modeling, inferential, and computational aspects via the likelihood-based and Bayesian approaches. We demonstrate the statistical and practical importance of correctly modeling the inflation at zero/one rather than ad hoc replacing them with values close to zero/one via simulation studies; the latter approach can lead to biased estimates and invalid inferences. We show via simulation studies that the likelihood-based approach is computationally faster in general than MCMC algorithms used in the Bayesian inferences, but runs the risk of non-convergence, large biases, and sensitivity to starting values in the optimization algorithm especially with clustered/correlated data, data with sparse inflation at zero and one, and data that warrant regularization of the likelihood. The disadvantages of the regular likelihood-based approach make the Bayesian approach an attractive alternative in these cases. Software packages and tools for fitting beta and zoib regressions in both the likelihood-based and Bayesian frameworks are also reviewed.

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

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 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

Application of a data-mining method based on Bayesian networks to lesion-deficit analysis

NASA Technical Reports Server (NTRS)

Herskovits, Edward H.; Gerring, Joan P.

2003-01-01

Although lesion-deficit analysis (LDA) has provided extensive information about structure-function associations in the human brain, LDA has suffered from the difficulties inherent to the analysis of spatial data, i.e., there are many more variables than subjects, and data may be difficult to model using standard distributions, such as the normal distribution. We herein describe a Bayesian method for LDA; this method is based on data-mining techniques that employ Bayesian networks to represent structure-function associations. These methods are computationally tractable, and can represent complex, nonlinear structure-function associations. When applied to the evaluation of data obtained from a study of the psychiatric sequelae of traumatic brain injury in children, this method generates a Bayesian network that demonstrates complex, nonlinear associations among lesions in the left caudate, right globus pallidus, right side of the corpus callosum, right caudate, and left thalamus, and subsequent development of attention-deficit hyperactivity disorder, confirming and extending our previous statistical analysis of these data. Furthermore, analysis of simulated data indicates that methods based on Bayesian networks may be more sensitive and specific for detecting associations among categorical variables than methods based on chi-square and Fisher exact statistics.

Sparse Event Modeling with Hierarchical Bayesian Kernel Methods

DTIC Science & Technology

2016-01-05

SECURITY CLASSIFICATION OF: The research objective of this proposal was to develop a predictive Bayesian kernel approach to model count data based on...several predictive variables. Such an approach, which we refer to as the Poisson Bayesian kernel model , is able to model the rate of occurrence of...which adds specificity to the model and can make nonlinear data more manageable. Early results show that the 1. REPORT DATE (DD-MM-YYYY) 4. TITLE

A Bayesian Approach for Analyzing Longitudinal Structural Equation Models

ERIC Educational Resources Information Center

Song, Xin-Yuan; Lu, Zhao-Hua; Hser, Yih-Ing; Lee, Sik-Yum

2011-01-01

This article considers a Bayesian approach for analyzing a longitudinal 2-level nonlinear structural equation model with covariates, and mixed continuous and ordered categorical variables. The first-level model is formulated for measures taken at each time point nested within individuals for investigating their characteristics that are dynamically…

A Robust Bayesian Random Effects Model for Nonlinear Calibration Problems

PubMed Central

Fong, Y.; Wakefield, J.; De Rosa, S.; Frahm, N.

2013-01-01

Summary In the context of a bioassay or an immunoassay, calibration means fitting a curve, usually nonlinear, through the observations collected on a set of samples containing known concentrations of a target substance, and then using the fitted curve and observations collected on samples of interest to predict the concentrations of the target substance in these samples. Recent technological advances have greatly improved our ability to quantify minute amounts of substance from a tiny volume of biological sample. This has in turn led to a need to improve statistical methods for calibration. In this paper, we focus on developing calibration methods robust to dependent outliers. We introduce a novel normal mixture model with dependent error terms to model the experimental noise. In addition, we propose a re-parameterization of the five parameter logistic nonlinear regression model that allows us to better incorporate prior information. We examine the performance of our methods with simulation studies and show that they lead to a substantial increase in performance measured in terms of mean squared error of estimation and a measure of the average prediction accuracy. A real data example from the HIV Vaccine Trials Network Laboratory is used to illustrate the methods. PMID:22551415

Bias in logistic regression due to imperfect diagnostic test results and practical correction approaches.

PubMed

Valle, Denis; Lima, Joanna M Tucker; Millar, Justin; Amratia, Punam; Haque, Ubydul

2015-11-04

Logistic regression is a statistical model widely used in cross-sectional and cohort studies to identify and quantify the effects of potential disease risk factors. However, the impact of imperfect tests on adjusted odds ratios (and thus on the identification of risk factors) is under-appreciated. The purpose of this article is to draw attention to the problem associated with modelling imperfect diagnostic tests, and propose simple Bayesian models to adequately address this issue. A systematic literature review was conducted to determine the proportion of malaria studies that appropriately accounted for false-negatives/false-positives in a logistic regression setting. Inference from the standard logistic regression was also compared with that from three proposed Bayesian models using simulations and malaria data from the western Brazilian Amazon. A systematic literature review suggests that malaria epidemiologists are largely unaware of the problem of using logistic regression to model imperfect diagnostic test results. Simulation results reveal that statistical inference can be substantially improved when using the proposed Bayesian models versus the standard logistic regression. Finally, analysis of original malaria data with one of the proposed Bayesian models reveals that microscopy sensitivity is strongly influenced by how long people have lived in the study region, and an important risk factor (i.e., participation in forest extractivism) is identified that would have been missed by standard logistic regression. Given the numerous diagnostic methods employed by malaria researchers and the ubiquitous use of logistic regression to model the results of these diagnostic tests, this paper provides critical guidelines to improve data analysis practice in the presence of misclassification error. Easy-to-use code that can be readily adapted to WinBUGS is provided, enabling straightforward implementation of the proposed Bayesian models.

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.

Bayesian Finite Mixtures for Nonlinear Modeling of Educational Data.

ERIC Educational Resources Information Center

Tirri, Henry; And Others

A Bayesian approach for finding latent classes in data is discussed. The approach uses finite mixture models to describe the underlying structure in the data and demonstrate that the possibility of using full joint probability models raises interesting new prospects for exploratory data analysis. The concepts and methods discussed are illustrated…

Model Comparison of Nonlinear Structural Equation Models with Fixed Covariates.

ERIC Educational Resources Information Center

Lee, Sik-Yum; Song, Xin-Yuan

2003-01-01

Proposed a new nonlinear structural equation model with fixed covariates to deal with some complicated substantive theory and developed a Bayesian path sampling procedure for model comparison. Illustrated the approach with an illustrative example using data from an international study. (SLD)

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…

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…

Analyzing degradation data with a random effects spline regression model

DOE PAGES

Fugate, Michael Lynn; Hamada, Michael Scott; Weaver, Brian Phillip

2017-03-17

This study proposes using a random effects spline regression model to analyze degradation data. Spline regression avoids having to specify a parametric function for the true degradation of an item. A distribution for the spline regression coefficients captures the variation of the true degradation curves from item to item. We illustrate the proposed methodology with a real example using a Bayesian approach. The Bayesian approach allows prediction of degradation of a population over time and estimation of reliability is easy to perform.

Analyzing degradation data with a random effects spline regression model

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

Fugate, Michael Lynn; Hamada, Michael Scott; Weaver, Brian Phillip

This study proposes using a random effects spline regression model to analyze degradation data. Spline regression avoids having to specify a parametric function for the true degradation of an item. A distribution for the spline regression coefficients captures the variation of the true degradation curves from item to item. We illustrate the proposed methodology with a real example using a Bayesian approach. The Bayesian approach allows prediction of degradation of a population over time and estimation of reliability is easy to perform.

Implications of Nonlinear Concentration Response Curve for Ozone related Mortality on Health Burden Assessment

EPA Science Inventory

We characterize the sensitivity of the ozone attributable health burden assessment with respect to different modeling strategies of concentration-response function. For this purpose, we develop a flexible Bayesian hierarchical model allowing for a nonlinear ozone risk curve with ...

A Bayesian methodological framework for accommodating interannual variability of nutrient loading with the SPARROW model

NASA Astrophysics Data System (ADS)

Wellen, Christopher; Arhonditsis, George B.; Labencki, Tanya; Boyd, Duncan

2012-10-01

Regression-type, hybrid empirical/process-based models (e.g., SPARROW, PolFlow) have assumed a prominent role in efforts to estimate the sources and transport of nutrient pollution at river basin scales. However, almost no attempts have been made to explicitly accommodate interannual nutrient loading variability in their structure, despite empirical and theoretical evidence indicating that the associated source/sink processes are quite variable at annual timescales. In this study, we present two methodological approaches to accommodate interannual variability with the Spatially Referenced Regressions on Watershed attributes (SPARROW) nonlinear regression model. The first strategy uses the SPARROW model to estimate a static baseline load and climatic variables (e.g., precipitation) to drive the interannual variability. The second approach allows the source/sink processes within the SPARROW model to vary at annual timescales using dynamic parameter estimation techniques akin to those used in dynamic linear models. Model parameterization is founded upon Bayesian inference techniques that explicitly consider calibration data and model uncertainty. Our case study is the Hamilton Harbor watershed, a mixed agricultural and urban residential area located at the western end of Lake Ontario, Canada. Our analysis suggests that dynamic parameter estimation is the more parsimonious of the two strategies tested and can offer insights into the temporal structural changes associated with watershed functioning. Consistent with empirical and theoretical work, model estimated annual in-stream attenuation rates varied inversely with annual discharge. Estimated phosphorus source areas were concentrated near the receiving water body during years of high in-stream attenuation and dispersed along the main stems of the streams during years of low attenuation, suggesting that nutrient source areas are subject to interannual variability.

Nonlinear-drifted Brownian motion with multiple hidden states for remaining useful life prediction of rechargeable batteries

NASA Astrophysics Data System (ADS)

Wang, Dong; Zhao, Yang; Yang, Fangfang; Tsui, Kwok-Leung

2017-09-01

Brownian motion with adaptive drift has attracted much attention in prognostics because its first hitting time is highly relevant to remaining useful life prediction and it follows the inverse Gaussian distribution. Besides linear degradation modeling, nonlinear-drifted Brownian motion has been developed to model nonlinear degradation. Moreover, the first hitting time distribution of the nonlinear-drifted Brownian motion has been approximated by time-space transformation. In the previous studies, the drift coefficient is the only hidden state used in state space modeling of the nonlinear-drifted Brownian motion. Besides the drift coefficient, parameters of a nonlinear function used in the nonlinear-drifted Brownian motion should be treated as additional hidden states of state space modeling to make the nonlinear-drifted Brownian motion more flexible. In this paper, a prognostic method based on nonlinear-drifted Brownian motion with multiple hidden states is proposed and then it is applied to predict remaining useful life of rechargeable batteries. 26 sets of rechargeable battery degradation samples are analyzed to validate the effectiveness of the proposed prognostic method. Moreover, some comparisons with a standard particle filter based prognostic method, a spherical cubature particle filter based prognostic method and two classic Bayesian prognostic methods are conducted to highlight the superiority of the proposed prognostic method. Results show that the proposed prognostic method has lower average prediction errors than the particle filter based prognostic methods and the classic Bayesian prognostic methods for battery remaining useful life prediction.

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.

Supervised nonlinear spectral unmixing using a postnonlinear mixing model for hyperspectral imagery.

PubMed

Altmann, Yoann; Halimi, Abderrahim; Dobigeon, Nicolas; Tourneret, Jean-Yves

2012-06-01

This paper presents a nonlinear mixing model for hyperspectral image unmixing. The proposed model assumes that the pixel reflectances are nonlinear functions of pure spectral components contaminated by an additive white Gaussian noise. These nonlinear functions are approximated using polynomial functions leading to a polynomial postnonlinear mixing model. A Bayesian algorithm and optimization methods are proposed to estimate the parameters involved in the model. The performance of the unmixing strategies is evaluated by simulations conducted on synthetic and real data.

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.

Bayesian Estimation of Panel Data Fractional Response Models with Endogeneity: An Application to Standardized Test Rates

ERIC Educational Resources Information Center

Kessler, Lawrence M.

2013-01-01

In this paper I propose Bayesian estimation of a nonlinear panel data model with a fractional dependent variable (bounded between 0 and 1). Specifically, I estimate a panel data fractional probit model which takes into account the bounded nature of the fractional response variable. I outline estimation under the assumption of strict exogeneity as…

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.

Prediction of maize phenotype based on whole-genome single nucleotide polymorphisms using deep belief networks

NASA Astrophysics Data System (ADS)

Rachmatia, H.; Kusuma, W. A.; Hasibuan, L. S.

2017-05-01

Selection in plant breeding could be more effective and more efficient if it is based on genomic data. Genomic selection (GS) is a new approach for plant-breeding selection that exploits genomic data through a mechanism called genomic prediction (GP). Most of GP models used linear methods that ignore effects of interaction among genes and effects of higher order nonlinearities. Deep belief network (DBN), one of the architectural in deep learning methods, is able to model data in high level of abstraction that involves nonlinearities effects of the data. This study implemented DBN for developing a GP model utilizing whole-genome Single Nucleotide Polymorphisms (SNPs) as data for training and testing. The case study was a set of traits in maize. The maize dataset was acquisitioned from CIMMYT’s (International Maize and Wheat Improvement Center) Global Maize program. Based on Pearson correlation, DBN is outperformed than other methods, kernel Hilbert space (RKHS) regression, Bayesian LASSO (BL), best linear unbiased predictor (BLUP), in case allegedly non-additive traits. DBN achieves correlation of 0.579 within -1 to 1 range.

Bayesian spatial analysis of childhood diseases in Zimbabwe.

PubMed

Tsiko, Rodney Godfrey

2015-09-02

Many sub-Saharan countries are confronted with persistently high levels of childhood morbidity and mortality because of the impact of a range of demographic, biological and social factors or situational events that directly precipitate ill health. In particular, under-five morbidity and mortality have increased in recent decades due to childhood diarrhoea, cough and fever. Understanding the geographic distribution of such diseases and their relationships to potential risk factors can be invaluable for cost effective intervention. Bayesian semi-parametric regression models were used to quantify the spatial risk of childhood diarrhoea, fever and cough, as well as associations between childhood diseases and a range of factors, after accounting for spatial correlation between neighbouring areas. Such semi-parametric regression models allow joint analysis of non-linear effects of continuous covariates, spatially structured variation, unstructured heterogeneity, and other fixed effects on childhood diseases. Modelling and inference made use of the fully Bayesian approach via Markov Chain Monte Carlo (MCMC) simulation techniques. The analysis was based on data derived from the 1999, 2005/6 and 2010/11 Zimbabwe Demographic and Health Surveys (ZDHS). The results suggest that until recently, sex of child had little or no significant association with childhood diseases. However, a higher proportion of male than female children within a given province had a significant association with childhood cough, fever and diarrhoea. Compared to their counterparts in rural areas, children raised in an urban setting had less exposure to cough, fever and diarrhoea across all the survey years with the exception of diarrhoea in 2010. In addition, the link between sanitation, parental education, antenatal care, vaccination and childhood diseases was found to be both intuitive and counterintuitive. Results also showed marked geographical differences in the prevalence of childhood diarrhoea, fever and cough. Across all the survey years Manicaland province reported the highest cases of childhood diseases. There is also clear evidence of significant high prevalence of childhood diseases in Mashonaland than in Matabeleland provinces.

Bayesian generalized least squares regression with application to log Pearson type 3 regional skew estimation

NASA Astrophysics Data System (ADS)

Reis, D. S.; Stedinger, J. R.; Martins, E. S.

2005-10-01

This paper develops a Bayesian approach to analysis of a generalized least squares (GLS) regression model for regional analyses of hydrologic data. The new approach allows computation of the posterior distributions of the parameters and the model error variance using a quasi-analytic approach. Two regional skew estimation studies illustrate the value of the Bayesian GLS approach for regional statistical analysis of a shape parameter and demonstrate that regional skew models can be relatively precise with effective record lengths in excess of 60 years. With Bayesian GLS the marginal posterior distribution of the model error variance and the corresponding mean and variance of the parameters can be computed directly, thereby providing a simple but important extension of the regional GLS regression procedures popularized by Tasker and Stedinger (1989), which is sensitive to the likely values of the model error variance when it is small relative to the sampling error in the at-site estimator.

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.

A simulation study on Bayesian Ridge regression models for several collinearity levels

NASA Astrophysics Data System (ADS)

Efendi, Achmad; Effrihan

2017-12-01

When analyzing data with multiple regression model if there are collinearities, then one or several predictor variables are usually omitted from the model. However, there sometimes some reasons, for instance medical or economic reasons, the predictors are all important and should be included in the model. Ridge regression model is not uncommon in some researches to use to cope with collinearity. Through this modeling, weights for predictor variables are used for estimating parameters. The next estimation process could follow the concept of likelihood. Furthermore, for the estimation nowadays the Bayesian version could be an alternative. This estimation method does not match likelihood one in terms of popularity due to some difficulties; computation and so forth. Nevertheless, with the growing improvement of computational methodology recently, this caveat should not at the moment become a problem. This paper discusses about simulation process for evaluating the characteristic of Bayesian Ridge regression parameter estimates. There are several simulation settings based on variety of collinearity levels and sample sizes. The results show that Bayesian method gives better performance for relatively small sample sizes, and for other settings the method does perform relatively similar to the likelihood method.

Bayesian model reduction and empirical Bayes for group (DCM) studies

PubMed Central

Friston, Karl J.; Litvak, Vladimir; Oswal, Ashwini; Razi, Adeel; Stephan, Klaas E.; van Wijk, Bernadette C.M.; Ziegler, Gabriel; Zeidman, Peter

2016-01-01

This technical note describes some Bayesian procedures for the analysis of group studies that use nonlinear models at the first (within-subject) level – e.g., dynamic causal models – and linear models at subsequent (between-subject) levels. Its focus is on using Bayesian model reduction to finesse the inversion of multiple models of a single dataset or a single (hierarchical or empirical Bayes) model of multiple datasets. These applications of Bayesian model reduction allow one to consider parametric random effects and make inferences about group effects very efficiently (in a few seconds). We provide the relatively straightforward theoretical background to these procedures and illustrate their application using a worked example. This example uses a simulated mismatch negativity study of schizophrenia. We illustrate the robustness of Bayesian model reduction to violations of the (commonly used) Laplace assumption in dynamic causal modelling and show how its recursive application can facilitate both classical and Bayesian inference about group differences. Finally, we consider the application of these empirical Bayesian procedures to classification and prediction. PMID:26569570

A Bayesian approach for estimating under-reported dengue incidence with a focus on non-linear associations between climate and dengue in Dhaka, Bangladesh.

PubMed

Sharmin, Sifat; Glass, Kathryn; Viennet, Elvina; Harley, David

2018-04-01

Determining the relation between climate and dengue incidence is challenging due to under-reporting of disease and consequent biased incidence estimates. Non-linear associations between climate and incidence compound this. Here, we introduce a modelling framework to estimate dengue incidence from passive surveillance data while incorporating non-linear climate effects. We estimated the true number of cases per month using a Bayesian generalised linear model, developed in stages to adjust for under-reporting. A semi-parametric thin-plate spline approach was used to quantify non-linear climate effects. The approach was applied to data collected from the national dengue surveillance system of Bangladesh. The model estimated that only 2.8% (95% credible interval 2.7-2.8) of all cases in the capital Dhaka were reported through passive case reporting. The optimal mean monthly temperature for dengue transmission is 29℃ and average monthly rainfall above 15 mm decreases transmission. Our approach provides an estimate of true incidence and an understanding of the effects of temperature and rainfall on dengue transmission in Dhaka, Bangladesh.

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

Assessment of parametric uncertainty for groundwater reactive transport modeling,

USGS Publications Warehouse

Shi, Xiaoqing; Ye, Ming; Curtis, Gary P.; Miller, Geoffery L.; Meyer, Philip D.; Kohler, Matthias; Yabusaki, Steve; Wu, Jichun

2014-01-01

The validity of using Gaussian assumptions for model residuals in uncertainty quantification of a groundwater reactive transport model was evaluated in this study. Least squares regression methods explicitly assume Gaussian residuals, and the assumption leads to Gaussian likelihood functions, model parameters, and model predictions. While the Bayesian methods do not explicitly require the Gaussian assumption, Gaussian residuals are widely used. This paper shows that the residuals of the reactive transport model are non-Gaussian, heteroscedastic, and correlated in time; characterizing them requires using a generalized likelihood function such as the formal generalized likelihood function developed by Schoups and Vrugt (2010). For the surface complexation model considered in this study for simulating uranium reactive transport in groundwater, parametric uncertainty is quantified using the least squares regression methods and Bayesian methods with both Gaussian and formal generalized likelihood functions. While the least squares methods and Bayesian methods with Gaussian likelihood function produce similar Gaussian parameter distributions, the parameter distributions of Bayesian uncertainty quantification using the formal generalized likelihood function are non-Gaussian. In addition, predictive performance of formal generalized likelihood function is superior to that of least squares regression and Bayesian methods with Gaussian likelihood function. The Bayesian uncertainty quantification is conducted using the differential evolution adaptive metropolis (DREAM(zs)) algorithm; as a Markov chain Monte Carlo (MCMC) method, it is a robust tool for quantifying uncertainty in groundwater reactive transport models. For the surface complexation model, the regression-based local sensitivity analysis and Morris- and DREAM(ZS)-based global sensitivity analysis yield almost identical ranking of parameter importance. The uncertainty analysis may help select appropriate likelihood functions, improve model calibration, and reduce predictive uncertainty in other groundwater reactive transport and environmental modeling.

Implementing informative priors for heterogeneity in meta-analysis using meta-regression and pseudo data.

PubMed

Rhodes, Kirsty M; Turner, Rebecca M; White, Ian R; Jackson, Dan; Spiegelhalter, David J; Higgins, Julian P T

2016-12-20

Many meta-analyses combine results from only a small number of studies, a situation in which the between-study variance is imprecisely estimated when standard methods are applied. Bayesian meta-analysis allows incorporation of external evidence on heterogeneity, providing the potential for more robust inference on the effect size of interest. We present a method for performing Bayesian meta-analysis using data augmentation, in which we represent an informative conjugate prior for between-study variance by pseudo data and use meta-regression for estimation. To assist in this, we derive predictive inverse-gamma distributions for the between-study variance expected in future meta-analyses. These may serve as priors for heterogeneity in new meta-analyses. In a simulation study, we compare approximate Bayesian methods using meta-regression and pseudo data against fully Bayesian approaches based on importance sampling techniques and Markov chain Monte Carlo (MCMC). We compare the frequentist properties of these Bayesian methods with those of the commonly used frequentist DerSimonian and Laird procedure. The method is implemented in standard statistical software and provides a less complex alternative to standard MCMC approaches. An importance sampling approach produces almost identical results to standard MCMC approaches, and results obtained through meta-regression and pseudo data are very similar. On average, data augmentation provides closer results to MCMC, if implemented using restricted maximum likelihood estimation rather than DerSimonian and Laird or maximum likelihood estimation. The methods are applied to real datasets, and an extension to network meta-analysis is described. The proposed method facilitates Bayesian meta-analysis in a way that is accessible to applied researchers. © 2016 The Authors. Statistics in Medicine Published by John Wiley & Sons Ltd. © 2016 The Authors. Statistics in Medicine Published by John Wiley & Sons Ltd.

A Bayesian goodness of fit test and semiparametric generalization of logistic regression with measurement data.

PubMed

Schörgendorfer, Angela; Branscum, Adam J; Hanson, Timothy E

2013-06-01

Logistic regression is a popular tool for risk analysis in medical and population health science. With continuous response data, it is common to create a dichotomous outcome for logistic regression analysis by specifying a threshold for positivity. Fitting a linear regression to the nondichotomized response variable assuming a logistic sampling model for the data has been empirically shown to yield more efficient estimates of odds ratios than ordinary logistic regression of the dichotomized endpoint. We illustrate that risk inference is not robust to departures from the parametric logistic distribution. Moreover, the model assumption of proportional odds is generally not satisfied when the condition of a logistic distribution for the data is violated, leading to biased inference from a parametric logistic analysis. We develop novel Bayesian semiparametric methodology for testing goodness of fit of parametric logistic regression with continuous measurement data. The testing procedures hold for any cutoff threshold and our approach simultaneously provides the ability to perform semiparametric risk estimation. Bayes factors are calculated using the Savage-Dickey ratio for testing the null hypothesis of logistic regression versus a semiparametric generalization. We propose a fully Bayesian and a computationally efficient empirical Bayesian approach to testing, and we present methods for semiparametric estimation of risks, relative risks, and odds ratios when parametric logistic regression fails. Theoretical results establish the consistency of the empirical Bayes test. Results from simulated data show that the proposed approach provides accurate inference irrespective of whether parametric assumptions hold or not. Evaluation of risk factors for obesity shows that different inferences are derived from an analysis of a real data set when deviations from a logistic distribution are permissible in a flexible semiparametric framework. © 2013, The International Biometric Society.

Comparing spatially varying coefficient models: a case study examining violent crime rates and their relationships to alcohol outlets and illegal drug arrests

NASA Astrophysics Data System (ADS)

Wheeler, David C.; Waller, Lance A.

2009-03-01

In this paper, we compare and contrast a Bayesian spatially varying coefficient process (SVCP) model with a geographically weighted regression (GWR) model for the estimation of the potentially spatially varying regression effects of alcohol outlets and illegal drug activity on violent crime in Houston, Texas. In addition, we focus on the inherent coefficient shrinkage properties of the Bayesian SVCP model as a way to address increased coefficient variance that follows from collinearity in GWR models. We outline the advantages of the Bayesian model in terms of reducing inflated coefficient variance, enhanced model flexibility, and more formal measuring of model uncertainty for prediction. We find spatially varying effects for alcohol outlets and drug violations, but the amount of variation depends on the type of model used. For the Bayesian model, this variation is controllable through the amount of prior influence placed on the variance of the coefficients. For example, the spatial pattern of coefficients is similar for the GWR and Bayesian models when a relatively large prior variance is used in the Bayesian model.

Bayesian analysis of non-linear differential equation models with application to a gut microbial ecosystem.

PubMed

Lawson, Daniel J; Holtrop, Grietje; Flint, Harry

2011-07-01

Process models specified by non-linear dynamic differential equations contain many parameters, which often must be inferred from a limited amount of data. We discuss a hierarchical Bayesian approach combining data from multiple related experiments in a meaningful way, which permits more powerful inference than treating each experiment as independent. The approach is illustrated with a simulation study and example data from experiments replicating the aspects of the human gut microbial ecosystem. A predictive model is obtained that contains prediction uncertainty caused by uncertainty in the parameters, and we extend the model to capture situations of interest that cannot easily be studied experimentally. Copyright © 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Genome-wide regression and prediction with the BGLR statistical package.

PubMed

Pérez, Paulino; de los Campos, Gustavo

2014-10-01

Many modern genomic data analyses require implementing regressions where the number of parameters (p, e.g., the number of marker effects) exceeds sample size (n). Implementing these large-p-with-small-n regressions poses several statistical and computational challenges, some of which can be confronted using Bayesian methods. This approach allows integrating various parametric and nonparametric shrinkage and variable selection procedures in a unified and consistent manner. The BGLR R-package implements a large collection of Bayesian regression models, including parametric variable selection and shrinkage methods and semiparametric procedures (Bayesian reproducing kernel Hilbert spaces regressions, RKHS). The software was originally developed for genomic applications; however, the methods implemented are useful for many nongenomic applications as well. The response can be continuous (censored or not) or categorical (either binary or ordinal). The algorithm is based on a Gibbs sampler with scalar updates and the implementation takes advantage of efficient compiled C and Fortran routines. In this article we describe the methods implemented in BGLR, present examples of the use of the package, and discuss practical issues emerging in real-data analysis. Copyright © 2014 by the Genetics Society of America.

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.

Additive Genetic Variability and the Bayesian Alphabet

PubMed Central

Gianola, Daniel; de los Campos, Gustavo; Hill, William G.; Manfredi, Eduardo; Fernando, Rohan

2009-01-01

The use of all available molecular markers in statistical models for prediction of quantitative traits has led to what could be termed a genomic-assisted selection paradigm in animal and plant breeding. This article provides a critical review of some theoretical and statistical concepts in the context of genomic-assisted genetic evaluation of animals and crops. First, relationships between the (Bayesian) variance of marker effects in some regression models and additive genetic variance are examined under standard assumptions. Second, the connection between marker genotypes and resemblance between relatives is explored, and linkages between a marker-based model and the infinitesimal model are reviewed. Third, issues associated with the use of Bayesian models for marker-assisted selection, with a focus on the role of the priors, are examined from a theoretical angle. The sensitivity of a Bayesian specification that has been proposed (called “Bayes A”) with respect to priors is illustrated with a simulation. Methods that can solve potential shortcomings of some of these Bayesian regression procedures are discussed briefly. PMID:19620397

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).

Sequential bearings-only-tracking initiation with particle filtering method.

PubMed

Liu, Bin; Hao, Chengpeng

2013-01-01

The tracking initiation problem is examined in the context of autonomous bearings-only-tracking (BOT) of a single appearing/disappearing target in the presence of clutter measurements. In general, this problem suffers from a combinatorial explosion in the number of potential tracks resulted from the uncertainty in the linkage between the target and the measurement (a.k.a the data association problem). In addition, the nonlinear measurements lead to a non-Gaussian posterior probability density function (pdf) in the optimal Bayesian sequential estimation framework. The consequence of this nonlinear/non-Gaussian context is the absence of a closed-form solution. This paper models the linkage uncertainty and the nonlinear/non-Gaussian estimation problem jointly with solid Bayesian formalism. A particle filtering (PF) algorithm is derived for estimating the model's parameters in a sequential manner. Numerical results show that the proposed solution provides a significant benefit over the most commonly used methods, IPDA and IMMPDA. The posterior Cramér-Rao bounds are also involved for performance evaluation.

Bayesian estimation of the discrete coefficient of determination.

PubMed

Chen, Ting; Braga-Neto, Ulisses M

2016-12-01

The discrete coefficient of determination (CoD) measures the nonlinear interaction between discrete predictor and target variables and has had far-reaching applications in Genomic Signal Processing. Previous work has addressed the inference of the discrete CoD using classical parametric and nonparametric approaches. In this paper, we introduce a Bayesian framework for the inference of the discrete CoD. We derive analytically the optimal minimum mean-square error (MMSE) CoD estimator, as well as a CoD estimator based on the Optimal Bayesian Predictor (OBP). For the latter estimator, exact expressions for its bias, variance, and root-mean-square (RMS) are given. The accuracy of both Bayesian CoD estimators with non-informative and informative priors, under fixed or random parameters, is studied via analytical and numerical approaches. We also demonstrate the application of the proposed Bayesian approach in the inference of gene regulatory networks, using gene-expression data from a previously published study on metastatic melanoma.

Hip fracture in the elderly: a re-analysis of the EPIDOS study with causal Bayesian networks.

PubMed

Caillet, Pascal; Klemm, Sarah; Ducher, Michel; Aussem, Alexandre; Schott, Anne-Marie

2015-01-01

Hip fractures commonly result in permanent disability, institutionalization or death in elderly. Existing hip-fracture predicting tools are underused in clinical practice, partly due to their lack of intuitive interpretation. By use of a graphical layer, Bayesian network models could increase the attractiveness of fracture prediction tools. Our aim was to study the potential contribution of a causal Bayesian network in this clinical setting. A logistic regression was performed as a standard control approach to check the robustness of the causal Bayesian network approach. EPIDOS is a multicenter study, conducted in an ambulatory care setting in five French cities between 1992 and 1996 and updated in 2010. The study included 7598 women aged 75 years or older, in which fractures were assessed quarterly during 4 years. A causal Bayesian network and a logistic regression were performed on EPIDOS data to describe major variables involved in hip fractures occurrences. Both models had similar association estimations and predictive performances. They detected gait speed and mineral bone density as variables the most involved in the fracture process. The causal Bayesian network showed that gait speed and bone mineral density were directly connected to fracture and seem to mediate the influence of all the other variables included in our model. The logistic regression approach detected multiple interactions involving psychotropic drug use, age and bone mineral density. Both approaches retrieved similar variables as predictors of hip fractures. However, Bayesian network highlighted the whole web of relation between the variables involved in the analysis, suggesting a possible mechanism leading to hip fracture. According to the latter results, intervention focusing concomitantly on gait speed and bone mineral density may be necessary for an optimal prevention of hip fracture occurrence in elderly people.

Bayesian model reduction and empirical Bayes for group (DCM) studies.

PubMed

Friston, Karl J; Litvak, Vladimir; Oswal, Ashwini; Razi, Adeel; Stephan, Klaas E; van Wijk, Bernadette C M; Ziegler, Gabriel; Zeidman, Peter

2016-03-01

This technical note describes some Bayesian procedures for the analysis of group studies that use nonlinear models at the first (within-subject) level - e.g., dynamic causal models - and linear models at subsequent (between-subject) levels. Its focus is on using Bayesian model reduction to finesse the inversion of multiple models of a single dataset or a single (hierarchical or empirical Bayes) model of multiple datasets. These applications of Bayesian model reduction allow one to consider parametric random effects and make inferences about group effects very efficiently (in a few seconds). We provide the relatively straightforward theoretical background to these procedures and illustrate their application using a worked example. This example uses a simulated mismatch negativity study of schizophrenia. We illustrate the robustness of Bayesian model reduction to violations of the (commonly used) Laplace assumption in dynamic causal modelling and show how its recursive application can facilitate both classical and Bayesian inference about group differences. Finally, we consider the application of these empirical Bayesian procedures to classification and prediction. Copyright © 2015 The Authors. Published by Elsevier Inc. All rights reserved.

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.

A computer program for uncertainty analysis integrating regression and Bayesian methods

USGS Publications Warehouse

Lu, Dan; Ye, Ming; Hill, Mary C.; Poeter, Eileen P.; Curtis, Gary

2014-01-01

This work develops a new functionality in UCODE_2014 to evaluate Bayesian credible intervals using the Markov Chain Monte Carlo (MCMC) method. The MCMC capability in UCODE_2014 is based on the FORTRAN version of the differential evolution adaptive Metropolis (DREAM) algorithm of Vrugt et al. (2009), which estimates the posterior probability density function of model parameters in high-dimensional and multimodal sampling problems. The UCODE MCMC capability provides eleven prior probability distributions and three ways to initialize the sampling process. It evaluates parametric and predictive uncertainties and it has parallel computing capability based on multiple chains to accelerate the sampling process. This paper tests and demonstrates the MCMC capability using a 10-dimensional multimodal mathematical function, a 100-dimensional Gaussian function, and a groundwater reactive transport model. The use of the MCMC capability is made straightforward and flexible by adopting the JUPITER API protocol. With the new MCMC capability, UCODE_2014 can be used to calculate three types of uncertainty intervals, which all can account for prior information: (1) linear confidence intervals which require linearity and Gaussian error assumptions and typically 10s–100s of highly parallelizable model runs after optimization, (2) nonlinear confidence intervals which require a smooth objective function surface and Gaussian observation error assumptions and typically 100s–1,000s of partially parallelizable model runs after optimization, and (3) MCMC Bayesian credible intervals which require few assumptions and commonly 10,000s–100,000s or more partially parallelizable model runs. Ready access allows users to select methods best suited to their work, and to compare methods in many circumstances.

Bayesian median regression for temporal gene expression data

NASA Astrophysics Data System (ADS)

Yu, Keming; Vinciotti, Veronica; Liu, Xiaohui; 't Hoen, Peter A. C.

2007-09-01

Most of the existing methods for the identification of biologically interesting genes in a temporal expression profiling dataset do not fully exploit the temporal ordering in the dataset and are based on normality assumptions for the gene expression. In this paper, we introduce a Bayesian median regression model to detect genes whose temporal profile is significantly different across a number of biological conditions. The regression model is defined by a polynomial function where both time and condition effects as well as interactions between the two are included. MCMC-based inference returns the posterior distribution of the polynomial coefficients. From this a simple Bayes factor test is proposed to test for significance. The estimation of the median rather than the mean, and within a Bayesian framework, increases the robustness of the method compared to a Hotelling T2-test previously suggested. This is shown on simulated data and on muscular dystrophy gene expression data.

Spatiotemporal Bayesian analysis of Lyme disease in New York state, 1990-2000.

PubMed

Chen, Haiyan; Stratton, Howard H; Caraco, Thomas B; White, Dennis J

2006-07-01

Mapping ordinarily increases our understanding of nontrivial spatial and temporal heterogeneities in disease rates. However, the large number of parameters required by the corresponding statistical models often complicates detailed analysis. This study investigates the feasibility of a fully Bayesian hierarchical regression approach to the problem and identifies how it outperforms two more popular methods: crude rate estimates (CRE) and empirical Bayes standardization (EBS). In particular, we apply a fully Bayesian approach to the spatiotemporal analysis of Lyme disease incidence in New York state for the period 1990-2000. These results are compared with those obtained by CRE and EBS in Chen et al. (2005). We show that the fully Bayesian regression model not only gives more reliable estimates of disease rates than the other two approaches but also allows for tractable models that can accommodate more numerous sources of variation and unknown parameters.

Non-stationary hydrologic frequency analysis using B-spline quantile regression

NASA Astrophysics Data System (ADS)

Nasri, B.; Bouezmarni, T.; St-Hilaire, A.; Ouarda, T. B. M. J.

2017-11-01

Hydrologic frequency analysis is commonly used by engineers and hydrologists to provide the basic information on planning, design and management of hydraulic and water resources systems under the assumption of stationarity. However, with increasing evidence of climate change, it is possible that the assumption of stationarity, which is prerequisite for traditional frequency analysis and hence, the results of conventional analysis would become questionable. In this study, we consider a framework for frequency analysis of extremes based on B-Spline quantile regression which allows to model data in the presence of non-stationarity and/or dependence on covariates with linear and non-linear dependence. A Markov Chain Monte Carlo (MCMC) algorithm was used to estimate quantiles and their posterior distributions. A coefficient of determination and Bayesian information criterion (BIC) for quantile regression are used in order to select the best model, i.e. for each quantile, we choose the degree and number of knots of the adequate B-spline quantile regression model. The method is applied to annual maximum and minimum streamflow records in Ontario, Canada. Climate indices are considered to describe the non-stationarity in the variable of interest and to estimate the quantiles in this case. The results show large differences between the non-stationary quantiles and their stationary equivalents for an annual maximum and minimum discharge with high annual non-exceedance probabilities.

A geometric approach to non-linear correlations with intrinsic scatter

NASA Astrophysics Data System (ADS)

Pihajoki, Pauli

2017-12-01

We propose a new mathematical model for n - k-dimensional non-linear correlations with intrinsic scatter in n-dimensional data. The model is based on Riemannian geometry and is naturally symmetric with respect to the measured variables and invariant under coordinate transformations. We combine the model with a Bayesian approach for estimating the parameters of the correlation relation and the intrinsic scatter. A side benefit of the approach is that censored and truncated data sets and independent, arbitrary measurement errors can be incorporated. We also derive analytic likelihoods for the typical astrophysical use case of linear relations in n-dimensional Euclidean space. We pay particular attention to the case of linear regression in two dimensions and compare our results to existing methods. Finally, we apply our methodology to the well-known MBH-σ correlation between the mass of a supermassive black hole in the centre of a galactic bulge and the corresponding bulge velocity dispersion. The main result of our analysis is that the most likely slope of this correlation is ∼6 for the data sets used, rather than the values in the range of ∼4-5 typically quoted in the literature for these data.

Bayesian dose-response analysis for epidemiological studies with complex uncertainty in dose estimation.

PubMed

Kwon, Deukwoo; Hoffman, F Owen; Moroz, Brian E; Simon, Steven L

2016-02-10

Most conventional risk analysis methods rely on a single best estimate of exposure per person, which does not allow for adjustment for exposure-related uncertainty. Here, we propose a Bayesian model averaging method to properly quantify the relationship between radiation dose and disease outcomes by accounting for shared and unshared uncertainty in estimated dose. Our Bayesian risk analysis method utilizes multiple realizations of sets (vectors) of doses generated by a two-dimensional Monte Carlo simulation method that properly separates shared and unshared errors in dose estimation. The exposure model used in this work is taken from a study of the risk of thyroid nodules among a cohort of 2376 subjects who were exposed to fallout from nuclear testing in Kazakhstan. We assessed the performance of our method through an extensive series of simulations and comparisons against conventional regression risk analysis methods. When the estimated doses contain relatively small amounts of uncertainty, the Bayesian method using multiple a priori plausible draws of dose vectors gave similar results to the conventional regression-based methods of dose-response analysis. However, when large and complex mixtures of shared and unshared uncertainties are present, the Bayesian method using multiple dose vectors had significantly lower relative bias than conventional regression-based risk analysis methods and better coverage, that is, a markedly increased capability to include the true risk coefficient within the 95% credible interval of the Bayesian-based risk estimate. An evaluation of the dose-response using our method is presented for an epidemiological study of thyroid disease following radiation exposure. Copyright © 2015 John Wiley & Sons, Ltd.

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

High correlations between MRI brain volume measurements based on NeuroQuant® and FreeSurfer.

PubMed

Ross, David E; Ochs, Alfred L; Tate, David F; Tokac, Umit; Seabaugh, John; Abildskov, Tracy J; Bigler, Erin D

2018-05-30

NeuroQuant ® (NQ) and FreeSurfer (FS) are commonly used computer-automated programs for measuring MRI brain volume. Previously they were reported to have high intermethod reliabilities but often large intermethod effect size differences. We hypothesized that linear transformations could be used to reduce the large effect sizes. This study was an extension of our previously reported study. We performed NQ and FS brain volume measurements on 60 subjects (including normal controls, patients with traumatic brain injury, and patients with Alzheimer's disease). We used two statistical approaches in parallel to develop methods for transforming FS volumes into NQ volumes: traditional linear regression, and Bayesian linear regression. For both methods, we used regression analyses to develop linear transformations of the FS volumes to make them more similar to the NQ volumes. The FS-to-NQ transformations based on traditional linear regression resulted in effect sizes which were small to moderate. The transformations based on Bayesian linear regression resulted in all effect sizes being trivially small. To our knowledge, this is the first report describing a method for transforming FS to NQ data so as to achieve high reliability and low effect size differences. Machine learning methods like Bayesian regression may be more useful than traditional methods. Copyright © 2018 Elsevier B.V. All rights reserved.

Neural network uncertainty assessment using Bayesian statistics: a remote sensing application

NASA Technical Reports Server (NTRS)

Aires, F.; Prigent, C.; Rossow, W. B.

2004-01-01

Neural network (NN) techniques have proved successful for many regression problems, in particular for remote sensing; however, uncertainty estimates are rarely provided. In this article, a Bayesian technique to evaluate uncertainties of the NN parameters (i.e., synaptic weights) is first presented. In contrast to more traditional approaches based on point estimation of the NN weights, we assess uncertainties on such estimates to monitor the robustness of the NN model. These theoretical developments are illustrated by applying them to the problem of retrieving surface skin temperature, microwave surface emissivities, and integrated water vapor content from a combined analysis of satellite microwave and infrared observations over land. The weight uncertainty estimates are then used to compute analytically the uncertainties in the network outputs (i.e., error bars and correlation structure of these errors). Such quantities are very important for evaluating any application of an NN model. The uncertainties on the NN Jacobians are then considered in the third part of this article. Used for regression fitting, NN models can be used effectively to represent highly nonlinear, multivariate functions. In this situation, most emphasis is put on estimating the output errors, but almost no attention has been given to errors associated with the internal structure of the regression model. The complex structure of dependency inside the NN is the essence of the model, and assessing its quality, coherency, and physical character makes all the difference between a blackbox model with small output errors and a reliable, robust, and physically coherent model. Such dependency structures are described to the first order by the NN Jacobians: they indicate the sensitivity of one output with respect to the inputs of the model for given input data. We use a Monte Carlo integration procedure to estimate the robustness of the NN Jacobians. A regularization strategy based on principal component analysis is proposed to suppress the multicollinearities in order to make these Jacobians robust and physically meaningful.

A spatiotemporal dengue fever early warning model accounting for nonlinear associations with meteorological factors: a Bayesian maximum entropy approach

NASA Astrophysics Data System (ADS)

Lee, Chieh-Han; Yu, Hwa-Lung; Chien, Lung-Chang

2014-05-01

Dengue fever has been identified as one of the most widespread vector-borne diseases in tropical and sub-tropical. In the last decade, dengue is an emerging infectious disease epidemic in Taiwan especially in the southern area where have annually high incidences. For the purpose of disease prevention and control, an early warning system is urgently needed. Previous studies have showed significant relationships between climate variables, in particular, rainfall and temperature, and the temporal epidemic patterns of dengue cases. However, the transmission of the dengue fever is a complex interactive process that mostly understated the composite space-time effects of dengue fever. This study proposes developing a one-week ahead warning system of dengue fever epidemics in the southern Taiwan that considered nonlinear associations between weekly dengue cases and meteorological factors across space and time. The early warning system based on an integration of distributed lag nonlinear model (DLNM) and stochastic Bayesian Maximum Entropy (BME) analysis. The study identified the most significant meteorological measures including weekly minimum temperature and maximum 24-hour rainfall with continuous 15-week lagged time to dengue cases variation under condition of uncertainty. Subsequently, the combination of nonlinear lagged effects of climate variables and space-time dependence function is implemented via a Bayesian framework to predict dengue fever occurrences in the southern Taiwan during 2012. The result shows the early warning system is useful for providing potential outbreak spatio-temporal prediction of dengue fever distribution. In conclusion, the proposed approach can provide a practical disease control tool for environmental regulators seeking more effective strategies for dengue fever prevention.

Parameter estimation of multivariate multiple regression model using bayesian with non-informative Jeffreys’ prior distribution

NASA Astrophysics Data System (ADS)

Saputro, D. R. S.; Amalia, F.; Widyaningsih, P.; Affan, R. C.

2018-05-01

Bayesian method is a method that can be used to estimate the parameters of multivariate multiple regression model. Bayesian method has two distributions, there are prior and posterior distributions. Posterior distribution is influenced by the selection of prior distribution. Jeffreys’ prior distribution is a kind of Non-informative prior distribution. This prior is used when the information about parameter not available. Non-informative Jeffreys’ prior distribution is combined with the sample information resulting the posterior distribution. Posterior distribution is used to estimate the parameter. The purposes of this research is to estimate the parameters of multivariate regression model using Bayesian method with Non-informative Jeffreys’ prior distribution. Based on the results and discussion, parameter estimation of β and Σ which were obtained from expected value of random variable of marginal posterior distribution function. The marginal posterior distributions for β and Σ are multivariate normal and inverse Wishart. However, in calculation of the expected value involving integral of a function which difficult to determine the value. Therefore, approach is needed by generating of random samples according to the posterior distribution characteristics of each parameter using Markov chain Monte Carlo (MCMC) Gibbs sampling algorithm.

BAYESIAN METHODS FOR REGIONAL-SCALE EUTROPHICATION MODELS. (R830887)

EPA Science Inventory

We demonstrate a Bayesian classification and regression tree (CART) approach to link multiple environmental stressors to biological responses and quantify uncertainty in model predictions. Such an approach can: (1) report prediction uncertainty, (2) be consistent with the amou...

Impact of Colic Pain as a Significant Factor for Predicting the Stone Free Rate of One-Session Shock Wave Lithotripsy for Treating Ureter Stones: A Bayesian Logistic Regression Model Analysis

PubMed Central

Chung, Doo Yong; Cho, Kang Su; Lee, Dae Hun; Han, Jang Hee; Kang, Dong Hyuk; Jung, Hae Do; Kown, Jong Kyou; Ham, Won Sik; Choi, Young Deuk; Lee, Joo Yong

2015-01-01

Purpose This study was conducted to evaluate colic pain as a prognostic pretreatment factor that can influence ureter stone clearance and to estimate the probability of stone-free status in shock wave lithotripsy (SWL) patients with a ureter stone. Materials and Methods We retrospectively reviewed the medical records of 1,418 patients who underwent their first SWL between 2005 and 2013. Among these patients, 551 had a ureter stone measuring 4–20 mm and were thus eligible for our analyses. The colic pain as the chief complaint was defined as either subjective flank pain during history taking and physical examination. Propensity-scores for established for colic pain was calculated for each patient using multivariate logistic regression based upon the following covariates: age, maximal stone length (MSL), and mean stone density (MSD). Each factor was evaluated as predictor for stone-free status by Bayesian and non-Bayesian logistic regression model. Results After propensity-score matching, 217 patients were extracted in each group from the total patient cohort. There were no statistical differences in variables used in propensity- score matching. One-session success and stone-free rate were also higher in the painful group (73.7% and 71.0%, respectively) than in the painless group (63.6% and 60.4%, respectively). In multivariate non-Bayesian and Bayesian logistic regression models, a painful stone, shorter MSL, and lower MSD were significant factors for one-session stone-free status in patients who underwent SWL. Conclusions Colic pain in patients with ureter calculi was one of the significant predicting factors including MSL and MSD for one-session stone-free status of SWL. PMID:25902059

An evaluation of Bayesian techniques for controlling model complexity and selecting inputs in a neural network for short-term load forecasting.

PubMed

Hippert, Henrique S; Taylor, James W

2010-04-01

Artificial neural networks have frequently been proposed for electricity load forecasting because of their capabilities for the nonlinear modelling of large multivariate data sets. Modelling with neural networks is not an easy task though; two of the main challenges are defining the appropriate level of model complexity, and choosing the input variables. This paper evaluates techniques for automatic neural network modelling within a Bayesian framework, as applied to six samples containing daily load and weather data for four different countries. We analyse input selection as carried out by the Bayesian 'automatic relevance determination', and the usefulness of the Bayesian 'evidence' for the selection of the best structure (in terms of number of neurones), as compared to methods based on cross-validation. Copyright 2009 Elsevier Ltd. All rights reserved.

Bayesian Inference for the Stereotype Regression Model: Application to a Case-control Study of Prostate Cancer

PubMed Central

Ahn, Jaeil; Mukherjee, Bhramar; Banerjee, Mousumi; Cooney, Kathleen A.

2011-01-01

Summary The stereotype regression model for categorical outcomes, proposed by Anderson (1984) is nested between the baseline category logits and adjacent category logits model with proportional odds structure. The stereotype model is more parsimonious than the ordinary baseline-category (or multinomial logistic) model due to a product representation of the log odds-ratios in terms of a common parameter corresponding to each predictor and category specific scores. The model could be used for both ordered and unordered outcomes. For ordered outcomes, the stereotype model allows more flexibility than the popular proportional odds model in capturing highly subjective ordinal scaling which does not result from categorization of a single latent variable, but are inherently multidimensional in nature. As pointed out by Greenland (1994), an additional advantage of the stereotype model is that it provides unbiased and valid inference under outcome-stratified sampling as in case-control studies. In addition, for matched case-control studies, the stereotype model is amenable to classical conditional likelihood principle, whereas there is no reduction due to sufficiency under the proportional odds model. In spite of these attractive features, the model has been applied less, as there are issues with maximum likelihood estimation and likelihood based testing approaches due to non-linearity and lack of identifiability of the parameters. We present comprehensive Bayesian inference and model comparison procedure for this class of models as an alternative to the classical frequentist approach. We illustrate our methodology by analyzing data from The Flint Men’s Health Study, a case-control study of prostate cancer in African-American men aged 40 to 79 years. We use clinical staging of prostate cancer in terms of Tumors, Nodes and Metastatsis (TNM) as the categorical response of interest. PMID:19731262

Detecting outliers when fitting data with nonlinear regression – a new method based on robust nonlinear regression and the false discovery rate

PubMed Central

Motulsky, Harvey J; Brown, Ronald E

2006-01-01

Background Nonlinear regression, like linear regression, assumes that the scatter of data around the ideal curve follows a Gaussian or normal distribution. This assumption leads to the familiar goal of regression: to minimize the sum of the squares of the vertical or Y-value distances between the points and the curve. Outliers can dominate the sum-of-the-squares calculation, and lead to misleading results. However, we know of no practical method for routinely identifying outliers when fitting curves with nonlinear regression. Results We describe a new method for identifying outliers when fitting data with nonlinear regression. We first fit the data using a robust form of nonlinear regression, based on the assumption that scatter follows a Lorentzian distribution. We devised a new adaptive method that gradually becomes more robust as the method proceeds. To define outliers, we adapted the false discovery rate approach to handling multiple comparisons. We then remove the outliers, and analyze the data using ordinary least-squares regression. Because the method combines robust regression and outlier removal, we call it the ROUT method. When analyzing simulated data, where all scatter is Gaussian, our method detects (falsely) one or more outlier in only about 1–3% of experiments. When analyzing data contaminated with one or several outliers, the ROUT method performs well at outlier identification, with an average False Discovery Rate less than 1%. Conclusion Our method, which combines a new method of robust nonlinear regression with a new method of outlier identification, identifies outliers from nonlinear curve fits with reasonable power and few false positives. PMID:16526949

Bayesian isotonic density regression

PubMed Central

Wang, Lianming; Dunson, David B.

2011-01-01

Density regression models allow the conditional distribution of the response given predictors to change flexibly over the predictor space. Such models are much more flexible than nonparametric mean regression models with nonparametric residual distributions, and are well supported in many applications. A rich variety of Bayesian methods have been proposed for density regression, but it is not clear whether such priors have full support so that any true data-generating model can be accurately approximated. This article develops a new class of density regression models that incorporate stochastic-ordering constraints which are natural when a response tends to increase or decrease monotonely with a predictor. Theory is developed showing large support. Methods are developed for hypothesis testing, with posterior computation relying on a simple Gibbs sampler. Frequentist properties are illustrated in a simulation study, and an epidemiology application is considered. PMID:22822259

Bowhead whale localization using time-difference-of-arrival data from asynchronous recorders.

PubMed

Warner, Graham A; Dosso, Stan E; Hannay, David E

2017-03-01

This paper estimates bowhead whale locations and uncertainties using nonlinear Bayesian inversion of the time-difference-of-arrival (TDOA) of low-frequency whale calls recorded on onmi-directional asynchronous recorders in the shallow waters of the northeastern Chukchi Sea, Alaska. A Y-shaped cluster of seven autonomous ocean-bottom hydrophones, separated by 0.5-9.2 km, was deployed for several months over which time their clocks drifted out of synchronization. Hundreds of recorded whale calls are manually associated between recorders. The TDOA between hydrophone pairs are calculated from filtered waveform cross correlations and depend on the whale locations, hydrophone locations, relative recorder clock offsets, and effective waveguide sound speed. A nonlinear Bayesian inversion estimates all of these parameters and their uncertainties as well as data error statistics. The problem is highly nonlinear and a linearized inversion did not produce physically realistic results. Whale location uncertainties from nonlinear inversion can be low enough to allow accurate tracking of migrating whales that vocalize repeatedly over several minutes. Estimates of clock drift rates are obtained from inversions of TDOA data over two weeks and agree with corresponding estimates obtained from long-time averaged ambient noise cross correlations. The inversion is suitable for application to large data sets of manually or automatically detected whale calls.

Genomic-Enabled Prediction of Ordinal Data with Bayesian Logistic Ordinal Regression.

PubMed

Montesinos-López, Osval A; Montesinos-López, Abelardo; Crossa, José; Burgueño, Juan; Eskridge, Kent

2015-08-18

Most genomic-enabled prediction models developed so far assume that the response variable is continuous and normally distributed. The exception is the probit model, developed for ordered categorical phenotypes. In statistical applications, because of the easy implementation of the Bayesian probit ordinal regression (BPOR) model, Bayesian logistic ordinal regression (BLOR) is implemented rarely in the context of genomic-enabled prediction [sample size (n) is much smaller than the number of parameters (p)]. For this reason, in this paper we propose a BLOR model using the Pólya-Gamma data augmentation approach that produces a Gibbs sampler with similar full conditional distributions of the BPOR model and with the advantage that the BPOR model is a particular case of the BLOR model. We evaluated the proposed model by using simulation and two real data sets. Results indicate that our BLOR model is a good alternative for analyzing ordinal data in the context of genomic-enabled prediction with the probit or logit link. Copyright © 2015 Montesinos-López et al.

Using Bayesian regression to test hypotheses about relationships between parameters and covariates in cognitive models.

PubMed

Boehm, Udo; Steingroever, Helen; Wagenmakers, Eric-Jan

2018-06-01

An important tool in the advancement of cognitive science are quantitative models that represent different cognitive variables in terms of model parameters. To evaluate such models, their parameters are typically tested for relationships with behavioral and physiological variables that are thought to reflect specific cognitive processes. However, many models do not come equipped with the statistical framework needed to relate model parameters to covariates. Instead, researchers often revert to classifying participants into groups depending on their values on the covariates, and subsequently comparing the estimated model parameters between these groups. Here we develop a comprehensive solution to the covariate problem in the form of a Bayesian regression framework. Our framework can be easily added to existing cognitive models and allows researchers to quantify the evidential support for relationships between covariates and model parameters using Bayes factors. Moreover, we present a simulation study that demonstrates the superiority of the Bayesian regression framework to the conventional classification-based approach.

Bayesian Estimation of Multivariate Latent Regression Models: Gauss versus Laplace

ERIC Educational Resources Information Center

Culpepper, Steven Andrew; Park, Trevor

2017-01-01

A latent multivariate regression model is developed that employs a generalized asymmetric Laplace (GAL) prior distribution for regression coefficients. The model is designed for high-dimensional applications where an approximate sparsity condition is satisfied, such that many regression coefficients are near zero after accounting for all the model…

Bayesian logistic regression approaches to predict incorrect DRG assignment.

PubMed

Suleiman, Mani; Demirhan, Haydar; Boyd, Leanne; Girosi, Federico; Aksakalli, Vural

2018-05-07

Episodes of care involving similar diagnoses and treatments and requiring similar levels of resource utilisation are grouped to the same Diagnosis-Related Group (DRG). In jurisdictions which implement DRG based payment systems, DRGs are a major determinant of funding for inpatient care. Hence, service providers often dedicate auditing staff to the task of checking that episodes have been coded to the correct DRG. The use of statistical models to estimate an episode's probability of DRG error can significantly improve the efficiency of clinical coding audits. This study implements Bayesian logistic regression models with weakly informative prior distributions to estimate the likelihood that episodes require a DRG revision, comparing these models with each other and to classical maximum likelihood estimates. All Bayesian approaches had more stable model parameters than maximum likelihood. The best performing Bayesian model improved overall classification per- formance by 6% compared to maximum likelihood, with a 34% gain compared to random classification, respectively. We found that the original DRG, coder and the day of coding all have a significant effect on the likelihood of DRG error. Use of Bayesian approaches has improved model parameter stability and classification accuracy. This method has already lead to improved audit efficiency in an operational capacity.

A Bayesian Approach for Evaluation of Determinants of Health System Efficiency Using Stochastic Frontier Analysis and Beta Regression.

PubMed

Şenel, Talat; Cengiz, Mehmet Ali

2016-01-01

In today's world, Public expenditures on health are one of the most important issues for governments. These increased expenditures are putting pressure on public budgets. Therefore, health policy makers have focused on the performance of their health systems and many countries have introduced reforms to improve the performance of their health systems. This study investigates the most important determinants of healthcare efficiency for OECD countries using second stage approach for Bayesian Stochastic Frontier Analysis (BSFA). There are two steps in this study. First we measure 29 OECD countries' healthcare efficiency by BSFA using the data from the OECD Health Database. At second stage, we expose the multiple relationships between the healthcare efficiency and characteristics of healthcare systems across OECD countries using Bayesian beta regression.

Multiscale Bayesian neural networks for soil water content estimation

NASA Astrophysics Data System (ADS)

Jana, Raghavendra B.; Mohanty, Binayak P.; Springer, Everett P.

2008-08-01

Artificial neural networks (ANN) have been used for some time now to estimate soil hydraulic parameters from other available or more easily measurable soil properties. However, most such uses of ANNs as pedotransfer functions (PTFs) have been at matching spatial scales (1:1) of inputs and outputs. This approach assumes that the outputs are only required at the same scale as the input data. Unfortunately, this is rarely true. Different hydrologic, hydroclimatic, and contaminant transport models require soil hydraulic parameter data at different spatial scales, depending upon their grid sizes. While conventional (deterministic) ANNs have been traditionally used in these studies, the use of Bayesian training of ANNs is a more recent development. In this paper, we develop a Bayesian framework to derive soil water retention function including its uncertainty at the point or local scale using PTFs trained with coarser-scale Soil Survey Geographic (SSURGO)-based soil data. The approach includes an ANN trained with Bayesian techniques as a PTF tool with training and validation data collected across spatial extents (scales) in two different regions in the United States. The two study areas include the Las Cruces Trench site in the Rio Grande basin of New Mexico, and the Southern Great Plains 1997 (SGP97) hydrology experimental region in Oklahoma. Each region-specific Bayesian ANN is trained using soil texture and bulk density data from the SSURGO database (scale 1:24,000), and predictions of the soil water contents at different pressure heads with point scale data (1:1) inputs are made. The resulting outputs are corrected for bias using both linear and nonlinear correction techniques. The results show good agreement between the soil water content values measured at the point scale and those predicted by the Bayesian ANN-based PTFs for both the study sites. Overall, Bayesian ANNs coupled with nonlinear bias correction are found to be very suitable tools for deriving soil hydraulic parameters at the local/fine scale from soil physical properties at coarser-scale and across different spatial extents. This approach could potentially be used for soil hydraulic properties estimation and downscaling.

Regional skew for California, and flood frequency for selected sites in the Sacramento-San Joaquin River Basin, based on data through water year 2006

USGS Publications Warehouse

Parrett, Charles; Veilleux, Andrea; Stedinger, J.R.; Barth, N.A.; Knifong, Donna L.; Ferris, J.C.

2011-01-01

Improved flood-frequency information is important throughout California in general and in the Sacramento-San Joaquin River Basin in particular, because of an extensive network of flood-control levees and the risk of catastrophic flooding. A key first step in updating flood-frequency information is determining regional skew. A Bayesian generalized least squares (GLS) regression method was used to derive a regional-skew model based on annual peak-discharge data for 158 long-term (30 or more years of record) stations throughout most of California. The desert areas in southeastern California had too few long-term stations to reliably determine regional skew for that hydrologically distinct region; therefore, the desert areas were excluded from the regional skew analysis for California. Of the 158 long-term stations used to determine regional skew, 145 have minimally regulated annual-peak discharges, and 13 stations are dam sites for which unregulated peak discharges were estimated from unregulated daily maximum discharge data furnished by the U.S. Army Corp of Engineers. Station skew was determined by using an expected moments algorithm (EMA) program for fitting the Pearson Type 3 flood-frequency distribution to the logarithms of annual peak-discharge data. The Bayesian GLS regression method previously developed was modified because of the large cross correlations among concurrent recorded peak discharges in California and the use of censored data and historical flood information with the new expected moments algorithm. In particular, to properly account for these cross-correlation problems and develop a suitable regression model and regression diagnostics, a combination of Bayesian weighted least squares and generalized least squares regression was adopted. This new methodology identified a nonlinear function relating regional skew to mean basin elevation. The regional skew values ranged from -0.62 for a mean basin elevation of zero to 0.61 for a mean basin elevation of 11,000 feet. This relation between skew and elevation reflects the interaction of snow with rain, which increases with increased elevation. The equivalent record length for the new regional skew ranges from 52 to 65 years of record, depending upon mean basin elevation. The old regional skew map in Bulletin 17B, published by the Hydrology Subcommittee of the Interagency Advisory Committee on Water Data (1982), reported an equivalent record length of only 17 years. The newly developed regional skew relation for California was used to update flood frequency for the 158 sites used in the regional skew analysis as well as 206 selected sites in the Sacramento-San Joaquin River Basin. For these sites, annual-peak discharges having recurrence intervals of 2, 5, 10, 25, 50, 100, 200, and 500 years were determined on the basis of data through water year 2006. The expected moments algorithm was used for determining the magnitude and frequency of floods at gaged sites by using regional skew values and using the basic approach outlined in Bulletin

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...

Comparison between Linear and Nonlinear Regression in a Laboratory Heat Transfer Experiment

ERIC Educational Resources Information Center

Gonçalves, Carine Messias; Schwaab, Marcio; Pinto, José Carlos

2013-01-01

In order to interpret laboratory experimental data, undergraduate students are used to perform linear regression through linearized versions of nonlinear models. However, the use of linearized models can lead to statistically biased parameter estimates. Even so, it is not an easy task to introduce nonlinear regression and show for the students…

Estimating Tree Height-Diameter Models with the Bayesian Method

PubMed Central

Duan, Aiguo; Zhang, Jianguo; Xiang, Congwei

2014-01-01

Six candidate height-diameter models were used to analyze the height-diameter relationships. The common methods for estimating the height-diameter models have taken the classical (frequentist) approach based on the frequency interpretation of probability, for example, the nonlinear least squares method (NLS) and the maximum likelihood method (ML). The Bayesian method has an exclusive advantage compared with classical method that the parameters to be estimated are regarded as random variables. In this study, the classical and Bayesian methods were used to estimate six height-diameter models, respectively. Both the classical method and Bayesian method showed that the Weibull model was the “best” model using data1. In addition, based on the Weibull model, data2 was used for comparing Bayesian method with informative priors with uninformative priors and classical method. The results showed that the improvement in prediction accuracy with Bayesian method led to narrower confidence bands of predicted value in comparison to that for the classical method, and the credible bands of parameters with informative priors were also narrower than uninformative priors and classical method. The estimated posterior distributions for parameters can be set as new priors in estimating the parameters using data2. PMID:24711733

Estimating tree height-diameter models with the Bayesian method.

PubMed

Zhang, Xiongqing; Duan, Aiguo; Zhang, Jianguo; Xiang, Congwei

2014-01-01

Six candidate height-diameter models were used to analyze the height-diameter relationships. The common methods for estimating the height-diameter models have taken the classical (frequentist) approach based on the frequency interpretation of probability, for example, the nonlinear least squares method (NLS) and the maximum likelihood method (ML). The Bayesian method has an exclusive advantage compared with classical method that the parameters to be estimated are regarded as random variables. In this study, the classical and Bayesian methods were used to estimate six height-diameter models, respectively. Both the classical method and Bayesian method showed that the Weibull model was the "best" model using data1. In addition, based on the Weibull model, data2 was used for comparing Bayesian method with informative priors with uninformative priors and classical method. The results showed that the improvement in prediction accuracy with Bayesian method led to narrower confidence bands of predicted value in comparison to that for the classical method, and the credible bands of parameters with informative priors were also narrower than uninformative priors and classical method. The estimated posterior distributions for parameters can be set as new priors in estimating the parameters using data2.

Incorporating approximation error in surrogate based Bayesian inversion

NASA Astrophysics Data System (ADS)

Zhang, J.; Zeng, L.; Li, W.; Wu, L.

2015-12-01

There are increasing interests in applying surrogates for inverse Bayesian modeling to reduce repetitive evaluations of original model. In this way, the computational cost is expected to be saved. However, the approximation error of surrogate model is usually overlooked. This is partly because that it is difficult to evaluate the approximation error for many surrogates. Previous studies have shown that, the direct combination of surrogates and Bayesian methods (e.g., Markov Chain Monte Carlo, MCMC) may lead to biased estimations when the surrogate cannot emulate the highly nonlinear original system. This problem can be alleviated by implementing MCMC in a two-stage manner. However, the computational cost is still high since a relatively large number of original model simulations are required. In this study, we illustrate the importance of incorporating approximation error in inverse Bayesian modeling. Gaussian process (GP) is chosen to construct the surrogate for its convenience in approximation error evaluation. Numerical cases of Bayesian experimental design and parameter estimation for contaminant source identification are used to illustrate this idea. It is shown that, once the surrogate approximation error is well incorporated into Bayesian framework, promising results can be obtained even when the surrogate is directly used, and no further original model simulations are required.

Additivity of nonlinear biomass equations

Treesearch

Bernard R. Parresol

2001-01-01

Two procedures that guarantee the property of additivity among the components of tree biomass and total tree biomass utilizing nonlinear functions are developed. Procedure 1 is a simple combination approach, and procedure 2 is based on nonlinear joint-generalized regression (nonlinear seemingly unrelated regressions) with parameter restrictions. Statistical theory is...

Reliability of a Bayesian network to predict an elevated aldosterone-to-renin ratio.

PubMed

Ducher, Michel; Mounier-Véhier, Claire; Lantelme, Pierre; Vaisse, Bernard; Baguet, Jean-Philippe; Fauvel, Jean-Pierre

2015-05-01

Resistant hypertension is common, mainly idiopathic, but sometimes related to primary aldosteronism. Thus, most hypertension specialists recommend screening for primary aldosteronism. To optimize the selection of patients whose aldosterone-to-renin ratio (ARR) is elevated from simple clinical and biological characteristics. Data from consecutive patients referred between 1 June 2008 and 30 May 2009 were collected retrospectively from five French 'European excellence hypertension centres' institutional registers. Patients were included if they had at least one of: onset of hypertension before age 40 years, resistant hypertension, history of hypokalaemia, efficient treatment by spironolactone, and potassium supplementation. An ARR>32 ng/L and aldosterone>160 ng/L in patients treated without agents altering the renin-angiotensin system was considered as elevated. Bayesian network and stepwise logistic regression were used to predict an elevated ARR. Of 334 patients, 89 were excluded (31 for incomplete data, 32 for taking agents that alter the renin-angiotensin system and 26 for other reasons). Among 245 included patients, 110 had an elevated ARR. Sensitivity reached 100% or 63.3% using Bayesian network or logistic regression, respectively, and specificity reached 89.6% or 67.2%, respectively. The area under the receiver-operating-characteristic curve obtained with the Bayesian network was significantly higher than that obtained by stepwise regression (0.93±0.02 vs. 0.70±0.03; P<0.001). In hypertension centres, Bayesian network efficiently detected patients with an elevated ARR. An external validation study is required before use in primary clinical settings. Copyright © 2015 Elsevier Masson SAS. All rights reserved.

Pseudo-second order models for the adsorption of safranin onto activated carbon: comparison of linear and non-linear regression methods.

PubMed

Kumar, K Vasanth

2007-04-02

Kinetic experiments were carried out for the sorption of safranin onto activated carbon particles. The kinetic data were fitted to pseudo-second order model of Ho, Sobkowsk and Czerwinski, Blanchard et al. and Ritchie by linear and non-linear regression methods. Non-linear method was found to be a better way of obtaining the parameters involved in the second order rate kinetic expressions. Both linear and non-linear regression showed that the Sobkowsk and Czerwinski and Ritchie's pseudo-second order models were the same. Non-linear regression analysis showed that both Blanchard et al. and Ho have similar ideas on the pseudo-second order model but with different assumptions. The best fit of experimental data in Ho's pseudo-second order expression by linear and non-linear regression method showed that Ho pseudo-second order model was a better kinetic expression when compared to other pseudo-second order kinetic expressions.

Bayesian Probability Theory

NASA Astrophysics Data System (ADS)

von der Linden, Wolfgang; Dose, Volker; von Toussaint, Udo

2014-06-01

Preface; Part I. Introduction: 1. The meaning of probability; 2. Basic definitions; 3. Bayesian inference; 4. Combinatrics; 5. Random walks; 6. Limit theorems; 7. Continuous distributions; 8. The central limit theorem; 9. Poisson processes and waiting times; Part II. Assigning Probabilities: 10. Transformation invariance; 11. Maximum entropy; 12. Qualified maximum entropy; 13. Global smoothness; Part III. Parameter Estimation: 14. Bayesian parameter estimation; 15. Frequentist parameter estimation; 16. The Cramer-Rao inequality; Part IV. Testing Hypotheses: 17. The Bayesian way; 18. The frequentist way; 19. Sampling distributions; 20. Bayesian vs frequentist hypothesis tests; Part V. Real World Applications: 21. Regression; 22. Inconsistent data; 23. Unrecognized signal contributions; 24. Change point problems; 25. Function estimation; 26. Integral equations; 27. Model selection; 28. Bayesian experimental design; Part VI. Probabilistic Numerical Techniques: 29. Numerical integration; 30. Monte Carlo methods; 31. Nested sampling; Appendixes; References; Index.

Nonlinear finite element model updating for damage identification of civil structures using batch Bayesian estimation

NASA Astrophysics Data System (ADS)

Ebrahimian, Hamed; Astroza, Rodrigo; Conte, Joel P.; de Callafon, Raymond A.

2017-02-01

This paper presents a framework for structural health monitoring (SHM) and damage identification of civil structures. This framework integrates advanced mechanics-based nonlinear finite element (FE) modeling and analysis techniques with a batch Bayesian estimation approach to estimate time-invariant model parameters used in the FE model of the structure of interest. The framework uses input excitation and dynamic response of the structure and updates a nonlinear FE model of the structure to minimize the discrepancies between predicted and measured response time histories. The updated FE model can then be interrogated to detect, localize, classify, and quantify the state of damage and predict the remaining useful life of the structure. As opposed to recursive estimation methods, in the batch Bayesian estimation approach, the entire time history of the input excitation and output response of the structure are used as a batch of data to estimate the FE model parameters through a number of iterations. In the case of non-informative prior, the batch Bayesian method leads to an extended maximum likelihood (ML) estimation method to estimate jointly time-invariant model parameters and the measurement noise amplitude. The extended ML estimation problem is solved efficiently using a gradient-based interior-point optimization algorithm. Gradient-based optimization algorithms require the FE response sensitivities with respect to the model parameters to be identified. The FE response sensitivities are computed accurately and efficiently using the direct differentiation method (DDM). The estimation uncertainties are evaluated based on the Cramer-Rao lower bound (CRLB) theorem by computing the exact Fisher Information matrix using the FE response sensitivities with respect to the model parameters. The accuracy of the proposed uncertainty quantification approach is verified using a sampling approach based on the unscented transformation. Two validation studies, based on realistic structural FE models of a bridge pier and a moment resisting steel frame, are performed to validate the performance and accuracy of the presented nonlinear FE model updating approach and demonstrate its application to SHM. These validation studies show the excellent performance of the proposed framework for SHM and damage identification even in the presence of high measurement noise and/or way-out initial estimates of the model parameters. Furthermore, the detrimental effects of the input measurement noise on the performance of the proposed framework are illustrated and quantified through one of the validation studies.

Economic policy optimization based on both one stochastic model and the parametric control theory

NASA Astrophysics Data System (ADS)

Ashimov, Abdykappar; Borovskiy, Yuriy; Onalbekov, Mukhit

2016-06-01

A nonlinear dynamic stochastic general equilibrium model with financial frictions is developed to describe two interacting national economies in the environment of the rest of the world. Parameters of nonlinear model are estimated based on its log-linearization by the Bayesian approach. The nonlinear model is verified by retroprognosis, estimation of stability indicators of mappings specified by the model, and estimation the degree of coincidence for results of internal and external shocks' effects on macroeconomic indicators on the basis of the estimated nonlinear model and its log-linearization. On the base of the nonlinear model, the parametric control problems of economic growth and volatility of macroeconomic indicators of Kazakhstan are formulated and solved for two exchange rate regimes (free floating and managed floating exchange rates)

Optimal design of clinical trials with biologics using dose-time-response models.

PubMed

Lange, Markus R; Schmidli, Heinz

2014-12-30

Biologics, in particular monoclonal antibodies, are important therapies in serious diseases such as cancer, psoriasis, multiple sclerosis, or rheumatoid arthritis. While most conventional drugs are given daily, the effect of monoclonal antibodies often lasts for months, and hence, these biologics require less frequent dosing. A good understanding of the time-changing effect of the biologic for different doses is needed to determine both an adequate dose and an appropriate time-interval between doses. Clinical trials provide data to estimate the dose-time-response relationship with semi-mechanistic nonlinear regression models. We investigate how to best choose the doses and corresponding sample size allocations in such clinical trials, so that the nonlinear dose-time-response model can be precisely estimated. We consider both local and conservative Bayesian D-optimality criteria for the design of clinical trials with biologics. For determining the optimal designs, computer-intensive numerical methods are needed, and we focus here on the particle swarm optimization algorithm. This metaheuristic optimizer has been successfully used in various areas but has only recently been applied in the optimal design context. The equivalence theorem is used to verify the optimality of the designs. The methodology is illustrated based on results from a clinical study in patients with gout, treated by a monoclonal antibody. Copyright © 2014 John Wiley & Sons, Ltd.

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.

BAYESIAN LARGE-SCALE MULTIPLE REGRESSION WITH SUMMARY STATISTICS FROM GENOME-WIDE ASSOCIATION STUDIES1

PubMed Central

Zhu, Xiang; Stephens, Matthew

2017-01-01

Bayesian methods for large-scale multiple regression provide attractive approaches to the analysis of genome-wide association studies (GWAS). For example, they can estimate heritability of complex traits, allowing for both polygenic and sparse models; and by incorporating external genomic data into the priors, they can increase power and yield new biological insights. However, these methods require access to individual genotypes and phenotypes, which are often not easily available. Here we provide a framework for performing these analyses without individual-level data. Specifically, we introduce a “Regression with Summary Statistics” (RSS) likelihood, which relates the multiple regression coefficients to univariate regression results that are often easily available. The RSS likelihood requires estimates of correlations among covariates (SNPs), which also can be obtained from public databases. We perform Bayesian multiple regression analysis by combining the RSS likelihood with previously proposed prior distributions, sampling posteriors by Markov chain Monte Carlo. In a wide range of simulations RSS performs similarly to analyses using the individual data, both for estimating heritability and detecting associations. We apply RSS to a GWAS of human height that contains 253,288 individuals typed at 1.06 million SNPs, for which analyses of individual-level data are practically impossible. Estimates of heritability (52%) are consistent with, but more precise, than previous results using subsets of these data. We also identify many previously unreported loci that show evidence for association with height in our analyses. Software is available at https://github.com/stephenslab/rss. PMID:29399241

Probabilistic numerical methods for PDE-constrained Bayesian inverse problems

NASA Astrophysics Data System (ADS)

Cockayne, Jon; Oates, Chris; Sullivan, Tim; Girolami, Mark

2017-06-01

This paper develops meshless methods for probabilistically describing discretisation error in the numerical solution of partial differential equations. This construction enables the solution of Bayesian inverse problems while accounting for the impact of the discretisation of the forward problem. In particular, this drives statistical inferences to be more conservative in the presence of significant solver error. Theoretical results are presented describing rates of convergence for the posteriors in both the forward and inverse problems. This method is tested on a challenging inverse problem with a nonlinear forward model.

Separation of the long-term thermal effects from the strain measurements in the Geodynamics Laboratory of Lanzarote

NASA Astrophysics Data System (ADS)

Venedikov, A. P.; Arnoso, J.; Cai, W.; Vieira, R.; Tan, S.; Velez, E. J.

2006-01-01

A 12-year series (1992-2004) of strain measurements recorded in the Geodynamics Laboratory of Lanzarote is investigated. Through a tidal analysis the non-tidal component of the data is separated in order to use it for studying signals, useful for monitoring of the volcanic activity on the island. This component contains various perturbations of meteorological and oceanic origin, which should be eliminated in order to make the useful signals discernible. The paper is devoted to the estimation and elimination of the effect of the air temperature inside the station, which strongly dominates the strainmeter data. For solving this task, a regression model is applied, which includes a linear relation with the temperature and time-dependant polynomials. The regression includes nonlinearly a set of parameters, which are estimated by a properly applied Bayesian approach. The results obtained are: the regression coefficient of the strain data on temperature is equal to (-367.4 ± 0.8) × 10 -9 °C -1, the curve of the non-tidal component reduced by the effect of the temperature and a polynomial approximation of the reduced curve. The technique used here can be helpful to investigators in the domain of the earthquake and volcano monitoring. However, the fundamental and extremely difficult problem of what kind of signals in the reduced curves might be useful in this field is not considered here.

Evaluating Spatial Variability in Sediment and Phosphorus Concentration-Discharge Relationships Using Bayesian Inference and Self-Organizing Maps

NASA Astrophysics Data System (ADS)

Underwood, Kristen L.; Rizzo, Donna M.; Schroth, Andrew W.; Dewoolkar, Mandar M.

2017-12-01

Given the variable biogeochemical, physical, and hydrological processes driving fluvial sediment and nutrient export, the water science and management communities need data-driven methods to identify regions prone to production and transport under variable hydrometeorological conditions. We use Bayesian analysis to segment concentration-discharge linear regression models for total suspended solids (TSS) and particulate and dissolved phosphorus (PP, DP) using 22 years of monitoring data from 18 Lake Champlain watersheds. Bayesian inference was leveraged to estimate segmented regression model parameters and identify threshold position. The identified threshold positions demonstrated a considerable range below and above the median discharge—which has been used previously as the default breakpoint in segmented regression models to discern differences between pre and post-threshold export regimes. We then applied a Self-Organizing Map (SOM), which partitioned the watersheds into clusters of TSS, PP, and DP export regimes using watershed characteristics, as well as Bayesian regression intercepts and slopes. A SOM defined two clusters of high-flux basins, one where PP flux was predominantly episodic and hydrologically driven; and another in which the sediment and nutrient sourcing and mobilization were more bimodal, resulting from both hydrologic processes at post-threshold discharges and reactive processes (e.g., nutrient cycling or lateral/vertical exchanges of fine sediment) at prethreshold discharges. A separate DP SOM defined two high-flux clusters exhibiting a bimodal concentration-discharge response, but driven by differing land use. Our novel framework shows promise as a tool with broad management application that provides insights into landscape drivers of riverine solute and sediment export.

Hierarchical Bayesian Logistic Regression to forecast metabolic control in type 2 DM patients.

PubMed

Dagliati, Arianna; Malovini, Alberto; Decata, Pasquale; Cogni, Giulia; Teliti, Marsida; Sacchi, Lucia; Cerra, Carlo; Chiovato, Luca; Bellazzi, Riccardo

2016-01-01

In this work we present our efforts in building a model able to forecast patients' changes in clinical conditions when repeated measurements are available. In this case the available risk calculators are typically not applicable. We propose a Hierarchical Bayesian Logistic Regression model, which allows taking into account individual and population variability in model parameters estimate. The model is used to predict metabolic control and its variation in type 2 diabetes mellitus. In particular we have analyzed a population of more than 1000 Italian type 2 diabetic patients, collected within the European project Mosaic. The results obtained in terms of Matthews Correlation Coefficient are significantly better than the ones gathered with standard logistic regression model, based on data pooling.

Predicting site locations for biomass using facilities with Bayesian methods

Treesearch

Timothy M. Young; James H. Perdue; Xia Huang

2017-01-01

Logistic regression models combined with Bayesian inference were developed to predict locations and quantify factors that influence the siting of biomass-using facilities that use woody biomass in the Southeastern United States. Predictions were developed for two groups of mills, one representing larger capacity mills similar to pulp and paper mills (Group II...

Priors in Whole-Genome Regression: The Bayesian Alphabet Returns

PubMed Central

Gianola, Daniel

2013-01-01

Whole-genome enabled prediction of complex traits has received enormous attention in animal and plant breeding and is making inroads into human and even Drosophila genetics. The term “Bayesian alphabet” denotes a growing number of letters of the alphabet used to denote various Bayesian linear regressions that differ in the priors adopted, while sharing the same sampling model. We explore the role of the prior distribution in whole-genome regression models for dissecting complex traits in what is now a standard situation with genomic data where the number of unknown parameters (p) typically exceeds sample size (n). Members of the alphabet aim to confront this overparameterization in various manners, but it is shown here that the prior is always influential, unless n ≫ p. This happens because parameters are not likelihood identified, so Bayesian learning is imperfect. Since inferences are not devoid of the influence of the prior, claims about genetic architecture from these methods should be taken with caution. However, all such procedures may deliver reasonable predictions of complex traits, provided that some parameters (“tuning knobs”) are assessed via a properly conducted cross-validation. It is concluded that members of the alphabet have a room in whole-genome prediction of phenotypes, but have somewhat doubtful inferential value, at least when sample size is such that n ≪ p. PMID:23636739

Exact and Approximate Statistical Inference for Nonlinear Regression and the Estimating Equation Approach.

PubMed

Demidenko, Eugene

2017-09-01

The exact density distribution of the nonlinear least squares estimator in the one-parameter regression model is derived in closed form and expressed through the cumulative distribution function of the standard normal variable. Several proposals to generalize this result are discussed. The exact density is extended to the estimating equation (EE) approach and the nonlinear regression with an arbitrary number of linear parameters and one intrinsically nonlinear parameter. For a very special nonlinear regression model, the derived density coincides with the distribution of the ratio of two normally distributed random variables previously obtained by Fieller (1932), unlike other approximations previously suggested by other authors. Approximations to the density of the EE estimators are discussed in the multivariate case. Numerical complications associated with the nonlinear least squares are illustrated, such as nonexistence and/or multiple solutions, as major factors contributing to poor density approximation. The nonlinear Markov-Gauss theorem is formulated based on the near exact EE density approximation.

Bayesian calibration for forensic age estimation.

PubMed

Ferrante, Luigi; Skrami, Edlira; Gesuita, Rosaria; Cameriere, Roberto

2015-05-10

Forensic medicine is increasingly called upon to assess the age of individuals. Forensic age estimation is mostly required in relation to illegal immigration and identification of bodies or skeletal remains. A variety of age estimation methods are based on dental samples and use of regression models, where the age of an individual is predicted by morphological tooth changes that take place over time. From the medico-legal point of view, regression models, with age as the dependent random variable entail that age tends to be overestimated in the young and underestimated in the old. To overcome this bias, we describe a new full Bayesian calibration method (asymmetric Laplace Bayesian calibration) for forensic age estimation that uses asymmetric Laplace distribution as the probability model. The method was compared with three existing approaches (two Bayesian and a classical method) using simulated data. Although its accuracy was comparable with that of the other methods, the asymmetric Laplace Bayesian calibration appears to be significantly more reliable and robust in case of misspecification of the probability model. The proposed method was also applied to a real dataset of values of the pulp chamber of the right lower premolar measured on x-ray scans of individuals of known age. Copyright © 2015 John Wiley & Sons, Ltd.

Nonlinear inversion of electrical resistivity imaging using pruning Bayesian neural networks

NASA Astrophysics Data System (ADS)

Jiang, Fei-Bo; Dai, Qian-Wei; Dong, Li

2016-06-01

Conventional artificial neural networks used to solve electrical resistivity imaging (ERI) inversion problem suffer from overfitting and local minima. To solve these problems, we propose to use a pruning Bayesian neural network (PBNN) nonlinear inversion method and a sample design method based on the K-medoids clustering algorithm. In the sample design method, the training samples of the neural network are designed according to the prior information provided by the K-medoids clustering results; thus, the training process of the neural network is well guided. The proposed PBNN, based on Bayesian regularization, is used to select the hidden layer structure by assessing the effect of each hidden neuron to the inversion results. Then, the hyperparameter α k , which is based on the generalized mean, is chosen to guide the pruning process according to the prior distribution of the training samples under the small-sample condition. The proposed algorithm is more efficient than other common adaptive regularization methods in geophysics. The inversion of synthetic data and field data suggests that the proposed method suppresses the noise in the neural network training stage and enhances the generalization. The inversion results with the proposed method are better than those of the BPNN, RBFNN, and RRBFNN inversion methods as well as the conventional least squares inversion.

Bayesian logistic regression in detection of gene-steroid interaction for cancer at PDLIM5 locus.

PubMed

Wang, Ke-Sheng; Owusu, Daniel; Pan, Yue; Xie, Changchun

2016-06-01

The PDZ and LIM domain 5 (PDLIM5) gene may play a role in cancer, bipolar disorder, major depression, alcohol dependence and schizophrenia; however, little is known about the interaction effect of steroid and PDLIM5 gene on cancer. This study examined 47 single-nucleotide polymorphisms (SNPs) within the PDLIM5 gene in the Marshfield sample with 716 cancer patients (any diagnosed cancer, excluding minor skin cancer) and 2848 noncancer controls. Multiple logistic regression model in PLINK software was used to examine the association of each SNP with cancer. Bayesian logistic regression in PROC GENMOD in SAS statistical software, ver. 9.4 was used to detect gene- steroid interactions influencing cancer. Single marker analysis using PLINK identified 12 SNPs associated with cancer (P< 0.05); especially, SNP rs6532496 revealed the strongest association with cancer (P = 6.84 × 10⁻³); while the next best signal was rs951613 (P = 7.46 × 10⁻³). Classic logistic regression in PROC GENMOD showed that both rs6532496 and rs951613 revealed strong gene-steroid interaction effects (OR=2.18, 95% CI=1.31-3.63 with P = 2.9 × 10⁻³ for rs6532496 and OR=2.07, 95% CI=1.24-3.45 with P = 5.43 × 10⁻³ for rs951613, respectively). Results from Bayesian logistic regression showed stronger interaction effects (OR=2.26, 95% CI=1.2-3.38 for rs6532496 and OR=2.14, 95% CI=1.14-3.2 for rs951613, respectively). All the 12 SNPs associated with cancer revealed significant gene-steroid interaction effects (P < 0.05); whereas 13 SNPs showed gene-steroid interaction effects without main effect on cancer. SNP rs4634230 revealed the strongest gene-steroid interaction effect (OR=2.49, 95% CI=1.5-4.13 with P = 4.0 × 10⁻⁴ based on the classic logistic regression and OR=2.59, 95% CI=1.4-3.97 from Bayesian logistic regression; respectively). This study provides evidence of common genetic variants within the PDLIM5 gene and interactions between PLDIM5 gene polymorphisms and steroid use influencing cancer.

Maximum Entropy Discrimination Poisson Regression for Software Reliability Modeling.

PubMed

Chatzis, Sotirios P; Andreou, Andreas S

2015-11-01

Reliably predicting software defects is one of the most significant tasks in software engineering. Two of the major components of modern software reliability modeling approaches are: 1) extraction of salient features for software system representation, based on appropriately designed software metrics and 2) development of intricate regression models for count data, to allow effective software reliability data modeling and prediction. Surprisingly, research in the latter frontier of count data regression modeling has been rather limited. More specifically, a lack of simple and efficient algorithms for posterior computation has made the Bayesian approaches appear unattractive, and thus underdeveloped in the context of software reliability modeling. In this paper, we try to address these issues by introducing a novel Bayesian regression model for count data, based on the concept of max-margin data modeling, effected in the context of a fully Bayesian model treatment with simple and efficient posterior distribution updates. Our novel approach yields a more discriminative learning technique, making more effective use of our training data during model inference. In addition, it allows of better handling uncertainty in the modeled data, which can be a significant problem when the training data are limited. We derive elegant inference algorithms for our model under the mean-field paradigm and exhibit its effectiveness using the publicly available benchmark data sets.

Bayesian evidence computation for model selection in non-linear geoacoustic inference problems.

PubMed

Dettmer, Jan; Dosso, Stan E; Osler, John C

2010-12-01

This paper applies a general Bayesian inference approach, based on Bayesian evidence computation, to geoacoustic inversion of interface-wave dispersion data. Quantitative model selection is carried out by computing the evidence (normalizing constants) for several model parameterizations using annealed importance sampling. The resulting posterior probability density estimate is compared to estimates obtained from Metropolis-Hastings sampling to ensure consistent results. The approach is applied to invert interface-wave dispersion data collected on the Scotian Shelf, off the east coast of Canada for the sediment shear-wave velocity profile. Results are consistent with previous work on these data but extend the analysis to a rigorous approach including model selection and uncertainty analysis. The results are also consistent with core samples and seismic reflection measurements carried out in the area.

Parameter and Structure Inference for Nonlinear Dynamical Systems

NASA Technical Reports Server (NTRS)

Morris, Robin D.; Smelyanskiy, Vadim N.; Millonas, Mark

2006-01-01

A great many systems can be modeled in the non-linear dynamical systems framework, as x = f(x) + xi(t), where f() is the potential function for the system, and xi is the excitation noise. Modeling the potential using a set of basis functions, we derive the posterior for the basis coefficients. A more challenging problem is to determine the set of basis functions that are required to model a particular system. We show that using the Bayesian Information Criteria (BIC) to rank models, and the beam search technique, that we can accurately determine the structure of simple non-linear dynamical system models, and the structure of the coupling between non-linear dynamical systems where the individual systems are known. This last case has important ecological applications.

Computation of nonlinear least squares estimator and maximum likelihood using principles in matrix calculus

NASA Astrophysics Data System (ADS)

Mahaboob, B.; Venkateswarlu, B.; Sankar, J. Ravi; Balasiddamuni, P.

2017-11-01

This paper uses matrix calculus techniques to obtain Nonlinear Least Squares Estimator (NLSE), Maximum Likelihood Estimator (MLE) and Linear Pseudo model for nonlinear regression model. David Pollard and Peter Radchenko [1] explained analytic techniques to compute the NLSE. However the present research paper introduces an innovative method to compute the NLSE using principles in multivariate calculus. This study is concerned with very new optimization techniques used to compute MLE and NLSE. Anh [2] derived NLSE and MLE of a heteroscedatistic regression model. Lemcoff [3] discussed a procedure to get linear pseudo model for nonlinear regression model. In this research article a new technique is developed to get the linear pseudo model for nonlinear regression model using multivariate calculus. The linear pseudo model of Edmond Malinvaud [4] has been explained in a very different way in this paper. David Pollard et.al used empirical process techniques to study the asymptotic of the LSE (Least-squares estimation) for the fitting of nonlinear regression function in 2006. In Jae Myung [13] provided a go conceptual for Maximum likelihood estimation in his work “Tutorial on maximum likelihood estimation

Spatial quantile regression using INLA with applications to childhood overweight in Malawi.

PubMed

Mtambo, Owen P L; Masangwi, Salule J; Kazembe, Lawrence N M

2015-04-01

Analyses of childhood overweight have mainly used mean regression. However, using quantile regression is more appropriate as it provides flexibility to analyse the determinants of overweight corresponding to quantiles of interest. The main objective of this study was to fit a Bayesian additive quantile regression model with structured spatial effects for childhood overweight in Malawi using the 2010 Malawi DHS data. Inference was fully Bayesian using R-INLA package. The significant determinants of childhood overweight ranged from socio-demographic factors such as type of residence to child and maternal factors such as child age and maternal BMI. We observed significant positive structured spatial effects on childhood overweight in some districts of Malawi. We recommended that the childhood malnutrition policy makers should consider timely interventions based on risk factors as identified in this paper including spatial targets of interventions. Copyright © 2015 Elsevier Ltd. All rights reserved.

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.

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.

Bayesian survival analysis in clinical trials: What methods are used in practice?

PubMed

Brard, Caroline; Le Teuff, Gwénaël; Le Deley, Marie-Cécile; Hampson, Lisa V

2017-02-01

Background Bayesian statistics are an appealing alternative to the traditional frequentist approach to designing, analysing, and reporting of clinical trials, especially in rare diseases. Time-to-event endpoints are widely used in many medical fields. There are additional complexities to designing Bayesian survival trials which arise from the need to specify a model for the survival distribution. The objective of this article was to critically review the use and reporting of Bayesian methods in survival trials. Methods A systematic review of clinical trials using Bayesian survival analyses was performed through PubMed and Web of Science databases. This was complemented by a full text search of the online repositories of pre-selected journals. Cost-effectiveness, dose-finding studies, meta-analyses, and methodological papers using clinical trials were excluded. Results In total, 28 articles met the inclusion criteria, 25 were original reports of clinical trials and 3 were re-analyses of a clinical trial. Most trials were in oncology (n = 25), were randomised controlled (n = 21) phase III trials (n = 13), and half considered a rare disease (n = 13). Bayesian approaches were used for monitoring in 14 trials and for the final analysis only in 14 trials. In the latter case, Bayesian survival analyses were used for the primary analysis in four cases, for the secondary analysis in seven cases, and for the trial re-analysis in three cases. Overall, 12 articles reported fitting Bayesian regression models (semi-parametric, n = 3; parametric, n = 9). Prior distributions were often incompletely reported: 20 articles did not define the prior distribution used for the parameter of interest. Over half of the trials used only non-informative priors for monitoring and the final analysis (n = 12) when it was specified. Indeed, no articles fitting Bayesian regression models placed informative priors on the parameter of interest. The prior for the treatment effect was based on historical data in only four trials. Decision rules were pre-defined in eight cases when trials used Bayesian monitoring, and in only one case when trials adopted a Bayesian approach to the final analysis. Conclusion Few trials implemented a Bayesian survival analysis and few incorporated external data into priors. There is scope to improve the quality of reporting of Bayesian methods in survival trials. Extension of the Consolidated Standards of Reporting Trials statement for reporting Bayesian clinical trials is recommended.

Nonparametric Bayesian Multiple Imputation for Incomplete Categorical Variables in Large-Scale Assessment Surveys

ERIC Educational Resources Information Center

Si, Yajuan; Reiter, Jerome P.

2013-01-01

In many surveys, the data comprise a large number of categorical variables that suffer from item nonresponse. Standard methods for multiple imputation, like log-linear models or sequential regression imputation, can fail to capture complex dependencies and can be difficult to implement effectively in high dimensions. We present a fully Bayesian,…

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

Semiparametric regression during 2003–2007*

PubMed Central

Ruppert, David; Wand, M.P.; Carroll, Raymond J.

2010-01-01

Semiparametric regression is a fusion between parametric regression and nonparametric regression that integrates low-rank penalized splines, mixed model and hierarchical Bayesian methodology – thus allowing more streamlined handling of longitudinal and spatial correlation. We review progress in the field over the five-year period between 2003 and 2007. We find semiparametric regression to be a vibrant field with substantial involvement and activity, continual enhancement and widespread application. PMID:20305800

Simultaneous Estimation of Regression Functions for Marine Corps Technical Training Specialties.

ERIC Educational Resources Information Center

Dunbar, Stephen B.; And Others

This paper considers the application of Bayesian techniques for simultaneous estimation to the specification of regression weights for selection tests used in various technical training courses in the Marine Corps. Results of a method for m-group regression developed by Molenaar and Lewis (1979) suggest that common weights for training courses…

Methods for identifying SNP interactions: a review on variations of Logic Regression, Random Forest and Bayesian logistic regression.

PubMed

Chen, Carla Chia-Ming; Schwender, Holger; Keith, Jonathan; Nunkesser, Robin; Mengersen, Kerrie; Macrossan, Paula

2011-01-01

Due to advancements in computational ability, enhanced technology and a reduction in the price of genotyping, more data are being generated for understanding genetic associations with diseases and disorders. However, with the availability of large data sets comes the inherent challenges of new methods of statistical analysis and modeling. Considering a complex phenotype may be the effect of a combination of multiple loci, various statistical methods have been developed for identifying genetic epistasis effects. Among these methods, logic regression (LR) is an intriguing approach incorporating tree-like structures. Various methods have built on the original LR to improve different aspects of the model. In this study, we review four variations of LR, namely Logic Feature Selection, Monte Carlo Logic Regression, Genetic Programming for Association Studies, and Modified Logic Regression-Gene Expression Programming, and investigate the performance of each method using simulated and real genotype data. We contrast these with another tree-like approach, namely Random Forests, and a Bayesian logistic regression with stochastic search variable selection.

Bayesian Methods for the Physical Sciences. Learning from Examples in Astronomy and Physics.

NASA Astrophysics Data System (ADS)

Andreon, Stefano; Weaver, Brian

2015-05-01

Chapter 1: This chapter presents some basic steps for performing a good statistical analysis, all summarized in about one page. Chapter 2: This short chapter introduces the basics of probability theory inan intuitive fashion using simple examples. It also illustrates, again with examples, how to propagate errors and the difference between marginal and profile likelihoods. Chapter 3: This chapter introduces the computational tools and methods that we use for sampling from the posterior distribution. Since all numerical computations, and Bayesian ones are no exception, may end in errors, we also provide a few tips to check that the numerical computation is sampling from the posterior distribution. Chapter 4: Many of the concepts of building, running, and summarizing the resultsof a Bayesian analysis are described with this step-by-step guide using a basic (Gaussian) model. The chapter also introduces examples using Poisson and Binomial likelihoods, and how to combine repeated independent measurements. Chapter 5: All statistical analyses make assumptions, and Bayesian analyses are no exception. This chapter emphasizes that results depend on data and priors (assumptions). We illustrate this concept with examples where the prior plays greatly different roles, from major to negligible. We also provide some advice on how to look for information useful for sculpting the prior. Chapter 6: In this chapter we consider examples for which we want to estimate more than a single parameter. These common problems include estimating location and spread. We also consider examples that require the modeling of two populations (one we are interested in and a nuisance population) or averaging incompatible measurements. We also introduce quite complex examples dealing with upper limits and with a larger-than-expected scatter. Chapter 7: Rarely is a sample randomly selected from the population we wish to study. Often, samples are affected by selection effects, e.g., easier-to-collect events or objects are over-represented in samples and difficult-to-collect are under-represented if not missing altogether. In this chapter we show how to account for non-random data collection to infer the properties of the population from the studied sample. Chapter 8: In this chapter we introduce regression models, i.e., how to fit (regress) one, or more quantities, against each other through a functional relationship and estimate any unknown parameters that dictate this relationship. Questions of interest include: how to deal with samples affected by selection effects? How does a rich data structure influence the fitted parameters? And what about non-linear multiple-predictor fits, upper/lower limits, measurements errors of different amplitudes and an intrinsic variety in the studied populations or an extra source of variability? A number of examples illustrate how to answer these questions and how to predict the value of an unavailable quantity by exploiting the existence of a trend with another, available, quantity. Chapter 9: This chapter provides some advice on how the careful scientist should perform model checking and sensitivity analysis, i.e., how to answer the following questions: is the considered model at odds with the current available data (the fitted data), for example because it is over-simplified compared to some specific complexity pointed out by the data? Furthermore, are the data informative about the quantity being measured or are results sensibly dependent on details of the fitted model? And, finally, what about if assumptions are uncertain? A number of examples illustrate how to answer these questions. Chapter 10: This chapter compares the performance of Bayesian methods against simple, non-Bayesian alternatives, such as maximum likelihood, minimal chi square, ordinary and weighted least square, bivariate correlated errors and intrinsic scatter, and robust estimates of location and scale. Performances are evaluated in terms of quality of the prediction, accuracy of the estimates, and fairness and noisiness of the quoted errors. We also focus on three failures of maximum likelihood methods occurring with small samples, with mixtures, and with regressions with errors in the predictor quantity.

Kalman filter approach for uncertainty quantification in time-resolved laser-induced incandescence.

PubMed

Hadwin, Paul J; Sipkens, Timothy A; Thomson, Kevin A; Liu, Fengshan; Daun, Kyle J

2018-03-01

Time-resolved laser-induced incandescence (TiRe-LII) data can be used to infer spatially and temporally resolved volume fractions and primary particle size distributions of soot-laden aerosols, but these estimates are corrupted by measurement noise as well as uncertainties in the spectroscopic and heat transfer submodels used to interpret the data. Estimates of the temperature, concentration, and size distribution of soot primary particles within a sample aerosol are typically made by nonlinear regression of modeled spectral incandescence decay, or effective temperature decay, to experimental data. In this work, we employ nonstationary Bayesian estimation techniques to infer aerosol properties from simulated and experimental LII signals, specifically the extended Kalman filter and Schmidt-Kalman filter. These techniques exploit the time-varying nature of both the measurements and the models, and they reveal how uncertainty in the estimates computed from TiRe-LII data evolves over time. Both techniques perform better when compared with standard deterministic estimates; however, we demonstrate that the Schmidt-Kalman filter produces more realistic uncertainty estimates.

Colossal photon bunching in quasiparticle-mediated nanodiamond cathodoluminescence

NASA Astrophysics Data System (ADS)

Feldman, Matthew A.; Dumitrescu, Eugene F.; Bridges, Denzel; Chisholm, Matthew F.; Davidson, Roderick B.; Evans, Philip G.; Hachtel, Jordan A.; Hu, Anming; Pooser, Raphael C.; Haglund, Richard F.; Lawrie, Benjamin J.

2018-02-01

Nanoscale control over the second-order photon correlation function g(2 )(τ ) is critical to emerging research in nonlinear nanophotonics and integrated quantum information science. Here we report on quasiparticle control of photon bunching with g(2 )(0 ) >45 in the cathodoluminescence of nanodiamond nitrogen vacancy (NV0) centers excited by a converged electron beam in an aberration-corrected scanning transmission electron microscope. Plasmon-mediated NV0 cathodoluminescence exhibits a 16-fold increase in luminescence intensity correlated with a threefold reduction in photon bunching compared with that of uncoupled NV0 centers. This effect is ascribed to the excitation of single temporally uncorrelated NV0 centers by single surface plasmon polaritons. Spectrally resolved Hanbury Brown-Twiss interferometry is employed to demonstrate that the bunching is mediated by the NV0 phonon sidebands, while no observable bunching is detected at the zero-phonon line. The data are consistent with fast phonon-mediated recombination dynamics, a conclusion substantiated by agreement between Bayesian regression and Monte Carlo models of superthermal NV0 luminescence.

Method for nonlinear exponential regression analysis

NASA Technical Reports Server (NTRS)

Junkin, B. G.

1972-01-01

Two computer programs developed according to two general types of exponential models for conducting nonlinear exponential regression analysis are described. Least squares procedure is used in which the nonlinear problem is linearized by expanding in a Taylor series. Program is written in FORTRAN 5 for the Univac 1108 computer.

Bayesian framework for modeling diffusion processes with nonlinear drift based on nonlinear and incomplete observations.

PubMed

Wu, Hao; Noé, Frank

2011-03-01

Diffusion processes are relevant for a variety of phenomena in the natural sciences, including diffusion of cells or biomolecules within cells, diffusion of molecules on a membrane or surface, and diffusion of a molecular conformation within a complex energy landscape. Many experimental tools exist now to track such diffusive motions in single cells or molecules, including high-resolution light microscopy, optical tweezers, fluorescence quenching, and Förster resonance energy transfer (FRET). Experimental observations are most often indirect and incomplete: (1) They do not directly reveal the potential or diffusion constants that govern the diffusion process, (2) they have limited time and space resolution, and (3) the highest-resolution experiments do not track the motion directly but rather probe it stochastically by recording single events, such as photons, whose properties depend on the state of the system under investigation. Here, we propose a general Bayesian framework to model diffusion processes with nonlinear drift based on incomplete observations as generated by various types of experiments. A maximum penalized likelihood estimator is given as well as a Gibbs sampling method that allows to estimate the trajectories that have caused the measurement, the nonlinear drift or potential function and the noise or diffusion matrices, as well as uncertainty estimates of these properties. The approach is illustrated on numerical simulations of FRET experiments where it is shown that trajectories, potentials, and diffusion constants can be efficiently and reliably estimated even in cases with little statistics or nonequilibrium measurement conditions.

Model Selection and Psychological Theory: A Discussion of the Differences between the Akaike Information Criterion (AIC) and the Bayesian Information Criterion (BIC)

ERIC Educational Resources Information Center

Vrieze, Scott I.

2012-01-01

This article reviews the Akaike information criterion (AIC) and the Bayesian information criterion (BIC) in model selection and the appraisal of psychological theory. The focus is on latent variable models, given their growing use in theory testing and construction. Theoretical statistical results in regression are discussed, and more important…

Application of Bayesian methods to habitat selection modeling of the northern spotted owl in California: new statistical methods for wildlife research

Treesearch

Howard B. Stauffer; Cynthia J. Zabel; Jeffrey R. Dunk

2005-01-01

We compared a set of competing logistic regression habitat selection models for Northern Spotted Owls (Strix occidentalis caurina) in California. The habitat selection models were estimated, compared, evaluated, and tested using multiple sample datasets collected on federal forestlands in northern California. We used Bayesian methods in interpreting...

Revisiting Isotherm Analyses Using R: Comparison of Linear, Non-linear, and Bayesian Techniques

EPA Science Inventory

Extensive adsorption isotherm data exist for an array of chemicals of concern on a variety of engineered and natural sorbents. Several isotherm models exist that can accurately describe these data from which the resultant fitting parameters may subsequently be used in numerical ...

Bayesian generalized linear mixed modeling of Tuberculosis using informative priors.

PubMed

Ojo, Oluwatobi Blessing; Lougue, Siaka; Woldegerima, Woldegebriel Assefa

2017-01-01

TB is rated as one of the world's deadliest diseases and South Africa ranks 9th out of the 22 countries with hardest hit of TB. Although many pieces of research have been carried out on this subject, this paper steps further by inculcating past knowledge into the model, using Bayesian approach with informative prior. Bayesian statistics approach is getting popular in data analyses. But, most applications of Bayesian inference technique are limited to situations of non-informative prior, where there is no solid external information about the distribution of the parameter of interest. The main aim of this study is to profile people living with TB in South Africa. In this paper, identical regression models are fitted for classical and Bayesian approach both with non-informative and informative prior, using South Africa General Household Survey (GHS) data for the year 2014. For the Bayesian model with informative prior, South Africa General Household Survey dataset for the year 2011 to 2013 are used to set up priors for the model 2014.

The Bayesian Decoding of Force Stimuli from Slowly Adapting Type I Fibers in Humans.

PubMed

Kasi, Patrick; Wright, James; Khamis, Heba; Birznieks, Ingvars; van Schaik, André

2016-01-01

It is well known that signals encoded by mechanoreceptors facilitate precise object manipulation in humans. It is therefore of interest to study signals encoded by the mechanoreceptors because this will contribute further towards the understanding of fundamental sensory mechanisms that are responsible for coordinating force components during object manipulation. From a practical point of view, this may suggest strategies for designing sensory-controlled biomedical devices and robotic manipulators. We use a two-stage nonlinear decoding paradigm to reconstruct the force stimulus given signals from slowly adapting type one (SA-I) tactile afferents. First, we describe a nonhomogeneous Poisson encoding model which is a function of the force stimulus and the force's rate of change. In the decoding phase, we use a recursive nonlinear Bayesian filter to reconstruct the force profile, given the SA-I spike patterns and parameters described by the encoding model. Under the current encoding model, the mode ratio of force to its derivative is: 1.26 to 1.02. This indicates that the force derivative contributes significantly to the rate of change to the SA-I afferent spike modulation. Furthermore, using recursive Bayesian decoding algorithms is advantageous because it can incorporate past and current information in order to make predictions--consistent with neural systems--with little computational resources. This makes it suitable for interfacing with prostheses.

The Bayesian Decoding of Force Stimuli from Slowly Adapting Type I Fibers in Humans

PubMed Central

Wright, James; Khamis, Heba; Birznieks, Ingvars; van Schaik, André

2016-01-01

It is well known that signals encoded by mechanoreceptors facilitate precise object manipulation in humans. It is therefore of interest to study signals encoded by the mechanoreceptors because this will contribute further towards the understanding of fundamental sensory mechanisms that are responsible for coordinating force components during object manipulation. From a practical point of view, this may suggest strategies for designing sensory-controlled biomedical devices and robotic manipulators. We use a two-stage nonlinear decoding paradigm to reconstruct the force stimulus given signals from slowly adapting type one (SA-I) tactile afferents. First, we describe a nonhomogeneous Poisson encoding model which is a function of the force stimulus and the force’s rate of change. In the decoding phase, we use a recursive nonlinear Bayesian filter to reconstruct the force profile, given the SA-I spike patterns and parameters described by the encoding model. Under the current encoding model, the mode ratio of force to its derivative is: 1.26 to 1.02. This indicates that the force derivative contributes significantly to the rate of change to the SA-I afferent spike modulation. Furthermore, using recursive Bayesian decoding algorithms is advantageous because it can incorporate past and current information in order to make predictions—consistent with neural systems—with little computational resources. This makes it suitable for interfacing with prostheses. PMID:27077750

Genomic Bayesian functional regression models with interactions for predicting wheat grain yield using hyper-spectral image data.

PubMed

Montesinos-López, Abelardo; Montesinos-López, Osval A; Cuevas, Jaime; Mata-López, Walter A; Burgueño, Juan; Mondal, Sushismita; Huerta, Julio; Singh, Ravi; Autrique, Enrique; González-Pérez, Lorena; Crossa, José

2017-01-01

Modern agriculture uses hyperspectral cameras that provide hundreds of reflectance data at discrete narrow bands in many environments. These bands often cover the whole visible light spectrum and part of the infrared and ultraviolet light spectra. With the bands, vegetation indices are constructed for predicting agronomically important traits such as grain yield and biomass. However, since vegetation indices only use some wavelengths (referred to as bands), we propose using all bands simultaneously as predictor variables for the primary trait grain yield; results of several multi-environment maize (Aguate et al. in Crop Sci 57(5):1-8, 2017) and wheat (Montesinos-López et al. in Plant Methods 13(4):1-23, 2017) breeding trials indicated that using all bands produced better prediction accuracy than vegetation indices. However, until now, these prediction models have not accounted for the effects of genotype × environment (G × E) and band × environment (B × E) interactions incorporating genomic or pedigree information. In this study, we propose Bayesian functional regression models that take into account all available bands, genomic or pedigree information, the main effects of lines and environments, as well as G × E and B × E interaction effects. The data set used is comprised of 976 wheat lines evaluated for grain yield in three environments (Drought, Irrigated and Reduced Irrigation). The reflectance data were measured in 250 discrete narrow bands ranging from 392 to 851 nm (nm). The proposed Bayesian functional regression models were implemented using two types of basis: B-splines and Fourier. Results of the proposed Bayesian functional regression models, including all the wavelengths for predicting grain yield, were compared with results from conventional models with and without bands. We observed that the models with B × E interaction terms were the most accurate models, whereas the functional regression models (with B-splines and Fourier basis) and the conventional models performed similarly in terms of prediction accuracy. However, the functional regression models are more parsimonious and computationally more efficient because the number of beta coefficients to be estimated is 21 (number of basis), rather than estimating the 250 regression coefficients for all bands. In this study adding pedigree or genomic information did not increase prediction accuracy.

When mechanism matters: Bayesian forecasting using models of ecological diffusion

USGS Publications Warehouse

Hefley, Trevor J.; Hooten, Mevin B.; Russell, Robin E.; Walsh, Daniel P.; Powell, James A.

2017-01-01

Ecological diffusion is a theory that can be used to understand and forecast spatio-temporal processes such as dispersal, invasion, and the spread of disease. Hierarchical Bayesian modelling provides a framework to make statistical inference and probabilistic forecasts, using mechanistic ecological models. To illustrate, we show how hierarchical Bayesian models of ecological diffusion can be implemented for large data sets that are distributed densely across space and time. The hierarchical Bayesian approach is used to understand and forecast the growth and geographic spread in the prevalence of chronic wasting disease in white-tailed deer (Odocoileus virginianus). We compare statistical inference and forecasts from our hierarchical Bayesian model to phenomenological regression-based methods that are commonly used to analyse spatial occurrence data. The mechanistic statistical model based on ecological diffusion led to important ecological insights, obviated a commonly ignored type of collinearity, and was the most accurate method for forecasting.

Bayesian estimation of seasonal course of canopy leaf area index from hyperspectral satellite data

NASA Astrophysics Data System (ADS)

Varvia, Petri; Rautiainen, Miina; Seppänen, Aku

2018-03-01

In this paper, Bayesian inversion of a physically-based forest reflectance model is investigated to estimate of boreal forest canopy leaf area index (LAI) from EO-1 Hyperion hyperspectral data. The data consist of multiple forest stands with different species compositions and structures, imaged in three phases of the growing season. The Bayesian estimates of canopy LAI are compared to reference estimates based on a spectral vegetation index. The forest reflectance model contains also other unknown variables in addition to LAI, for example leaf single scattering albedo and understory reflectance. In the Bayesian approach, these variables are estimated simultaneously with LAI. The feasibility and seasonal variation of these estimates is also examined. Credible intervals for the estimates are also calculated and evaluated. The results show that the Bayesian inversion approach is significantly better than using a comparable spectral vegetation index regression.

Uncertainty plus Prior Equals Rational Bias: An Intuitive Bayesian Probability Weighting Function

ERIC Educational Resources Information Center

Fennell, John; Baddeley, Roland

2012-01-01

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…

Non-Linear Modeling of Growth Prerequisites in a Finnish Polytechnic Institution of Higher Education

ERIC Educational Resources Information Center

Nokelainen, Petri; Ruohotie, Pekka

2009-01-01

Purpose: This study aims to examine the factors of growth-oriented atmosphere in a Finnish polytechnic institution of higher education with categorical exploratory factor analysis, multidimensional scaling and Bayesian unsupervised model-based visualization. Design/methodology/approach: This study was designed to examine employee perceptions of…

Bayesian feature selection for high-dimensional linear regression via the Ising approximation with applications to genomics.

PubMed

Fisher, Charles K; Mehta, Pankaj

2015-06-01

Feature selection, identifying a subset of variables that are relevant for predicting a response, is an important and challenging component of many methods in statistics and machine learning. Feature selection is especially difficult and computationally intensive when the number of variables approaches or exceeds the number of samples, as is often the case for many genomic datasets. Here, we introduce a new approach--the Bayesian Ising Approximation (BIA)-to rapidly calculate posterior probabilities for feature relevance in L2 penalized linear regression. In the regime where the regression problem is strongly regularized by the prior, we show that computing the marginal posterior probabilities for features is equivalent to computing the magnetizations of an Ising model with weak couplings. Using a mean field approximation, we show it is possible to rapidly compute the feature selection path described by the posterior probabilities as a function of the L2 penalty. We present simulations and analytical results illustrating the accuracy of the BIA on some simple regression problems. Finally, we demonstrate the applicability of the BIA to high-dimensional regression by analyzing a gene expression dataset with nearly 30 000 features. These results also highlight the impact of correlations between features on Bayesian feature selection. An implementation of the BIA in C++, along with data for reproducing our gene expression analyses, are freely available at http://physics.bu.edu/∼pankajm/BIACode. © The Author 2015. Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions@oup.com.

Bayesian Lagrangian Data Assimilation and Drifter Deployment Strategies

NASA Astrophysics Data System (ADS)

Dutt, A.; Lermusiaux, P. F. J.

2017-12-01

Ocean currents transport a variety of natural (e.g. water masses, phytoplankton, zooplankton, sediments, etc.) and man-made materials and other objects (e.g. pollutants, floating debris, search and rescue, etc.). Lagrangian Coherent Structures (LCSs) or the most influential/persistent material lines in a flow, provide a robust approach to characterize such Lagrangian transports and organize classic trajectories. Using the flow-map stochastic advection and a dynamically-orthogonal decomposition, we develop uncertainty prediction schemes for both Eulerian and Lagrangian variables. We then extend our Bayesian Gaussian Mixture Model (GMM)-DO filter to a joint Eulerian-Lagrangian Bayesian data assimilation scheme. The resulting nonlinear filter allows the simultaneous non-Gaussian estimation of Eulerian variables (e.g. velocity, temperature, salinity, etc.) and Lagrangian variables (e.g. drifter/float positions, trajectories, LCSs, etc.). Its results are showcased using a double-gyre flow with a random frequency, a stochastic flow past a cylinder, and realistic ocean examples. We further show how our Bayesian mutual information and adaptive sampling equations provide a rigorous efficient methodology to plan optimal drifter deployment strategies and predict the optimal times, locations, and types of measurements to be collected.

Dynamic Dimensionality Selection for Bayesian Classifier Ensembles

DTIC Science & Technology

2015-03-19

learning of weights in an otherwise generatively learned naive Bayes classifier. WANBIA-C is very cometitive to Logistic Regression but much more...classifier, Generative learning, Discriminative learning, Naïve Bayes, Feature selection, Logistic regression , higher order attribute independence 16...discriminative learning of weights in an otherwise generatively learned naive Bayes classifier. WANBIA-C is very cometitive to Logistic Regression but

Spatial Double Generalized Beta Regression Models: Extensions and Application to Study Quality of Education in Colombia

ERIC Educational Resources Information Center

Cepeda-Cuervo, Edilberto; Núñez-Antón, Vicente

2013-01-01

In this article, a proposed Bayesian extension of the generalized beta spatial regression models is applied to the analysis of the quality of education in Colombia. We briefly revise the beta distribution and describe the joint modeling approach for the mean and dispersion parameters in the spatial regression models' setting. Finally, we motivate…

Model selection and parameter estimation in structural dynamics using approximate Bayesian computation

NASA Astrophysics Data System (ADS)

Ben Abdessalem, Anis; Dervilis, Nikolaos; Wagg, David; Worden, Keith

2018-01-01

This paper will introduce the use of the approximate Bayesian computation (ABC) algorithm for model selection and parameter estimation in structural dynamics. ABC is a likelihood-free method typically used when the likelihood function is either intractable or cannot be approached in a closed form. To circumvent the evaluation of the likelihood function, simulation from a forward model is at the core of the ABC algorithm. The algorithm offers the possibility to use different metrics and summary statistics representative of the data to carry out Bayesian inference. The efficacy of the algorithm in structural dynamics is demonstrated through three different illustrative examples of nonlinear system identification: cubic and cubic-quintic models, the Bouc-Wen model and the Duffing oscillator. The obtained results suggest that ABC is a promising alternative to deal with model selection and parameter estimation issues, specifically for systems with complex behaviours.

Mining pharmacovigilance data using Bayesian logistic regression with James-Stein type shrinkage estimation.

PubMed

An, Lihua; Fung, Karen Y; Krewski, Daniel

2010-09-01

Spontaneous adverse event reporting systems are widely used to identify adverse reactions to drugs following their introduction into the marketplace. In this article, a James-Stein type shrinkage estimation strategy was developed in a Bayesian logistic regression model to analyze pharmacovigilance data. This method is effective in detecting signals as it combines information and borrows strength across medically related adverse events. Computer simulation demonstrated that the shrinkage estimator is uniformly better than the maximum likelihood estimator in terms of mean squared error. This method was used to investigate the possible association of a series of diabetic drugs and the risk of cardiovascular events using data from the Canada Vigilance Online Database.

New insights into faster computation of uncertainties

NASA Astrophysics Data System (ADS)

Bhattacharya, Atreyee

2012-11-01

Heavy computation power, lengthy simulations, and an exhaustive number of model runs—often these seem like the only statistical tools that scientists have at their disposal when computing uncertainties associated with predictions, particularly in cases of environmental processes such as groundwater movement. However, calculation of uncertainties need not be as lengthy, a new study shows. Comparing two approaches—the classical Bayesian “credible interval” and a less commonly used regression-based “confidence interval” method—Lu et al. show that for many practical purposes both methods provide similar estimates of uncertainties. The advantage of the regression method is that it demands 10-1000 model runs, whereas the classical Bayesian approach requires 10,000 to millions of model runs.

Heuristics as Bayesian inference under extreme priors.

PubMed

Parpart, Paula; Jones, Matt; Love, Bradley C

2018-05-01

Simple heuristics are often regarded as tractable decision strategies because they ignore a great deal of information in the input data. One puzzle is why heuristics can outperform full-information models, such as linear regression, which make full use of the available information. These "less-is-more" effects, in which a relatively simpler model outperforms a more complex model, are prevalent throughout cognitive science, and are frequently argued to demonstrate an inherent advantage of simplifying computation or ignoring information. In contrast, we show at the computational level (where algorithmic restrictions are set aside) that it is never optimal to discard information. Through a formal Bayesian analysis, we prove that popular heuristics, such as tallying and take-the-best, are formally equivalent to Bayesian inference under the limit of infinitely strong priors. Varying the strength of the prior yields a continuum of Bayesian models with the heuristics at one end and ordinary regression at the other. Critically, intermediate models perform better across all our simulations, suggesting that down-weighting information with the appropriate prior is preferable to entirely ignoring it. Rather than because of their simplicity, our analyses suggest heuristics perform well because they implement strong priors that approximate the actual structure of the environment. We end by considering how new heuristics could be derived by infinitely strengthening the priors of other Bayesian models. These formal results have implications for work in psychology, machine learning and economics. Copyright © 2017 The Authors. Published by Elsevier Inc. All rights reserved.

Criterion for evaluating the predictive ability of nonlinear regression models without cross-validation.

PubMed

Kaneko, Hiromasa; Funatsu, Kimito

2013-09-23

We propose predictive performance criteria for nonlinear regression models without cross-validation. The proposed criteria are the determination coefficient and the root-mean-square error for the midpoints between k-nearest-neighbor data points. These criteria can be used to evaluate predictive ability after the regression models are updated, whereas cross-validation cannot be performed in such a situation. The proposed method is effective and helpful in handling big data when cross-validation cannot be applied. By analyzing data from numerical simulations and quantitative structural relationships, we confirm that the proposed criteria enable the predictive ability of the nonlinear regression models to be appropriately quantified.

Rigorous Approach in Investigation of Seismic Structure and Source Characteristicsin Northeast Asia: Hierarchical and Trans-dimensional Bayesian Inversion

NASA Astrophysics Data System (ADS)

Mustac, M.; Kim, S.; Tkalcic, H.; Rhie, J.; Chen, Y.; Ford, S. R.; Sebastian, N.

2015-12-01

Conventional approaches to inverse problems suffer from non-linearity and non-uniqueness in estimations of seismic structures and source properties. Estimated results and associated uncertainties are often biased by applied regularizations and additional constraints, which are commonly introduced to solve such problems. Bayesian methods, however, provide statistically meaningful estimations of models and their uncertainties constrained by data information. In addition, hierarchical and trans-dimensional (trans-D) techniques are inherently implemented in the Bayesian framework to account for involved error statistics and model parameterizations, and, in turn, allow more rigorous estimations of the same. Here, we apply Bayesian methods throughout the entire inference process to estimate seismic structures and source properties in Northeast Asia including east China, the Korean peninsula, and the Japanese islands. Ambient noise analysis is first performed to obtain a base three-dimensional (3-D) heterogeneity model using continuous broadband waveforms from more than 300 stations. As for the tomography of surface wave group and phase velocities in the 5-70 s band, we adopt a hierarchical and trans-D Bayesian inversion method using Voronoi partition. The 3-D heterogeneity model is further improved by joint inversions of teleseismic receiver functions and dispersion data using a newly developed high-efficiency Bayesian technique. The obtained model is subsequently used to prepare 3-D structural Green's functions for the source characterization. A hierarchical Bayesian method for point source inversion using regional complete waveform data is applied to selected events from the region. The seismic structure and source characteristics with rigorously estimated uncertainties from the novel Bayesian methods provide enhanced monitoring and discrimination of seismic events in northeast Asia.

BFLCRM: A BAYESIAN FUNCTIONAL LINEAR COX REGRESSION MODEL FOR PREDICTING TIME TO CONVERSION TO ALZHEIMER’S DISEASE*

PubMed Central

Lee, Eunjee; Zhu, Hongtu; Kong, Dehan; Wang, Yalin; Giovanello, Kelly Sullivan; Ibrahim, Joseph G

2015-01-01

The aim of this paper is to develop a Bayesian functional linear Cox regression model (BFLCRM) with both functional and scalar covariates. This new development is motivated by establishing the likelihood of conversion to Alzheimer’s disease (AD) in 346 patients with mild cognitive impairment (MCI) enrolled in the Alzheimer’s Disease Neuroimaging Initiative 1 (ADNI-1) and the early markers of conversion. These 346 MCI patients were followed over 48 months, with 161 MCI participants progressing to AD at 48 months. The functional linear Cox regression model was used to establish that functional covariates including hippocampus surface morphology and scalar covariates including brain MRI volumes, cognitive performance (ADAS-Cog), and APOE status can accurately predict time to onset of AD. Posterior computation proceeds via an efficient Markov chain Monte Carlo algorithm. A simulation study is performed to evaluate the finite sample performance of BFLCRM. PMID:26900412

Classification of emotional states from electrocardiogram signals: a non-linear approach based on hurst

PubMed Central

2013-01-01

Background Identifying the emotional state is helpful in applications involving patients with autism and other intellectual disabilities; computer-based training, human computer interaction etc. Electrocardiogram (ECG) signals, being an activity of the autonomous nervous system (ANS), reflect the underlying true emotional state of a person. However, the performance of various methods developed so far lacks accuracy, and more robust methods need to be developed to identify the emotional pattern associated with ECG signals. Methods Emotional ECG data was obtained from sixty participants by inducing the six basic emotional states (happiness, sadness, fear, disgust, surprise and neutral) using audio-visual stimuli. The non-linear feature ‘Hurst’ was computed using Rescaled Range Statistics (RRS) and Finite Variance Scaling (FVS) methods. New Hurst features were proposed by combining the existing RRS and FVS methods with Higher Order Statistics (HOS). The features were then classified using four classifiers – Bayesian Classifier, Regression Tree, K- nearest neighbor and Fuzzy K-nearest neighbor. Seventy percent of the features were used for training and thirty percent for testing the algorithm. Results Analysis of Variance (ANOVA) conveyed that Hurst and the proposed features were statistically significant (p < 0.001). Hurst computed using RRS and FVS methods showed similar classification accuracy. The features obtained by combining FVS and HOS performed better with a maximum accuracy of 92.87% and 76.45% for classifying the six emotional states using random and subject independent validation respectively. Conclusions The results indicate that the combination of non-linear analysis and HOS tend to capture the finer emotional changes that can be seen in healthy ECG data. This work can be further fine tuned to develop a real time system. PMID:23680041

Bayesian Analysis of High Dimensional Classification

NASA Astrophysics Data System (ADS)

Mukhopadhyay, Subhadeep; Liang, Faming

2009-12-01

Modern data mining and bioinformatics have presented an important playground for statistical learning techniques, where the number of input variables is possibly much larger than the sample size of the training data. In supervised learning, logistic regression or probit regression can be used to model a binary output and form perceptron classification rules based on Bayesian inference. In these cases , there is a lot of interest in searching for sparse model in High Dimensional regression(/classification) setup. we first discuss two common challenges for analyzing high dimensional data. The first one is the curse of dimensionality. The complexity of many existing algorithms scale exponentially with the dimensionality of the space and by virtue of that algorithms soon become computationally intractable and therefore inapplicable in many real applications. secondly, multicollinearities among the predictors which severely slowdown the algorithm. In order to make Bayesian analysis operational in high dimension we propose a novel 'Hierarchical stochastic approximation monte carlo algorithm' (HSAMC), which overcomes the curse of dimensionality, multicollinearity of predictors in high dimension and also it possesses the self-adjusting mechanism to avoid the local minima separated by high energy barriers. Models and methods are illustrated by simulation inspired from from the feild of genomics. Numerical results indicate that HSAMC can work as a general model selection sampler in high dimensional complex model space.

Spatial distribution of psychotic disorders in an urban area of France: an ecological study.

PubMed

Pignon, Baptiste; Schürhoff, Franck; Baudin, Grégoire; Ferchiou, Aziz; Richard, Jean-Romain; Saba, Ghassen; Leboyer, Marion; Kirkbride, James B; Szöke, Andrei

2016-05-18

Previous analyses of neighbourhood variations of non-affective psychotic disorders (NAPD) have focused mainly on incidence. However, prevalence studies provide important insights on factors associated with disease evolution as well as for healthcare resource allocation. This study aimed to investigate the distribution of prevalent NAPD cases in an urban area in France. The number of cases in each neighbourhood was modelled as a function of potential confounders and ecological variables, namely: migrant density, economic deprivation and social fragmentation. This was modelled using statistical models of increasing complexity: frequentist models (using Poisson and negative binomial regressions), and several Bayesian models. For each model, assumptions validity were checked and compared as to how this fitted to the data, in order to test for possible spatial variation in prevalence. Data showed significant overdispersion (invalidating the Poisson regression model) and residual autocorrelation (suggesting the need to use Bayesian models). The best Bayesian model was Leroux's model (i.e. a model with both strong correlation between neighbouring areas and weaker correlation between areas further apart), with economic deprivation as an explanatory variable (OR = 1.13, 95% CI [1.02-1.25]). In comparison with frequentist methods, the Bayesian model showed a better fit. The number of cases showed non-random spatial distribution and was linked to economic deprivation.

Bayesian dynamical systems modelling in the social sciences.

PubMed

Ranganathan, Shyam; Spaiser, Viktoria; Mann, Richard P; Sumpter, David J T

2014-01-01

Data arising from social systems is often highly complex, involving non-linear relationships between the macro-level variables that characterize these systems. We present a method for analyzing this type of longitudinal or panel data using differential equations. We identify the best non-linear functions that capture interactions between variables, employing Bayes factor to decide how many interaction terms should be included in the model. This method punishes overly complicated models and identifies models with the most explanatory power. We illustrate our approach on the classic example of relating democracy and economic growth, identifying non-linear relationships between these two variables. We show how multiple variables and variable lags can be accounted for and provide a toolbox in R to implement our approach.

Using Structured Additive Regression Models to Estimate Risk Factors of Malaria: Analysis of 2010 Malawi Malaria Indicator Survey Data

PubMed Central

Chirombo, James; Lowe, Rachel; Kazembe, Lawrence

2014-01-01

Background After years of implementing Roll Back Malaria (RBM) interventions, the changing landscape of malaria in terms of risk factors and spatial pattern has not been fully investigated. This paper uses the 2010 malaria indicator survey data to investigate if known malaria risk factors remain relevant after many years of interventions. Methods We adopted a structured additive logistic regression model that allowed for spatial correlation, to more realistically estimate malaria risk factors. Our model included child and household level covariates, as well as climatic and environmental factors. Continuous variables were modelled by assuming second order random walk priors, while spatial correlation was specified as a Markov random field prior, with fixed effects assigned diffuse priors. Inference was fully Bayesian resulting in an under five malaria risk map for Malawi. Results Malaria risk increased with increasing age of the child. With respect to socio-economic factors, the greater the household wealth, the lower the malaria prevalence. A general decline in malaria risk was observed as altitude increased. Minimum temperatures and average total rainfall in the three months preceding the survey did not show a strong association with disease risk. Conclusions The structured additive regression model offered a flexible extension to standard regression models by enabling simultaneous modelling of possible nonlinear effects of continuous covariates, spatial correlation and heterogeneity, while estimating usual fixed effects of categorical and continuous observed variables. Our results confirmed that malaria epidemiology is a complex interaction of biotic and abiotic factors, both at the individual, household and community level and that risk factors are still relevant many years after extensive implementation of RBM activities. PMID:24991915

Using structured additive regression models to estimate risk factors of malaria: analysis of 2010 Malawi malaria indicator survey data.

PubMed

Chirombo, James; Lowe, Rachel; Kazembe, Lawrence

2014-01-01

After years of implementing Roll Back Malaria (RBM) interventions, the changing landscape of malaria in terms of risk factors and spatial pattern has not been fully investigated. This paper uses the 2010 malaria indicator survey data to investigate if known malaria risk factors remain relevant after many years of interventions. We adopted a structured additive logistic regression model that allowed for spatial correlation, to more realistically estimate malaria risk factors. Our model included child and household level covariates, as well as climatic and environmental factors. Continuous variables were modelled by assuming second order random walk priors, while spatial correlation was specified as a Markov random field prior, with fixed effects assigned diffuse priors. Inference was fully Bayesian resulting in an under five malaria risk map for Malawi. Malaria risk increased with increasing age of the child. With respect to socio-economic factors, the greater the household wealth, the lower the malaria prevalence. A general decline in malaria risk was observed as altitude increased. Minimum temperatures and average total rainfall in the three months preceding the survey did not show a strong association with disease risk. The structured additive regression model offered a flexible extension to standard regression models by enabling simultaneous modelling of possible nonlinear effects of continuous covariates, spatial correlation and heterogeneity, while estimating usual fixed effects of categorical and continuous observed variables. Our results confirmed that malaria epidemiology is a complex interaction of biotic and abiotic factors, both at the individual, household and community level and that risk factors are still relevant many years after extensive implementation of RBM activities.

Bayesian generalized linear mixed modeling of Tuberculosis using informative priors

PubMed Central

Woldegerima, Woldegebriel Assefa

2017-01-01

TB is rated as one of the world’s deadliest diseases and South Africa ranks 9th out of the 22 countries with hardest hit of TB. Although many pieces of research have been carried out on this subject, this paper steps further by inculcating past knowledge into the model, using Bayesian approach with informative prior. Bayesian statistics approach is getting popular in data analyses. But, most applications of Bayesian inference technique are limited to situations of non-informative prior, where there is no solid external information about the distribution of the parameter of interest. The main aim of this study is to profile people living with TB in South Africa. In this paper, identical regression models are fitted for classical and Bayesian approach both with non-informative and informative prior, using South Africa General Household Survey (GHS) data for the year 2014. For the Bayesian model with informative prior, South Africa General Household Survey dataset for the year 2011 to 2013 are used to set up priors for the model 2014. PMID:28257437

Testing students' e-learning via Facebook through Bayesian structural equation modeling.

PubMed

Salarzadeh Jenatabadi, Hashem; Moghavvemi, Sedigheh; Wan Mohamed Radzi, Che Wan Jasimah Bt; Babashamsi, Parastoo; Arashi, Mohammad

2017-01-01

Learning is an intentional activity, with several factors affecting students' intention to use new learning technology. Researchers have investigated technology acceptance in different contexts by developing various theories/models and testing them by a number of means. Although most theories/models developed have been examined through regression or structural equation modeling, Bayesian analysis offers more accurate data analysis results. To address this gap, the unified theory of acceptance and technology use in the context of e-learning via Facebook are re-examined in this study using Bayesian analysis. The data (S1 Data) were collected from 170 students enrolled in a business statistics course at University of Malaya, Malaysia, and tested with the maximum likelihood and Bayesian approaches. The difference between the two methods' results indicates that performance expectancy and hedonic motivation are the strongest factors influencing the intention to use e-learning via Facebook. The Bayesian estimation model exhibited better data fit than the maximum likelihood estimator model. The results of the Bayesian and maximum likelihood estimator approaches are compared and the reasons for the result discrepancy are deliberated.

Testing students’ e-learning via Facebook through Bayesian structural equation modeling

PubMed Central

Moghavvemi, Sedigheh; Wan Mohamed Radzi, Che Wan Jasimah Bt; Babashamsi, Parastoo; Arashi, Mohammad

2017-01-01

Learning is an intentional activity, with several factors affecting students’ intention to use new learning technology. Researchers have investigated technology acceptance in different contexts by developing various theories/models and testing them by a number of means. Although most theories/models developed have been examined through regression or structural equation modeling, Bayesian analysis offers more accurate data analysis results. To address this gap, the unified theory of acceptance and technology use in the context of e-learning via Facebook are re-examined in this study using Bayesian analysis. The data (S1 Data) were collected from 170 students enrolled in a business statistics course at University of Malaya, Malaysia, and tested with the maximum likelihood and Bayesian approaches. The difference between the two methods’ results indicates that performance expectancy and hedonic motivation are the strongest factors influencing the intention to use e-learning via Facebook. The Bayesian estimation model exhibited better data fit than the maximum likelihood estimator model. The results of the Bayesian and maximum likelihood estimator approaches are compared and the reasons for the result discrepancy are deliberated. PMID:28886019

Semiparametric time varying coefficient model for matched case-crossover studies.

PubMed

Ortega-Villa, Ana Maria; Kim, Inyoung; Kim, H

2017-03-15

In matched case-crossover studies, it is generally accepted that the covariates on which a case and associated controls are matched cannot exert a confounding effect on independent predictors included in the conditional logistic regression model. This is because any stratum effect is removed by the conditioning on the fixed number of sets of the case and controls in the stratum. Hence, the conditional logistic regression model is not able to detect any effects associated with the matching covariates by stratum. However, some matching covariates such as time often play an important role as an effect modification leading to incorrect statistical estimation and prediction. Therefore, we propose three approaches to evaluate effect modification by time. The first is a parametric approach, the second is a semiparametric penalized approach, and the third is a semiparametric Bayesian approach. Our parametric approach is a two-stage method, which uses conditional logistic regression in the first stage and then estimates polynomial regression in the second stage. Our semiparametric penalized and Bayesian approaches are one-stage approaches developed by using regression splines. Our semiparametric one stage approach allows us to not only detect the parametric relationship between the predictor and binary outcomes, but also evaluate nonparametric relationships between the predictor and time. We demonstrate the advantage of our semiparametric one-stage approaches using both a simulation study and an epidemiological example of a 1-4 bi-directional case-crossover study of childhood aseptic meningitis with drinking water turbidity. We also provide statistical inference for the semiparametric Bayesian approach using Bayes Factors. Copyright © 2016 John Wiley & Sons, Ltd. Copyright © 2016 John Wiley & Sons, Ltd.

Mixed linear-nonlinear fault slip inversion: Bayesian inference of model, weighting, and smoothing parameters

NASA Astrophysics Data System (ADS)

Fukuda, J.; Johnson, K. M.

2009-12-01

Studies utilizing inversions of geodetic data for the spatial distribution of coseismic slip on faults typically present the result as a single fault plane and slip distribution. Commonly the geometry of the fault plane is assumed to be known a priori and the data are inverted for slip. However, sometimes there is not strong a priori information on the geometry of the fault that produced the earthquake and the data is not always strong enough to completely resolve the fault geometry. We develop a method to solve for the full posterior probability distribution of fault slip and fault geometry parameters in a Bayesian framework using Monte Carlo methods. The slip inversion problem is particularly challenging because it often involves multiple data sets with unknown relative weights (e.g. InSAR, GPS), model parameters that are related linearly (slip) and nonlinearly (fault geometry) through the theoretical model to surface observations, prior information on model parameters, and a regularization prior to stabilize the inversion. We present the theoretical framework and solution method for a Bayesian inversion that can handle all of these aspects of the problem. The method handles the mixed linear/nonlinear nature of the problem through combination of both analytical least-squares solutions and Monte Carlo methods. We first illustrate and validate the inversion scheme using synthetic data sets. We then apply the method to inversion of geodetic data from the 2003 M6.6 San Simeon, California earthquake. We show that the uncertainty in strike and dip of the fault plane is over 20 degrees. We characterize the uncertainty in the slip estimate with a volume around the mean fault solution in which the slip most likely occurred. Slip likely occurred somewhere in a volume that extends 5-10 km in either direction normal to the fault plane. We implement slip inversions with both traditional, kinematic smoothing constraints on slip and a simple physical condition of uniform stress drop.

Detangling complex relationships in forensic data: principles and use of causal networks and their application to clinical forensic science.

PubMed

Lefèvre, Thomas; Lepresle, Aude; Chariot, Patrick

2015-09-01

The search for complex, nonlinear relationships and causality in data is hindered by the availability of techniques in many domains, including forensic science. Linear multivariable techniques are useful but present some shortcomings. In the past decade, Bayesian approaches have been introduced in forensic science. To date, authors have mainly focused on providing an alternative to classical techniques for quantifying effects and dealing with uncertainty. Causal networks, including Bayesian networks, can help detangle complex relationships in data. A Bayesian network estimates the joint probability distribution of data and graphically displays dependencies between variables and the circulation of information between these variables. In this study, we illustrate the interest in utilizing Bayesian networks for dealing with complex data through an application in clinical forensic science. Evaluating the functional impairment of assault survivors is a complex task for which few determinants are known. As routinely estimated in France, the duration of this impairment can be quantified by days of 'Total Incapacity to Work' ('Incapacité totale de travail,' ITT). In this study, we used a Bayesian network approach to identify the injury type, victim category and time to evaluation as the main determinants of the 'Total Incapacity to Work' (TIW). We computed the conditional probabilities associated with the TIW node and its parents. We compared this approach with a multivariable analysis, and the results of both techniques were converging. Thus, Bayesian networks should be considered a reliable means to detangle complex relationships in data.

Bayesian Nonparametric Prediction and Statistical Inference

DTIC Science & Technology

1989-09-07

Kadane, J. (1980), "Bayesian decision theory and the sim- plification of models," in Evaluation of Econometric Models, J. Kmenta and J. Ramsey , eds...the random model and weighted least squares regression," in Evaluation of Econometric Models, ed. by J. Kmenta and J. Ramsey , Academic Press, 197-217...likelihood function. On the other hand, H. Jeffreys’s theory of hypothesis testing covers the most important situations in which the prior is not diffuse. See

Current and Future Constraints on Higgs Couplings in the Nonlinear Effective Theory

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

de Blas, Jorge; Eberhardt, Otto; Krause, Claudius

We perform a Bayesian statistical analysis of the constraints on the nonlinear Effective Theory given by the Higgs electroweak chiral Lagrangian. We obtain bounds on the effective coefficients entering in Higgs observables at the leading order, using all available Higgs-boson signal strengths from the LHC runs 1 and 2. Using a prior dependence study of the solutions, we discuss the results within the context of natural-sized Wilson coefficients. We further study the expected sensitivities to the different Wilson coefficients at various possible future colliders. Finally, we interpret our results in terms of some minimal composite Higgs models.

Cardiovascular oscillations: in search of a nonlinear parametric model

NASA Astrophysics Data System (ADS)

Bandrivskyy, Andriy; Luchinsky, Dmitry; McClintock, Peter V.; Smelyanskiy, Vadim; Stefanovska, Aneta; Timucin, Dogan

2003-05-01

We suggest a fresh approach to the modeling of the human cardiovascular system. Taking advantage of a new Bayesian inference technique, able to deal with stochastic nonlinear systems, we show that one can estimate parameters for models of the cardiovascular system directly from measured time series. We present preliminary results of inference of parameters of a model of coupled oscillators from measured cardiovascular data addressing cardiorespiratory interaction. We argue that the inference technique offers a very promising tool for the modeling, able to contribute significantly towards the solution of a long standing challenge -- development of new diagnostic techniques based on noninvasive measurements.

Development of regional skews for selected flood durations for the Central Valley Region, California, based on data through water year 2008

USGS Publications Warehouse

Lamontagne, Jonathan R.; Stedinger, Jery R.; Berenbrock, Charles; Veilleux, Andrea G.; Ferris, Justin C.; Knifong, Donna L.

2012-01-01

Flood-frequency information is important in the Central Valley region of California because of the high risk of catastrophic flooding. Most traditional flood-frequency studies focus on peak flows, but for the assessment of the adequacy of reservoirs, levees, other flood control structures, sustained flood flow (flood duration) frequency data are needed. This study focuses on rainfall or rain-on-snow floods, rather than the annual maximum, because rain events produce the largest floods in the region. A key to estimating flood-duration frequency is determining the regional skew for such data. Of the 50 sites used in this study to determine regional skew, 28 sites were considered to have little to no significant regulated flows, and for the 22 sites considered significantly regulated, unregulated daily flow data were synthesized by using reservoir storage changes and diversion records. The unregulated, annual maximum rainfall flood flows for selected durations (1-day, 3-day, 7-day, 15-day, and 30-day) for all 50 sites were furnished by the U.S. Army Corps of Engineers. Station skew was determined by using the expected moments algorithm program for fitting the Pearson Type 3 flood-frequency distribution to the logarithms of annual flood-duration data. Bayesian generalized least squares regression procedures used in earlier studies were modified to address problems caused by large cross correlations among concurrent rainfall floods in California and to address the extensive censoring of low outliers at some sites, by using the new expected moments algorithm for fitting the LP3 distribution to rainfall flood-duration data. To properly account for these problems and to develop suitable regional-skew regression models and regression diagnostics, a combination of ordinary least squares, weighted least squares, and Bayesian generalized least squares regressions were adopted. This new methodology determined that a nonlinear model relating regional skew to mean basin elevation was the best model for each flood duration. The regional-skew values ranged from -0.74 for a flood duration of 1-day and a mean basin elevation less than 2,500 feet to values near 0 for a flood duration of 7-days and a mean basin elevation greater than 4,500 feet. This relation between skew and elevation reflects the interaction of snow and rain, which increases with increased elevation. The regional skews are more accurate, and the mean squared errors are less than in the Interagency Advisory Committee on Water Data's National skew map of Bulletin 17B.

Examining the influence of link function misspecification in conventional regression models for developing crash modification factors.

PubMed

Wu, Lingtao; Lord, Dominique

2017-05-01

This study further examined the use of regression models for developing crash modification factors (CMFs), specifically focusing on the misspecification in the link function. The primary objectives were to validate the accuracy of CMFs derived from the commonly used regression models (i.e., generalized linear models or GLMs with additive linear link functions) when some of the variables have nonlinear relationships and quantify the amount of bias as a function of the nonlinearity. Using the concept of artificial realistic data, various linear and nonlinear crash modification functions (CM-Functions) were assumed for three variables. Crash counts were randomly generated based on these CM-Functions. CMFs were then derived from regression models for three different scenarios. The results were compared with the assumed true values. The main findings are summarized as follows: (1) when some variables have nonlinear relationships with crash risk, the CMFs for these variables derived from the commonly used GLMs are all biased, especially around areas away from the baseline conditions (e.g., boundary areas); (2) with the increase in nonlinearity (i.e., nonlinear relationship becomes stronger), the bias becomes more significant; (3) the quality of CMFs for other variables having linear relationships can be influenced when mixed with those having nonlinear relationships, but the accuracy may still be acceptable; and (4) the misuse of the link function for one or more variables can also lead to biased estimates for other parameters. This study raised the importance of the link function when using regression models for developing CMFs. Copyright © 2017 Elsevier Ltd. All rights reserved.

Comparing models for quantitative risk assessment: an application to the European Registry of foreign body injuries in children.

PubMed

Berchialla, Paola; Scarinzi, Cecilia; Snidero, Silvia; Gregori, Dario

2016-08-01

Risk Assessment is the systematic study of decisions subject to uncertain consequences. An increasing interest has been focused on modeling techniques like Bayesian Networks since their capability of (1) combining in the probabilistic framework different type of evidence including both expert judgments and objective data; (2) overturning previous beliefs in the light of the new information being received and (3) making predictions even with incomplete data. In this work, we proposed a comparison among Bayesian Networks and other classical Quantitative Risk Assessment techniques such as Neural Networks, Classification Trees, Random Forests and Logistic Regression models. Hybrid approaches, combining both Classification Trees and Bayesian Networks, were also considered. Among Bayesian Networks, a clear distinction between purely data-driven approach and combination of expert knowledge with objective data is made. The aim of this paper consists in evaluating among this models which best can be applied, in the framework of Quantitative Risk Assessment, to assess the safety of children who are exposed to the risk of inhalation/insertion/aspiration of consumer products. The issue of preventing injuries in children is of paramount importance, in particular where product design is involved: quantifying the risk associated to product characteristics can be of great usefulness in addressing the product safety design regulation. Data of the European Registry of Foreign Bodies Injuries formed the starting evidence for risk assessment. Results showed that Bayesian Networks appeared to have both the ease of interpretability and accuracy in making prediction, even if simpler models like logistic regression still performed well. © The Author(s) 2013.

Pseudo second order kinetics and pseudo isotherms for malachite green onto activated carbon: comparison of linear and non-linear regression methods.

PubMed

Kumar, K Vasanth; Sivanesan, S

2006-08-25

Pseudo second order kinetic expressions of Ho, Sobkowsk and Czerwinski, Blanachard et al. and Ritchie were fitted to the experimental kinetic data of malachite green onto activated carbon by non-linear and linear method. Non-linear method was found to be a better way of obtaining the parameters involved in the second order rate kinetic expressions. Both linear and non-linear regression showed that the Sobkowsk and Czerwinski and Ritchie's pseudo second order model were the same. Non-linear regression analysis showed that both Blanachard et al. and Ho have similar ideas on the pseudo second order model but with different assumptions. The best fit of experimental data in Ho's pseudo second order expression by linear and non-linear regression method showed that Ho pseudo second order model was a better kinetic expression when compared to other pseudo second order kinetic expressions. The amount of dye adsorbed at equilibrium, q(e), was predicted from Ho pseudo second order expression and were fitted to the Langmuir, Freundlich and Redlich Peterson expressions by both linear and non-linear method to obtain the pseudo isotherms. The best fitting pseudo isotherm was found to be the Langmuir and Redlich Peterson isotherm. Redlich Peterson is a special case of Langmuir when the constant g equals unity.

A Bayesian Nonparametric Causal Model for Regression Discontinuity Designs

ERIC Educational Resources Information Center

Karabatsos, George; Walker, Stephen G.

2013-01-01

The regression discontinuity (RD) design (Thistlewaite & Campbell, 1960; Cook, 2008) provides a framework to identify and estimate causal effects from a non-randomized design. Each subject of a RD design is assigned to the treatment (versus assignment to a non-treatment) whenever her/his observed value of the assignment variable equals or…

On the null distribution of Bayes factors in linear regression

USDA-ARS?s Scientific Manuscript database

We show that under the null, the 2 log (Bayes factor) is asymptotically distributed as a weighted sum of chi-squared random variables with a shifted mean. This claim holds for Bayesian multi-linear regression with a family of conjugate priors, namely, the normal-inverse-gamma prior, the g-prior, and...

Simultaneous Estimation of Regression Functions for Marine Corps Technical Training Specialties.

DTIC Science & Technology

1985-01-03

Edmonton, Alberta CANADA 1 Dr. Frederic M. Lord Educational Testing Service 1 Dr. Earl Hunt Princeton, NJ 08541 Dept, of Psychology University of...111111-1.6 MICROCOPY RESOLUTION TEST CHART NATIONAL BUREAU OF STANDARDS-1963-A SIMIULTANEOUS ESTIMATION OF REGRESSION FUNCTIONS FOR MARINE CORPS...Bayesian techniques for simul- taneous estimation to the specification of regression weights for selection tests used in various technical training courses

Detection of Differential Item Functioning with Nonlinear Regression: A Non-IRT Approach Accounting for Guessing

ERIC Educational Resources Information Center

Drabinová, Adéla; Martinková, Patrícia

2017-01-01

In this article we present a general approach not relying on item response theory models (non-IRT) to detect differential item functioning (DIF) in dichotomous items with presence of guessing. The proposed nonlinear regression (NLR) procedure for DIF detection is an extension of method based on logistic regression. As a non-IRT approach, NLR can…

Almost but not quite 2D, Non-linear Bayesian Inversion of CSEM Data

NASA Astrophysics Data System (ADS)

Ray, A.; Key, K.; Bodin, T.

2013-12-01

The geophysical inverse problem can be elegantly stated in a Bayesian framework where a probability distribution can be viewed as a statement of information regarding a random variable. After all, the goal of geophysical inversion is to provide information on the random variables of interest - physical properties of the earth's subsurface. However, though it may be simple to postulate, a practical difficulty of fully non-linear Bayesian inversion is the computer time required to adequately sample the model space and extract the information we seek. As a consequence, in geophysical problems where evaluation of a full 2D/3D forward model is computationally expensive, such as marine controlled source electromagnetic (CSEM) mapping of the resistivity of seafloor oil and gas reservoirs, Bayesian studies have largely been conducted with 1D forward models. While the 1D approximation is indeed appropriate for exploration targets with planar geometry and geological stratification, it only provides a limited, site-specific idea of uncertainty in resistivity with depth. In this work, we extend our fully non-linear 1D Bayesian inversion to a 2D model framework, without requiring the usual regularization of model resistivities in the horizontal or vertical directions used to stabilize quasi-2D inversions. In our approach, we use the reversible jump Markov-chain Monte-Carlo (RJ-MCMC) or trans-dimensional method and parameterize the subsurface in a 2D plane with Voronoi cells. The method is trans-dimensional in that the number of cells required to parameterize the subsurface is variable, and the cells dynamically move around and multiply or combine as demanded by the data being inverted. This approach allows us to expand our uncertainty analysis of resistivity at depth to more than a single site location, allowing for interactions between model resistivities at different horizontal locations along a traverse over an exploration target. While the model is parameterized in 2D, we efficiently evaluate the forward response using 1D profiles extracted from the model at the common-midpoints of the EM source-receiver pairs. Since the 1D approximation is locally valid at different midpoint locations, the computation time is far lower than is required by a full 2D or 3D simulation. We have applied this method to both synthetic and real CSEM survey data from the Scarborough gas field on the Northwest shelf of Australia, resulting in a spatially variable quantification of resistivity and its uncertainty in 2D. This Bayesian approach results in a large database of 2D models that comprise a posterior probability distribution, which we can subset to test various hypotheses about the range of model structures compatible with the data. For example, we can subset the model distributions to examine the hypothesis that a resistive reservoir extends overs a certain spatial extent. Depending on how this conditions other parts of the model space, light can be shed on the geological viability of the hypothesis. Since tackling spatially variable uncertainty and trade-offs in 2D and 3D is a challenging research problem, the insights gained from this work may prove valuable for subsequent full 2D and 3D Bayesian inversions.

Variational dynamic background model for keyword spotting in handwritten documents

NASA Astrophysics Data System (ADS)

Kumar, Gaurav; Wshah, Safwan; Govindaraju, Venu

2013-12-01

We propose a bayesian framework for keyword spotting in handwritten documents. This work is an extension to our previous work where we proposed dynamic background model, DBM for keyword spotting that takes into account the local character level scores and global word level scores to learn a logistic regression classifier to separate keywords from non-keywords. In this work, we add a bayesian layer on top of the DBM called the variational dynamic background model, VDBM. The logistic regression classifier uses the sigmoid function to separate keywords from non-keywords. The sigmoid function being neither convex nor concave, exact inference of VDBM becomes intractable. An expectation maximization step is proposed to do approximate inference. The advantage of VDBM over the DBM is multi-fold. Firstly, being bayesian, it prevents over-fitting of data. Secondly, it provides better modeling of data and an improved prediction of unseen data. VDBM is evaluated on the IAM dataset and the results prove that it outperforms our prior work and other state of the art line based word spotting system.

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.

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.

Improved parameter inference in catchment models: 1. Evaluating parameter uncertainty

NASA Astrophysics Data System (ADS)

Kuczera, George

1983-10-01

A Bayesian methodology is developed to evaluate parameter uncertainty in catchment models fitted to a hydrologic response such as runoff, the goal being to improve the chance of successful regionalization. The catchment model is posed as a nonlinear regression model with stochastic errors possibly being both autocorrelated and heteroscedastic. The end result of this methodology, which may use Box-Cox power transformations and ARMA error models, is the posterior distribution, which summarizes what is known about the catchment model parameters. This can be simplified to a multivariate normal provided a linearization in parameter space is acceptable; means of checking and improving this assumption are discussed. The posterior standard deviations give a direct measure of parameter uncertainty, and study of the posterior correlation matrix can indicate what kinds of data are required to improve the precision of poorly determined parameters. Finally, a case study involving a nine-parameter catchment model fitted to monthly runoff and soil moisture data is presented. It is shown that use of ordinary least squares when its underlying error assumptions are violated gives an erroneous description of parameter uncertainty.

Gaussian processes: a method for automatic QSAR modeling of ADME properties.

PubMed

Obrezanova, Olga; Csanyi, Gabor; Gola, Joelle M R; Segall, Matthew D

2007-01-01

In this article, we discuss the application of the Gaussian Process method for the prediction of absorption, distribution, metabolism, and excretion (ADME) properties. On the basis of a Bayesian probabilistic approach, the method is widely used in the field of machine learning but has rarely been applied in quantitative structure-activity relationship and ADME modeling. The method is suitable for modeling nonlinear relationships, does not require subjective determination of the model parameters, works for a large number of descriptors, and is inherently resistant to overtraining. The performance of Gaussian Processes compares well with and often exceeds that of artificial neural networks. Due to these features, the Gaussian Processes technique is eminently suitable for automatic model generation-one of the demands of modern drug discovery. Here, we describe the basic concept of the method in the context of regression problems and illustrate its application to the modeling of several ADME properties: blood-brain barrier, hERG inhibition, and aqueous solubility at pH 7.4. We also compare Gaussian Processes with other modeling techniques.

Statistical tools for analysis and modeling of cosmic populations and astronomical time series: CUDAHM and TSE

NASA Astrophysics Data System (ADS)

Loredo, Thomas; Budavari, Tamas; Scargle, Jeffrey D.

2018-01-01

This presentation provides an overview of open-source software packages addressing two challenging classes of astrostatistics problems. (1) CUDAHM is a C++ framework for hierarchical Bayesian modeling of cosmic populations, leveraging graphics processing units (GPUs) to enable applying this computationally challenging paradigm to large datasets. CUDAHM is motivated by measurement error problems in astronomy, where density estimation and linear and nonlinear regression must be addressed for populations of thousands to millions of objects whose features are measured with possibly complex uncertainties, potentially including selection effects. An example calculation demonstrates accurate GPU-accelerated luminosity function estimation for simulated populations of $10^6$ objects in about two hours using a single NVIDIA Tesla K40c GPU. (2) Time Series Explorer (TSE) is a collection of software in Python and MATLAB for exploratory analysis and statistical modeling of astronomical time series. It comprises a library of stand-alone functions and classes, as well as an application environment for interactive exploration of times series data. The presentation will summarize key capabilities of this emerging project, including new algorithms for analysis of irregularly-sampled time series.

A Bayesian estimation of a stochastic predator-prey model of economic fluctuations

NASA Astrophysics Data System (ADS)

Dibeh, Ghassan; Luchinsky, Dmitry G.; Luchinskaya, Daria D.; Smelyanskiy, Vadim N.

2007-06-01

In this paper, we develop a Bayesian framework for the empirical estimation of the parameters of one of the best known nonlinear models of the business cycle: The Marx-inspired model of a growth cycle introduced by R. M. Goodwin. The model predicts a series of closed cycles representing the dynamics of labor's share and the employment rate in the capitalist economy. The Bayesian framework is used to empirically estimate a modified Goodwin model. The original model is extended in two ways. First, we allow for exogenous periodic variations of the otherwise steady growth rates of the labor force and productivity per worker. Second, we allow for stochastic variations of those parameters. The resultant modified Goodwin model is a stochastic predator-prey model with periodic forcing. The model is then estimated using a newly developed Bayesian estimation method on data sets representing growth cycles in France and Italy during the years 1960-2005. Results show that inference of the parameters of the stochastic Goodwin model can be achieved. The comparison of the dynamics of the Goodwin model with the inferred values of parameters demonstrates quantitative agreement with the growth cycle empirical data.

Bayesian regression analyses of radiation modality effects on pericardial and pleural effusion and survival in esophageal cancer.

PubMed

He, Liru; Chapple, Andrew; Liao, Zhongxing; Komaki, Ritsuko; Thall, Peter F; Lin, Steven H

2016-10-01

To evaluate radiation modality effects on pericardial effusion (PCE), pleural effusion (PE) and survival in esophageal cancer (EC) patients. We analyzed data from 470 EC patients treated with definitive concurrent chemoradiotherapy (CRT). Bayesian semi-competing risks (SCR) regression models were fit to assess effects of radiation modality and prognostic covariates on the risks of PCE and PE, and death either with or without these preceding events. Bayesian piecewise exponential regression models were fit for overall survival, the time to PCE or death, and the time to PE or death. All models included propensity score as a covariate to correct for potential selection bias. Median times to onset of PCE and PE after RT were 7.1 and 6.1months for IMRT, and 6.5 and 5.4months for 3DCRT, respectively. Compared to 3DCRT, the IMRT group had significantly lower risks of PE, PCE, and death. The respective probabilities of a patient being alive without either PCE or PE at 3-years and 5-years were 0.29 and 0.21 for IMRT compared to 0.13 and 0.08 for 3DCRT. In the SCR regression analyses, IMRT was associated with significantly lower risks of PCE (HR=0.26) and PE (HR=0.49), and greater overall survival (probability of beneficial effect (pbe)>0.99), after controlling for known clinical prognostic factors. IMRT reduces the incidence and postpones the onset of PCE and PE, and increases survival probability, compared to 3DCRT. Copyright © 2016 Elsevier Ireland Ltd. All rights reserved.

Micromechanical response of articular cartilage to tensile load measured using nonlinear microscopy.

PubMed

Bell, J S; Christmas, J; Mansfield, J C; Everson, R M; Winlove, C P

2014-06-01

Articular cartilage (AC) is a highly anisotropic biomaterial, and its complex mechanical properties have been a topic of intense investigation for over 60 years. Recent advances in the field of nonlinear optics allow the individual constituents of AC to be imaged in living tissue without the need for exogenous contrast agents. Combining mechanical testing with nonlinear microscopy provides a wealth of information about microscopic responses to load. This work investigates the inhomogeneous distribution of strain in loaded AC by tracking the movement and morphological changes of individual chondrocytes using point pattern matching and Bayesian modeling. This information can be used to inform models of mechanotransduction and pathogenesis, and is readily extendable to various other connective tissues. Copyright © 2014 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

Soft sensor modeling based on variable partition ensemble method for nonlinear batch processes

NASA Astrophysics Data System (ADS)

Wang, Li; Chen, Xiangguang; Yang, Kai; Jin, Huaiping

2017-01-01

Batch processes are always characterized by nonlinear and system uncertain properties, therefore, the conventional single model may be ill-suited. A local learning strategy soft sensor based on variable partition ensemble method is developed for the quality prediction of nonlinear and non-Gaussian batch processes. A set of input variable sets are obtained by bootstrapping and PMI criterion. Then, multiple local GPR models are developed based on each local input variable set. When a new test data is coming, the posterior probability of each best performance local model is estimated based on Bayesian inference and used to combine these local GPR models to get the final prediction result. The proposed soft sensor is demonstrated by applying to an industrial fed-batch chlortetracycline fermentation process.

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.

A Bayesian Meta-Analysis on Prevalence of Hepatitis B Virus Infection among Chinese Volunteer Blood Donors

PubMed Central

Liu, Guang-ying; Zheng, Yang; Deng, Yan; Gao, Yan-yan; Wang, Lie

2013-01-01

Background Although transfusion-transmitted infection of hepatitis B virus (HBV) threatens the blood safety of China, the nationwide circumstance of HBV infection among blood donors is still unclear. Objectives To comprehensively estimate the prevalence of HBsAg positive and HBV occult infection (OBI) among Chinese volunteer blood donors through bayesian meta-analysis. Methods We performed an electronic search in Pub-Med, Web of Knowledge, Medline, Wanfang Data and CNKI, complemented by a hand search of relevant reference lists. Two authors independently extracted data from the eligible studies. Then two bayesian random-effect meta-analyses were performed, followed by bayesian meta-regressions. Results 5957412 and 571227 donors were identified in HBsAg group and OBI group, respectively. The pooled prevalence of HBsAg group and OBI group among donors is 1.085% (95% credible interval [CI] 0.859%∼1.398%) and 0.094% (95% CI 0.0578%∼0.1655%). For HBsAg group, subgroup analysis shows the more developed area has a lower prevalence than the less developed area; meta-regression indicates there is a significant decreasing trend in HBsAg positive prevalence with sampling year (beta = −0.1202, 95% −0.2081∼−0.0312). Conclusion Blood safety against HBV infection in China is suffering serious threats and the government should take effective measures to improve this situation. PMID:24236110

Comparing methods of measuring geographic patterns in temporal trends: an application to county-level heart disease mortality in the United States, 1973 to 2010.

PubMed

Vaughan, Adam S; Kramer, Michael R; Waller, Lance A; Schieb, Linda J; Greer, Sophia; Casper, Michele

2015-05-01

To demonstrate the implications of choosing analytical methods for quantifying spatiotemporal trends, we compare the assumptions, implementation, and outcomes of popular methods using county-level heart disease mortality in the United States between 1973 and 2010. We applied four regression-based approaches (joinpoint regression, both aspatial and spatial generalized linear mixed models, and Bayesian space-time model) and compared resulting inferences for geographic patterns of local estimates of annual percent change and associated uncertainty. The average local percent change in heart disease mortality from each method was -4.5%, with the Bayesian model having the smallest range of values. The associated uncertainty in percent change differed markedly across the methods, with the Bayesian space-time model producing the narrowest range of variance (0.0-0.8). The geographic pattern of percent change was consistent across methods with smaller declines in the South Central United States and larger declines in the Northeast and Midwest. However, the geographic patterns of uncertainty differed markedly between methods. The similarity of results, including geographic patterns, for magnitude of percent change across these methods validates the underlying spatial pattern of declines in heart disease mortality. However, marked differences in degree of uncertainty indicate that Bayesian modeling offers substantially more precise estimates. Copyright © 2015 Elsevier Inc. All rights reserved.

Bayesian hierarchical models for cost-effectiveness analyses that use data from cluster randomized trials.

PubMed

Grieve, Richard; Nixon, Richard; Thompson, Simon G

2010-01-01

Cost-effectiveness analyses (CEA) may be undertaken alongside cluster randomized trials (CRTs) where randomization is at the level of the cluster (for example, the hospital or primary care provider) rather than the individual. Costs (and outcomes) within clusters may be correlated so that the assumption made by standard bivariate regression models, that observations are independent, is incorrect. This study develops a flexible modeling framework to acknowledge the clustering in CEA that use CRTs. The authors extend previous Bayesian bivariate models for CEA of multicenter trials to recognize the specific form of clustering in CRTs. They develop new Bayesian hierarchical models (BHMs) that allow mean costs and outcomes, and also variances, to differ across clusters. They illustrate how each model can be applied using data from a large (1732 cases, 70 primary care providers) CRT evaluating alternative interventions for reducing postnatal depression. The analyses compare cost-effectiveness estimates from BHMs with standard bivariate regression models that ignore the data hierarchy. The BHMs show high levels of cost heterogeneity across clusters (intracluster correlation coefficient, 0.17). Compared with standard regression models, the BHMs yield substantially increased uncertainty surrounding the cost-effectiveness estimates, and altered point estimates. The authors conclude that ignoring clustering can lead to incorrect inferences. The BHMs that they present offer a flexible modeling framework that can be applied more generally to CEA that use CRTs.

Regression modeling of ground-water flow

USGS Publications Warehouse

Cooley, R.L.; Naff, R.L.

1985-01-01

Nonlinear multiple regression methods are developed to model and analyze groundwater flow systems. Complete descriptions of regression methodology as applied to groundwater flow models allow scientists and engineers engaged in flow modeling to apply the methods to a wide range of problems. Organization of the text proceeds from an introduction that discusses the general topic of groundwater flow modeling, to a review of basic statistics necessary to properly apply regression techniques, and then to the main topic: exposition and use of linear and nonlinear regression to model groundwater flow. Statistical procedures are given to analyze and use the regression models. A number of exercises and answers are included to exercise the student on nearly all the methods that are presented for modeling and statistical analysis. Three computer programs implement the more complex methods. These three are a general two-dimensional, steady-state regression model for flow in an anisotropic, heterogeneous porous medium, a program to calculate a measure of model nonlinearity with respect to the regression parameters, and a program to analyze model errors in computed dependent variables such as hydraulic head. (USGS)

Itô-SDE MCMC method for Bayesian characterization of errors associated with data limitations in stochastic expansion methods for uncertainty quantification

NASA Astrophysics Data System (ADS)

Arnst, M.; Abello Álvarez, B.; Ponthot, J.-P.; Boman, R.

2017-11-01

This paper is concerned with the characterization and the propagation of errors associated with data limitations in polynomial-chaos-based stochastic methods for uncertainty quantification. Such an issue can arise in uncertainty quantification when only a limited amount of data is available. When the available information does not suffice to accurately determine the probability distributions that must be assigned to the uncertain variables, the Bayesian method for assigning these probability distributions becomes attractive because it allows the stochastic model to account explicitly for insufficiency of the available information. In previous work, such applications of the Bayesian method had already been implemented by using the Metropolis-Hastings and Gibbs Markov Chain Monte Carlo (MCMC) methods. In this paper, we present an alternative implementation, which uses an alternative MCMC method built around an Itô stochastic differential equation (SDE) that is ergodic for the Bayesian posterior. We draw together from the mathematics literature a number of formal properties of this Itô SDE that lend support to its use in the implementation of the Bayesian method, and we describe its discretization, including the choice of the free parameters, by using the implicit Euler method. We demonstrate the proposed methodology on a problem of uncertainty quantification in a complex nonlinear engineering application relevant to metal forming.

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.

An adaptive sparse-grid high-order stochastic collocation method for Bayesian inference in groundwater reactive transport modeling

NASA Astrophysics Data System (ADS)

Zhang, Guannan; Lu, Dan; Ye, Ming; Gunzburger, Max; Webster, Clayton

2013-10-01

Bayesian analysis has become vital to uncertainty quantification in groundwater modeling, but its application has been hindered by the computational cost associated with numerous model executions required by exploring the posterior probability density function (PPDF) of model parameters. This is particularly the case when the PPDF is estimated using Markov Chain Monte Carlo (MCMC) sampling. In this study, a new approach is developed to improve the computational efficiency of Bayesian inference by constructing a surrogate of the PPDF, using an adaptive sparse-grid high-order stochastic collocation (aSG-hSC) method. Unlike previous works using first-order hierarchical basis, this paper utilizes a compactly supported higher-order hierarchical basis to construct the surrogate system, resulting in a significant reduction in the number of required model executions. In addition, using the hierarchical surplus as an error indicator allows locally adaptive refinement of sparse grids in the parameter space, which further improves computational efficiency. To efficiently build the surrogate system for the PPDF with multiple significant modes, optimization techniques are used to identify the modes, for which high-probability regions are defined and components of the aSG-hSC approximation are constructed. After the surrogate is determined, the PPDF can be evaluated by sampling the surrogate system directly without model execution, resulting in improved efficiency of the surrogate-based MCMC compared with conventional MCMC. The developed method is evaluated using two synthetic groundwater reactive transport models. The first example involves coupled linear reactions and demonstrates the accuracy of our high-order hierarchical basis approach in approximating high-dimensional posteriori distribution. The second example is highly nonlinear because of the reactions of uranium surface complexation, and demonstrates how the iterative aSG-hSC method is able to capture multimodal and non-Gaussian features of PPDF caused by model nonlinearity. Both experiments show that aSG-hSC is an effective and efficient tool for Bayesian inference.

Finite-sample and asymptotic sign-based tests for parameters of non-linear quantile regression with Markov noise

NASA Astrophysics Data System (ADS)

Sirenko, M. A.; Tarasenko, P. F.; Pushkarev, M. I.

2017-01-01

One of the most noticeable features of sign-based statistical procedures is an opportunity to build an exact test for simple hypothesis testing of parameters in a regression model. In this article, we expanded a sing-based approach to the nonlinear case with dependent noise. The examined model is a multi-quantile regression, which makes it possible to test hypothesis not only of regression parameters, but of noise parameters as well.

Bayesian Group Bridge for Bi-level Variable Selection.

PubMed

Mallick, Himel; Yi, Nengjun

2017-06-01

A Bayesian bi-level variable selection method (BAGB: Bayesian Analysis of Group Bridge) is developed for regularized regression and classification. This new development is motivated by grouped data, where generic variables can be divided into multiple groups, with variables in the same group being mechanistically related or statistically correlated. As an alternative to frequentist group variable selection methods, BAGB incorporates structural information among predictors through a group-wise shrinkage prior. Posterior computation proceeds via an efficient MCMC algorithm. In addition to the usual ease-of-interpretation of hierarchical linear models, the Bayesian formulation produces valid standard errors, a feature that is notably absent in the frequentist framework. Empirical evidence of the attractiveness of the method is illustrated by extensive Monte Carlo simulations and real data analysis. Finally, several extensions of this new approach are presented, providing a unified framework for bi-level variable selection in general models with flexible penalties.

Uncertainty Management for Diagnostics and Prognostics of Batteries using Bayesian Techniques

NASA Technical Reports Server (NTRS)

Saha, Bhaskar; Goebel, kai

2007-01-01

Uncertainty management has always been the key hurdle faced by diagnostics and prognostics algorithms. A Bayesian treatment of this problem provides an elegant and theoretically sound approach to the modern Condition- Based Maintenance (CBM)/Prognostic Health Management (PHM) paradigm. The application of the Bayesian techniques to regression and classification in the form of Relevance Vector Machine (RVM), and to state estimation as in Particle Filters (PF), provides a powerful tool to integrate the diagnosis and prognosis of battery health. The RVM, which is a Bayesian treatment of the Support Vector Machine (SVM), is used for model identification, while the PF framework uses the learnt model, statistical estimates of noise and anticipated operational conditions to provide estimates of remaining useful life (RUL) in the form of a probability density function (PDF). This type of prognostics generates a significant value addition to the management of any operation involving electrical systems.

Clinical judgment to estimate pretest probability in the diagnosis of Cushing's syndrome under a Bayesian perspective.

PubMed

Cipoli, Daniel E; Martinez, Edson Z; Castro, Margaret de; Moreira, Ayrton C

2012-12-01

To estimate the pretest probability of Cushing's syndrome (CS) diagnosis by a Bayesian approach using intuitive clinical judgment. Physicians were requested, in seven endocrinology meetings, to answer three questions: "Based on your personal expertise, after obtaining clinical history and physical examination, without using laboratorial tests, what is your probability of diagnosing Cushing's Syndrome?"; "For how long have you been practicing Endocrinology?"; and "Where do you work?". A Bayesian beta regression, using the WinBugs software was employed. We obtained 294 questionnaires. The mean pretest probability of CS diagnosis was 51.6% (95%CI: 48.7-54.3). The probability was directly related to experience in endocrinology, but not with the place of work. Pretest probability of CS diagnosis was estimated using a Bayesian methodology. Although pretest likelihood can be context-dependent, experience based on years of practice may help the practitioner to diagnosis CS.

Bayesian inference of interaction properties of noisy dynamical systems with time-varying coupling: capabilities and limitations

NASA Astrophysics Data System (ADS)

Wilting, Jens; Lehnertz, Klaus

2015-08-01

We investigate a recently published analysis framework based on Bayesian inference for the time-resolved characterization of interaction properties of noisy, coupled dynamical systems. It promises wide applicability and a better time resolution than well-established methods. At the example of representative model systems, we show that the analysis framework has the same weaknesses as previous methods, particularly when investigating interacting, structurally different non-linear oscillators. We also inspect the tracking of time-varying interaction properties and propose a further modification of the algorithm, which improves the reliability of obtained results. We exemplarily investigate the suitability of this algorithm to infer strength and direction of interactions between various regions of the human brain during an epileptic seizure. Within the limitations of the applicability of this analysis tool, we show that the modified algorithm indeed allows a better time resolution through Bayesian inference when compared to previous methods based on least square fits.

Comparing Families of Dynamic Causal Models

PubMed Central

Penny, Will D.; Stephan, Klaas E.; Daunizeau, Jean; Rosa, Maria J.; Friston, Karl J.; Schofield, Thomas M.; Leff, Alex P.

2010-01-01

Mathematical models of scientific data can be formally compared using Bayesian model evidence. Previous applications in the biological sciences have mainly focussed on model selection in which one first selects the model with the highest evidence and then makes inferences based on the parameters of that model. This “best model” approach is very useful but can become brittle if there are a large number of models to compare, and if different subjects use different models. To overcome this shortcoming we propose the combination of two further approaches: (i) family level inference and (ii) Bayesian model averaging within families. Family level inference removes uncertainty about aspects of model structure other than the characteristic of interest. For example: What are the inputs to the system? Is processing serial or parallel? Is it linear or nonlinear? Is it mediated by a single, crucial connection? We apply Bayesian model averaging within families to provide inferences about parameters that are independent of further assumptions about model structure. We illustrate the methods using Dynamic Causal Models of brain imaging data. PMID:20300649

An Excel Solver Exercise to Introduce Nonlinear Regression

ERIC Educational Resources Information Center

Pinder, Jonathan P.

2013-01-01

Business students taking business analytics courses that have significant predictive modeling components, such as marketing research, data mining, forecasting, and advanced financial modeling, are introduced to nonlinear regression using application software that is a "black box" to the students. Thus, although correct models are…

Mixed effect Poisson log-linear models for clinical and epidemiological sleep hypnogram data

PubMed Central

Swihart, Bruce J.; Caffo, Brian S.; Crainiceanu, Ciprian; Punjabi, Naresh M.

2013-01-01

Bayesian Poisson log-linear multilevel models scalable to epidemiological studies are proposed to investigate population variability in sleep state transition rates. Hierarchical random effects are used to account for pairings of subjects and repeated measures within those subjects, as comparing diseased to non-diseased subjects while minimizing bias is of importance. Essentially, non-parametric piecewise constant hazards are estimated and smoothed, allowing for time-varying covariates and segment of the night comparisons. The Bayesian Poisson regression is justified through a re-derivation of a classical algebraic likelihood equivalence of Poisson regression with a log(time) offset and survival regression assuming exponentially distributed survival times. Such re-derivation allows synthesis of two methods currently used to analyze sleep transition phenomena: stratified multi-state proportional hazards models and log-linear models with GEE for transition counts. An example data set from the Sleep Heart Health Study is analyzed. Supplementary material includes the analyzed data set as well as the code for a reproducible analysis. PMID:22241689

Does Nonlinear Modeling Play a Role in Plasmid Bioprocess Monitoring Using Fourier Transform Infrared Spectra?

PubMed

Lopes, Marta B; Calado, Cecília R C; Figueiredo, Mário A T; Bioucas-Dias, José M

2017-06-01

The monitoring of biopharmaceutical products using Fourier transform infrared (FT-IR) spectroscopy relies on calibration techniques involving the acquisition of spectra of bioprocess samples along the process. The most commonly used method for that purpose is partial least squares (PLS) regression, under the assumption that a linear model is valid. Despite being successful in the presence of small nonlinearities, linear methods may fail in the presence of strong nonlinearities. This paper studies the potential usefulness of nonlinear regression methods for predicting, from in situ near-infrared (NIR) and mid-infrared (MIR) spectra acquired in high-throughput mode, biomass and plasmid concentrations in Escherichia coli DH5-α cultures producing the plasmid model pVAX-LacZ. The linear methods PLS and ridge regression (RR) are compared with their kernel (nonlinear) versions, kPLS and kRR, as well as with the (also nonlinear) relevance vector machine (RVM) and Gaussian process regression (GPR). For the systems studied, RR provided better predictive performances compared to the remaining methods. Moreover, the results point to further investigation based on larger data sets whenever differences in predictive accuracy between a linear method and its kernelized version could not be found. The use of nonlinear methods, however, shall be judged regarding the additional computational cost required to tune their additional parameters, especially when the less computationally demanding linear methods herein studied are able to successfully monitor the variables under study.

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

Learning accurate and interpretable models based on regularized random forests regression

PubMed Central

2014-01-01

Background Many biology related research works combine data from multiple sources in an effort to understand the underlying problems. It is important to find and interpret the most important information from these sources. Thus it will be beneficial to have an effective algorithm that can simultaneously extract decision rules and select critical features for good interpretation while preserving the prediction performance. Methods In this study, we focus on regression problems for biological data where target outcomes are continuous. In general, models constructed from linear regression approaches are relatively easy to interpret. However, many practical biological applications are nonlinear in essence where we can hardly find a direct linear relationship between input and output. Nonlinear regression techniques can reveal nonlinear relationship of data, but are generally hard for human to interpret. We propose a rule based regression algorithm that uses 1-norm regularized random forests. The proposed approach simultaneously extracts a small number of rules from generated random forests and eliminates unimportant features. Results We tested the approach on some biological data sets. The proposed approach is able to construct a significantly smaller set of regression rules using a subset of attributes while achieving prediction performance comparable to that of random forests regression. Conclusion It demonstrates high potential in aiding prediction and interpretation of nonlinear relationships of the subject being studied. PMID:25350120

A stepwise regression tree for nonlinear approximation: applications to estimating subpixel land cover

USGS Publications Warehouse

Huang, C.; Townshend, J.R.G.

2003-01-01

A stepwise regression tree (SRT) algorithm was developed for approximating complex nonlinear relationships. Based on the regression tree of Breiman et al . (BRT) and a stepwise linear regression (SLR) method, this algorithm represents an improvement over SLR in that it can approximate nonlinear relationships and over BRT in that it gives more realistic predictions. The applicability of this method to estimating subpixel forest was demonstrated using three test data sets, on all of which it gave more accurate predictions than SLR and BRT. SRT also generated more compact trees and performed better than or at least as well as BRT at all 10 equal forest proportion interval ranging from 0 to 100%. This method is appealing to estimating subpixel land cover over large areas.

An offline approach for output-only Bayesian identification of stochastic nonlinear systems using unscented Kalman filtering

NASA Astrophysics Data System (ADS)

Erazo, Kalil; Nagarajaiah, Satish

2017-06-01

In this paper an offline approach for output-only Bayesian identification of stochastic nonlinear systems is presented. The approach is based on a re-parameterization of the joint posterior distribution of the parameters that define a postulated state-space stochastic model class. In the re-parameterization the state predictive distribution is included, marginalized, and estimated recursively in a state estimation step using an unscented Kalman filter, bypassing state augmentation as required by existing online methods. In applications expectations of functions of the parameters are of interest, which requires the evaluation of potentially high-dimensional integrals; Markov chain Monte Carlo is adopted to sample the posterior distribution and estimate the expectations. The proposed approach is suitable for nonlinear systems subjected to non-stationary inputs whose realization is unknown, and that are modeled as stochastic processes. Numerical verification and experimental validation examples illustrate the effectiveness and advantages of the approach, including: (i) an increased numerical stability with respect to augmented-state unscented Kalman filtering, avoiding divergence of the estimates when the forcing input is unmeasured; (ii) the ability to handle arbitrary prior and posterior distributions. The experimental validation of the approach is conducted using data from a large-scale structure tested on a shake table. It is shown that the approach is robust to inherent modeling errors in the description of the system and forcing input, providing accurate prediction of the dynamic response when the excitation history is unknown.

Multimodal, high-dimensional, model-based, Bayesian inverse problems with applications in biomechanics

NASA Astrophysics Data System (ADS)

Franck, I. M.; Koutsourelakis, P. S.

2017-01-01

This paper is concerned with the numerical solution of model-based, Bayesian inverse problems. We are particularly interested in cases where the cost of each likelihood evaluation (forward-model call) is expensive and the number of unknown (latent) variables is high. This is the setting in many problems in computational physics where forward models with nonlinear PDEs are used and the parameters to be calibrated involve spatio-temporarily varying coefficients, which upon discretization give rise to a high-dimensional vector of unknowns. One of the consequences of the well-documented ill-posedness of inverse problems is the possibility of multiple solutions. While such information is contained in the posterior density in Bayesian formulations, the discovery of a single mode, let alone multiple, poses a formidable computational task. The goal of the present paper is two-fold. On one hand, we propose approximate, adaptive inference strategies using mixture densities to capture multi-modal posteriors. On the other, we extend our work in [1] with regard to effective dimensionality reduction techniques that reveal low-dimensional subspaces where the posterior variance is mostly concentrated. We validate the proposed model by employing Importance Sampling which confirms that the bias introduced is small and can be efficiently corrected if the analyst wishes to do so. We demonstrate the performance of the proposed strategy in nonlinear elastography where the identification of the mechanical properties of biological materials can inform non-invasive, medical diagnosis. The discovery of multiple modes (solutions) in such problems is critical in achieving the diagnostic objectives.

A gradient-based model parametrization using Bernstein polynomials in Bayesian inversion of surface wave dispersion

NASA Astrophysics Data System (ADS)

Gosselin, Jeremy M.; Dosso, Stan E.; Cassidy, John F.; Quijano, Jorge E.; Molnar, Sheri; Dettmer, Jan

2017-10-01

This paper develops and applies a Bernstein-polynomial parametrization to efficiently represent general, gradient-based profiles in nonlinear geophysical inversion, with application to ambient-noise Rayleigh-wave dispersion data. Bernstein polynomials provide a stable parametrization in that small perturbations to the model parameters (basis-function coefficients) result in only small perturbations to the geophysical parameter profile. A fully nonlinear Bayesian inversion methodology is applied to estimate shear wave velocity (VS) profiles and uncertainties from surface wave dispersion data extracted from ambient seismic noise. The Bayesian information criterion is used to determine the appropriate polynomial order consistent with the resolving power of the data. Data error correlations are accounted for in the inversion using a parametric autoregressive model. The inversion solution is defined in terms of marginal posterior probability profiles for VS as a function of depth, estimated using Metropolis-Hastings sampling with parallel tempering. This methodology is applied to synthetic dispersion data as well as data processed from passive array recordings collected on the Fraser River Delta in British Columbia, Canada. Results from this work are in good agreement with previous studies, as well as with co-located invasive measurements. The approach considered here is better suited than `layered' modelling approaches in applications where smooth gradients in geophysical parameters are expected, such as soil/sediment profiles. Further, the Bernstein polynomial representation is more general than smooth models based on a fixed choice of gradient type (e.g. power-law gradient) because the form of the gradient is determined objectively by the data, rather than by a subjective parametrization choice.

Validation of Bayesian analysis of compartmental kinetic models in medical imaging.

PubMed

Sitek, Arkadiusz; Li, Quanzheng; El Fakhri, Georges; Alpert, Nathaniel M

2016-10-01

Kinetic compartmental analysis is frequently used to compute physiologically relevant quantitative values from time series of images. In this paper, a new approach based on Bayesian analysis to obtain information about these parameters is presented and validated. The closed-form of the posterior distribution of kinetic parameters is derived with a hierarchical prior to model the standard deviation of normally distributed noise. Markov chain Monte Carlo methods are used for numerical estimation of the posterior distribution. Computer simulations of the kinetics of F18-fluorodeoxyglucose (FDG) are used to demonstrate drawing statistical inferences about kinetic parameters and to validate the theory and implementation. Additionally, point estimates of kinetic parameters and covariance of those estimates are determined using the classical non-linear least squares approach. Posteriors obtained using methods proposed in this work are accurate as no significant deviation from the expected shape of the posterior was found (one-sided P>0.08). It is demonstrated that the results obtained by the standard non-linear least-square methods fail to provide accurate estimation of uncertainty for the same data set (P<0.0001). The results of this work validate new methods for a computer simulations of FDG kinetics. Results show that in situations where the classical approach fails in accurate estimation of uncertainty, Bayesian estimation provides an accurate information about the uncertainties in the parameters. Although a particular example of FDG kinetics was used in the paper, the methods can be extended for different pharmaceuticals and imaging modalities. Copyright © 2016 Associazione Italiana di Fisica Medica. Published by Elsevier Ltd. All rights reserved.

Application of nonlinear least-squares regression to ground-water flow modeling, west-central Florida

USGS Publications Warehouse

Yobbi, D.K.

2000-01-01

A nonlinear least-squares regression technique for estimation of ground-water flow model parameters was applied to an existing model of the regional aquifer system underlying west-central Florida. The regression technique minimizes the differences between measured and simulated water levels. Regression statistics, including parameter sensitivities and correlations, were calculated for reported parameter values in the existing model. Optimal parameter values for selected hydrologic variables of interest are estimated by nonlinear regression. Optimal estimates of parameter values are about 140 times greater than and about 0.01 times less than reported values. Independently estimating all parameters by nonlinear regression was impossible, given the existing zonation structure and number of observations, because of parameter insensitivity and correlation. Although the model yields parameter values similar to those estimated by other methods and reproduces the measured water levels reasonably accurately, a simpler parameter structure should be considered. Some possible ways of improving model calibration are to: (1) modify the defined parameter-zonation structure by omitting and/or combining parameters to be estimated; (2) carefully eliminate observation data based on evidence that they are likely to be biased; (3) collect additional water-level data; (4) assign values to insensitive parameters, and (5) estimate the most sensitive parameters first, then, using the optimized values for these parameters, estimate the entire data set.

Time series forecasting using ERNN and QR based on Bayesian model averaging

NASA Astrophysics Data System (ADS)

Pwasong, Augustine; Sathasivam, Saratha

2017-08-01

The Bayesian model averaging technique is a multi-model combination technique. The technique was employed to amalgamate the Elman recurrent neural network (ERNN) technique with the quadratic regression (QR) technique. The amalgamation produced a hybrid technique known as the hybrid ERNN-QR technique. The potentials of forecasting with the hybrid technique are compared with the forecasting capabilities of individual techniques of ERNN and QR. The outcome revealed that the hybrid technique is superior to the individual techniques in the mean square error sense.

A comparative study between nonlinear regression and nonparametric approaches for modelling Phalaris paradoxa seedling emergence

USDA-ARS?s Scientific Manuscript database

Parametric non-linear regression (PNR) techniques commonly are used to develop weed seedling emergence models. Such techniques, however, require statistical assumptions that are difficult to meet. To examine and overcome these limitations, we compared PNR with a nonparametric estimation technique. F...

Predicting motor vehicle collisions using Bayesian neural network models: an empirical analysis.

PubMed

Xie, Yuanchang; Lord, Dominique; Zhang, Yunlong

2007-09-01

Statistical models have frequently been used in highway safety studies. They can be utilized for various purposes, including establishing relationships between variables, screening covariates and predicting values. Generalized linear models (GLM) and hierarchical Bayes models (HBM) have been the most common types of model favored by transportation safety analysts. Over the last few years, researchers have proposed the back-propagation neural network (BPNN) model for modeling the phenomenon under study. Compared to GLMs and HBMs, BPNNs have received much less attention in highway safety modeling. The reasons are attributed to the complexity for estimating this kind of model as well as the problem related to "over-fitting" the data. To circumvent the latter problem, some statisticians have proposed the use of Bayesian neural network (BNN) models. These models have been shown to perform better than BPNN models while at the same time reducing the difficulty associated with over-fitting the data. The objective of this study is to evaluate the application of BNN models for predicting motor vehicle crashes. To accomplish this objective, a series of models was estimated using data collected on rural frontage roads in Texas. Three types of models were compared: BPNN, BNN and the negative binomial (NB) regression models. The results of this study show that in general both types of neural network models perform better than the NB regression model in terms of data prediction. Although the BPNN model can occasionally provide better or approximately equivalent prediction performance compared to the BNN model, in most cases its prediction performance is worse than the BNN model. In addition, the data fitting performance of the BPNN model is consistently worse than the BNN model, which suggests that the BNN model has better generalization abilities than the BPNN model and can effectively alleviate the over-fitting problem without significantly compromising the nonlinear approximation ability. The results also show that BNNs could be used for other useful analyses in highway safety, including the development of accident modification factors and for improving the prediction capabilities for evaluating different highway design alternatives.

Estimation of Fine Particulate Matter in Taipei Using Landuse Regression and Bayesian Maximum Entropy Methods

PubMed Central

Yu, Hwa-Lung; Wang, Chih-Hsih; Liu, Ming-Che; Kuo, Yi-Ming

2011-01-01

Fine airborne particulate matter (PM2.5) has adverse effects on human health. Assessing the long-term effects of PM2.5 exposure on human health and ecology is often limited by a lack of reliable PM2.5 measurements. In Taipei, PM2.5 levels were not systematically measured until August, 2005. Due to the popularity of geographic information systems (GIS), the landuse regression method has been widely used in the spatial estimation of PM concentrations. This method accounts for the potential contributing factors of the local environment, such as traffic volume. Geostatistical methods, on other hand, account for the spatiotemporal dependence among the observations of ambient pollutants. This study assesses the performance of the landuse regression model for the spatiotemporal estimation of PM2.5 in the Taipei area. Specifically, this study integrates the landuse regression model with the geostatistical approach within the framework of the Bayesian maximum entropy (BME) method. The resulting epistemic framework can assimilate knowledge bases including: (a) empirical-based spatial trends of PM concentration based on landuse regression, (b) the spatio-temporal dependence among PM observation information, and (c) site-specific PM observations. The proposed approach performs the spatiotemporal estimation of PM2.5 levels in the Taipei area (Taiwan) from 2005–2007. PMID:21776223

Estimation of fine particulate matter in Taipei using landuse regression and bayesian maximum entropy methods.

PubMed

Yu, Hwa-Lung; Wang, Chih-Hsih; Liu, Ming-Che; Kuo, Yi-Ming

2011-06-01

Fine airborne particulate matter (PM2.5) has adverse effects on human health. Assessing the long-term effects of PM2.5 exposure on human health and ecology is often limited by a lack of reliable PM2.5 measurements. In Taipei, PM2.5 levels were not systematically measured until August, 2005. Due to the popularity of geographic information systems (GIS), the landuse regression method has been widely used in the spatial estimation of PM concentrations. This method accounts for the potential contributing factors of the local environment, such as traffic volume. Geostatistical methods, on other hand, account for the spatiotemporal dependence among the observations of ambient pollutants. This study assesses the performance of the landuse regression model for the spatiotemporal estimation of PM2.5 in the Taipei area. Specifically, this study integrates the landuse regression model with the geostatistical approach within the framework of the Bayesian maximum entropy (BME) method. The resulting epistemic framework can assimilate knowledge bases including: (a) empirical-based spatial trends of PM concentration based on landuse regression, (b) the spatio-temporal dependence among PM observation information, and (c) site-specific PM observations. The proposed approach performs the spatiotemporal estimation of PM2.5 levels in the Taipei area (Taiwan) from 2005-2007.

Automating approximate Bayesian computation by local linear regression.

PubMed

Thornton, Kevin R

2009-07-07

In several biological contexts, parameter inference often relies on computationally-intensive techniques. "Approximate Bayesian Computation", or ABC, methods based on summary statistics have become increasingly popular. A particular flavor of ABC based on using a linear regression to approximate the posterior distribution of the parameters, conditional on the summary statistics, is computationally appealing, yet no standalone tool exists to automate the procedure. Here, I describe a program to implement the method. The software package ABCreg implements the local linear-regression approach to ABC. The advantages are: 1. The code is standalone, and fully-documented. 2. The program will automatically process multiple data sets, and create unique output files for each (which may be processed immediately in R), facilitating the testing of inference procedures on simulated data, or the analysis of multiple data sets. 3. The program implements two different transformation methods for the regression step. 4. Analysis options are controlled on the command line by the user, and the program is designed to output warnings for cases where the regression fails. 5. The program does not depend on any particular simulation machinery (coalescent, forward-time, etc.), and therefore is a general tool for processing the results from any simulation. 6. The code is open-source, and modular.Examples of applying the software to empirical data from Drosophila melanogaster, and testing the procedure on simulated data, are shown. In practice, the ABCreg simplifies implementing ABC based on local-linear regression.

Bayesian analysis of non-homogeneous Markov chains: application to mental health data.

PubMed

Sung, Minje; Soyer, Refik; Nhan, Nguyen

2007-07-10

In this paper we present a formal treatment of non-homogeneous Markov chains by introducing a hierarchical Bayesian framework. Our work is motivated by the analysis of correlated categorical data which arise in assessment of psychiatric treatment programs. In our development, we introduce a Markovian structure to describe the non-homogeneity of transition patterns. In doing so, we introduce a logistic regression set-up for Markov chains and incorporate covariates in our model. We present a Bayesian model using Markov chain Monte Carlo methods and develop inference procedures to address issues encountered in the analyses of data from psychiatric treatment programs. Our model and inference procedures are implemented to some real data from a psychiatric treatment study. Copyright 2006 John Wiley & Sons, Ltd.

Kernel Partial Least Squares for Nonlinear Regression and Discrimination

NASA Technical Reports Server (NTRS)

Rosipal, Roman; Clancy, Daniel (Technical Monitor)

2002-01-01

This paper summarizes recent results on applying the method of partial least squares (PLS) in a reproducing kernel Hilbert space (RKHS). A previously proposed kernel PLS regression model was proven to be competitive with other regularized regression methods in RKHS. The family of nonlinear kernel-based PLS models is extended by considering the kernel PLS method for discrimination. Theoretical and experimental results on a two-class discrimination problem indicate usefulness of the method.

Bayesian B-spline mapping for dynamic quantitative traits.

PubMed

Xing, Jun; Li, Jiahan; Yang, Runqing; Zhou, Xiaojing; Xu, Shizhong

2012-04-01

Owing to their ability and flexibility to describe individual gene expression at different time points, random regression (RR) analyses have become a popular procedure for the genetic analysis of dynamic traits whose phenotypes are collected over time. Specifically, when modelling the dynamic patterns of gene expressions in the RR framework, B-splines have been proved successful as an alternative to orthogonal polynomials. In the so-called Bayesian B-spline quantitative trait locus (QTL) mapping, B-splines are used to characterize the patterns of QTL effects and individual-specific time-dependent environmental errors over time, and the Bayesian shrinkage estimation method is employed to estimate model parameters. Extensive simulations demonstrate that (1) in terms of statistical power, Bayesian B-spline mapping outperforms the interval mapping based on the maximum likelihood; (2) for the simulated dataset with complicated growth curve simulated by B-splines, Legendre polynomial-based Bayesian mapping is not capable of identifying the designed QTLs accurately, even when higher-order Legendre polynomials are considered and (3) for the simulated dataset using Legendre polynomials, the Bayesian B-spline mapping can find the same QTLs as those identified by Legendre polynomial analysis. All simulation results support the necessity and flexibility of B-spline in Bayesian mapping of dynamic traits. The proposed method is also applied to a real dataset, where QTLs controlling the growth trajectory of stem diameters in Populus are located.

Bayesian quantitative precipitation forecasts in terms of quantiles

NASA Astrophysics Data System (ADS)

Bentzien, Sabrina; Friederichs, Petra

2014-05-01

Ensemble prediction systems (EPS) for numerical weather predictions on the mesoscale are particularly developed to obtain probabilistic guidance for high impact weather. An EPS not only issues a deterministic future state of the atmosphere but a sample of possible future states. Ensemble postprocessing then translates such a sample of forecasts into probabilistic measures. This study focus on probabilistic quantitative precipitation forecasts in terms of quantiles. Quantiles are particular suitable to describe precipitation at various locations, since no assumption is required on the distribution of precipitation. The focus is on the prediction during high-impact events and related to the Volkswagen Stiftung funded project WEX-MOP (Mesoscale Weather Extremes - Theory, Spatial Modeling and Prediction). Quantile forecasts are derived from the raw ensemble and via quantile regression. Neighborhood method and time-lagging are effective tools to inexpensively increase the ensemble spread, which results in more reliable forecasts especially for extreme precipitation events. Since an EPS provides a large amount of potentially informative predictors, a variable selection is required in order to obtain a stable statistical model. A Bayesian formulation of quantile regression allows for inference about the selection of predictive covariates by the use of appropriate prior distributions. Moreover, the implementation of an additional process layer for the regression parameters accounts for spatial variations of the parameters. Bayesian quantile regression and its spatially adaptive extension is illustrated for the German-focused mesoscale weather prediction ensemble COSMO-DE-EPS, which runs (pre)operationally since December 2010 at the German Meteorological Service (DWD). Objective out-of-sample verification uses the quantile score (QS), a weighted absolute error between quantile forecasts and observations. The QS is a proper scoring function and can be decomposed into reliability, resolutions and uncertainty parts. A quantile reliability plot gives detailed insights in the predictive performance of the quantile forecasts.

Estimation of Logistic Regression Models in Small Samples. A Simulation Study Using a Weakly Informative Default Prior Distribution

ERIC Educational Resources Information Center

Gordovil-Merino, Amalia; Guardia-Olmos, Joan; Pero-Cebollero, Maribel

2012-01-01

In this paper, we used simulations to compare the performance of classical and Bayesian estimations in logistic regression models using small samples. In the performed simulations, conditions were varied, including the type of relationship between independent and dependent variable values (i.e., unrelated and related values), the type of variable…

Bayesian quantile regression-based partially linear mixed-effects joint models for longitudinal data with multiple features.

PubMed

Zhang, Hanze; Huang, Yangxin; Wang, Wei; Chen, Henian; Langland-Orban, Barbara

2017-01-01

In longitudinal AIDS studies, it is of interest to investigate the relationship between HIV viral load and CD4 cell counts, as well as the complicated time effect. Most of common models to analyze such complex longitudinal data are based on mean-regression, which fails to provide efficient estimates due to outliers and/or heavy tails. Quantile regression-based partially linear mixed-effects models, a special case of semiparametric models enjoying benefits of both parametric and nonparametric models, have the flexibility to monitor the viral dynamics nonparametrically and detect the varying CD4 effects parametrically at different quantiles of viral load. Meanwhile, it is critical to consider various data features of repeated measurements, including left-censoring due to a limit of detection, covariate measurement error, and asymmetric distribution. In this research, we first establish a Bayesian joint models that accounts for all these data features simultaneously in the framework of quantile regression-based partially linear mixed-effects models. The proposed models are applied to analyze the Multicenter AIDS Cohort Study (MACS) data. Simulation studies are also conducted to assess the performance of the proposed methods under different scenarios.

Linearity versus Nonlinearity of Offspring-Parent Regression: An Experimental Study of Drosophila Melanogaster

PubMed Central

Gimelfarb, A.; Willis, J. H.

1994-01-01

An experiment was conducted to investigate the offspring-parent regression for three quantitative traits (weight, abdominal bristles and wing length) in Drosophila melanogaster. Linear and polynomial models were fitted for the regressions of a character in offspring on both parents. It is demonstrated that responses by the characters to selection predicted by the nonlinear regressions may differ substantially from those predicted by the linear regressions. This is true even, and especially, if selection is weak. The realized heritability for a character under selection is shown to be determined not only by the offspring-parent regression but also by the distribution of the character and by the form and strength of selection. PMID:7828818

Analysis of Feature Intervisibility and Cumulative Visibility Using GIS, Bayesian and Spatial Statistics: A Study from the Mandara Mountains, Northern Cameroon

PubMed Central

Wright, David K.; MacEachern, Scott; Lee, Jaeyong

2014-01-01

The locations of diy-geδ-bay (DGB) sites in the Mandara Mountains, northern Cameroon are hypothesized to occur as a function of their ability to see and be seen from points on the surrounding landscape. A series of geostatistical, two-way and Bayesian logistic regression analyses were performed to test two hypotheses related to the intervisibility of the sites to one another and their visual prominence on the landscape. We determine that the intervisibility of the sites to one another is highly statistically significant when compared to 10 stratified-random permutations of DGB sites. Bayesian logistic regression additionally demonstrates that the visibility of the sites to points on the surrounding landscape is statistically significant. The location of sites appears to have also been selected on the basis of lower slope than random permutations of sites. Using statistical measures, many of which are not commonly employed in archaeological research, to evaluate aspects of visibility on the landscape, we conclude that the placement of DGB sites improved their conspicuousness for enhanced ritual, social cooperation and/or competition purposes. PMID:25383883

Bayesian estimation of extreme flood quantiles using a rainfall-runoff model and a stochastic daily rainfall generator

NASA Astrophysics Data System (ADS)

Costa, Veber; Fernandes, Wilson

2017-11-01

Extreme flood estimation has been a key research topic in hydrological sciences. Reliable estimates of such events are necessary as structures for flood conveyance are continuously evolving in size and complexity and, as a result, their failure-associated hazards become more and more pronounced. Due to this fact, several estimation techniques intended to improve flood frequency analysis and reducing uncertainty in extreme quantile estimation have been addressed in the literature in the last decades. In this paper, we develop a Bayesian framework for the indirect estimation of extreme flood quantiles from rainfall-runoff models. In the proposed approach, an ensemble of long daily rainfall series is simulated with a stochastic generator, which models extreme rainfall amounts with an upper-bounded distribution function, namely, the 4-parameter lognormal model. The rationale behind the generation model is that physical limits for rainfall amounts, and consequently for floods, exist and, by imposing an appropriate upper bound for the probabilistic model, more plausible estimates can be obtained for those rainfall quantiles with very low exceedance probabilities. Daily rainfall time series are converted into streamflows by routing each realization of the synthetic ensemble through a conceptual hydrologic model, the Rio Grande rainfall-runoff model. Calibration of parameters is performed through a nonlinear regression model, by means of the specification of a statistical model for the residuals that is able to accommodate autocorrelation, heteroscedasticity and nonnormality. By combining the outlined steps in a Bayesian structure of analysis, one is able to properly summarize the resulting uncertainty and estimating more accurate credible intervals for a set of flood quantiles of interest. The method for extreme flood indirect estimation was applied to the American river catchment, at the Folsom dam, in the state of California, USA. Results show that most floods, including exceptionally large non-systematic events, were reasonably estimated with the proposed approach. In addition, by accounting for uncertainties in each modeling step, one is able to obtain a better understanding of the influential factors in large flood formation dynamics.

A Development of Nonstationary Regional Frequency Analysis Model with Large-scale Climate Information: Its Application to Korean Watershed

NASA Astrophysics Data System (ADS)

Kim, Jin-Young; Kwon, Hyun-Han; Kim, Hung-Soo

2015-04-01

The existing regional frequency analysis has disadvantages in that it is difficult to consider geographical characteristics in estimating areal rainfall. In this regard, this study aims to develop a hierarchical Bayesian model based nonstationary regional frequency analysis in that spatial patterns of the design rainfall with geographical information (e.g. latitude, longitude and altitude) are explicitly incorporated. This study assumes that the parameters of Gumbel (or GEV distribution) are a function of geographical characteristics within a general linear regression framework. Posterior distribution of the regression parameters are estimated by Bayesian Markov Chain Monte Carlo (MCMC) method, and the identified functional relationship is used to spatially interpolate the parameters of the distributions by using digital elevation models (DEM) as inputs. The proposed model is applied to derive design rainfalls over the entire Han-river watershed. It was found that the proposed Bayesian regional frequency analysis model showed similar results compared to L-moment based regional frequency analysis. In addition, the model showed an advantage in terms of quantifying uncertainty of the design rainfall and estimating the area rainfall considering geographical information. Finally, comprehensive discussion on design rainfall in the context of nonstationary will be presented. KEYWORDS: Regional frequency analysis, Nonstationary, Spatial information, Bayesian Acknowledgement This research was supported by a grant (14AWMP-B082564-01) from Advanced Water Management Research Program funded by Ministry of Land, Infrastructure and Transport of Korean government.

Boosting Bayesian parameter inference of stochastic differential equation models with methods from statistical physics

NASA Astrophysics Data System (ADS)

Albert, Carlo; Ulzega, Simone; Stoop, Ruedi

2016-04-01

Measured time-series of both precipitation and runoff are known to exhibit highly non-trivial statistical properties. For making reliable probabilistic predictions in hydrology, it is therefore desirable to have stochastic models with output distributions that share these properties. When parameters of such models have to be inferred from data, we also need to quantify the associated parametric uncertainty. For non-trivial stochastic models, however, this latter step is typically very demanding, both conceptually and numerically, and always never done in hydrology. Here, we demonstrate that methods developed in statistical physics make a large class of stochastic differential equation (SDE) models amenable to a full-fledged Bayesian parameter inference. For concreteness we demonstrate these methods by means of a simple yet non-trivial toy SDE model. We consider a natural catchment that can be described by a linear reservoir, at the scale of observation. All the neglected processes are assumed to happen at much shorter time-scales and are therefore modeled with a Gaussian white noise term, the standard deviation of which is assumed to scale linearly with the system state (water volume in the catchment). Even for constant input, the outputs of this simple non-linear SDE model show a wealth of desirable statistical properties, such as fat-tailed distributions and long-range correlations. Standard algorithms for Bayesian inference fail, for models of this kind, because their likelihood functions are extremely high-dimensional intractable integrals over all possible model realizations. The use of Kalman filters is illegitimate due to the non-linearity of the model. Particle filters could be used but become increasingly inefficient with growing number of data points. Hamiltonian Monte Carlo algorithms allow us to translate this inference problem to the problem of simulating the dynamics of a statistical mechanics system and give us access to most sophisticated methods that have been developed in the statistical physics community over the last few decades. We demonstrate that such methods, along with automated differentiation algorithms, allow us to perform a full-fledged Bayesian inference, for a large class of SDE models, in a highly efficient and largely automatized manner. Furthermore, our algorithm is highly parallelizable. For our toy model, discretized with a few hundred points, a full Bayesian inference can be performed in a matter of seconds on a standard PC.

Entropy-Bayesian Inversion of Time-Lapse Tomographic GPR data for Monitoring Dielectric Permittivity and Soil Moisture Variations

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

Hou, Z; Terry, N; Hubbard, S S

2013-02-12

In this study, we evaluate the possibility of monitoring soil moisture variation using tomographic ground penetrating radar travel time data through Bayesian inversion, which is integrated with entropy memory function and pilot point concepts, as well as efficient sampling approaches. It is critical to accurately estimate soil moisture content and variations in vadose zone studies. Many studies have illustrated the promise and value of GPR tomographic data for estimating soil moisture and associated changes, however, challenges still exist in the inversion of GPR tomographic data in a manner that quantifies input and predictive uncertainty, incorporates multiple data types, handles non-uniquenessmore » and nonlinearity, and honors time-lapse tomograms collected in a series. To address these challenges, we develop a minimum relative entropy (MRE)-Bayesian based inverse modeling framework that non-subjectively defines prior probabilities, incorporates information from multiple sources, and quantifies uncertainty. The framework enables us to estimate dielectric permittivity at pilot point locations distributed within the tomogram, as well as the spatial correlation range. In the inversion framework, MRE is first used to derive prior probability distribution functions (pdfs) of dielectric permittivity based on prior information obtained from a straight-ray GPR inversion. The probability distributions are then sampled using a Quasi-Monte Carlo (QMC) approach, and the sample sets provide inputs to a sequential Gaussian simulation (SGSim) algorithm that constructs a highly resolved permittivity/velocity field for evaluation with a curved-ray GPR forward model. The likelihood functions are computed as a function of misfits, and posterior pdfs are constructed using a Gaussian kernel. Inversion of subsequent time-lapse datasets combines the Bayesian estimates from the previous inversion (as a memory function) with new data. The memory function and pilot point design takes advantage of the spatial-temporal correlation of the state variables. We first apply the inversion framework to a static synthetic example and then to a time-lapse GPR tomographic dataset collected during a dynamic experiment conducted at the Hanford Site in Richland, WA. We demonstrate that the MRE-Bayesian inversion enables us to merge various data types, quantify uncertainty, evaluate nonlinear models, and produce more detailed and better resolved estimates than straight-ray based inversion; therefore, it has the potential to improve estimates of inter-wellbore dielectric permittivity and soil moisture content and to monitor their temporal dynamics more accurately.« less

Entropy-Bayesian Inversion of Time-Lapse Tomographic GPR data for Monitoring Dielectric Permittivity and Soil Moisture Variations

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

Hou, Zhangshuan; Terry, Neil C.; Hubbard, Susan S.

2013-02-22

In this study, we evaluate the possibility of monitoring soil moisture variation using tomographic ground penetrating radar travel time data through Bayesian inversion, which is integrated with entropy memory function and pilot point concepts, as well as efficient sampling approaches. It is critical to accurately estimate soil moisture content and variations in vadose zone studies. Many studies have illustrated the promise and value of GPR tomographic data for estimating soil moisture and associated changes, however, challenges still exist in the inversion of GPR tomographic data in a manner that quantifies input and predictive uncertainty, incorporates multiple data types, handles non-uniquenessmore » and nonlinearity, and honors time-lapse tomograms collected in a series. To address these challenges, we develop a minimum relative entropy (MRE)-Bayesian based inverse modeling framework that non-subjectively defines prior probabilities, incorporates information from multiple sources, and quantifies uncertainty. The framework enables us to estimate dielectric permittivity at pilot point locations distributed within the tomogram, as well as the spatial correlation range. In the inversion framework, MRE is first used to derive prior probability density functions (pdfs) of dielectric permittivity based on prior information obtained from a straight-ray GPR inversion. The probability distributions are then sampled using a Quasi-Monte Carlo (QMC) approach, and the sample sets provide inputs to a sequential Gaussian simulation (SGSIM) algorithm that constructs a highly resolved permittivity/velocity field for evaluation with a curved-ray GPR forward model. The likelihood functions are computed as a function of misfits, and posterior pdfs are constructed using a Gaussian kernel. Inversion of subsequent time-lapse datasets combines the Bayesian estimates from the previous inversion (as a memory function) with new data. The memory function and pilot point design takes advantage of the spatial-temporal correlation of the state variables. We first apply the inversion framework to a static synthetic example and then to a time-lapse GPR tomographic dataset collected during a dynamic experiment conducted at the Hanford Site in Richland, WA. We demonstrate that the MRE-Bayesian inversion enables us to merge various data types, quantify uncertainty, evaluate nonlinear models, and produce more detailed and better resolved estimates than straight-ray based inversion; therefore, it has the potential to improve estimates of inter-wellbore dielectric permittivity and soil moisture content and to monitor their temporal dynamics more accurately.« less

Methods for calculating confidence and credible intervals for the residual between-study variance in random effects meta-regression models

PubMed Central

2014-01-01

Background Meta-regression is becoming increasingly used to model study level covariate effects. However this type of statistical analysis presents many difficulties and challenges. Here two methods for calculating confidence intervals for the magnitude of the residual between-study variance in random effects meta-regression models are developed. A further suggestion for calculating credible intervals using informative prior distributions for the residual between-study variance is presented. Methods Two recently proposed and, under the assumptions of the random effects model, exact methods for constructing confidence intervals for the between-study variance in random effects meta-analyses are extended to the meta-regression setting. The use of Generalised Cochran heterogeneity statistics is extended to the meta-regression setting and a Newton-Raphson procedure is developed to implement the Q profile method for meta-analysis and meta-regression. WinBUGS is used to implement informative priors for the residual between-study variance in the context of Bayesian meta-regressions. Results Results are obtained for two contrasting examples, where the first example involves a binary covariate and the second involves a continuous covariate. Intervals for the residual between-study variance are wide for both examples. Conclusions Statistical methods, and R computer software, are available to compute exact confidence intervals for the residual between-study variance under the random effects model for meta-regression. These frequentist methods are almost as easily implemented as their established counterparts for meta-analysis. Bayesian meta-regressions are also easily performed by analysts who are comfortable using WinBUGS. Estimates of the residual between-study variance in random effects meta-regressions should be routinely reported and accompanied by some measure of their uncertainty. Confidence and/or credible intervals are well-suited to this purpose. PMID:25196829

A comparative study between nonlinear regression and artificial neural network approaches for modelling wild oat (Avena fatua) field emergence

USDA-ARS?s Scientific Manuscript database

Non-linear regression techniques are used widely to fit weed field emergence patterns to soil microclimatic indices using S-type functions. Artificial neural networks present interesting and alternative features for such modeling purposes. In this work, a univariate hydrothermal-time based Weibull m...

Hierarchical cluster-based partial least squares regression (HC-PLSR) is an efficient tool for metamodelling of nonlinear dynamic models.

PubMed

Tøndel, Kristin; Indahl, Ulf G; Gjuvsland, Arne B; Vik, Jon Olav; Hunter, Peter; Omholt, Stig W; Martens, Harald

2011-06-01

Deterministic dynamic models of complex biological systems contain a large number of parameters and state variables, related through nonlinear differential equations with various types of feedback. A metamodel of such a dynamic model is a statistical approximation model that maps variation in parameters and initial conditions (inputs) to variation in features of the trajectories of the state variables (outputs) throughout the entire biologically relevant input space. A sufficiently accurate mapping can be exploited both instrumentally and epistemically. Multivariate regression methodology is a commonly used approach for emulating dynamic models. However, when the input-output relations are highly nonlinear or non-monotone, a standard linear regression approach is prone to give suboptimal results. We therefore hypothesised that a more accurate mapping can be obtained by locally linear or locally polynomial regression. We present here a new method for local regression modelling, Hierarchical Cluster-based PLS regression (HC-PLSR), where fuzzy C-means clustering is used to separate the data set into parts according to the structure of the response surface. We compare the metamodelling performance of HC-PLSR with polynomial partial least squares regression (PLSR) and ordinary least squares (OLS) regression on various systems: six different gene regulatory network models with various types of feedback, a deterministic mathematical model of the mammalian circadian clock and a model of the mouse ventricular myocyte function. Our results indicate that multivariate regression is well suited for emulating dynamic models in systems biology. The hierarchical approach turned out to be superior to both polynomial PLSR and OLS regression in all three test cases. The advantage, in terms of explained variance and prediction accuracy, was largest in systems with highly nonlinear functional relationships and in systems with positive feedback loops. HC-PLSR is a promising approach for metamodelling in systems biology, especially for highly nonlinear or non-monotone parameter to phenotype maps. The algorithm can be flexibly adjusted to suit the complexity of the dynamic model behaviour, inviting automation in the metamodelling of complex systems.

Hierarchical Cluster-based Partial Least Squares Regression (HC-PLSR) is an efficient tool for metamodelling of nonlinear dynamic models

PubMed Central

2011-01-01

Background Deterministic dynamic models of complex biological systems contain a large number of parameters and state variables, related through nonlinear differential equations with various types of feedback. A metamodel of such a dynamic model is a statistical approximation model that maps variation in parameters and initial conditions (inputs) to variation in features of the trajectories of the state variables (outputs) throughout the entire biologically relevant input space. A sufficiently accurate mapping can be exploited both instrumentally and epistemically. Multivariate regression methodology is a commonly used approach for emulating dynamic models. However, when the input-output relations are highly nonlinear or non-monotone, a standard linear regression approach is prone to give suboptimal results. We therefore hypothesised that a more accurate mapping can be obtained by locally linear or locally polynomial regression. We present here a new method for local regression modelling, Hierarchical Cluster-based PLS regression (HC-PLSR), where fuzzy C-means clustering is used to separate the data set into parts according to the structure of the response surface. We compare the metamodelling performance of HC-PLSR with polynomial partial least squares regression (PLSR) and ordinary least squares (OLS) regression on various systems: six different gene regulatory network models with various types of feedback, a deterministic mathematical model of the mammalian circadian clock and a model of the mouse ventricular myocyte function. Results Our results indicate that multivariate regression is well suited for emulating dynamic models in systems biology. The hierarchical approach turned out to be superior to both polynomial PLSR and OLS regression in all three test cases. The advantage, in terms of explained variance and prediction accuracy, was largest in systems with highly nonlinear functional relationships and in systems with positive feedback loops. Conclusions HC-PLSR is a promising approach for metamodelling in systems biology, especially for highly nonlinear or non-monotone parameter to phenotype maps. The algorithm can be flexibly adjusted to suit the complexity of the dynamic model behaviour, inviting automation in the metamodelling of complex systems. PMID:21627852

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

A Gibbs sampler for Bayesian analysis of site-occupancy data

USGS Publications Warehouse

Dorazio, Robert M.; Rodriguez, Daniel Taylor

2012-01-01

1. A Bayesian analysis of site-occupancy data containing covariates of species occurrence and species detection probabilities is usually completed using Markov chain Monte Carlo methods in conjunction with software programs that can implement those methods for any statistical model, not just site-occupancy models. Although these software programs are quite flexible, considerable experience is often required to specify a model and to initialize the Markov chain so that summaries of the posterior distribution can be estimated efficiently and accurately. 2. As an alternative to these programs, we develop a Gibbs sampler for Bayesian analysis of site-occupancy data that include covariates of species occurrence and species detection probabilities. This Gibbs sampler is based on a class of site-occupancy models in which probabilities of species occurrence and detection are specified as probit-regression functions of site- and survey-specific covariate measurements. 3. To illustrate the Gibbs sampler, we analyse site-occupancy data of the blue hawker, Aeshna cyanea (Odonata, Aeshnidae), a common dragonfly species in Switzerland. Our analysis includes a comparison of results based on Bayesian and classical (non-Bayesian) methods of inference. We also provide code (based on the R software program) for conducting Bayesian and classical analyses of site-occupancy data.

Lagged kernel machine regression for identifying time windows of susceptibility to exposures of complex mixtures.

PubMed

Liu, Shelley H; Bobb, Jennifer F; Lee, Kyu Ha; Gennings, Chris; Claus Henn, Birgit; Bellinger, David; Austin, Christine; Schnaas, Lourdes; Tellez-Rojo, Martha M; Hu, Howard; Wright, Robert O; Arora, Manish; Coull, Brent A

2018-07-01

The impact of neurotoxic chemical mixtures on children's health is a critical public health concern. It is well known that during early life, toxic exposures may impact cognitive function during critical time intervals of increased vulnerability, known as windows of susceptibility. Knowledge on time windows of susceptibility can help inform treatment and prevention strategies, as chemical mixtures may affect a developmental process that is operating at a specific life phase. There are several statistical challenges in estimating the health effects of time-varying exposures to multi-pollutant mixtures, such as: multi-collinearity among the exposures both within time points and across time points, and complex exposure-response relationships. To address these concerns, we develop a flexible statistical method, called lagged kernel machine regression (LKMR). LKMR identifies critical exposure windows of chemical mixtures, and accounts for complex non-linear and non-additive effects of the mixture at any given exposure window. Specifically, LKMR estimates how the effects of a mixture of exposures change with the exposure time window using a Bayesian formulation of a grouped, fused lasso penalty within a kernel machine regression (KMR) framework. A simulation study demonstrates the performance of LKMR under realistic exposure-response scenarios, and demonstrates large gains over approaches that consider each time window separately, particularly when serial correlation among the time-varying exposures is high. Furthermore, LKMR demonstrates gains over another approach that inputs all time-specific chemical concentrations together into a single KMR. We apply LKMR to estimate associations between neurodevelopment and metal mixtures in Early Life Exposures in Mexico and Neurotoxicology, a prospective cohort study of child health in Mexico City.

Multilayer Perceptron for Robust Nonlinear Interval Regression Analysis Using Genetic Algorithms

PubMed Central

2014-01-01

On the basis of fuzzy regression, computational models in intelligence such as neural networks have the capability to be applied to nonlinear interval regression analysis for dealing with uncertain and imprecise data. When training data are not contaminated by outliers, computational models perform well by including almost all given training data in the data interval. Nevertheless, since training data are often corrupted by outliers, robust learning algorithms employed to resist outliers for interval regression analysis have been an interesting area of research. Several approaches involving computational intelligence are effective for resisting outliers, but the required parameters for these approaches are related to whether the collected data contain outliers or not. Since it seems difficult to prespecify the degree of contamination beforehand, this paper uses multilayer perceptron to construct the robust nonlinear interval regression model using the genetic algorithm. Outliers beyond or beneath the data interval will impose slight effect on the determination of data interval. Simulation results demonstrate that the proposed method performs well for contaminated datasets. PMID:25110755

Multilayer perceptron for robust nonlinear interval regression analysis using genetic algorithms.

PubMed

Hu, Yi-Chung

2014-01-01

On the basis of fuzzy regression, computational models in intelligence such as neural networks have the capability to be applied to nonlinear interval regression analysis for dealing with uncertain and imprecise data. When training data are not contaminated by outliers, computational models perform well by including almost all given training data in the data interval. Nevertheless, since training data are often corrupted by outliers, robust learning algorithms employed to resist outliers for interval regression analysis have been an interesting area of research. Several approaches involving computational intelligence are effective for resisting outliers, but the required parameters for these approaches are related to whether the collected data contain outliers or not. Since it seems difficult to prespecify the degree of contamination beforehand, this paper uses multilayer perceptron to construct the robust nonlinear interval regression model using the genetic algorithm. Outliers beyond or beneath the data interval will impose slight effect on the determination of data interval. Simulation results demonstrate that the proposed method performs well for contaminated datasets.

Evaluation of AUC(0-4) predictive methods for cyclosporine in kidney transplant patients.

PubMed

Aoyama, Takahiko; Matsumoto, Yoshiaki; Shimizu, Makiko; Fukuoka, Masamichi; Kimura, Toshimi; Kokubun, Hideya; Yoshida, Kazunari; Yago, Kazuo

2005-05-01

Cyclosporine (CyA) is the most commonly used immunosuppressive agent in patients who undergo kidney transplantation. Dosage adjustment of CyA is usually based on trough levels. Recently, trough levels have been replacing the area under the concentration-time curve during the first 4 h after CyA administration (AUC(0-4)). The aim of this study was to compare the predictive values obtained using three different methods of AUC(0-4) monitoring. AUC(0-4) was calculated from 0 to 4 h in early and stable renal transplant patients using the trapezoidal rule. The predicted AUC(0-4) was calculated using three different methods: the multiple regression equation reported by Uchida et al.; Bayesian estimation for modified population pharmacokinetic parameters reported by Yoshida et al.; and modified population pharmacokinetic parameters reported by Cremers et al. The predicted AUC(0-4) was assessed on the basis of predictive bias, precision, and correlation coefficient. The predicted AUC(0-4) values obtained using three methods through measurement of three blood samples showed small differences in predictive bias, precision, and correlation coefficient. In the prediction of AUC(0-4) measurement of one blood sample from stable renal transplant patients, the performance of the regression equation reported by Uchida depended on sampling time. On the other hand, the performance of Bayesian estimation with modified pharmacokinetic parameters reported by Yoshida through measurement of one blood sample, which is not dependent on sampling time, showed a small difference in the correlation coefficient. The prediction of AUC(0-4) using a regression equation required accurate sampling time. In this study, the prediction of AUC(0-4) using Bayesian estimation did not require accurate sampling time in the AUC(0-4) monitoring of CyA. Thus Bayesian estimation is assumed to be clinically useful in the dosage adjustment of CyA.

New methods of testing nonlinear hypothesis using iterative NLLS estimator

NASA Astrophysics Data System (ADS)

Mahaboob, B.; Venkateswarlu, B.; Mokeshrayalu, G.; Balasiddamuni, P.

2017-11-01

This research paper discusses the method of testing nonlinear hypothesis using iterative Nonlinear Least Squares (NLLS) estimator. Takeshi Amemiya [1] explained this method. However in the present research paper, a modified Wald test statistic due to Engle, Robert [6] is proposed to test the nonlinear hypothesis using iterative NLLS estimator. An alternative method for testing nonlinear hypothesis using iterative NLLS estimator based on nonlinear hypothesis using iterative NLLS estimator based on nonlinear studentized residuals has been proposed. In this research article an innovative method of testing nonlinear hypothesis using iterative restricted NLLS estimator is derived. Pesaran and Deaton [10] explained the methods of testing nonlinear hypothesis. This paper uses asymptotic properties of nonlinear least squares estimator proposed by Jenrich [8]. The main purpose of this paper is to provide very innovative methods of testing nonlinear hypothesis using iterative NLLS estimator, iterative NLLS estimator based on nonlinear studentized residuals and iterative restricted NLLS estimator. Eakambaram et al. [12] discussed least absolute deviation estimations versus nonlinear regression model with heteroscedastic errors and also they studied the problem of heteroscedasticity with reference to nonlinear regression models with suitable illustration. William Grene [13] examined the interaction effect in nonlinear models disused by Ai and Norton [14] and suggested ways to examine the effects that do not involve statistical testing. Peter [15] provided guidelines for identifying composite hypothesis and addressing the probability of false rejection for multiple hypotheses.

Detecting a Change in School Performance: A Bayesian Analysis for a Multilevel Join Point Problem. CSE Technical Report 542.

ERIC Educational Resources Information Center

Thum, Yeow Meng; Bhattacharya, Suman Kumar

To better describe individual behavior within a system, this paper uses a sample of longitudinal test scores from a large urban school system to consider hierarchical Bayes estimation of a multilevel linear regression model in which each individual regression slope of test score on time switches at some unknown point in time, "kj."…

A Fast Solution of the Lindley Equations for the M-Group Regression Problem. Technical Report 78-3, October 1977 through May 1978.

ERIC Educational Resources Information Center

Molenaar, Ivo W.

The technical problems involved in obtaining Bayesian model estimates for the regression parameters in m similar groups are studied. The available computer programs, BPREP (BASIC), and BAYREG, both written in FORTRAN, require an amount of computer processing that does not encourage regular use. These programs are analyzed so that the performance…

Bayesian Nonparametric Inference – Why and How

PubMed Central

Müller, Peter; Mitra, Riten

2013-01-01

We review inference under models with nonparametric Bayesian (BNP) priors. The discussion follows a set of examples for some common inference problems. The examples are chosen to highlight problems that are challenging for standard parametric inference. We discuss inference for density estimation, clustering, regression and for mixed effects models with random effects distributions. While we focus on arguing for the need for the flexibility of BNP models, we also review some of the more commonly used BNP models, thus hopefully answering a bit of both questions, why and how to use BNP. PMID:24368932

Recursive Bayesian recurrent neural networks for time-series modeling.

PubMed

Mirikitani, Derrick T; Nikolaev, Nikolay

2010-02-01

This paper develops a probabilistic approach to recursive second-order training of recurrent neural networks (RNNs) for improved time-series modeling. A general recursive Bayesian Levenberg-Marquardt algorithm is derived to sequentially update the weights and the covariance (Hessian) matrix. The main strengths of the approach are a principled handling of the regularization hyperparameters that leads to better generalization, and stable numerical performance. The framework involves the adaptation of a noise hyperparameter and local weight prior hyperparameters, which represent the noise in the data and the uncertainties in the model parameters. Experimental investigations using artificial and real-world data sets show that RNNs equipped with the proposed approach outperform standard real-time recurrent learning and extended Kalman training algorithms for recurrent networks, as well as other contemporary nonlinear neural models, on time-series modeling.

Does the high–tech industry consistently reduce CO{sub 2} emissions? Results from nonparametric additive regression model

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

Xu, Bin; Research Center of Applied Statistics, Jiangxi University of Finance and Economics, Nanchang, Jiangxi 330013; Lin, Boqiang, E-mail: bqlin@xmu.edu.cn

China is currently the world's largest carbon dioxide (CO{sub 2}) emitter. Moreover, total energy consumption and CO{sub 2} emissions in China will continue to increase due to the rapid growth of industrialization and urbanization. Therefore, vigorously developing the high–tech industry becomes an inevitable choice to reduce CO{sub 2} emissions at the moment or in the future. However, ignoring the existing nonlinear links between economic variables, most scholars use traditional linear models to explore the impact of the high–tech industry on CO{sub 2} emissions from an aggregate perspective. Few studies have focused on nonlinear relationships and regional differences in China. Basedmore » on panel data of 1998–2014, this study uses the nonparametric additive regression model to explore the nonlinear effect of the high–tech industry from a regional perspective. The estimated results show that the residual sum of squares (SSR) of the nonparametric additive regression model in the eastern, central and western regions are 0.693, 0.054 and 0.085 respectively, which are much less those that of the traditional linear regression model (3.158, 4.227 and 7.196). This verifies that the nonparametric additive regression model has a better fitting effect. Specifically, the high–tech industry produces an inverted “U–shaped” nonlinear impact on CO{sub 2} emissions in the eastern region, but a positive “U–shaped” nonlinear effect in the central and western regions. Therefore, the nonlinear impact of the high–tech industry on CO{sub 2} emissions in the three regions should be given adequate attention in developing effective abatement policies. - Highlights: • The nonlinear effect of the high–tech industry on CO{sub 2} emissions was investigated. • The high–tech industry yields an inverted “U–shaped” effect in the eastern region. • The high–tech industry has a positive “U–shaped” nonlinear effect in other regions. • The linear impact of the high–tech industry in the eastern region is the strongest.« less

Using Recursive Regression to Explore Nonlinear Relationships and Interactions: A Tutorial Applied to a Multicultural Education Study

ERIC Educational Resources Information Center

Strang, Kenneth David

2009-01-01

This paper discusses how a seldom-used statistical procedure, recursive regression (RR), can numerically and graphically illustrate data-driven nonlinear relationships and interaction of variables. This routine falls into the family of exploratory techniques, yet a few interesting features make it a valuable compliment to factor analysis and…

The ice age cycle and the deglaciations: an application of nonlinear regression modelling

NASA Astrophysics Data System (ADS)

Dalgleish, A. N.; Boulton, G. S.; Renshaw, E.

2000-03-01

We have applied the nonlinear regression technique known as additivity and variance stabilisation (AVAS) to time series which reflect Earth's climate over the last 600 ka. AVAS estimates a smooth, nonlinear transform for each variable, under the assumption of an additive model. The Earth's orbital parameters and insolation variations have been used as regression variables. Analysis of the contribution of each variable shows that the deglaciations are characterised by periods of increasing obliquity and perihelion approaching the vernal equinox, but not by any systematic change in eccentricity. The magnitude of insolation changes also plays no role. By approximating the transforms we can obtain a future prediction, with a glacial maximum at 60 ka AP, and a subsequent obliquity and precession forced deglaciation.

Multiple-Shrinkage Multinomial Probit Models with Applications to Simulating Geographies in Public Use Data.

PubMed

Burgette, Lane F; Reiter, Jerome P

2013-06-01

Multinomial outcomes with many levels can be challenging to model. Information typically accrues slowly with increasing sample size, yet the parameter space expands rapidly with additional covariates. Shrinking all regression parameters towards zero, as often done in models of continuous or binary response variables, is unsatisfactory, since setting parameters equal to zero in multinomial models does not necessarily imply "no effect." We propose an approach to modeling multinomial outcomes with many levels based on a Bayesian multinomial probit (MNP) model and a multiple shrinkage prior distribution for the regression parameters. The prior distribution encourages the MNP regression parameters to shrink toward a number of learned locations, thereby substantially reducing the dimension of the parameter space. Using simulated data, we compare the predictive performance of this model against two other recently-proposed methods for big multinomial models. The results suggest that the fully Bayesian, multiple shrinkage approach can outperform these other methods. We apply the multiple shrinkage MNP to simulating replacement values for areal identifiers, e.g., census tract indicators, in order to protect data confidentiality in public use datasets.

Genomic Prediction of Genotype × Environment Interaction Kernel Regression Models.

PubMed

Cuevas, Jaime; Crossa, José; Soberanis, Víctor; Pérez-Elizalde, Sergio; Pérez-Rodríguez, Paulino; Campos, Gustavo de Los; Montesinos-López, O A; Burgueño, Juan

2016-11-01

In genomic selection (GS), genotype × environment interaction (G × E) can be modeled by a marker × environment interaction (M × E). The G × E may be modeled through a linear kernel or a nonlinear (Gaussian) kernel. In this study, we propose using two nonlinear Gaussian kernels: the reproducing kernel Hilbert space with kernel averaging (RKHS KA) and the Gaussian kernel with the bandwidth estimated through an empirical Bayesian method (RKHS EB). We performed single-environment analyses and extended to account for G × E interaction (GBLUP-G × E, RKHS KA-G × E and RKHS EB-G × E) in wheat ( L.) and maize ( L.) data sets. For single-environment analyses of wheat and maize data sets, RKHS EB and RKHS KA had higher prediction accuracy than GBLUP for all environments. For the wheat data, the RKHS KA-G × E and RKHS EB-G × E models did show up to 60 to 68% superiority over the corresponding single environment for pairs of environments with positive correlations. For the wheat data set, the models with Gaussian kernels had accuracies up to 17% higher than that of GBLUP-G × E. For the maize data set, the prediction accuracy of RKHS EB-G × E and RKHS KA-G × E was, on average, 5 to 6% higher than that of GBLUP-G × E. The superiority of the Gaussian kernel models over the linear kernel is due to more flexible kernels that accounts for small, more complex marker main effects and marker-specific interaction effects. Copyright © 2016 Crop Science Society of America.

Pathway analysis of high-throughput biological data within a Bayesian network framework.

PubMed

Isci, Senol; Ozturk, Cengizhan; Jones, Jon; Otu, Hasan H

2011-06-15

Most current approaches to high-throughput biological data (HTBD) analysis either perform individual gene/protein analysis or, gene/protein set enrichment analysis for a list of biologically relevant molecules. Bayesian Networks (BNs) capture linear and non-linear interactions, handle stochastic events accounting for noise, and focus on local interactions, which can be related to causal inference. Here, we describe for the first time an algorithm that models biological pathways as BNs and identifies pathways that best explain given HTBD by scoring fitness of each network. Proposed method takes into account the connectivity and relatedness between nodes of the pathway through factoring pathway topology in its model. Our simulations using synthetic data demonstrated robustness of our approach. We tested proposed method, Bayesian Pathway Analysis (BPA), on human microarray data regarding renal cell carcinoma (RCC) and compared our results with gene set enrichment analysis. BPA was able to find broader and more specific pathways related to RCC. Accompanying BPA software (BPAS) package is freely available for academic use at http://bumil.boun.edu.tr/bpa.

An efficient method for model refinement in diffuse optical tomography

NASA Astrophysics Data System (ADS)

Zirak, A. R.; Khademi, M.

2007-11-01

Diffuse optical tomography (DOT) is a non-linear, ill-posed, boundary value and optimization problem which necessitates regularization. Also, Bayesian methods are suitable owing to measurements data are sparse and correlated. In such problems which are solved with iterative methods, for stabilization and better convergence, the solution space must be small. These constraints subject to extensive and overdetermined system of equations which model retrieving criteria specially total least squares (TLS) must to refine model error. Using TLS is limited to linear systems which is not achievable when applying traditional Bayesian methods. This paper presents an efficient method for model refinement using regularized total least squares (RTLS) for treating on linearized DOT problem, having maximum a posteriori (MAP) estimator and Tikhonov regulator. This is done with combination Bayesian and regularization tools as preconditioner matrices, applying them to equations and then using RTLS to the resulting linear equations. The preconditioning matrixes are guided by patient specific information as well as a priori knowledge gained from the training set. Simulation results illustrate that proposed method improves the image reconstruction performance and localize the abnormally well.

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.

Prediction of residual feed intake for first-lactation dairy cows using orthogonal polynomial random regression.

PubMed

Manafiazar, G; McFadden, T; Goonewardene, L; Okine, E; Basarab, J; Li, P; Wang, Z

2013-01-01

Residual Feed Intake (RFI) is a measure of energy efficiency. Developing an appropriate model to predict expected energy intake while accounting for multifunctional energy requirements of metabolic body weight (MBW), empty body weight (EBW), milk production energy requirements (MPER), and their nonlinear lactation profiles, is the key to successful prediction of RFI in dairy cattle. Individual daily actual energy intake and monthly body weight of 281 first-lactation dairy cows from 1 to 305 d in milk were recorded at the Dairy Research and Technology Centre of the University of Alberta (Edmonton, AB, Canada); individual monthly milk yield and compositions were obtained from the Dairy Herd Improvement Program. Combinations of different orders (1-5) of fixed (F) and random (R) factors were fitted using Legendre polynomial regression to model the nonlinear lactation profiles of MBW, EBW, and MPER over 301 d. The F5R3, F5R3, and F5R2 (subscripts indicate the order fitted) models were selected, based on the combination of the log-likelihood ratio test and the Bayesian information criterion, as the best prediction equations for MBW, EBW, and MPER, respectively. The selected models were used to predict daily individual values for these traits. To consider the body reserve changes, the differences of predicted EBW between 2 consecutive days were considered as the EBW change between these days. The smoothed total 301-d actual energy intake was then linearly regressed on the total 301-d predicted traits of MBW, EBW change, and MPER to obtain the first-lactation RFI (coefficient of determination=0.68). The mean of predicted daily average lactation RFI was 0 and ranged from -6.58 to 8.64 Mcal of NE(L)/d. Fifty-one percent of the animals had an RFI value below the mean (efficient) and 49% of them had an RFI value above the mean (inefficient). These results indicate that the first-lactation RFI can be predicted from its component traits with a reasonable coefficient of determination. The predicted RFI could be used in the dairy breeding program to increase profitability by selecting animals that are genetically superior in energy efficiency based on RFI, or through routinely measured traits, which are genetically correlated with RFI. Copyright © 2013 American Dairy Science Association. Published by Elsevier Inc. All rights reserved.

Sampling schemes and parameter estimation for nonlinear Bernoulli-Gaussian sparse models

NASA Astrophysics Data System (ADS)

Boudineau, Mégane; Carfantan, Hervé; Bourguignon, Sébastien; Bazot, Michael

2016-06-01

We address the sparse approximation problem in the case where the data are approximated by the linear combination of a small number of elementary signals, each of these signals depending non-linearly on additional parameters. Sparsity is explicitly expressed through a Bernoulli-Gaussian hierarchical model in a Bayesian framework. Posterior mean estimates are computed using Markov Chain Monte-Carlo algorithms. We generalize the partially marginalized Gibbs sampler proposed in the linear case in [1], and build an hybrid Hastings-within-Gibbs algorithm in order to account for the nonlinear parameters. All model parameters are then estimated in an unsupervised procedure. The resulting method is evaluated on a sparse spectral analysis problem. It is shown to converge more efficiently than the classical joint estimation procedure, with only a slight increase of the computational cost per iteration, consequently reducing the global cost of the estimation procedure.

A method for nonlinear exponential regression analysis

NASA Technical Reports Server (NTRS)

Junkin, B. G.

1971-01-01

A computer-oriented technique is presented for performing a nonlinear exponential regression analysis on decay-type experimental data. The technique involves the least squares procedure wherein the nonlinear problem is linearized by expansion in a Taylor series. A linear curve fitting procedure for determining the initial nominal estimates for the unknown exponential model parameters is included as an integral part of the technique. A correction matrix was derived and then applied to the nominal estimate to produce an improved set of model parameters. The solution cycle is repeated until some predetermined criterion is satisfied.

Ozone and childhood respiratory disease in three US cities: evaluation of effect measure modification by neighborhood socioeconomic status using a Bayesian hierarchical approach.

PubMed

O' Lenick, Cassandra R; Chang, Howard H; Kramer, Michael R; Winquist, Andrea; Mulholland, James A; Friberg, Mariel D; Sarnat, Stefanie Ebelt

2017-04-05

Ground-level ozone is a potent airway irritant and a determinant of respiratory morbidity. Susceptibility to the health effects of ambient ozone may be influenced by both intrinsic and extrinsic factors, such as neighborhood socioeconomic status (SES). Questions remain regarding the manner and extent that factors such as SES influence ozone-related health effects, particularly across different study areas. Using a 2-stage modeling approach we evaluated neighborhood SES as a modifier of ozone-related pediatric respiratory morbidity in Atlanta, Dallas, & St. Louis. We acquired multi-year data on emergency department (ED) visits among 5-18 year olds with a primary diagnosis of respiratory disease in each city. Daily concentrations of 8-h maximum ambient ozone were estimated for all ZIP Code Tabulation Areas (ZCTA) in each city by fusing observed concentration data from available network monitors with simulations from an emissions-based chemical transport model. In the first stage, we used conditional logistic regression to estimate ZCTA-specific odds ratios (OR) between ozone and respiratory ED visits, controlling for temporal trends and meteorology. In the second stage, we combined ZCTA-level estimates in a Bayesian hierarchical model to assess overall associations and effect modification by neighborhood SES considering categorical and continuous SES indicators (e.g., ZCTA-specific levels of poverty). We estimated ORs and 95% posterior intervals (PI) for a 25 ppb increase in ozone. The hierarchical model combined effect estimates from 179 ZCTAs in Atlanta, 205 ZCTAs in Dallas, and 151 ZCTAs in St. Louis. The strongest overall association of ozone and pediatric respiratory disease was in Atlanta (OR = 1.08, 95% PI: 1.06, 1.11), followed by Dallas (OR = 1.04, 95% PI: 1.01, 1.07) and St. Louis (OR = 1.03, 95% PI: 0.99, 1.07). Patterns of association across levels of neighborhood SES in each city suggested stronger ORs in low compared to high SES areas, with some evidence of non-linear effect modification. Results suggest that ozone is associated with pediatric respiratory morbidity in multiple US cities; neighborhood SES may modify this association in a non-linear manner. In each city, children living in low SES environments appear to be especially vulnerable given positive ORs and high underlying rates of respiratory morbidity.

Bayesian Factor Analysis as a Variable Selection Problem: Alternative Priors and Consequences

PubMed Central

Lu, Zhao-Hua; Chow, Sy-Miin; Loken, Eric

2016-01-01

Factor analysis is a popular statistical technique for multivariate data analysis. Developments in the structural equation modeling framework have enabled the use of hybrid confirmatory/exploratory approaches in which factor loading structures can be explored relatively flexibly within a confirmatory factor analysis (CFA) framework. Recently, a Bayesian structural equation modeling (BSEM) approach (Muthén & Asparouhov, 2012) has been proposed as a way to explore the presence of cross-loadings in CFA models. We show that the issue of determining factor loading patterns may be formulated as a Bayesian variable selection problem in which Muthén and Asparouhov’s approach can be regarded as a BSEM approach with ridge regression prior (BSEM-RP). We propose another Bayesian approach, denoted herein as the Bayesian structural equation modeling with spike and slab prior (BSEM-SSP), which serves as a one-stage alternative to the BSEM-RP. We review the theoretical advantages and disadvantages of both approaches and compare their empirical performance relative to two modification indices-based approaches and exploratory factor analysis with target rotation. A teacher stress scale data set (Byrne, 2012; Pettegrew & Wolf, 1982) is used to demonstrate our approach. PMID:27314566

Bayesian Scalar-on-Image Regression with Application to Association Between Intracranial DTI and Cognitive Outcomes

PubMed Central

Huang, Lei; Goldsmith, Jeff; Reiss, Philip T.; Reich, Daniel S.; Crainiceanu, Ciprian M.

2013-01-01

Diffusion tensor imaging (DTI) measures water diffusion within white matter, allowing for in vivo quantification of brain pathways. These pathways often subserve specific functions, and impairment of those functions is often associated with imaging abnormalities. As a method for predicting clinical disability from DTI images, we propose a hierarchical Bayesian “scalar-on-image” regression procedure. Our procedure introduces a latent binary map that estimates the locations of predictive voxels and penalizes the magnitude of effect sizes in these voxels, thereby resolving the ill-posed nature of the problem. By inducing a spatial prior structure, the procedure yields a sparse association map that also maintains spatial continuity of predictive regions. The method is demonstrated on a simulation study and on a study of association between fractional anisotropy and cognitive disability in a cross-sectional sample of 135 multiple sclerosis patients. PMID:23792220

Bayesian function-on-function regression for multilevel functional data.

PubMed

Meyer, Mark J; Coull, Brent A; Versace, Francesco; Cinciripini, Paul; Morris, Jeffrey S

2015-09-01

Medical and public health research increasingly involves the collection of complex and high dimensional data. In particular, functional data-where the unit of observation is a curve or set of curves that are finely sampled over a grid-is frequently obtained. Moreover, researchers often sample multiple curves per person resulting in repeated functional measures. A common question is how to analyze the relationship between two functional variables. We propose a general function-on-function regression model for repeatedly sampled functional data on a fine grid, presenting a simple model as well as a more extensive mixed model framework, and introducing various functional Bayesian inferential procedures that account for multiple testing. We examine these models via simulation and a data analysis with data from a study that used event-related potentials to examine how the brain processes various types of images. © 2015, The International Biometric Society.

Bayesian Ensemble Trees (BET) for Clustering and Prediction in Heterogeneous Data

PubMed Central

Duan, Leo L.; Clancy, John P.; Szczesniak, Rhonda D.

2016-01-01

We propose a novel “tree-averaging” model that utilizes the ensemble of classification and regression trees (CART). Each constituent tree is estimated with a subset of similar data. We treat this grouping of subsets as Bayesian Ensemble Trees (BET) and model them as a Dirichlet process. We show that BET determines the optimal number of trees by adapting to the data heterogeneity. Compared with the other ensemble methods, BET requires much fewer trees and shows equivalent prediction accuracy using weighted averaging. Moreover, each tree in BET provides variable selection criterion and interpretation for each subset. We developed an efficient estimating procedure with improved estimation strategies in both CART and mixture models. We demonstrate these advantages of BET with simulations and illustrate the approach with a real-world data example involving regression of lung function measurements obtained from patients with cystic fibrosis. Supplemental materials are available online. PMID:27524872

A flexible Bayesian assessment for the expected impact of data on prediction confidence for optimal sampling designs

NASA Astrophysics Data System (ADS)

Leube, Philipp; Geiges, Andreas; Nowak, Wolfgang

2010-05-01

Incorporating hydrogeological data, such as head and tracer data, into stochastic models of subsurface flow and transport helps to reduce prediction uncertainty. Considering limited financial resources available for the data acquisition campaign, information needs towards the prediction goal should be satisfied in a efficient and task-specific manner. For finding the best one among a set of design candidates, an objective function is commonly evaluated, which measures the expected impact of data on prediction confidence, prior to their collection. An appropriate approach to this task should be stochastically rigorous, master non-linear dependencies between data, parameters and model predictions, and allow for a wide variety of different data types. Existing methods fail to fulfill all these requirements simultaneously. For this reason, we introduce a new method, denoted as CLUE (Cross-bred Likelihood Uncertainty Estimator), that derives the essential distributions and measures of data utility within a generalized, flexible and accurate framework. The method makes use of Bayesian GLUE (Generalized Likelihood Uncertainty Estimator) and extends it to an optimal design method by marginalizing over the yet unknown data values. Operating in a purely Bayesian Monte-Carlo framework, CLUE is a strictly formal information processing scheme free of linearizations. It provides full flexibility associated with the type of measurements (linear, non-linear, direct, indirect) and accounts for almost arbitrary sources of uncertainty (e.g. heterogeneity, geostatistical assumptions, boundary conditions, model concepts) via stochastic simulation and Bayesian model averaging. This helps to minimize the strength and impact of possible subjective prior assumptions, that would be hard to defend prior to data collection. Our study focuses on evaluating two different uncertainty measures: (i) expected conditional variance and (ii) expected relative entropy of a given prediction goal. The applicability and advantages are shown in a synthetic example. Therefor, we consider a contaminant source, posing a threat on a drinking water well in an aquifer. Furthermore, we assume uncertainty in geostatistical parameters, boundary conditions and hydraulic gradient. The two mentioned measures evaluate the sensitivity of (1) general prediction confidence and (2) exceedance probability of a legal regulatory threshold value on sampling locations.

Supervised Time Series Event Detector for Building Data

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

2016-04-13

A machine learning based approach is developed to detect events that have rarely been seen in the historical data. The data can include building energy consumption, sensor data, environmental data and any data that may affect the building's energy consumption. The algorithm is a modified nonlinear Bayesian support vector machine, which examines daily energy consumption profile, detect the days with abnormal events, and diagnose the cause of the events.

Bayesian regression models outperform partial least squares methods for predicting milk components and technological properties using infrared spectral data

PubMed Central

Ferragina, A.; de los Campos, G.; Vazquez, A. I.; Cecchinato, A.; Bittante, G.

2017-01-01

The aim of this study was to assess the performance of Bayesian models commonly used for genomic selection to predict “difficult-to-predict” dairy traits, such as milk fatty acid (FA) expressed as percentage of total fatty acids, and technological properties, such as fresh cheese yield and protein recovery, using Fourier-transform infrared (FTIR) spectral data. Our main hypothesis was that Bayesian models that can estimate shrinkage and perform variable selection may improve our ability to predict FA traits and technological traits above and beyond what can be achieved using the current calibration models (e.g., partial least squares, PLS). To this end, we assessed a series of Bayesian methods and compared their prediction performance with that of PLS. The comparison between models was done using the same sets of data (i.e., same samples, same variability, same spectral treatment) for each trait. Data consisted of 1,264 individual milk samples collected from Brown Swiss cows for which gas chromatographic FA composition, milk coagulation properties, and cheese-yield traits were available. For each sample, 2 spectra in the infrared region from 5,011 to 925 cm−1 were available and averaged before data analysis. Three Bayesian models: Bayesian ridge regression (Bayes RR), Bayes A, and Bayes B, and 2 reference models: PLS and modified PLS (MPLS) procedures, were used to calibrate equations for each of the traits. The Bayesian models used were implemented in the R package BGLR (http://cran.r-project.org/web/packages/BGLR/index.html), whereas the PLS and MPLS were those implemented in the WinISI II software (Infrasoft International LLC, State College, PA). Prediction accuracy was estimated for each trait and model using 25 replicates of a training-testing validation procedure. Compared with PLS, which is currently the most widely used calibration method, MPLS and the 3 Bayesian methods showed significantly greater prediction accuracy. Accuracy increased in moving from calibration to external validation methods, and in moving from PLS and MPLS to Bayesian methods, particularly Bayes A and Bayes B. The maximum R2 value of validation was obtained with Bayes B and Bayes A. For the FA, C10:0 (% of each FA on total FA basis) had the highest R2 (0.75, achieved with Bayes A and Bayes B), and among the technological traits, fresh cheese yield R2 of 0.82 (achieved with Bayes B). These 2 methods have proven to be useful instruments in shrinking and selecting very informative wavelengths and inferring the structure and functions of the analyzed traits. We conclude that Bayesian models are powerful tools for deriving calibration equations, and, importantly, these equations can be easily developed using existing open-source software. As part of our study, we provide scripts based on the open source R software BGLR, which can be used to train customized prediction equations for other traits or populations. PMID:26387015

Bayesian integration and non-linear feedback control in a full-body motor task.

PubMed

Stevenson, Ian H; Fernandes, Hugo L; Vilares, Iris; Wei, Kunlin; Körding, Konrad P

2009-12-01

A large number of experiments have asked to what degree human reaching movements can be understood as being close to optimal in a statistical sense. However, little is known about whether these principles are relevant for other classes of movements. Here we analyzed movement in a task that is similar to surfing or snowboarding. Human subjects stand on a force plate that measures their center of pressure. This center of pressure affects the acceleration of a cursor that is displayed in a noisy fashion (as a cloud of dots) on a projection screen while the subject is incentivized to keep the cursor close to a fixed position. We find that salient aspects of observed behavior are well-described by optimal control models where a Bayesian estimation model (Kalman filter) is combined with an optimal controller (either a Linear-Quadratic-Regulator or Bang-bang controller). We find evidence that subjects integrate information over time taking into account uncertainty. However, behavior in this continuous steering task appears to be a highly non-linear function of the visual feedback. While the nervous system appears to implement Bayes-like mechanisms for a full-body, dynamic task, it may additionally take into account the specific costs and constraints of the task.

Nonlinear dynamic model for visual object tracking on Grassmann manifolds with partial occlusion handling.

PubMed

Khan, Zulfiqar Hasan; Gu, Irene Yu-Hua

2013-12-01

This paper proposes a novel Bayesian online learning and tracking scheme for video objects on Grassmann manifolds. Although manifold visual object tracking is promising, large and fast nonplanar (or out-of-plane) pose changes and long-term partial occlusions of deformable objects in video remain a challenge that limits the tracking performance. The proposed method tackles these problems with the main novelties on: 1) online estimation of object appearances on Grassmann manifolds; 2) optimal criterion-based occlusion handling for online updating of object appearances; 3) a nonlinear dynamic model for both the appearance basis matrix and its velocity; and 4) Bayesian formulations, separately for the tracking process and the online learning process, that are realized by employing two particle filters: one is on the manifold for generating appearance particles and another on the linear space for generating affine box particles. Tracking and online updating are performed in an alternating fashion to mitigate the tracking drift. Experiments using the proposed tracker on videos captured by a single dynamic/static camera have shown robust tracking performance, particularly for scenarios when target objects contain significant nonplanar pose changes and long-term partial occlusions. Comparisons with eight existing state-of-the-art/most relevant manifold/nonmanifold trackers with evaluations have provided further support to the proposed scheme.

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.

"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.

Quasi-Likelihood Techniques in a Logistic Regression Equation for Identifying Simulium damnosum s.l. Larval Habitats Intra-cluster Covariates in Togo.

PubMed

Jacob, Benjamin G; Novak, Robert J; Toe, Laurent; Sanfo, Moussa S; Afriyie, Abena N; Ibrahim, Mohammed A; Griffith, Daniel A; Unnasch, Thomas R

2012-01-01

The standard methods for regression analyses of clustered riverine larval habitat data of Simulium damnosum s.l. a major black-fly vector of Onchoceriasis, postulate models relating observational ecological-sampled parameter estimators to prolific habitats without accounting for residual intra-cluster error correlation effects. Generally, this correlation comes from two sources: (1) the design of the random effects and their assumed covariance from the multiple levels within the regression model; and, (2) the correlation structure of the residuals. Unfortunately, inconspicuous errors in residual intra-cluster correlation estimates can overstate precision in forecasted S.damnosum s.l. riverine larval habitat explanatory attributes regardless how they are treated (e.g., independent, autoregressive, Toeplitz, etc). In this research, the geographical locations for multiple riverine-based S. damnosum s.l. larval ecosystem habitats sampled from 2 pre-established epidemiological sites in Togo were identified and recorded from July 2009 to June 2010. Initially the data was aggregated into proc genmod. An agglomerative hierarchical residual cluster-based analysis was then performed. The sampled clustered study site data was then analyzed for statistical correlations using Monthly Biting Rates (MBR). Euclidean distance measurements and terrain-related geomorphological statistics were then generated in ArcGIS. A digital overlay was then performed also in ArcGIS using the georeferenced ground coordinates of high and low density clusters stratified by Annual Biting Rates (ABR). This data was overlain onto multitemporal sub-meter pixel resolution satellite data (i.e., QuickBird 0.61m wavbands ). Orthogonal spatial filter eigenvectors were then generated in SAS/GIS. Univariate and non-linear regression-based models (i.e., Logistic, Poisson and Negative Binomial) were also employed to determine probability distributions and to identify statistically significant parameter estimators from the sampled data. Thereafter, Durbin-Watson test statistics were used to test the null hypothesis that the regression residuals were not autocorrelated against the alternative that the residuals followed an autoregressive process in AUTOREG. Bayesian uncertainty matrices were also constructed employing normal priors for each of the sampled estimators in PROC MCMC. The residuals revealed both spatially structured and unstructured error effects in the high and low ABR-stratified clusters. The analyses also revealed that the estimators, levels of turbidity and presence of rocks were statistically significant for the high-ABR-stratified clusters, while the estimators distance between habitats and floating vegetation were important for the low-ABR-stratified cluster. Varying and constant coefficient regression models, ABR- stratified GIS-generated clusters, sub-meter resolution satellite imagery, a robust residual intra-cluster diagnostic test, MBR-based histograms, eigendecomposition spatial filter algorithms and Bayesian matrices can enable accurate autoregressive estimation of latent uncertainity affects and other residual error probabilities (i.e., heteroskedasticity) for testing correlations between georeferenced S. damnosum s.l. riverine larval habitat estimators. The asymptotic distribution of the resulting residual adjusted intra-cluster predictor error autocovariate coefficients can thereafter be established while estimates of the asymptotic variance can lead to the construction of approximate confidence intervals for accurately targeting productive S. damnosum s.l habitats based on spatiotemporal field-sampled count data.

Non-ignorable missingness in logistic regression.

PubMed

Wang, Joanna J J; Bartlett, Mark; Ryan, Louise

2017-08-30

Nonresponses and missing data are common in observational studies. Ignoring or inadequately handling missing data may lead to biased parameter estimation, incorrect standard errors and, as a consequence, incorrect statistical inference and conclusions. We present a strategy for modelling non-ignorable missingness where the probability of nonresponse depends on the outcome. Using a simple case of logistic regression, we quantify the bias in regression estimates and show the observed likelihood is non-identifiable under non-ignorable missing data mechanism. We then adopt a selection model factorisation of the joint distribution as the basis for a sensitivity analysis to study changes in estimated parameters and the robustness of study conclusions against different assumptions. A Bayesian framework for model estimation is used as it provides a flexible approach for incorporating different missing data assumptions and conducting sensitivity analysis. Using simulated data, we explore the performance of the Bayesian selection model in correcting for bias in a logistic regression. We then implement our strategy using survey data from the 45 and Up Study to investigate factors associated with worsening health from the baseline to follow-up survey. Our findings have practical implications for the use of the 45 and Up Study data to answer important research questions relating to health and quality-of-life. Copyright © 2017 John Wiley & Sons, Ltd. Copyright © 2017 John Wiley & Sons, Ltd.

Determinants of medication adherence in older people with dementia from the caregivers' perspective.

PubMed

El-Saifi, Najwan; Moyle, Wendy; Jones, Cindy; Alston-Knox, Clair

2018-05-11

ABSTRACTBackground:Adherence to treatment is a primary determinant of treatment success. Caregiver support can influence medication adherence in people with cognitive impairment. This study sought to characterize medication adherence in older people with dementia from the caregivers' perspective, and to identify influencing factors. Caregivers caring for a person with dementia and living in the community were eligible to complete the survey. Bayesian profile regression was applied to identify determinants of medication adherence measured using the Adherence to Refills and Medication Scale. Out of the 320 caregivers who participated in the survey, Bayesian profile regression on 221 participants identified two groups: Profile 1 (55 caregivers) with a mean adherence rate of 0.69 (80% Credible Interval (CrI): 0.61-0.77), and Profile 2 (166 caregivers) with a mean adherence rate of 0.80 (80% CrI: 0.77-0.84). Caregivers in Profile 1 were characterized with below data average scores for the following: cognitive functioning, commitment or intention, self-efficacy, and health knowledge, which were all above the data average in Profile 2, except for health knowledge. Caregivers in Profile 1 had a greater proportion of care recipients taking more than five medications and with late-stage dementia. Trade, technical, or vocational training was more common among the caregivers in Profile 1. Profile 2 caregivers had a better patient-provider relationship and less medical problems. Bayesian profile regression was useful in understanding caregiver factors that influence medication adherence. Tailored interventions to the determinants of medication adherence can guide the development of evidence-based interventions.

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

A Bayesian Hierarchical Modeling Approach to Predicting Flow in Ungauged Basins

EPA Science Inventory

Recent innovative approaches to identifying and applying regression-based relationships between land use patterns (such as increasing impervious surface area and decreasing vegetative cover) and rainfall-runoff model parameters represent novel and promising improvements to predic...

Bayesian models for comparative analysis integrating phylogenetic uncertainty.

PubMed

de Villemereuil, Pierre; Wells, Jessie A; Edwards, Robert D; Blomberg, Simon P

2012-06-28

Uncertainty in comparative analyses can come from at least two sources: a) phylogenetic uncertainty in the tree topology or branch lengths, and b) uncertainty due to intraspecific variation in trait values, either due to measurement error or natural individual variation. Most phylogenetic comparative methods do not account for such uncertainties. Not accounting for these sources of uncertainty leads to false perceptions of precision (confidence intervals will be too narrow) and inflated significance in hypothesis testing (e.g. p-values will be too small). Although there is some application-specific software for fitting Bayesian models accounting for phylogenetic error, more general and flexible software is desirable. We developed models to directly incorporate phylogenetic uncertainty into a range of analyses that biologists commonly perform, using a Bayesian framework and Markov Chain Monte Carlo analyses. We demonstrate applications in linear regression, quantification of phylogenetic signal, and measurement error models. Phylogenetic uncertainty was incorporated by applying a prior distribution for the phylogeny, where this distribution consisted of the posterior tree sets from Bayesian phylogenetic tree estimation programs. The models were analysed using simulated data sets, and applied to a real data set on plant traits, from rainforest plant species in Northern Australia. Analyses were performed using the free and open source software OpenBUGS and JAGS. Incorporating phylogenetic uncertainty through an empirical prior distribution of trees leads to more precise estimation of regression model parameters than using a single consensus tree and enables a more realistic estimation of confidence intervals. In addition, models incorporating measurement errors and/or individual variation, in one or both variables, are easily formulated in the Bayesian framework. We show that BUGS is a useful, flexible general purpose tool for phylogenetic comparative analyses, particularly for modelling in the face of phylogenetic uncertainty and accounting for measurement error or individual variation in explanatory variables. Code for all models is provided in the BUGS model description language.

Bayesian models for comparative analysis integrating phylogenetic uncertainty

PubMed Central

2012-01-01

Background Uncertainty in comparative analyses can come from at least two sources: a) phylogenetic uncertainty in the tree topology or branch lengths, and b) uncertainty due to intraspecific variation in trait values, either due to measurement error or natural individual variation. Most phylogenetic comparative methods do not account for such uncertainties. Not accounting for these sources of uncertainty leads to false perceptions of precision (confidence intervals will be too narrow) and inflated significance in hypothesis testing (e.g. p-values will be too small). Although there is some application-specific software for fitting Bayesian models accounting for phylogenetic error, more general and flexible software is desirable. Methods We developed models to directly incorporate phylogenetic uncertainty into a range of analyses that biologists commonly perform, using a Bayesian framework and Markov Chain Monte Carlo analyses. Results We demonstrate applications in linear regression, quantification of phylogenetic signal, and measurement error models. Phylogenetic uncertainty was incorporated by applying a prior distribution for the phylogeny, where this distribution consisted of the posterior tree sets from Bayesian phylogenetic tree estimation programs. The models were analysed using simulated data sets, and applied to a real data set on plant traits, from rainforest plant species in Northern Australia. Analyses were performed using the free and open source software OpenBUGS and JAGS. Conclusions Incorporating phylogenetic uncertainty through an empirical prior distribution of trees leads to more precise estimation of regression model parameters than using a single consensus tree and enables a more realistic estimation of confidence intervals. In addition, models incorporating measurement errors and/or individual variation, in one or both variables, are easily formulated in the Bayesian framework. We show that BUGS is a useful, flexible general purpose tool for phylogenetic comparative analyses, particularly for modelling in the face of phylogenetic uncertainty and accounting for measurement error or individual variation in explanatory variables. Code for all models is provided in the BUGS model description language. PMID:22741602

Bayesian Statistics and Uncertainty Quantification for Safety Boundary Analysis in Complex Systems

NASA Technical Reports Server (NTRS)

He, Yuning; Davies, Misty Dawn

2014-01-01

The analysis of a safety-critical system often requires detailed knowledge of safe regions and their highdimensional non-linear boundaries. We present a statistical approach to iteratively detect and characterize the boundaries, which are provided as parameterized shape candidates. Using methods from uncertainty quantification and active learning, we incrementally construct a statistical model from only few simulation runs and obtain statistically sound estimates of the shape parameters for safety boundaries.

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.

Detecting influential observations in nonlinear regression modeling of groundwater flow

USGS Publications Warehouse

Yager, Richard M.

1998-01-01

Nonlinear regression is used to estimate optimal parameter values in models of groundwater flow to ensure that differences between predicted and observed heads and flows do not result from nonoptimal parameter values. Parameter estimates can be affected, however, by observations that disproportionately influence the regression, such as outliers that exert undue leverage on the objective function. Certain statistics developed for linear regression can be used to detect influential observations in nonlinear regression if the models are approximately linear. This paper discusses the application of Cook's D, which measures the effect of omitting a single observation on a set of estimated parameter values, and the statistical parameter DFBETAS, which quantifies the influence of an observation on each parameter. The influence statistics were used to (1) identify the influential observations in the calibration of a three-dimensional, groundwater flow model of a fractured-rock aquifer through nonlinear regression, and (2) quantify the effect of omitting influential observations on the set of estimated parameter values. Comparison of the spatial distribution of Cook's D with plots of model sensitivity shows that influential observations correspond to areas where the model heads are most sensitive to certain parameters, and where predicted groundwater flow rates are largest. Five of the six discharge observations were identified as influential, indicating that reliable measurements of groundwater flow rates are valuable data in model calibration. DFBETAS are computed and examined for an alternative model of the aquifer system to identify a parameterization error in the model design that resulted in overestimation of the effect of anisotropy on horizontal hydraulic conductivity.

Estimating monotonic rates from biological data using local linear regression.

PubMed

Olito, Colin; White, Craig R; Marshall, Dustin J; Barneche, Diego R

2017-03-01

Accessing many fundamental questions in biology begins with empirical estimation of simple monotonic rates of underlying biological processes. Across a variety of disciplines, ranging from physiology to biogeochemistry, these rates are routinely estimated from non-linear and noisy time series data using linear regression and ad hoc manual truncation of non-linearities. Here, we introduce the R package LoLinR, a flexible toolkit to implement local linear regression techniques to objectively and reproducibly estimate monotonic biological rates from non-linear time series data, and demonstrate possible applications using metabolic rate data. LoLinR provides methods to easily and reliably estimate monotonic rates from time series data in a way that is statistically robust, facilitates reproducible research and is applicable to a wide variety of research disciplines in the biological sciences. © 2017. Published by The Company of Biologists Ltd.

Order Selection for General Expression of Nonlinear Autoregressive Model Based on Multivariate Stepwise Regression

NASA Astrophysics Data System (ADS)

Shi, Jinfei; Zhu, Songqing; Chen, Ruwen

2017-12-01

An order selection method based on multiple stepwise regressions is proposed for General Expression of Nonlinear Autoregressive model which converts the model order problem into the variable selection of multiple linear regression equation. The partial autocorrelation function is adopted to define the linear term in GNAR model. The result is set as the initial model, and then the nonlinear terms are introduced gradually. Statistics are chosen to study the improvements of both the new introduced and originally existed variables for the model characteristics, which are adopted to determine the model variables to retain or eliminate. So the optimal model is obtained through data fitting effect measurement or significance test. The simulation and classic time-series data experiment results show that the method proposed is simple, reliable and can be applied to practical engineering.

Robust, Adaptive Functional Regression in Functional Mixed Model Framework.

PubMed

Zhu, Hongxiao; Brown, Philip J; Morris, Jeffrey S

2011-09-01

Functional data are increasingly encountered in scientific studies, and their high dimensionality and complexity lead to many analytical challenges. Various methods for functional data analysis have been developed, including functional response regression methods that involve regression of a functional response on univariate/multivariate predictors with nonparametrically represented functional coefficients. In existing methods, however, the functional regression can be sensitive to outlying curves and outlying regions of curves, so is not robust. In this paper, we introduce a new Bayesian method, robust functional mixed models (R-FMM), for performing robust functional regression within the general functional mixed model framework, which includes multiple continuous or categorical predictors and random effect functions accommodating potential between-function correlation induced by the experimental design. The underlying model involves a hierarchical scale mixture model for the fixed effects, random effect and residual error functions. These modeling assumptions across curves result in robust nonparametric estimators of the fixed and random effect functions which down-weight outlying curves and regions of curves, and produce statistics that can be used to flag global and local outliers. These assumptions also lead to distributions across wavelet coefficients that have outstanding sparsity and adaptive shrinkage properties, with great flexibility for the data to determine the sparsity and the heaviness of the tails. Together with the down-weighting of outliers, these within-curve properties lead to fixed and random effect function estimates that appear in our simulations to be remarkably adaptive in their ability to remove spurious features yet retain true features of the functions. We have developed general code to implement this fully Bayesian method that is automatic, requiring the user to only provide the functional data and design matrices. It is efficient enough to handle large data sets, and yields posterior samples of all model parameters that can be used to perform desired Bayesian estimation and inference. Although we present details for a specific implementation of the R-FMM using specific distributional choices in the hierarchical model, 1D functions, and wavelet transforms, the method can be applied more generally using other heavy-tailed distributions, higher dimensional functions (e.g. images), and using other invertible transformations as alternatives to wavelets.

Robust, Adaptive Functional Regression in Functional Mixed Model Framework

PubMed Central

Zhu, Hongxiao; Brown, Philip J.; Morris, Jeffrey S.

2012-01-01

Functional data are increasingly encountered in scientific studies, and their high dimensionality and complexity lead to many analytical challenges. Various methods for functional data analysis have been developed, including functional response regression methods that involve regression of a functional response on univariate/multivariate predictors with nonparametrically represented functional coefficients. In existing methods, however, the functional regression can be sensitive to outlying curves and outlying regions of curves, so is not robust. In this paper, we introduce a new Bayesian method, robust functional mixed models (R-FMM), for performing robust functional regression within the general functional mixed model framework, which includes multiple continuous or categorical predictors and random effect functions accommodating potential between-function correlation induced by the experimental design. The underlying model involves a hierarchical scale mixture model for the fixed effects, random effect and residual error functions. These modeling assumptions across curves result in robust nonparametric estimators of the fixed and random effect functions which down-weight outlying curves and regions of curves, and produce statistics that can be used to flag global and local outliers. These assumptions also lead to distributions across wavelet coefficients that have outstanding sparsity and adaptive shrinkage properties, with great flexibility for the data to determine the sparsity and the heaviness of the tails. Together with the down-weighting of outliers, these within-curve properties lead to fixed and random effect function estimates that appear in our simulations to be remarkably adaptive in their ability to remove spurious features yet retain true features of the functions. We have developed general code to implement this fully Bayesian method that is automatic, requiring the user to only provide the functional data and design matrices. It is efficient enough to handle large data sets, and yields posterior samples of all model parameters that can be used to perform desired Bayesian estimation and inference. Although we present details for a specific implementation of the R-FMM using specific distributional choices in the hierarchical model, 1D functions, and wavelet transforms, the method can be applied more generally using other heavy-tailed distributions, higher dimensional functions (e.g. images), and using other invertible transformations as alternatives to wavelets. PMID:22308015

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.

A simplified competition data analysis for radioligand specific activity determination.

PubMed

Venturino, A; Rivera, E S; Bergoc, R M; Caro, R A

1990-01-01

Non-linear regression and two-step linear fit methods were developed to determine the actual specific activity of 125I-ovine prolactin by radioreceptor self-displacement analysis. The experimental results obtained by the different methods are superposable. The non-linear regression method is considered to be the most adequate procedure to calculate the specific activity, but if its software is not available, the other described methods are also suitable.

Bayesian kernel machine regression for estimating the health effects of multi-pollutant mixtures.

PubMed

Bobb, Jennifer F; Valeri, Linda; Claus Henn, Birgit; Christiani, David C; Wright, Robert O; Mazumdar, Maitreyi; Godleski, John J; Coull, Brent A

2015-07-01

Because humans are invariably exposed to complex chemical mixtures, estimating the health effects of multi-pollutant exposures is of critical concern in environmental epidemiology, and to regulatory agencies such as the U.S. Environmental Protection Agency. However, most health effects studies focus on single agents or consider simple two-way interaction models, in part because we lack the statistical methodology to more realistically capture the complexity of mixed exposures. We introduce Bayesian kernel machine regression (BKMR) as a new approach to study mixtures, in which the health outcome is regressed on a flexible function of the mixture (e.g. air pollution or toxic waste) components that is specified using a kernel function. In high-dimensional settings, a novel hierarchical variable selection approach is incorporated to identify important mixture components and account for the correlated structure of the mixture. Simulation studies demonstrate the success of BKMR in estimating the exposure-response function and in identifying the individual components of the mixture responsible for health effects. We demonstrate the features of the method through epidemiology and toxicology applications. © The Author 2014. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: journals.permissions@oup.com.

The Bayesian group lasso for confounded spatial data

USGS Publications Warehouse

Hefley, Trevor J.; Hooten, Mevin B.; Hanks, Ephraim M.; Russell, Robin E.; Walsh, Daniel P.

2017-01-01

Generalized linear mixed models for spatial processes are widely used in applied statistics. In many applications of the spatial generalized linear mixed model (SGLMM), the goal is to obtain inference about regression coefficients while achieving optimal predictive ability. When implementing the SGLMM, multicollinearity among covariates and the spatial random effects can make computation challenging and influence inference. We present a Bayesian group lasso prior with a single tuning parameter that can be chosen to optimize predictive ability of the SGLMM and jointly regularize the regression coefficients and spatial random effect. We implement the group lasso SGLMM using efficient Markov chain Monte Carlo (MCMC) algorithms and demonstrate how multicollinearity among covariates and the spatial random effect can be monitored as a derived quantity. To test our method, we compared several parameterizations of the SGLMM using simulated data and two examples from plant ecology and disease ecology. In all examples, problematic levels multicollinearity occurred and influenced sampling efficiency and inference. We found that the group lasso prior resulted in roughly twice the effective sample size for MCMC samples of regression coefficients and can have higher and less variable predictive accuracy based on out-of-sample data when compared to the standard SGLMM.

Predicting Rotator Cuff Tears Using Data Mining and Bayesian Likelihood Ratios

PubMed Central

Lu, Hsueh-Yi; Huang, Chen-Yuan; Su, Chwen-Tzeng; Lin, Chen-Chiang

2014-01-01

Objectives Rotator cuff tear is a common cause of shoulder diseases. Correct diagnosis of rotator cuff tears can save patients from further invasive, costly and painful tests. This study used predictive data mining and Bayesian theory to improve the accuracy of diagnosing rotator cuff tears by clinical examination alone. Methods In this retrospective study, 169 patients who had a preliminary diagnosis of rotator cuff tear on the basis of clinical evaluation followed by confirmatory MRI between 2007 and 2011 were identified. MRI was used as a reference standard to classify rotator cuff tears. The predictor variable was the clinical assessment results, which consisted of 16 attributes. This study employed 2 data mining methods (ANN and the decision tree) and a statistical method (logistic regression) to classify the rotator cuff diagnosis into “tear” and “no tear” groups. Likelihood ratio and Bayesian theory were applied to estimate the probability of rotator cuff tears based on the results of the prediction models. Results Our proposed data mining procedures outperformed the classic statistical method. The correction rate, sensitivity, specificity and area under the ROC curve of predicting a rotator cuff tear were statistical better in the ANN and decision tree models compared to logistic regression. Based on likelihood ratios derived from our prediction models, Fagan's nomogram could be constructed to assess the probability of a patient who has a rotator cuff tear using a pretest probability and a prediction result (tear or no tear). Conclusions Our predictive data mining models, combined with likelihood ratios and Bayesian theory, appear to be good tools to classify rotator cuff tears as well as determine the probability of the presence of the disease to enhance diagnostic decision making for rotator cuff tears. PMID:24733553

Comparison of 3 estimation methods of mycophenolic acid AUC based on a limited sampling strategy in renal transplant patients.

PubMed

Hulin, Anne; Blanchet, Benoît; Audard, Vincent; Barau, Caroline; Furlan, Valérie; Durrbach, Antoine; Taïeb, Fabrice; Lang, Philippe; Grimbert, Philippe; Tod, Michel

2009-04-01

A significant relationship between mycophenolic acid (MPA) area under the plasma concentration-time curve (AUC) and the risk for rejection has been reported. Based on 3 concentration measurements, 3 approaches have been proposed for the estimation of MPA AUC, involving either a multilinear regression approach model (MLRA) or a Bayesian estimation using either gamma absorption or zero-order absorption population models. The aim of the study was to compare the 3 approaches for the estimation of MPA AUC in 150 renal transplant patients treated with mycophenolate mofetil and tacrolimus. The population parameters were determined in 77 patients (learning study). The AUC estimation methods were compared in the learning population and in 73 patients from another center (validation study). In the latter study, the reference AUCs were estimated by the trapezoidal rule on 8 measurements. MPA concentrations were measured by liquid chromatography. The gamma absorption model gave the best fit. In the learning study, the AUCs estimated by both Bayesian methods were very similar, whereas the multilinear approach was highly correlated but yielded estimates about 20% lower than Bayesian methods. This resulted in dosing recommendations differing by 250 mg/12 h or more in 27% of cases. In the validation study, AUC estimates based on the Bayesian method with gamma absorption model and multilinear regression approach model were, respectively, 12% higher and 7% lower than the reference values. To conclude, the bicompartmental model with gamma absorption rate gave the best fit. The 3 AUC estimation methods are highly correlated but not concordant. For a given patient, the same estimation method should always be used.

Learning Instance-Specific Predictive Models

PubMed Central

Visweswaran, Shyam; Cooper, Gregory F.

2013-01-01

This paper introduces a Bayesian algorithm for constructing predictive models from data that are optimized to predict a target variable well for a particular instance. This algorithm learns Markov blanket models, carries out Bayesian model averaging over a set of models to predict a target variable of the instance at hand, and employs an instance-specific heuristic to locate a set of suitable models to average over. We call this method the instance-specific Markov blanket (ISMB) algorithm. The ISMB algorithm was evaluated on 21 UCI data sets using five different performance measures and its performance was compared to that of several commonly used predictive algorithms, including nave Bayes, C4.5 decision tree, logistic regression, neural networks, k-Nearest Neighbor, Lazy Bayesian Rules, and AdaBoost. Over all the data sets, the ISMB algorithm performed better on average on all performance measures against all the comparison algorithms. PMID:25045325

Generalizability of Evidence-Based Assessment Recommendations for Pediatric Bipolar Disorder

PubMed Central

Jenkins, Melissa M.; Youngstrom, Eric A.; Youngstrom, Jennifer Kogos; Feeny, Norah C.; Findling, Robert L.

2013-01-01

Bipolar disorder is frequently clinically diagnosed in youths who do not actually satisfy DSM-IV criteria, yet cases that would satisfy full DSM-IV criteria are often undetected clinically. Evidence-based assessment methods that incorporate Bayesian reasoning have demonstrated improved diagnostic accuracy, and consistency; however, their clinical utility is largely unexplored. The present study examines the effectiveness of promising evidence-based decision-making compared to the clinical gold standard. Participants were 562 youth, ages 5-17 and predominantly African American, drawn from a community mental health clinic. Research diagnoses combined semi-structured interview with youths’ psychiatric, developmental, and family mental health histories. Independent Bayesian estimates relied on published risk estimates from other samples discriminated bipolar diagnoses, Area Under Curve=.75, p<.00005. The Bayes and confidence ratings correlated rs =.30. Agreement about an evidence-based assessment intervention “threshold model” (wait/assess/treat) had K=.24, p<.05. No potential moderators of agreement between the Bayesian estimates and confidence ratings, including type of bipolar illness, were significant. Bayesian risk estimates were highly correlated with logistic regression estimates using optimal sample weights, r=.81, p<.0005. Clinical and Bayesian approaches agree in terms of overall concordance and deciding next clinical action, even when Bayesian predictions are based on published estimates from clinically and demographically different samples. Evidence-based assessment methods may be useful in settings that cannot routinely employ gold standard assessments, and they may help decrease rates of overdiagnosis while promoting earlier identification of true cases. PMID:22004538

Bayesian analysis of time-series data under case-crossover designs: posterior equivalence and inference.

PubMed

Li, Shi; Mukherjee, Bhramar; Batterman, Stuart; Ghosh, Malay

2013-12-01

Case-crossover designs are widely used to study short-term exposure effects on the risk of acute adverse health events. While the frequentist literature on this topic is vast, there is no Bayesian work in this general area. The contribution of this paper is twofold. First, the paper establishes Bayesian equivalence results that require characterization of the set of priors under which the posterior distributions of the risk ratio parameters based on a case-crossover and time-series analysis are identical. Second, the paper studies inferential issues under case-crossover designs in a Bayesian framework. Traditionally, a conditional logistic regression is used for inference on risk-ratio parameters in case-crossover studies. We consider instead a more general full likelihood-based approach which makes less restrictive assumptions on the risk functions. Formulation of a full likelihood leads to growth in the number of parameters proportional to the sample size. We propose a semi-parametric Bayesian approach using a Dirichlet process prior to handle the random nuisance parameters that appear in a full likelihood formulation. We carry out a simulation study to compare the Bayesian methods based on full and conditional likelihood with the standard frequentist approaches for case-crossover and time-series analysis. The proposed methods are illustrated through the Detroit Asthma Morbidity, Air Quality and Traffic study, which examines the association between acute asthma risk and ambient air pollutant concentrations. © 2013, The International Biometric Society.

Data-driven methods towards learning the highly nonlinear inverse kinematics of tendon-driven surgical manipulators.

PubMed

Xu, Wenjun; Chen, Jie; Lau, Henry Y K; Ren, Hongliang

2017-09-01

Accurate motion control of flexible surgical manipulators is crucial in tissue manipulation tasks. The tendon-driven serpentine manipulator (TSM) is one of the most widely adopted flexible mechanisms in minimally invasive surgery because of its enhanced maneuverability in torturous environments. TSM, however, exhibits high nonlinearities and conventional analytical kinematics model is insufficient to achieve high accuracy. To account for the system nonlinearities, we applied a data driven approach to encode the system inverse kinematics. Three regression methods: extreme learning machine (ELM), Gaussian mixture regression (GMR) and K-nearest neighbors regression (KNNR) were implemented to learn a nonlinear mapping from the robot 3D position states to the control inputs. The performance of the three algorithms was evaluated both in simulation and physical trajectory tracking experiments. KNNR performed the best in the tracking experiments, with the lowest RMSE of 2.1275 mm. The proposed inverse kinematics learning methods provide an alternative and efficient way to accurately model the tendon driven flexible manipulator. Copyright © 2016 John Wiley & Sons, Ltd.

Bayesian regression models outperform partial least squares methods for predicting milk components and technological properties using infrared spectral data.

PubMed

Ferragina, A; de los Campos, G; Vazquez, A I; Cecchinato, A; Bittante, G

2015-11-01

The aim of this study was to assess the performance of Bayesian models commonly used for genomic selection to predict "difficult-to-predict" dairy traits, such as milk fatty acid (FA) expressed as percentage of total fatty acids, and technological properties, such as fresh cheese yield and protein recovery, using Fourier-transform infrared (FTIR) spectral data. Our main hypothesis was that Bayesian models that can estimate shrinkage and perform variable selection may improve our ability to predict FA traits and technological traits above and beyond what can be achieved using the current calibration models (e.g., partial least squares, PLS). To this end, we assessed a series of Bayesian methods and compared their prediction performance with that of PLS. The comparison between models was done using the same sets of data (i.e., same samples, same variability, same spectral treatment) for each trait. Data consisted of 1,264 individual milk samples collected from Brown Swiss cows for which gas chromatographic FA composition, milk coagulation properties, and cheese-yield traits were available. For each sample, 2 spectra in the infrared region from 5,011 to 925 cm(-1) were available and averaged before data analysis. Three Bayesian models: Bayesian ridge regression (Bayes RR), Bayes A, and Bayes B, and 2 reference models: PLS and modified PLS (MPLS) procedures, were used to calibrate equations for each of the traits. The Bayesian models used were implemented in the R package BGLR (http://cran.r-project.org/web/packages/BGLR/index.html), whereas the PLS and MPLS were those implemented in the WinISI II software (Infrasoft International LLC, State College, PA). Prediction accuracy was estimated for each trait and model using 25 replicates of a training-testing validation procedure. Compared with PLS, which is currently the most widely used calibration method, MPLS and the 3 Bayesian methods showed significantly greater prediction accuracy. Accuracy increased in moving from calibration to external validation methods, and in moving from PLS and MPLS to Bayesian methods, particularly Bayes A and Bayes B. The maximum R(2) value of validation was obtained with Bayes B and Bayes A. For the FA, C10:0 (% of each FA on total FA basis) had the highest R(2) (0.75, achieved with Bayes A and Bayes B), and among the technological traits, fresh cheese yield R(2) of 0.82 (achieved with Bayes B). These 2 methods have proven to be useful instruments in shrinking and selecting very informative wavelengths and inferring the structure and functions of the analyzed traits. We conclude that Bayesian models are powerful tools for deriving calibration equations, and, importantly, these equations can be easily developed using existing open-source software. As part of our study, we provide scripts based on the open source R software BGLR, which can be used to train customized prediction equations for other traits or populations. Copyright © 2015 American Dairy Science Association. Published by Elsevier Inc. All rights reserved.

Demonstration of leapfrogging for implementing nonlinear model predictive control on a heat exchanger.

PubMed

Sridhar, Upasana Manimegalai; Govindarajan, Anand; Rhinehart, R Russell

2016-01-01

This work reveals the applicability of a relatively new optimization technique, Leapfrogging, for both nonlinear regression modeling and a methodology for nonlinear model-predictive control. Both are relatively simple, yet effective. The application on a nonlinear, pilot-scale, shell-and-tube heat exchanger reveals practicability of the techniques. Copyright © 2015 ISA. Published by Elsevier Ltd. All rights reserved.

Fast Bayesian experimental design: Laplace-based importance sampling for the expected information gain

NASA Astrophysics Data System (ADS)

Beck, Joakim; Dia, Ben Mansour; Espath, Luis F. R.; Long, Quan; Tempone, Raúl

2018-06-01

In calculating expected information gain in optimal Bayesian experimental design, the computation of the inner loop in the classical double-loop Monte Carlo requires a large number of samples and suffers from underflow if the number of samples is small. These drawbacks can be avoided by using an importance sampling approach. We present a computationally efficient method for optimal Bayesian experimental design that introduces importance sampling based on the Laplace method to the inner loop. We derive the optimal values for the method parameters in which the average computational cost is minimized according to the desired error tolerance. We use three numerical examples to demonstrate the computational efficiency of our method compared with the classical double-loop Monte Carlo, and a more recent single-loop Monte Carlo method that uses the Laplace method as an approximation of the return value of the inner loop. The first example is a scalar problem that is linear in the uncertain parameter. The second example is a nonlinear scalar problem. The third example deals with the optimal sensor placement for an electrical impedance tomography experiment to recover the fiber orientation in laminate composites.

Regression of non-linear coupling of noise in LIGO detectors

NASA Astrophysics Data System (ADS)

Da Silva Costa, C. F.; Billman, C.; Effler, A.; Klimenko, S.; Cheng, H.-P.

2018-03-01

In 2015, after their upgrade, the advanced Laser Interferometer Gravitational-Wave Observatory (LIGO) detectors started acquiring data. The effort to improve their sensitivity has never stopped since then. The goal to achieve design sensitivity is challenging. Environmental and instrumental noise couple to the detector output with different, linear and non-linear, coupling mechanisms. The noise regression method we use is based on the Wiener–Kolmogorov filter, which uses witness channels to make noise predictions. We present here how this method helped to determine complex non-linear noise couplings in the output mode cleaner and in the mirror suspension system of the LIGO detector.

A controlled experiment in ground water flow model calibration

USGS Publications Warehouse

Hill, M.C.; Cooley, R.L.; Pollock, D.W.

1998-01-01

Nonlinear regression was introduced to ground water modeling in the 1970s, but has been used very little to calibrate numerical models of complicated ground water systems. Apparently, nonlinear regression is thought by many to be incapable of addressing such complex problems. With what we believe to be the most complicated synthetic test case used for such a study, this work investigates using nonlinear regression in ground water model calibration. Results of the study fall into two categories. First, the study demonstrates how systematic use of a well designed nonlinear regression method can indicate the importance of different types of data and can lead to successive improvement of models and their parameterizations. Our method differs from previous methods presented in the ground water literature in that (1) weighting is more closely related to expected data errors than is usually the case; (2) defined diagnostic statistics allow for more effective evaluation of the available data, the model, and their interaction; and (3) prior information is used more cautiously. Second, our results challenge some commonly held beliefs about model calibration. For the test case considered, we show that (1) field measured values of hydraulic conductivity are not as directly applicable to models as their use in some geostatistical methods imply; (2) a unique model does not necessarily need to be identified to obtain accurate predictions; and (3) in the absence of obvious model bias, model error was normally distributed. The complexity of the test case involved implies that the methods used and conclusions drawn are likely to be powerful in practice.Nonlinear regression was introduced to ground water modeling in the 1970s, but has been used very little to calibrate numerical models of complicated ground water systems. Apparently, nonlinear regression is thought by many to be incapable of addressing such complex problems. With what we believe to be the most complicated synthetic test case used for such a study, this work investigates using nonlinear regression in ground water model calibration. Results of the study fall into two categories. First, the study demonstrates how systematic use of a well designed nonlinear regression method can indicate the importance of different types of data and can lead to successive improvement of models and their parameterizations. Our method differs from previous methods presented in the ground water literature in that (1) weighting is more closely related to expected data errors than is usually the case; (2) defined diagnostic statistics allow for more effective evaluation of the available data, the model, and their interaction; and (3) prior information is used more cautiously. Second, our results challenge some commonly held beliefs about model calibration. For the test case considered, we show that (1) field measured values of hydraulic conductivity are not as directly applicable to models as their use in some geostatistical methods imply; (2) a unique model does not necessarily need to be identified to obtain accurate predictions; and (3) in the absence of obvious model bias, model error was normally distributed. The complexity of the test case involved implies that the methods used and conclusions drawn are likely to be powerful in practice.

Spatial variability of the effect of air pollution on term birth weight: evaluating influential factors using Bayesian hierarchical models.

PubMed

Li, Lianfa; Laurent, Olivier; Wu, Jun

2016-02-05

Epidemiological studies suggest that air pollution is adversely associated with pregnancy outcomes. Such associations may be modified by spatially-varying factors including socio-demographic characteristics, land-use patterns and unaccounted exposures. Yet, few studies have systematically investigated the impact of these factors on spatial variability of the air pollution's effects. This study aimed to examine spatial variability of the effects of air pollution on term birth weight across Census tracts and the influence of tract-level factors on such variability. We obtained over 900,000 birth records from 2001 to 2008 in Los Angeles County, California, USA. Air pollution exposure was modeled at individual level for nitrogen dioxide (NO2) and nitrogen oxides (NOx) using spatiotemporal models. Two-stage Bayesian hierarchical non-linear models were developed to (1) quantify the associations between air pollution exposure and term birth weight within each tract; and (2) examine the socio-demographic, land-use, and exposure-related factors contributing to the between-tract variability of the associations between air pollution and term birth weight. Higher air pollution exposure was associated with lower term birth weight (average posterior effects: -14.7 (95 % CI: -19.8, -9.7) g per 10 ppb increment in NO2 and -6.9 (95 % CI: -12.9, -0.9) g per 10 ppb increment in NOx). The variation of the association across Census tracts was significantly influenced by the tract-level socio-demographic, exposure-related and land-use factors. Our models captured the complex non-linear relationship between these factors and the associations between air pollution and term birth weight: we observed the thresholds from which the influence of the tract-level factors was markedly exacerbated or attenuated. Exacerbating factors might reflect additional exposure to environmental insults or lower socio-economic status with higher vulnerability, whereas attenuating factors might indicate reduced exposure or higher socioeconomic status with lower vulnerability. Our Bayesian models effectively combined a priori knowledge with training data to infer the posterior association of air pollution with term birth weight and to evaluate the influence of the tract-level factors on spatial variability of such association. This study contributes new findings about non-linear influences of socio-demographic factors, land-use patterns, and unaccounted exposures on spatial variability of the effects of air pollution.

Improving near-infrared prediction model robustness with support vector machine regression: a pharmaceutical tablet assay example.

PubMed

Igne, Benoît; Drennen, James K; Anderson, Carl A

2014-01-01

Changes in raw materials and process wear and tear can have significant effects on the prediction error of near-infrared calibration models. When the variability that is present during routine manufacturing is not included in the calibration, test, and validation sets, the long-term performance and robustness of the model will be limited. Nonlinearity is a major source of interference. In near-infrared spectroscopy, nonlinearity can arise from light path-length differences that can come from differences in particle size or density. The usefulness of support vector machine (SVM) regression to handle nonlinearity and improve the robustness of calibration models in scenarios where the calibration set did not include all the variability present in test was evaluated. Compared to partial least squares (PLS) regression, SVM regression was less affected by physical (particle size) and chemical (moisture) differences. The linearity of the SVM predicted values was also improved. Nevertheless, although visualization and interpretation tools have been developed to enhance the usability of SVM-based methods, work is yet to be done to provide chemometricians in the pharmaceutical industry with a regression method that can supplement PLS-based methods.

Artificial and Bayesian Neural Networks

PubMed

Korhani Kangi, Azam; Bahrampour, Abbas

2018-02-26

Introduction and purpose: In recent years the use of neural networks without any premises for investigation of prognosis in analyzing survival data has increased. Artificial neural networks (ANN) use small processors with a continuous network to solve problems inspired by the human brain. Bayesian neural networks (BNN) constitute a neural-based approach to modeling and non-linearization of complex issues using special algorithms and statistical methods. Gastric cancer incidence is the first and third ranking for men and women in Iran, respectively. The aim of the present study was to assess the value of an artificial neural network and a Bayesian neural network for modeling and predicting of probability of gastric cancer patient death. Materials and Methods: In this study, we used information on 339 patients aged from 20 to 90 years old with positive gastric cancer, referred to Afzalipoor and Shahid Bahonar Hospitals in Kerman City from 2001 to 2015. The three layers perceptron neural network (ANN) and the Bayesian neural network (BNN) were used for predicting the probability of mortality using the available data. To investigate differences between the models, sensitivity, specificity, accuracy and the area under receiver operating characteristic curves (AUROCs) were generated. Results: In this study, the sensitivity and specificity of the artificial neural network and Bayesian neural network models were 0.882, 0.903 and 0.954, 0.909, respectively. Prediction accuracy and the area under curve ROC for the two models were 0.891, 0.944 and 0.935, 0.961. The age at diagnosis of gastric cancer was most important for predicting survival, followed by tumor grade, morphology, gender, smoking history, opium consumption, receiving chemotherapy, presence of metastasis, tumor stage, receiving radiotherapy, and being resident in a village. Conclusion: The findings of the present study indicated that the Bayesian neural network is preferable to an artificial neural network for predicting survival of gastric cancer patients in Iran. Creative Commons Attribution License

The Use of Linear Instrumental Variables Methods in Health Services Research and Health Economics: A Cautionary Note

PubMed Central

Terza, Joseph V; Bradford, W David; Dismuke, Clara E

2008-01-01

Objective To investigate potential bias in the use of the conventional linear instrumental variables (IV) method for the estimation of causal effects in inherently nonlinear regression settings. Data Sources Smoking Supplement to the 1979 National Health Interview Survey, National Longitudinal Alcohol Epidemiologic Survey, and simulated data. Study Design Potential bias from the use of the linear IV method in nonlinear models is assessed via simulation studies and real world data analyses in two commonly encountered regression setting: (1) models with a nonnegative outcome (e.g., a count) and a continuous endogenous regressor; and (2) models with a binary outcome and a binary endogenous regressor. Principle Findings The simulation analyses show that substantial bias in the estimation of causal effects can result from applying the conventional IV method in inherently nonlinear regression settings. Moreover, the bias is not attenuated as the sample size increases. This point is further illustrated in the survey data analyses in which IV-based estimates of the relevant causal effects diverge substantially from those obtained with appropriate nonlinear estimation methods. Conclusions We offer this research as a cautionary note to those who would opt for the use of linear specifications in inherently nonlinear settings involving endogeneity. PMID:18546544

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.

Single-case experimental design yielded an effect estimate corresponding to a randomized controlled trial.

PubMed

Shadish, William R; Rindskopf, David M; Boyajian, Jonathan G

2016-08-01

We reanalyzed data from a previous randomized crossover design that administered high or low doses of intravenous immunoglobulin (IgG) to 12 patients with hypogammaglobulinaemia over 12 time points, with crossover after time 6. The objective was to see if results corresponded when analyzed as a set of single-case experimental designs vs. as a usual randomized controlled trial (RCT). Two blinded statisticians independently analyzed results. One analyzed the RCT comparing mean outcomes of group A (high dose IgG) to group B (low dose IgG) at the usual trial end point (time 6 in this case). The other analyzed all 12 time points for the group B patients as six single-case experimental designs analyzed together in a Bayesian nonlinear framework. In the randomized trial, group A [M = 794.93; standard deviation (SD) = 90.48] had significantly higher serum IgG levels at time six than group B (M = 283.89; SD = 71.10) (t = 10.88; df = 10; P < 0.001), yielding a mean difference of MD = 511.05 [standard error (SE) = 46.98]. For the single-case experimental designs, the effect from an intrinsically nonlinear regression was also significant and comparable in size with overlapping confidence intervals: MD = 495.00, SE = 54.41, and t = 495.00/54.41 = 9.10. Subsequent exploratory analyses indicated that how trend was modeled made a difference to these conclusions. The results of single-case experimental designs accurately approximated results from an RCT, although more work is needed to understand the conditions under which this holds. Copyright © 2016 Elsevier Inc. All rights reserved.

Model selection for logistic regression models

NASA Astrophysics Data System (ADS)

Duller, Christine

2012-09-01

Model selection for logistic regression models decides which of some given potential regressors have an effect and hence should be included in the final model. The second interesting question is whether a certain factor is heterogeneous among some subsets, i.e. whether the model should include a random intercept or not. In this paper these questions will be answered with classical as well as with Bayesian methods. The application show some results of recent research projects in medicine and business administration.

Methods for estimating annual exceedance probability discharges for streams in Arkansas, based on data through water year 2013

USGS Publications Warehouse

Wagner, Daniel M.; Krieger, Joshua D.; Veilleux, Andrea G.

2016-08-04

In 2013, the U.S. Geological Survey initiated a study to update regional skew, annual exceedance probability discharges, and regional regression equations used to estimate annual exceedance probability discharges for ungaged locations on streams in the study area with the use of recent geospatial data, new analytical methods, and available annual peak-discharge data through the 2013 water year. An analysis of regional skew using Bayesian weighted least-squares/Bayesian generalized-least squares regression was performed for Arkansas, Louisiana, and parts of Missouri and Oklahoma. The newly developed constant regional skew of -0.17 was used in the computation of annual exceedance probability discharges for 281 streamgages used in the regional regression analysis. Based on analysis of covariance, four flood regions were identified for use in the generation of regional regression models. Thirty-nine basin characteristics were considered as potential explanatory variables, and ordinary least-squares regression techniques were used to determine the optimum combinations of basin characteristics for each of the four regions. Basin characteristics in candidate models were evaluated based on multicollinearity with other basin characteristics (variance inflation factor < 2.5) and statistical significance at the 95-percent confidence level (p ≤ 0.05). Generalized least-squares regression was used to develop the final regression models for each flood region. Average standard errors of prediction of the generalized least-squares models ranged from 32.76 to 59.53 percent, with the largest range in flood region D. Pseudo coefficients of determination of the generalized least-squares models ranged from 90.29 to 97.28 percent, with the largest range also in flood region D. The regional regression equations apply only to locations on streams in Arkansas where annual peak discharges are not substantially affected by regulation, diversion, channelization, backwater, or urbanization. The applicability and accuracy of the regional regression equations depend on the basin characteristics measured for an ungaged location on a stream being within range of those used to develop the equations.

Bayesian design criteria: computation, comparison, and application to a pharmacokinetic and a pharmacodynamic model.

PubMed

Merlé, Y; Mentré, F

1995-02-01

In this paper 3 criteria to design experiments for Bayesian estimation of the parameters of nonlinear models with respect to their parameters, when a prior distribution is available, are presented: the determinant of the Bayesian information matrix, the determinant of the pre-posterior covariance matrix, and the expected information provided by an experiment. A procedure to simplify the computation of these criteria is proposed in the case of continuous prior distributions and is compared with the criterion obtained from a linearization of the model about the mean of the prior distribution for the parameters. This procedure is applied to two models commonly encountered in the area of pharmacokinetics and pharmacodynamics: the one-compartment open model with bolus intravenous single-dose injection and the Emax model. They both involve two parameters. Additive as well as multiplicative gaussian measurement errors are considered with normal prior distributions. Various combinations of the variances of the prior distribution and of the measurement error are studied. Our attention is restricted to designs with limited numbers of measurements (1 or 2 measurements). This situation often occurs in practice when Bayesian estimation is performed. The optimal Bayesian designs that result vary with the variances of the parameter distribution and with the measurement error. The two-point optimal designs sometimes differ from the D-optimal designs for the mean of the prior distribution and may consist of replicating measurements. For the studied cases, the determinant of the Bayesian information matrix and its linearized form lead to the same optimal designs. In some cases, the pre-posterior covariance matrix can be far from its lower bound, namely, the inverse of the Bayesian information matrix, especially for the Emax model and a multiplicative measurement error. The expected information provided by the experiment and the determinant of the pre-posterior covariance matrix generally lead to the same designs except for the Emax model and the multiplicative measurement error. Results show that these criteria can be easily computed and that they could be incorporated in modules for designing experiments.

Empirical intrinsic geometry for nonlinear modeling and time series filtering.

PubMed

Talmon, Ronen; Coifman, Ronald R

2013-07-30

In this paper, we present a method for time series analysis based on empirical intrinsic geometry (EIG). EIG enables one to reveal the low-dimensional parametric manifold as well as to infer the underlying dynamics of high-dimensional time series. By incorporating concepts of information geometry, this method extends existing geometric analysis tools to support stochastic settings and parametrizes the geometry of empirical distributions. However, the statistical models are not required as priors; hence, EIG may be applied to a wide range of real signals without existing definitive models. We show that the inferred model is noise-resilient and invariant under different observation and instrumental modalities. In addition, we show that it can be extended efficiently to newly acquired measurements in a sequential manner. These two advantages enable us to revisit the Bayesian approach and incorporate empirical dynamics and intrinsic geometry into a nonlinear filtering framework. We show applications to nonlinear and non-Gaussian tracking problems as well as to acoustic signal localization.

Joint model-based clustering of nonlinear longitudinal trajectories and associated time-to-event data analysis, linked by latent class membership: with application to AIDS clinical studies.

PubMed

Huang, Yangxin; Lu, Xiaosun; Chen, Jiaqing; Liang, Juan; Zangmeister, Miriam

2017-10-27

Longitudinal and time-to-event data are often observed together. Finite mixture models are currently used to analyze nonlinear heterogeneous longitudinal data, which, by releasing the homogeneity restriction of nonlinear mixed-effects (NLME) models, can cluster individuals into one of the pre-specified classes with class membership probabilities. This clustering may have clinical significance, and be associated with clinically important time-to-event data. This article develops a joint modeling approach to a finite mixture of NLME models for longitudinal data and proportional hazard Cox model for time-to-event data, linked by individual latent class indicators, under a Bayesian framework. The proposed joint models and method are applied to a real AIDS clinical trial data set, followed by simulation studies to assess the performance of the proposed joint model and a naive two-step model, in which finite mixture model and Cox model are fitted separately.

Robust ridge regression estimators for nonlinear models with applications to high throughput screening assay data.

PubMed

Lim, Changwon

2015-03-30

Nonlinear regression is often used to evaluate the toxicity of a chemical or a drug by fitting data from a dose-response study. Toxicologists and pharmacologists may draw a conclusion about whether a chemical is toxic by testing the significance of the estimated parameters. However, sometimes the null hypothesis cannot be rejected even though the fit is quite good. One possible reason for such cases is that the estimated standard errors of the parameter estimates are extremely large. In this paper, we propose robust ridge regression estimation procedures for nonlinear models to solve this problem. The asymptotic properties of the proposed estimators are investigated; in particular, their mean squared errors are derived. The performances of the proposed estimators are compared with several standard estimators using simulation studies. The proposed methodology is also illustrated using high throughput screening assay data obtained from the National Toxicology Program. Copyright © 2014 John Wiley & Sons, Ltd.

Predictions of Performance in Career Education.

ERIC Educational Resources Information Center

Novick, M. R.; And Others

Prediction weights for educational programs in 22 vocational and technical fields are provided using ability scores from the American College Testing Program (ACT) Career Planning Profile and a Bayesian regression theory. The criterion variable studies was first-semester grade-point average. Each vocational-technical program analyzed was…

Improving satellite-based PM2.5 estimates in China using Gaussian processes modeling in a Bayesian hierarchical setting.

PubMed

Yu, Wenxi; Liu, Yang; Ma, Zongwei; Bi, Jun

2017-08-01

Using satellite-based aerosol optical depth (AOD) measurements and statistical models to estimate ground-level PM 2.5 is a promising way to fill the areas that are not covered by ground PM 2.5 monitors. The statistical models used in previous studies are primarily Linear Mixed Effects (LME) and Geographically Weighted Regression (GWR) models. In this study, we developed a new regression model between PM 2.5 and AOD using Gaussian processes in a Bayesian hierarchical setting. Gaussian processes model the stochastic nature of the spatial random effects, where the mean surface and the covariance function is specified. The spatial stochastic process is incorporated under the Bayesian hierarchical framework to explain the variation of PM 2.5 concentrations together with other factors, such as AOD, spatial and non-spatial random effects. We evaluate the results of our model and compare them with those of other, conventional statistical models (GWR and LME) by within-sample model fitting and out-of-sample validation (cross validation, CV). The results show that our model possesses a CV result (R 2  = 0.81) that reflects higher accuracy than that of GWR and LME (0.74 and 0.48, respectively). Our results indicate that Gaussian process models have the potential to improve the accuracy of satellite-based PM 2.5 estimates.

Quantile regression and Bayesian cluster detection to identify radon prone areas.

PubMed

Sarra, Annalina; Fontanella, Lara; Valentini, Pasquale; Palermi, Sergio

2016-11-01

Albeit the dominant source of radon in indoor environments is the geology of the territory, many studies have demonstrated that indoor radon concentrations also depend on dwelling-specific characteristics. Following a stepwise analysis, in this study we propose a combined approach to delineate radon prone areas. We first investigate the impact of various building covariates on indoor radon concentrations. To achieve a more complete picture of this association, we exploit the flexible formulation of a Bayesian spatial quantile regression, which is also equipped with parameters that controls the spatial dependence across data. The quantitative knowledge of the influence of each significant building-specific factor on the measured radon levels is employed to predict the radon concentrations that would have been found if the sampled buildings had possessed standard characteristics. Those normalised radon measures should reflect the geogenic radon potential of the underlying ground, which is a quantity directly related to the geological environment. The second stage of the analysis is aimed at identifying radon prone areas, and to this end, we adopt a Bayesian model for spatial cluster detection using as reference unit the building with standard characteristics. The case study is based on a data set of more than 2000 indoor radon measures, available for the Abruzzo region (Central Italy) and collected by the Agency of Environmental Protection of Abruzzo, during several indoor radon monitoring surveys. Copyright © 2016 Elsevier Ltd. All rights reserved.

Bayesian data fusion for spatial prediction of categorical variables in environmental sciences

NASA Astrophysics Data System (ADS)

Gengler, Sarah; Bogaert, Patrick

2014-12-01

First developed to predict continuous variables, Bayesian Maximum Entropy (BME) has become a complete framework in the context of space-time prediction since it has been extended to predict categorical variables and mixed random fields. This method proposes solutions to combine several sources of data whatever the nature of the information. However, the various attempts that were made for adapting the BME methodology to categorical variables and mixed random fields faced some limitations, as a high computational burden. The main objective of this paper is to overcome this limitation by generalizing the Bayesian Data Fusion (BDF) theoretical framework to categorical variables, which is somehow a simplification of the BME method through the convenient conditional independence hypothesis. The BDF methodology for categorical variables is first described and then applied to a practical case study: the estimation of soil drainage classes using a soil map and point observations in the sandy area of Flanders around the city of Mechelen (Belgium). The BDF approach is compared to BME along with more classical approaches, as Indicator CoKringing (ICK) and logistic regression. Estimators are compared using various indicators, namely the Percentage of Correctly Classified locations (PCC) and the Average Highest Probability (AHP). Although BDF methodology for categorical variables is somehow a simplification of BME approach, both methods lead to similar results and have strong advantages compared to ICK and logistic regression.

Bayesian inference for the spatio-temporal invasion of alien species.

PubMed

Cook, Alex; Marion, Glenn; Butler, Adam; Gibson, Gavin

2007-08-01

In this paper we develop a Bayesian approach to parameter estimation in a stochastic spatio-temporal model of the spread of invasive species across a landscape. To date, statistical techniques, such as logistic and autologistic regression, have outstripped stochastic spatio-temporal models in their ability to handle large numbers of covariates. Here we seek to address this problem by making use of a range of covariates describing the bio-geographical features of the landscape. Relative to regression techniques, stochastic spatio-temporal models are more transparent in their representation of biological processes. They also explicitly model temporal change, and therefore do not require the assumption that the species' distribution (or other spatial pattern) has already reached equilibrium as is often the case with standard statistical approaches. In order to illustrate the use of such techniques we apply them to the analysis of data detailing the spread of an invasive plant, Heracleum mantegazzianum, across Britain in the 20th Century using geo-referenced covariate information describing local temperature, elevation and habitat type. The use of Markov chain Monte Carlo sampling within a Bayesian framework facilitates statistical assessments of differences in the suitability of different habitat classes for H. mantegazzianum, and enables predictions of future spread to account for parametric uncertainty and system variability. Our results show that ignoring such covariate information may lead to biased estimates of key processes and implausible predictions of future distributions.

Logistic Mixed Models to Investigate Implicit and Explicit Belief Tracking.

PubMed

Lages, Martin; Scheel, Anne

2016-01-01

We investigated the proposition of a two-systems Theory of Mind in adults' belief tracking. A sample of N = 45 participants predicted the choice of one of two opponent players after observing several rounds in an animated card game. Three matches of this card game were played and initial gaze direction on target and subsequent choice predictions were recorded for each belief task and participant. We conducted logistic regressions with mixed effects on the binary data and developed Bayesian logistic mixed models to infer implicit and explicit mentalizing in true belief and false belief tasks. Although logistic regressions with mixed effects predicted the data well a Bayesian logistic mixed model with latent task- and subject-specific parameters gave a better account of the data. As expected explicit choice predictions suggested a clear understanding of true and false beliefs (TB/FB). Surprisingly, however, model parameters for initial gaze direction also indicated belief tracking. We discuss why task-specific parameters for initial gaze directions are different from choice predictions yet reflect second-order perspective taking.

Commensurate Priors for Incorporating Historical Information in Clinical Trials Using General and Generalized Linear Models

PubMed Central

Hobbs, Brian P.; Sargent, Daniel J.; Carlin, Bradley P.

2014-01-01

Assessing between-study variability in the context of conventional random-effects meta-analysis is notoriously difficult when incorporating data from only a small number of historical studies. In order to borrow strength, historical and current data are often assumed to be fully homogeneous, but this can have drastic consequences for power and Type I error if the historical information is biased. In this paper, we propose empirical and fully Bayesian modifications of the commensurate prior model (Hobbs et al., 2011) extending Pocock (1976), and evaluate their frequentist and Bayesian properties for incorporating patient-level historical data using general and generalized linear mixed regression models. Our proposed commensurate prior models lead to preposterior admissible estimators that facilitate alternative bias-variance trade-offs than those offered by pre-existing methodologies for incorporating historical data from a small number of historical studies. We also provide a sample analysis of a colon cancer trial comparing time-to-disease progression using a Weibull regression model. PMID:24795786

On Bayesian methods of exploring qualitative interactions for targeted treatment.

PubMed

Chen, Wei; Ghosh, Debashis; Raghunathan, Trivellore E; Norkin, Maxim; Sargent, Daniel J; Bepler, Gerold

2012-12-10

Providing personalized treatments designed to maximize benefits and minimizing harms is of tremendous current medical interest. One problem in this area is the evaluation of the interaction between the treatment and other predictor variables. Treatment effects in subgroups having the same direction but different magnitudes are called quantitative interactions, whereas those having opposite directions in subgroups are called qualitative interactions (QIs). Identifying QIs is challenging because they are rare and usually unknown among many potential biomarkers. Meanwhile, subgroup analysis reduces the power of hypothesis testing and multiple subgroup analyses inflate the type I error rate. We propose a new Bayesian approach to search for QI in a multiple regression setting with adaptive decision rules. We consider various regression models for the outcome. We illustrate this method in two examples of phase III clinical trials. The algorithm is straightforward and easy to implement using existing software packages. We provide a sample code in Appendix A. Copyright © 2012 John Wiley & Sons, Ltd.

Integrated Data Analysis for Fusion: A Bayesian Tutorial for Fusion Diagnosticians

NASA Astrophysics Data System (ADS)

Dinklage, Andreas; Dreier, Heiko; Fischer, Rainer; Gori, Silvio; Preuss, Roland; Toussaint, Udo von

2008-03-01

Integrated Data Analysis (IDA) offers a unified way of combining information relevant to fusion experiments. Thereby, IDA meets with typical issues arising in fusion data analysis. In IDA, all information is consistently formulated as probability density functions quantifying uncertainties in the analysis within the Bayesian probability theory. For a single diagnostic, IDA allows the identification of faulty measurements and improvements in the setup. For a set of diagnostics, IDA gives joint error distributions allowing the comparison and integration of different diagnostics results. Validation of physics models can be performed by model comparison techniques. Typical data analysis applications benefit from IDA capabilities of nonlinear error propagation, the inclusion of systematic effects and the comparison of different physics models. Applications range from outlier detection, background discrimination, model assessment and design of diagnostics. In order to cope with next step fusion device requirements, appropriate techniques are explored for fast analysis applications.

Generative models for discovering sparse distributed representations.

PubMed Central

Hinton, G E; Ghahramani, Z

1997-01-01

We describe a hierarchical, generative model that can be viewed as a nonlinear generalization of factor analysis and can be implemented in a neural network. The model uses bottom-up, top-down and lateral connections to perform Bayesian perceptual inference correctly. Once perceptual inference has been performed the connection strengths can be updated using a very simple learning rule that only requires locally available information. We demonstrate that the network learns to extract sparse, distributed, hierarchical representations. PMID:9304685

From Birdsong to Human Speech Recognition: Bayesian Inference on a Hierarchy of Nonlinear Dynamical Systems

PubMed Central

Yildiz, Izzet B.; von Kriegstein, Katharina; Kiebel, Stefan J.

2013-01-01

Our knowledge about the computational mechanisms underlying human learning and recognition of sound sequences, especially speech, is still very limited. One difficulty in deciphering the exact means by which humans recognize speech is that there are scarce experimental findings at a neuronal, microscopic level. Here, we show that our neuronal-computational understanding of speech learning and recognition may be vastly improved by looking at an animal model, i.e., the songbird, which faces the same challenge as humans: to learn and decode complex auditory input, in an online fashion. Motivated by striking similarities between the human and songbird neural recognition systems at the macroscopic level, we assumed that the human brain uses the same computational principles at a microscopic level and translated a birdsong model into a novel human sound learning and recognition model with an emphasis on speech. We show that the resulting Bayesian model with a hierarchy of nonlinear dynamical systems can learn speech samples such as words rapidly and recognize them robustly, even in adverse conditions. In addition, we show that recognition can be performed even when words are spoken by different speakers and with different accents—an everyday situation in which current state-of-the-art speech recognition models often fail. The model can also be used to qualitatively explain behavioral data on human speech learning and derive predictions for future experiments. PMID:24068902

From birdsong to human speech recognition: bayesian inference on a hierarchy of nonlinear dynamical systems.

PubMed

Yildiz, Izzet B; von Kriegstein, Katharina; Kiebel, Stefan J

2013-01-01

Our knowledge about the computational mechanisms underlying human learning and recognition of sound sequences, especially speech, is still very limited. One difficulty in deciphering the exact means by which humans recognize speech is that there are scarce experimental findings at a neuronal, microscopic level. Here, we show that our neuronal-computational understanding of speech learning and recognition may be vastly improved by looking at an animal model, i.e., the songbird, which faces the same challenge as humans: to learn and decode complex auditory input, in an online fashion. Motivated by striking similarities between the human and songbird neural recognition systems at the macroscopic level, we assumed that the human brain uses the same computational principles at a microscopic level and translated a birdsong model into a novel human sound learning and recognition model with an emphasis on speech. We show that the resulting Bayesian model with a hierarchy of nonlinear dynamical systems can learn speech samples such as words rapidly and recognize them robustly, even in adverse conditions. In addition, we show that recognition can be performed even when words are spoken by different speakers and with different accents-an everyday situation in which current state-of-the-art speech recognition models often fail. The model can also be used to qualitatively explain behavioral data on human speech learning and derive predictions for future experiments.

Nonlinear Bayesian cue integration explains the dynamics of vocal learning

NASA Astrophysics Data System (ADS)

Zhou, Baohua; Sober, Samuel; Nemenman, Ilya

The acoustics of vocal production in songbirds is tightly regulated during both development and adulthood as birds progressively refine their song using sensory feedback to match an acoustic target. Here, we perturb this sensory feedback using headphones to shift the pitch (fundamental frequency) of song. When the pitch is shifted upwards (downwards), birds eventually learn to compensate and sing lower (higher), bringing the experienced pitch closer to the target. Paradoxically, the speed and amplitude of this motor learning decrease with increases in the introduced error size, so that birds respond rapidly to a small sensory perturbation, while seemingly never correcting a much bigger one. Similar results are observed broadly across the animal kingdom, and they do not derive from a limited plasticity of the adult brain since birds can compensate for a large error as long as the error is imposed gradually. We develop a mathematical model based on nonlinear Bayesian integration of two sensory modalities (one perturbed and the other not) that quantitatively explains all of these observations. The model makes predictions about the structure of the probability distribution of the pitches sung by birds during the pitch shift experiments, which we confirm using experimental data. This work was supported in part by James S. McDonnell Foundation Grant # 220020321, NSF Grant # IOS/1208126, NSF Grant # IOS/1456912 and NIH Grants # R01NS084844.

A Learning Progression Should Address Regression: Insights from Developing Non-Linear Reasoning in Ecology

ERIC Educational Resources Information Center

Hovardas, Tasos

2016-01-01

Although ecological systems at varying scales involve non-linear interactions, learners insist thinking in a linear fashion when they deal with ecological phenomena. The overall objective of the present contribution was to propose a hypothetical learning progression for developing non-linear reasoning in prey-predator systems and to provide…

Evaluating Bayesian spatial methods for modelling species distributions with clumped and restricted occurrence data.

PubMed

Redding, David W; Lucas, Tim C D; Blackburn, Tim M; Jones, Kate E

2017-01-01

Statistical approaches for inferring the spatial distribution of taxa (Species Distribution Models, SDMs) commonly rely on available occurrence data, which is often clumped and geographically restricted. Although available SDM methods address some of these factors, they could be more directly and accurately modelled using a spatially-explicit approach. Software to fit models with spatial autocorrelation parameters in SDMs are now widely available, but whether such approaches for inferring SDMs aid predictions compared to other methodologies is unknown. Here, within a simulated environment using 1000 generated species' ranges, we compared the performance of two commonly used non-spatial SDM methods (Maximum Entropy Modelling, MAXENT and boosted regression trees, BRT), to a spatial Bayesian SDM method (fitted using R-INLA), when the underlying data exhibit varying combinations of clumping and geographic restriction. Finally, we tested how any recommended methodological settings designed to account for spatially non-random patterns in the data impact inference. Spatial Bayesian SDM method was the most consistently accurate method, being in the top 2 most accurate methods in 7 out of 8 data sampling scenarios. Within high-coverage sample datasets, all methods performed fairly similarly. When sampling points were randomly spread, BRT had a 1-3% greater accuracy over the other methods and when samples were clumped, the spatial Bayesian SDM method had a 4%-8% better AUC score. Alternatively, when sampling points were restricted to a small section of the true range all methods were on average 10-12% less accurate, with greater variation among the methods. Model inference under the recommended settings to account for autocorrelation was not impacted by clumping or restriction of data, except for the complexity of the spatial regression term in the spatial Bayesian model. Methods, such as those made available by R-INLA, can be successfully used to account for spatial autocorrelation in an SDM context and, by taking account of random effects, produce outputs that can better elucidate the role of covariates in predicting species occurrence. Given that it is often unclear what the drivers are behind data clumping in an empirical occurrence dataset, or indeed how geographically restricted these data are, spatially-explicit Bayesian SDMs may be the better choice when modelling the spatial distribution of target species.

Development of non-linear models predicting daily fine particle concentrations using aerosol optical depth retrievals and ground-based measurements at a municipality in the Brazilian Amazon region

NASA Astrophysics Data System (ADS)

Gonçalves, Karen dos Santos; Winkler, Mirko S.; Benchimol-Barbosa, Paulo Roberto; de Hoogh, Kees; Artaxo, Paulo Eduardo; de Souza Hacon, Sandra; Schindler, Christian; Künzli, Nino

2018-07-01

Epidemiological studies generally use particulate matter measurements with diameter less 2.5 μm (PM2.5) from monitoring networks. Satellite aerosol optical depth (AOD) data has considerable potential in predicting PM2.5 concentrations, and thus provides an alternative method for producing knowledge regarding the level of pollution and its health impact in areas where no ground PM2.5 measurements are available. This is the case in the Brazilian Amazon rainforest region where forest fires are frequent sources of high pollution. In this study, we applied a non-linear model for predicting PM2.5 concentration from AOD retrievals using interaction terms between average temperature, relative humidity, sine, cosine of date in a period of 365,25 days and the square of the lagged relative residual. Regression performance statistics were tested comparing the goodness of fit and R2 based on results from linear regression and non-linear regression for six different models. The regression results for non-linear prediction showed the best performance, explaining on average 82% of the daily PM2.5 concentrations when considering the whole period studied. In the context of Amazonia, it was the first study predicting PM2.5 concentrations using the latest high-resolution AOD products also in combination with the testing of a non-linear model performance. Our results permitted a reliable prediction considering the AOD-PM2.5 relationship and set the basis for further investigations on air pollution impacts in the complex context of Brazilian Amazon Region.

On the regularization for nonlinear tomographic absorption spectroscopy

NASA Astrophysics Data System (ADS)

Dai, Jinghang; Yu, Tao; Xu, Lijun; Cai, Weiwei

2018-02-01

Tomographic absorption spectroscopy (TAS) has attracted increased research efforts recently due to the development in both hardware and new imaging concepts such as nonlinear tomography and compressed sensing. Nonlinear TAS is one of the emerging modality that bases on the concept of nonlinear tomography and has been successfully demonstrated both numerically and experimentally. However, all the previous demonstrations were realized using only two orthogonal projections simply for ease of implementation. In this work, we examine the performance of nonlinear TAS using other beam arrangements and test the effectiveness of the beam optimization technique that has been developed for linear TAS. In addition, so far only smoothness prior has been adopted and applied in nonlinear TAS. Nevertheless, there are also other useful priors such as sparseness and model-based prior which have not been investigated yet. This work aims to show how these priors can be implemented and included in the reconstruction process. Regularization through Bayesian formulation will be introduced specifically for this purpose, and a method for the determination of a proper regularization factor will be proposed. The comparative studies performed with different beam arrangements and regularization schemes on a few representative phantoms suggest that the beam optimization method developed for linear TAS also works for the nonlinear counterpart and the regularization scheme should be selected properly according to the available a priori information under specific application scenarios so as to achieve the best reconstruction fidelity. Though this work is conducted under the context of nonlinear TAS, it can also provide useful insights for other tomographic modalities.

Revisiting tests for neglected nonlinearity using artificial neural networks.

PubMed

Cho, Jin Seo; Ishida, Isao; White, Halbert

2011-05-01

Tests for regression neglected nonlinearity based on artificial neural networks (ANNs) have so far been studied by separately analyzing the two ways in which the null of regression linearity can hold. This implies that the asymptotic behavior of general ANN-based tests for neglected nonlinearity is still an open question. Here we analyze a convenient ANN-based quasi-likelihood ratio statistic for testing neglected nonlinearity, paying careful attention to both components of the null. We derive the asymptotic null distribution under each component separately and analyze their interaction. Somewhat remarkably, it turns out that the previously known asymptotic null distribution for the type 1 case still applies, but under somewhat stronger conditions than previously recognized. We present Monte Carlo experiments corroborating our theoretical results and showing that standard methods can yield misleading inference when our new, stronger regularity conditions are violated.

Incorporation of prior information on parameters into nonlinear regression groundwater flow models: 1. Theory

USGS Publications Warehouse

Cooley, Richard L.

1982-01-01

Prior information on the parameters of a groundwater flow model can be used to improve parameter estimates obtained from nonlinear regression solution of a modeling problem. Two scales of prior information can be available: (1) prior information having known reliability (that is, bias and random error structure) and (2) prior information consisting of best available estimates of unknown reliability. A regression method that incorporates the second scale of prior information assumes the prior information to be fixed for any particular analysis to produce improved, although biased, parameter estimates. Approximate optimization of two auxiliary parameters of the formulation is used to help minimize the bias, which is almost always much smaller than that resulting from standard ridge regression. It is shown that if both scales of prior information are available, then a combined regression analysis may be made.

A Bayesian approach for parameter estimation and prediction using a computationally intensive model

DOE PAGES

Higdon, Dave; McDonnell, Jordan D.; Schunck, Nicolas; ...

2015-02-05

Bayesian methods have been successful in quantifying uncertainty in physics-based problems in parameter estimation and prediction. In these cases, physical measurements y are modeled as the best fit of a physics-based modelmore » $$\\eta (\\theta )$$, where θ denotes the uncertain, best input setting. Hence the statistical model is of the form $$y=\\eta (\\theta )+\\epsilon ,$$ where $$\\epsilon $$ accounts for measurement, and possibly other, error sources. When nonlinearity is present in $$\\eta (\\cdot )$$, the resulting posterior distribution for the unknown parameters in the Bayesian formulation is typically complex and nonstandard, requiring computationally demanding computational approaches such as Markov chain Monte Carlo (MCMC) to produce multivariate draws from the posterior. Although generally applicable, MCMC requires thousands (or even millions) of evaluations of the physics model $$\\eta (\\cdot )$$. This requirement is problematic if the model takes hours or days to evaluate. To overcome this computational bottleneck, we present an approach adapted from Bayesian model calibration. This approach combines output from an ensemble of computational model runs with physical measurements, within a statistical formulation, to carry out inference. A key component of this approach is a statistical response surface, or emulator, estimated from the ensemble of model runs. We demonstrate this approach with a case study in estimating parameters for a density functional theory model, using experimental mass/binding energy measurements from a collection of atomic nuclei. Lastly, we also demonstrate how this approach produces uncertainties in predictions for recent mass measurements obtained at Argonne National Laboratory.« less

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.

Convergence analysis of surrogate-based methods for Bayesian inverse problems

NASA Astrophysics Data System (ADS)

Yan, Liang; Zhang, Yuan-Xiang

2017-12-01

The major challenges in the Bayesian inverse problems arise from the need for repeated evaluations of the forward model, as required by Markov chain Monte Carlo (MCMC) methods for posterior sampling. Many attempts at accelerating Bayesian inference have relied on surrogates for the forward model, typically constructed through repeated forward simulations that are performed in an offline phase. Although such approaches can be quite effective at reducing computation cost, there has been little analysis of the approximation on posterior inference. In this work, we prove error bounds on the Kullback-Leibler (KL) distance between the true posterior distribution and the approximation based on surrogate models. Our rigorous error analysis show that if the forward model approximation converges at certain rate in the prior-weighted L 2 norm, then the posterior distribution generated by the approximation converges to the true posterior at least two times faster in the KL sense. The error bound on the Hellinger distance is also provided. To provide concrete examples focusing on the use of the surrogate model based methods, we present an efficient technique for constructing stochastic surrogate models to accelerate the Bayesian inference approach. The Christoffel least squares algorithms, based on generalized polynomial chaos, are used to construct a polynomial approximation of the forward solution over the support of the prior distribution. The numerical strategy and the predicted convergence rates are then demonstrated on the nonlinear inverse problems, involving the inference of parameters appearing in partial differential equations.

IMNN: Information Maximizing Neural Networks

NASA Astrophysics Data System (ADS)

Charnock, Tom; Lavaux, Guilhem; Wandelt, Benjamin D.

2018-04-01

This software trains artificial neural networks to find non-linear functionals of data that maximize Fisher information: information maximizing neural networks (IMNNs). As compressing large data sets vastly simplifies both frequentist and Bayesian inference, important information may be inadvertently missed. Likelihood-free inference based on automatically derived IMNN summaries produces summaries that are good approximations to sufficient statistics. IMNNs are robustly capable of automatically finding optimal, non-linear summaries of the data even in cases where linear compression fails: inferring the variance of Gaussian signal in the presence of noise, inferring cosmological parameters from mock simulations of the Lyman-α forest in quasar spectra, and inferring frequency-domain parameters from LISA-like detections of gravitational waveforms. In this final case, the IMNN summary outperforms linear data compression by avoiding the introduction of spurious likelihood maxima.

Non-linear Parameter Estimates from Non-stationary MEG Data

PubMed Central

Martínez-Vargas, Juan D.; López, Jose D.; Baker, Adam; Castellanos-Dominguez, German; Woolrich, Mark W.; Barnes, Gareth

2016-01-01

We demonstrate a method to estimate key electrophysiological parameters from resting state data. In this paper, we focus on the estimation of head-position parameters. The recovery of these parameters is especially challenging as they are non-linearly related to the measured field. In order to do this we use an empirical Bayesian scheme to estimate the cortical current distribution due to a range of laterally shifted head-models. We compare different methods of approaching this problem from the division of M/EEG data into stationary sections and performing separate source inversions, to explaining all of the M/EEG data with a single inversion. We demonstrate this through estimation of head position in both simulated and empirical resting state MEG data collected using a head-cast. PMID:27597815

Data Mining in Child Welfare.

ERIC Educational Resources Information Center

Schoech, Dick; Quinn, Andrew; Rycraft, Joan R.

2000-01-01

Examines the historical and larger context of data mining and describes data mining processes, techniques, and tools. Illustrates these using a child welfare dataset concerning the employee turnover that is mined, using logistic regression and a Bayesian neural network. Discusses the data mining process, the resulting models, their predictive…

Regression estimators for generic health-related quality of life and quality-adjusted life years.

PubMed

Basu, Anirban; Manca, Andrea

2012-01-01

To develop regression models for outcomes with truncated supports, such as health-related quality of life (HRQoL) data, and account for features typical of such data such as a skewed distribution, spikes at 1 or 0, and heteroskedasticity. Regression estimators based on features of the Beta distribution. First, both a single equation and a 2-part model are presented, along with estimation algorithms based on maximum-likelihood, quasi-likelihood, and Bayesian Markov-chain Monte Carlo methods. A novel Bayesian quasi-likelihood estimator is proposed. Second, a simulation exercise is presented to assess the performance of the proposed estimators against ordinary least squares (OLS) regression for a variety of HRQoL distributions that are encountered in practice. Finally, the performance of the proposed estimators is assessed by using them to quantify the treatment effect on QALYs in the EVALUATE hysterectomy trial. Overall model fit is studied using several goodness-of-fit tests such as Pearson's correlation test, link and reset tests, and a modified Hosmer-Lemeshow test. The simulation results indicate that the proposed methods are more robust in estimating covariate effects than OLS, especially when the effects are large or the HRQoL distribution has a large spike at 1. Quasi-likelihood techniques are more robust than maximum likelihood estimators. When applied to the EVALUATE trial, all but the maximum likelihood estimators produce unbiased estimates of the treatment effect. One and 2-part Beta regression models provide flexible approaches to regress the outcomes with truncated supports, such as HRQoL, on covariates, after accounting for many idiosyncratic features of the outcomes distribution. This work will provide applied researchers with a practical set of tools to model outcomes in cost-effectiveness analysis.

PFIM 4.0, an extended R program for design evaluation and optimization in nonlinear mixed-effect models.

PubMed

Dumont, Cyrielle; Lestini, Giulia; Le Nagard, Hervé; Mentré, France; Comets, Emmanuelle; Nguyen, Thu Thuy; Group, For The Pfim

2018-03-01

Nonlinear mixed-effect models (NLMEMs) are increasingly used for the analysis of longitudinal studies during drug development. When designing these studies, the expected Fisher information matrix (FIM) can be used instead of performing time-consuming clinical trial simulations. The function PFIM is the first tool for design evaluation and optimization that has been developed in R. In this article, we present an extended version, PFIM 4.0, which includes several new features. Compared with version 3.0, PFIM 4.0 includes a more complete pharmacokinetic/pharmacodynamic library of models and accommodates models including additional random effects for inter-occasion variability as well as discrete covariates. A new input method has been added to specify user-defined models through an R function. Optimization can be performed assuming some fixed parameters or some fixed sampling times. New outputs have been added regarding the FIM such as eigenvalues, conditional numbers, and the option of saving the matrix obtained after evaluation or optimization. Previously obtained results, which are summarized in a FIM, can be taken into account in evaluation or optimization of one-group protocols. This feature enables the use of PFIM for adaptive designs. The Bayesian individual FIM has been implemented, taking into account a priori distribution of random effects. Designs for maximum a posteriori Bayesian estimation of individual parameters can now be evaluated or optimized and the predicted shrinkage is also reported. It is also possible to visualize the graphs of the model and the sensitivity functions without performing evaluation or optimization. The usefulness of these approaches and the simplicity of use of PFIM 4.0 are illustrated by two examples: (i) an example of designing a population pharmacokinetic study accounting for previous results, which highlights the advantage of adaptive designs; (ii) an example of Bayesian individual design optimization for a pharmacodynamic study, showing that the Bayesian individual FIM can be a useful tool in therapeutic drug monitoring, allowing efficient prediction of estimation precision and shrinkage for individual parameters. PFIM 4.0 is a useful tool for design evaluation and optimization of longitudinal studies in pharmacometrics and is freely available at http://www.pfim.biostat.fr. Copyright © 2018 Elsevier B.V. All rights reserved.

A full-spectral Bayesian reconstruction approach based on the material decomposition model applied in dual-energy computed tomography.

PubMed

Cai, C; Rodet, T; Legoupil, S; Mohammad-Djafari, A

2013-11-01

Dual-energy computed tomography (DECT) makes it possible to get two fractions of basis materials without segmentation. One is the soft-tissue equivalent water fraction and the other is the hard-matter equivalent bone fraction. Practical DECT measurements are usually obtained with polychromatic x-ray beams. Existing reconstruction approaches based on linear forward models without counting the beam polychromaticity fail to estimate the correct decomposition fractions and result in beam-hardening artifacts (BHA). The existing BHA correction approaches either need to refer to calibration measurements or suffer from the noise amplification caused by the negative-log preprocessing and the ill-conditioned water and bone separation problem. To overcome these problems, statistical DECT reconstruction approaches based on nonlinear forward models counting the beam polychromaticity show great potential for giving accurate fraction images. This work proposes a full-spectral Bayesian reconstruction approach which allows the reconstruction of high quality fraction images from ordinary polychromatic measurements. This approach is based on a Gaussian noise model with unknown variance assigned directly to the projections without taking negative-log. Referring to Bayesian inferences, the decomposition fractions and observation variance are estimated by using the joint maximum a posteriori (MAP) estimation method. Subject to an adaptive prior model assigned to the variance, the joint estimation problem is then simplified into a single estimation problem. It transforms the joint MAP estimation problem into a minimization problem with a nonquadratic cost function. To solve it, the use of a monotone conjugate gradient algorithm with suboptimal descent steps is proposed. The performance of the proposed approach is analyzed with both simulated and experimental data. The results show that the proposed Bayesian approach is robust to noise and materials. It is also necessary to have the accurate spectrum information about the source-detector system. When dealing with experimental data, the spectrum can be predicted by a Monte Carlo simulator. For the materials between water and bone, less than 5% separation errors are observed on the estimated decomposition fractions. The proposed approach is a statistical reconstruction approach based on a nonlinear forward model counting the full beam polychromaticity and applied directly to the projections without taking negative-log. Compared to the approaches based on linear forward models and the BHA correction approaches, it has advantages in noise robustness and reconstruction accuracy.

Combined state and parameter identification of nonlinear structural dynamical systems based on Rao-Blackwellization and Markov chain Monte Carlo simulations

NASA Astrophysics Data System (ADS)

Abhinav, S.; Manohar, C. S.

2018-03-01

The problem of combined state and parameter estimation in nonlinear state space models, based on Bayesian filtering methods, is considered. A novel approach, which combines Rao-Blackwellized particle filters for state estimation with Markov chain Monte Carlo (MCMC) simulations for parameter identification, is proposed. In order to ensure successful performance of the MCMC samplers, in situations involving large amount of dynamic measurement data and (or) low measurement noise, the study employs a modified measurement model combined with an importance sampling based correction. The parameters of the process noise covariance matrix are also included as quantities to be identified. The study employs the Rao-Blackwellization step at two stages: one, associated with the state estimation problem in the particle filtering step, and, secondly, in the evaluation of the ratio of likelihoods in the MCMC run. The satisfactory performance of the proposed method is illustrated on three dynamical systems: (a) a computational model of a nonlinear beam-moving oscillator system, (b) a laboratory scale beam traversed by a loaded trolley, and (c) an earthquake shake table study on a bending-torsion coupled nonlinear frame subjected to uniaxial support motion.

Selected aspects of prior and likelihood information for a Bayesian classifier in a road safety analysis.

PubMed

Nowakowska, Marzena

2017-04-01

The development of the Bayesian logistic regression model classifying the road accident severity is discussed. The already exploited informative priors (method of moments, maximum likelihood estimation, and two-stage Bayesian updating), along with the original idea of a Boot prior proposal, are investigated when no expert opinion has been available. In addition, two possible approaches to updating the priors, in the form of unbalanced and balanced training data sets, are presented. The obtained logistic Bayesian models are assessed on the basis of a deviance information criterion (DIC), highest probability density (HPD) intervals, and coefficients of variation estimated for the model parameters. The verification of the model accuracy has been based on sensitivity, specificity and the harmonic mean of sensitivity and specificity, all calculated from a test data set. The models obtained from the balanced training data set have a better classification quality than the ones obtained from the unbalanced training data set. The two-stage Bayesian updating prior model and the Boot prior model, both identified with the use of the balanced training data set, outperform the non-informative, method of moments, and maximum likelihood estimation prior models. It is important to note that one should be careful when interpreting the parameters since different priors can lead to different models. Copyright © 2017 Elsevier Ltd. All rights reserved.

Using Bayesian neural networks to classify forest scenes

NASA Astrophysics Data System (ADS)

Vehtari, Aki; Heikkonen, Jukka; Lampinen, Jouko; Juujarvi, Jouni

1998-10-01

We present results that compare the performance of Bayesian learning methods for neural networks on the task of classifying forest scenes into trees and background. Classification task is demanding due to the texture richness of the trees, occlusions of the forest scene objects and diverse lighting conditions under operation. This makes it difficult to determine which are optimal image features for the classification. A natural way to proceed is to extract many different types of potentially suitable features, and to evaluate their usefulness in later processing stages. One approach to cope with large number of features is to use Bayesian methods to control the model complexity. Bayesian learning uses a prior on model parameters, combines this with evidence from a training data, and the integrates over the resulting posterior to make predictions. With this method, we can use large networks and many features without fear of overfitting. For this classification task we compare two Bayesian learning methods for multi-layer perceptron (MLP) neural networks: (1) The evidence framework of MacKay uses a Gaussian approximation to the posterior weight distribution and maximizes with respect to hyperparameters. (2) In a Markov Chain Monte Carlo (MCMC) method due to Neal, the posterior distribution of the network parameters is numerically integrated using the MCMC method. As baseline classifiers for comparison we use (3) MLP early stop committee, (4) K-nearest-neighbor and (5) Classification And Regression Tree.

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.

Free will in Bayesian and inverse Bayesian inference-driven endo-consciousness.

PubMed

Gunji, Yukio-Pegio; Minoura, Mai; Kojima, Kei; Horry, Yoichi

2017-12-01

How can we link challenging issues related to consciousness and/or qualia with natural science? The introduction of endo-perspective, instead of exo-perspective, as proposed by Matsuno, Rössler, and Gunji, is considered one of the most promising candidate approaches. Here, we distinguish the endo-from the exo-perspective in terms of whether the external is or is not directly operated. In the endo-perspective, the external can be neither perceived nor recognized directly; rather, one can only indirectly summon something outside of the perspective, which can be illustrated by a causation-reversal pair. On one hand, causation logically proceeds from the cause to the effect. On the other hand, a reversal from the effect to the cause is non-logical and is equipped with a metaphorical structure. We argue that the differences in exo- and endo-perspectives result not from the difference between Western and Eastern cultures, but from differences between modernism and animism. Here, a causation-reversal pair described using a pair of upward (from premise to consequence) and downward (from consequence to premise) causation and a pair of Bayesian and inverse Bayesian inference (BIB inference). Accordingly, the notion of endo-consciousness is proposed as an agent equipped with BIB inference. We also argue that BIB inference can yield both highly efficient computations through Bayesian interference and robust computations through inverse Bayesian inference. By adapting a logical model of the free will theorem to the BIB inference, we show that endo-consciousness can explain free will as a regression of the controllability of voluntary action. Copyright © 2017. Published by Elsevier Ltd.

A different approach to estimate nonlinear regression model using numerical methods

NASA Astrophysics Data System (ADS)

Mahaboob, B.; Venkateswarlu, B.; Mokeshrayalu, G.; Balasiddamuni, P.

2017-11-01

This research paper concerns with the computational methods namely the Gauss-Newton method, Gradient algorithm methods (Newton-Raphson method, Steepest Descent or Steepest Ascent algorithm method, the Method of Scoring, the Method of Quadratic Hill-Climbing) based on numerical analysis to estimate parameters of nonlinear regression model in a very different way. Principles of matrix calculus have been used to discuss the Gradient-Algorithm methods. Yonathan Bard [1] discussed a comparison of gradient methods for the solution of nonlinear parameter estimation problems. However this article discusses an analytical approach to the gradient algorithm methods in a different way. This paper describes a new iterative technique namely Gauss-Newton method which differs from the iterative technique proposed by Gorden K. Smyth [2]. Hans Georg Bock et.al [10] proposed numerical methods for parameter estimation in DAE’s (Differential algebraic equation). Isabel Reis Dos Santos et al [11], Introduced weighted least squares procedure for estimating the unknown parameters of a nonlinear regression metamodel. For large-scale non smooth convex minimization the Hager and Zhang (HZ) conjugate gradient Method and the modified HZ (MHZ) method were presented by Gonglin Yuan et al [12].

An evaluation of bias in propensity score-adjusted non-linear regression models.

PubMed

Wan, Fei; Mitra, Nandita

2018-03-01

Propensity score methods are commonly used to adjust for observed confounding when estimating the conditional treatment effect in observational studies. One popular method, covariate adjustment of the propensity score in a regression model, has been empirically shown to be biased in non-linear models. However, no compelling underlying theoretical reason has been presented. We propose a new framework to investigate bias and consistency of propensity score-adjusted treatment effects in non-linear models that uses a simple geometric approach to forge a link between the consistency of the propensity score estimator and the collapsibility of non-linear models. Under this framework, we demonstrate that adjustment of the propensity score in an outcome model results in the decomposition of observed covariates into the propensity score and a remainder term. Omission of this remainder term from a non-collapsible regression model leads to biased estimates of the conditional odds ratio and conditional hazard ratio, but not for the conditional rate ratio. We further show, via simulation studies, that the bias in these propensity score-adjusted estimators increases with larger treatment effect size, larger covariate effects, and increasing dissimilarity between the coefficients of the covariates in the treatment model versus the outcome model.

Nitrate variability in groundwater of North Carolina using monitoring and private well data models.

PubMed

Messier, Kyle P; Kane, Evan; Bolich, Rick; Serre, Marc L

2014-09-16

Nitrate (NO3-) is a widespread contaminant of groundwater and surface water across the United States that has deleterious effects to human and ecological health. This study develops a model for predicting point-level groundwater NO3- at a state scale for monitoring wells and private wells of North Carolina. A land use regression (LUR) model selection procedure is developed for determining nonlinear model explanatory variables when they are known to be correlated. Bayesian Maximum Entropy (BME) is used to integrate the LUR model to create a LUR-BME model of spatial/temporal varying groundwater NO3- concentrations. LUR-BME results in a leave-one-out cross-validation r2 of 0.74 and 0.33 for monitoring and private wells, effectively predicting within spatial covariance ranges. Results show significant differences in the spatial distribution of groundwater NO3- contamination in monitoring versus private wells; high NO3- concentrations in the southeastern plains of North Carolina; and wastewater treatment residuals and swine confined animal feeding operations as local sources of NO3- in monitoring wells. Results are of interest to agencies that regulate drinking water sources or monitor health outcomes from ingestion of drinking water. Lastly, LUR-BME model estimates can be integrated into surface water models for more accurate management of nonpoint sources of nitrogen.

Nonlinear system identification for prostate cancer and optimality of intermittent androgen suppression therapy.

PubMed

Suzuki, Taiji; Aihara, Kazuyuki

2013-09-01

These days prostate cancer is one of the most common types of malignant neoplasm in men. Androgen ablation therapy (hormone therapy) has been shown to be effective for advanced prostate cancer. However, continuous hormone therapy often causes recurrence. This results from the progression of androgen-dependent cancer cells to androgen-independent cancer cells during the continuous hormone therapy. One possible method to prevent the progression to the androgen-independent state is intermittent androgen suppression (IAS) therapy, which ceases dosing intermittently. In this paper, we propose two methods to estimate the dynamics of prostate cancer, and investigate the IAS therapy from the viewpoint of optimality. The two methods that we propose for dynamics estimation are a variational Bayesian method for a piecewise affine (PWA) system and a Gaussian process regression method. We apply the proposed methods to real clinical data and compare their predictive performances. Then, using the estimated dynamics of prostate cancer, we observe how prostate cancer behaves for various dosing schedules. It can be seen that the conventional IAS therapy is a way of imposing high cost for dosing while keeping the prostate cancer in a safe state. We would like to dedicate this paper to the memory of Professor Luigi M. Ricciardi. Copyright © 2013 The Authors. Published by Elsevier Inc. All rights reserved.

A Bayesian Approach to Identifying Structural Nonlinearity using Free-Decay Response: Application to Damage Detection in Composites

DTIC Science & Technology

2010-03-03

obtainable while for the free-decay problem we simply have to include the initial conditions as random variables to be predicted. A different approach that...important and useful properties of MLEs is that, under regularity conditions , they are asymptotically unbiased and possess the minimum possible...becomes pLðzjh;s2G;MiÞ (i.e. the likelihood is conditional on the specified model). However, in this work we will only consider a single model and drop the

Hybrid Cubature Kalman filtering for identifying nonlinear models from sampled recording: Estimation of neuronal dynamics.

PubMed

Madi, Mahmoud K; Karameh, Fadi N

2017-01-01

Kalman filtering methods have long been regarded as efficient adaptive Bayesian techniques for estimating hidden states in models of linear dynamical systems under Gaussian uncertainty. Recent advents of the Cubature Kalman filter (CKF) have extended this efficient estimation property to nonlinear systems, and also to hybrid nonlinear problems where by the processes are continuous and the observations are discrete (continuous-discrete CD-CKF). Employing CKF techniques, therefore, carries high promise for modeling many biological phenomena where the underlying processes exhibit inherently nonlinear, continuous, and noisy dynamics and the associated measurements are uncertain and time-sampled. This paper investigates the performance of cubature filtering (CKF and CD-CKF) in two flagship problems arising in the field of neuroscience upon relating brain functionality to aggregate neurophysiological recordings: (i) estimation of the firing dynamics and the neural circuit model parameters from electric potentials (EP) observations, and (ii) estimation of the hemodynamic model parameters and the underlying neural drive from BOLD (fMRI) signals. First, in simulated neural circuit models, estimation accuracy was investigated under varying levels of observation noise (SNR), process noise structures, and observation sampling intervals (dt). When compared to the CKF, the CD-CKF consistently exhibited better accuracy for a given SNR, sharp accuracy increase with higher SNR, and persistent error reduction with smaller dt. Remarkably, CD-CKF accuracy shows only a mild deterioration for non-Gaussian process noise, specifically with Poisson noise, a commonly assumed form of background fluctuations in neuronal systems. Second, in simulated hemodynamic models, parametric estimates were consistently improved under CD-CKF. Critically, time-localization of the underlying neural drive, a determinant factor in fMRI-based functional connectivity studies, was significantly more accurate under CD-CKF. In conclusion, and with the CKF recently benchmarked against other advanced Bayesian techniques, the CD-CKF framework could provide significant gains in robustness and accuracy when estimating a variety of biological phenomena models where the underlying process dynamics unfold at time scales faster than those seen in collected measurements.

Hybrid Cubature Kalman filtering for identifying nonlinear models from sampled recording: Estimation of neuronal dynamics

PubMed Central

2017-01-01

Kalman filtering methods have long been regarded as efficient adaptive Bayesian techniques for estimating hidden states in models of linear dynamical systems under Gaussian uncertainty. Recent advents of the Cubature Kalman filter (CKF) have extended this efficient estimation property to nonlinear systems, and also to hybrid nonlinear problems where by the processes are continuous and the observations are discrete (continuous-discrete CD-CKF). Employing CKF techniques, therefore, carries high promise for modeling many biological phenomena where the underlying processes exhibit inherently nonlinear, continuous, and noisy dynamics and the associated measurements are uncertain and time-sampled. This paper investigates the performance of cubature filtering (CKF and CD-CKF) in two flagship problems arising in the field of neuroscience upon relating brain functionality to aggregate neurophysiological recordings: (i) estimation of the firing dynamics and the neural circuit model parameters from electric potentials (EP) observations, and (ii) estimation of the hemodynamic model parameters and the underlying neural drive from BOLD (fMRI) signals. First, in simulated neural circuit models, estimation accuracy was investigated under varying levels of observation noise (SNR), process noise structures, and observation sampling intervals (dt). When compared to the CKF, the CD-CKF consistently exhibited better accuracy for a given SNR, sharp accuracy increase with higher SNR, and persistent error reduction with smaller dt. Remarkably, CD-CKF accuracy shows only a mild deterioration for non-Gaussian process noise, specifically with Poisson noise, a commonly assumed form of background fluctuations in neuronal systems. Second, in simulated hemodynamic models, parametric estimates were consistently improved under CD-CKF. Critically, time-localization of the underlying neural drive, a determinant factor in fMRI-based functional connectivity studies, was significantly more accurate under CD-CKF. In conclusion, and with the CKF recently benchmarked against other advanced Bayesian techniques, the CD-CKF framework could provide significant gains in robustness and accuracy when estimating a variety of biological phenomena models where the underlying process dynamics unfold at time scales faster than those seen in collected measurements. PMID:28727850

Multi-Target Regression via Robust Low-Rank Learning.

PubMed

Zhen, Xiantong; Yu, Mengyang; He, Xiaofei; Li, Shuo

2018-02-01

Multi-target regression has recently regained great popularity due to its capability of simultaneously learning multiple relevant regression tasks and its wide applications in data mining, computer vision and medical image analysis, while great challenges arise from jointly handling inter-target correlations and input-output relationships. In this paper, we propose Multi-layer Multi-target Regression (MMR) which enables simultaneously modeling intrinsic inter-target correlations and nonlinear input-output relationships in a general framework via robust low-rank learning. Specifically, the MMR can explicitly encode inter-target correlations in a structure matrix by matrix elastic nets (MEN); the MMR can work in conjunction with the kernel trick to effectively disentangle highly complex nonlinear input-output relationships; the MMR can be efficiently solved by a new alternating optimization algorithm with guaranteed convergence. The MMR leverages the strength of kernel methods for nonlinear feature learning and the structural advantage of multi-layer learning architectures for inter-target correlation modeling. More importantly, it offers a new multi-layer learning paradigm for multi-target regression which is endowed with high generality, flexibility and expressive ability. Extensive experimental evaluation on 18 diverse real-world datasets demonstrates that our MMR can achieve consistently high performance and outperforms representative state-of-the-art algorithms, which shows its great effectiveness and generality for multivariate prediction.

A Bayesian Semiparametric Latent Variable Model for Mixed Responses

ERIC Educational Resources Information Center

Fahrmeir, Ludwig; Raach, Alexander

2007-01-01

In this paper we introduce a latent variable model (LVM) for mixed ordinal and continuous responses, where covariate effects on the continuous latent variables are modelled through a flexible semiparametric Gaussian regression model. We extend existing LVMs with the usual linear covariate effects by including nonparametric components for nonlinear…

Development of a real-time crash risk prediction model incorporating the various crash mechanisms across different traffic states.

PubMed

Xu, Chengcheng; Wang, Wei; Liu, Pan; Zhang, Fangwei

2015-01-01

This study aimed to identify the traffic flow variables contributing to crash risks under different traffic states and to develop a real-time crash risk model incorporating the varying crash mechanisms across different traffic states. The crash, traffic, and geometric data were collected on the I-880N freeway in California in 2008 and 2009. This study considered 4 different traffic states in Wu's 4-phase traffic theory. They are free fluid traffic, bunched fluid traffic, bunched congested traffic, and standing congested traffic. Several different statistical methods were used to accomplish the research objective. The preliminary analysis showed that traffic states significantly affected crash likelihood, collision type, and injury severity. Nonlinear canonical correlation analysis (NLCCA) was conducted to identify the underlying phenomena that made certain traffic states more hazardous than others. The results suggested that different traffic states were associated with various collision types and injury severities. The matching of traffic flow characteristics and crash characteristics in NLCCA revealed how traffic states affected traffic safety. The logistic regression analyses showed that the factors contributing to crash risks were quite different across various traffic states. To incorporate the varying crash mechanisms across different traffic states, random parameters logistic regression was used to develop a real-time crash risk model. Bayesian inference based on Markov chain Monte Carlo simulations was used for model estimation. The parameters of traffic flow variables in the model were allowed to vary across different traffic states. Compared with the standard logistic regression model, the proposed model significantly improved the goodness-of-fit and predictive performance. These results can promote a better understanding of the relationship between traffic flow characteristics and crash risks, which is valuable knowledge in the pursuit of improving traffic safety on freeways through the use of dynamic safety management systems.

Analysis of Blood Transfusion Data Using Bivariate Zero-Inflated Poisson Model: A Bayesian Approach.

PubMed

Mohammadi, Tayeb; Kheiri, Soleiman; Sedehi, Morteza

2016-01-01

Recognizing the factors affecting the number of blood donation and blood deferral has a major impact on blood transfusion. There is a positive correlation between the variables "number of blood donation" and "number of blood deferral": as the number of return for donation increases, so does the number of blood deferral. On the other hand, due to the fact that many donors never return to donate, there is an extra zero frequency for both of the above-mentioned variables. In this study, in order to apply the correlation and to explain the frequency of the excessive zero, the bivariate zero-inflated Poisson regression model was used for joint modeling of the number of blood donation and number of blood deferral. The data was analyzed using the Bayesian approach applying noninformative priors at the presence and absence of covariates. Estimating the parameters of the model, that is, correlation, zero-inflation parameter, and regression coefficients, was done through MCMC simulation. Eventually double-Poisson model, bivariate Poisson model, and bivariate zero-inflated Poisson model were fitted on the data and were compared using the deviance information criteria (DIC). The results showed that the bivariate zero-inflated Poisson regression model fitted the data better than the other models.

Analysis of Blood Transfusion Data Using Bivariate Zero-Inflated Poisson Model: A Bayesian Approach

PubMed Central

Mohammadi, Tayeb; Sedehi, Morteza

2016-01-01

Recognizing the factors affecting the number of blood donation and blood deferral has a major impact on blood transfusion. There is a positive correlation between the variables “number of blood donation” and “number of blood deferral”: as the number of return for donation increases, so does the number of blood deferral. On the other hand, due to the fact that many donors never return to donate, there is an extra zero frequency for both of the above-mentioned variables. In this study, in order to apply the correlation and to explain the frequency of the excessive zero, the bivariate zero-inflated Poisson regression model was used for joint modeling of the number of blood donation and number of blood deferral. The data was analyzed using the Bayesian approach applying noninformative priors at the presence and absence of covariates. Estimating the parameters of the model, that is, correlation, zero-inflation parameter, and regression coefficients, was done through MCMC simulation. Eventually double-Poisson model, bivariate Poisson model, and bivariate zero-inflated Poisson model were fitted on the data and were compared using the deviance information criteria (DIC). The results showed that the bivariate zero-inflated Poisson regression model fitted the data better than the other models. PMID:27703493

Geographical variation of cerebrovascular disease in New York State: the correlation with income

PubMed Central

Han, Daikwon; Carrow, Shannon S; Rogerson, Peter A; Munschauer, Frederick E

2005-01-01

Background Income is known to be associated with cerebrovascular disease; however, little is known about the more detailed relationship between cerebrovascular disease and income. We examined the hypothesis that the geographical distribution of cerebrovascular disease in New York State may be predicted by a nonlinear model using income as a surrogate socioeconomic risk factor. Results We used spatial clustering methods to identify areas with high and low prevalence of cerebrovascular disease at the ZIP code level after smoothing rates and correcting for edge effects; geographic locations of high and low clusters of cerebrovascular disease in New York State were identified with and without income adjustment. To examine effects of income, we calculated the excess number of cases using a non-linear regression with cerebrovascular disease rates taken as the dependent variable and income and income squared taken as independent variables. The resulting regression equation was: excess rate = 32.075 - 1.22*10-4(income) + 8.068*10-10(income2), and both income and income squared variables were significant at the 0.01 level. When income was included as a covariate in the non-linear regression, the number and size of clusters of high cerebrovascular disease prevalence decreased. Some 87 ZIP codes exceeded the critical value of the local statistic yielding a relative risk of 1.2. The majority of low cerebrovascular disease prevalence geographic clusters disappeared when the non-linear income effect was included. For linear regression, the excess rate of cerebrovascular disease falls with income; each $10,000 increase in median income of each ZIP code resulted in an average reduction of 3.83 observed cases. The significant nonlinear effect indicates a lessening of this income effect with increasing income. Conclusion Income is a non-linear predictor of excess cerebrovascular disease rates, with both low and high observed cerebrovascular disease rate areas associated with higher income. Income alone explains a significant amount of the geographical variance in cerebrovascular disease across New York State since both high and low clusters of cerebrovascular disease dissipate or disappear with income adjustment. Geographical modeling, including non-linear effects of income, may allow for better identification of other non-traditional risk factors. PMID:16242043

A phenomenological biological dose model for proton therapy based on linear energy transfer spectra.

PubMed

Rørvik, Eivind; Thörnqvist, Sara; Stokkevåg, Camilla H; Dahle, Tordis J; Fjaera, Lars Fredrik; Ytre-Hauge, Kristian S

2017-06-01

The relative biological effectiveness (RBE) of protons varies with the radiation quality, quantified by the linear energy transfer (LET). Most phenomenological models employ a linear dependency of the dose-averaged LET (LET d ) to calculate the biological dose. However, several experiments have indicated a possible non-linear trend. Our aim was to investigate if biological dose models including non-linear LET dependencies should be considered, by introducing a LET spectrum based dose model. The RBE-LET relationship was investigated by fitting of polynomials from 1st to 5th degree to a database of 85 data points from aerobic in vitro experiments. We included both unweighted and weighted regression, the latter taking into account experimental uncertainties. Statistical testing was performed to decide whether higher degree polynomials provided better fits to the data as compared to lower degrees. The newly developed models were compared to three published LET d based models for a simulated spread out Bragg peak (SOBP) scenario. The statistical analysis of the weighted regression analysis favored a non-linear RBE-LET relationship, with the quartic polynomial found to best represent the experimental data (P = 0.010). The results of the unweighted regression analysis were on the borderline of statistical significance for non-linear functions (P = 0.053), and with the current database a linear dependency could not be rejected. For the SOBP scenario, the weighted non-linear model estimated a similar mean RBE value (1.14) compared to the three established models (1.13-1.17). The unweighted model calculated a considerably higher RBE value (1.22). The analysis indicated that non-linear models could give a better representation of the RBE-LET relationship. However, this is not decisive, as inclusion of the experimental uncertainties in the regression analysis had a significant impact on the determination and ranking of the models. As differences between the models were observed for the SOBP scenario, both non-linear LET spectrum- and linear LET d based models should be further evaluated in clinically realistic scenarios. © 2017 American Association of Physicists in Medicine.

Poisson Mixture Regression Models for Heart Disease Prediction.

PubMed

Mufudza, Chipo; Erol, Hamza

2016-01-01

Early heart disease control can be achieved by high disease prediction and diagnosis efficiency. This paper focuses on the use of model based clustering techniques to predict and diagnose heart disease via Poisson mixture regression models. Analysis and application of Poisson mixture regression models is here addressed under two different classes: standard and concomitant variable mixture regression models. Results show that a two-component concomitant variable Poisson mixture regression model predicts heart disease better than both the standard Poisson mixture regression model and the ordinary general linear Poisson regression model due to its low Bayesian Information Criteria value. Furthermore, a Zero Inflated Poisson Mixture Regression model turned out to be the best model for heart prediction over all models as it both clusters individuals into high or low risk category and predicts rate to heart disease componentwise given clusters available. It is deduced that heart disease prediction can be effectively done by identifying the major risks componentwise using Poisson mixture regression model.

Poisson Mixture Regression Models for Heart Disease Prediction

PubMed Central

Erol, Hamza

2016-01-01

Early heart disease control can be achieved by high disease prediction and diagnosis efficiency. This paper focuses on the use of model based clustering techniques to predict and diagnose heart disease via Poisson mixture regression models. Analysis and application of Poisson mixture regression models is here addressed under two different classes: standard and concomitant variable mixture regression models. Results show that a two-component concomitant variable Poisson mixture regression model predicts heart disease better than both the standard Poisson mixture regression model and the ordinary general linear Poisson regression model due to its low Bayesian Information Criteria value. Furthermore, a Zero Inflated Poisson Mixture Regression model turned out to be the best model for heart prediction over all models as it both clusters individuals into high or low risk category and predicts rate to heart disease componentwise given clusters available. It is deduced that heart disease prediction can be effectively done by identifying the major risks componentwise using Poisson mixture regression model. PMID:27999611

Reaction norm model with unknown environmental covariate to analyze heterosis by environment interaction.

PubMed

Su, G; Madsen, P; Lund, M S

2009-05-01

Crossbreeding is currently increasing in dairy cattle production. Several studies have shown an environment-dependent heterosis [i.e., an interaction between heterosis and environment (H x E)]. An H x E interaction is usually estimated from a few discrete environment levels. The present study proposes a reaction norm model to describe H x E interaction, which can deal with a large number of environment levels using few parameters. In the proposed model, total heterosis consists of an environment-independent part, which is described as a function of heterozygosity, and an environment-dependent part, which is described as a function of heterozygosity and environmental value (e.g., herd-year effect). A Bayesian approach is developed to estimate the environmental covariates, the regression coefficients of the reaction norm, and other parameters of the model simultaneously in both linear and nonlinear reaction norms. In the nonlinear reaction norm model, the H x E is approximated using linear splines. The approach was tested using simulated data, which were generated using an animal model with a reaction norm for heterosis. The simulation study includes 4 scenarios (the combinations of moderate vs. low heritability and moderate vs. low herd-year variation) of H x E interaction in a nonlinear form. In all scenarios, the proposed model predicted total heterosis very well. The correlation between true heterosis and predicted heterosis was 0.98 in the scenarios with low herd-year variation and 0.99 in the scenarios with moderate herd-year variation. This suggests that the proposed model and method could be a good approach to analyze H x E interactions and predict breeding values in situations in which heterosis changes gradually and continuously over an environmental gradient. On the other hand, it was found that a model ignoring H x E interaction did not significantly harm the prediction of breeding value under the simulated scenarios in which the variance for environment-dependent heterosis effects was small (as it generally is), and sires were randomly used over production environments.

Non-Linear Approach in Kinesiology Should Be Preferred to the Linear--A Case of Basketball.

PubMed

Trninić, Marko; Jeličić, Mario; Papić, Vladan

2015-07-01

In kinesiology, medicine, biology and psychology, in which research focus is on dynamical self-organized systems, complex connections exist between variables. Non-linear nature of complex systems has been discussed and explained by the example of non-linear anthropometric predictors of performance in basketball. Previous studies interpreted relations between anthropometric features and measures of effectiveness in basketball by (a) using linear correlation models, and by (b) including all basketball athletes in the same sample of participants regardless of their playing position. In this paper the significance and character of linear and non-linear relations between simple anthropometric predictors (AP) and performance criteria consisting of situation-related measures of effectiveness (SE) in basketball were determined and evaluated. The sample of participants consisted of top-level junior basketball players divided in three groups according to their playing time (8 minutes and more per game) and playing position: guards (N = 42), forwards (N = 26) and centers (N = 40). Linear (general model) and non-linear (general model) regression models were calculated simultaneously and separately for each group. The conclusion is viable: non-linear regressions are frequently superior to linear correlations when interpreting actual association logic among research variables.

LiDAR based prediction of forest biomass using hierarchical models with spatially varying coefficients

USGS Publications Warehouse

Babcock, Chad; Finley, Andrew O.; Bradford, John B.; Kolka, Randall K.; Birdsey, Richard A.; Ryan, Michael G.

2015-01-01

Many studies and production inventory systems have shown the utility of coupling covariates derived from Light Detection and Ranging (LiDAR) data with forest variables measured on georeferenced inventory plots through regression models. The objective of this study was to propose and assess the use of a Bayesian hierarchical modeling framework that accommodates both residual spatial dependence and non-stationarity of model covariates through the introduction of spatial random effects. We explored this objective using four forest inventory datasets that are part of the North American Carbon Program, each comprising point-referenced measures of above-ground forest biomass and discrete LiDAR. For each dataset, we considered at least five regression model specifications of varying complexity. Models were assessed based on goodness of fit criteria and predictive performance using a 10-fold cross-validation procedure. Results showed that the addition of spatial random effects to the regression model intercept improved fit and predictive performance in the presence of substantial residual spatial dependence. Additionally, in some cases, allowing either some or all regression slope parameters to vary spatially, via the addition of spatial random effects, further improved model fit and predictive performance. In other instances, models showed improved fit but decreased predictive performance—indicating over-fitting and underscoring the need for cross-validation to assess predictive ability. The proposed Bayesian modeling framework provided access to pixel-level posterior predictive distributions that were useful for uncertainty mapping, diagnosing spatial extrapolation issues, revealing missing model covariates, and discovering locally significant parameters.

Parametric and Nonparametric Statistical Methods for Genomic Selection of Traits with Additive and Epistatic Genetic Architectures

PubMed Central

Howard, Réka; Carriquiry, Alicia L.; Beavis, William D.

2014-01-01

Parametric and nonparametric methods have been developed for purposes of predicting phenotypes. These methods are based on retrospective analyses of empirical data consisting of genotypic and phenotypic scores. Recent reports have indicated that parametric methods are unable to predict phenotypes of traits with known epistatic genetic architectures. Herein, we review parametric methods including least squares regression, ridge regression, Bayesian ridge regression, least absolute shrinkage and selection operator (LASSO), Bayesian LASSO, best linear unbiased prediction (BLUP), Bayes A, Bayes B, Bayes C, and Bayes Cπ. We also review nonparametric methods including Nadaraya-Watson estimator, reproducing kernel Hilbert space, support vector machine regression, and neural networks. We assess the relative merits of these 14 methods in terms of accuracy and mean squared error (MSE) using simulated genetic architectures consisting of completely additive or two-way epistatic interactions in an F2 population derived from crosses of inbred lines. Each simulated genetic architecture explained either 30% or 70% of the phenotypic variability. The greatest impact on estimates of accuracy and MSE was due to genetic architecture. Parametric methods were unable to predict phenotypic values when the underlying genetic architecture was based entirely on epistasis. Parametric methods were slightly better than nonparametric methods for additive genetic architectures. Distinctions among parametric methods for additive genetic architectures were incremental. Heritability, i.e., proportion of phenotypic variability, had the second greatest impact on estimates of accuracy and MSE. PMID:24727289

A voxel-based investigation for MRI-only radiotherapy of the brain using ultra short echo times

NASA Astrophysics Data System (ADS)

Edmund, Jens M.; Kjer, Hans M.; Van Leemput, Koen; Hansen, Rasmus H.; Andersen, Jon AL; Andreasen, Daniel

2014-12-01

Radiotherapy (RT) based on magnetic resonance imaging (MRI) as the only modality, so-called MRI-only RT, would remove the systematic registration error between MR and computed tomography (CT), and provide co-registered MRI for assessment of treatment response and adaptive RT. Electron densities, however, need to be assigned to the MRI images for dose calculation and patient setup based on digitally reconstructed radiographs (DRRs). Here, we investigate the geometric and dosimetric performance for a number of popular voxel-based methods to generate a so-called pseudo CT (pCT). Five patients receiving cranial irradiation, each containing a co-registered MRI and CT scan, were included. An ultra short echo time MRI sequence for bone visualization was used. Six methods were investigated for three popular types of voxel-based approaches; (1) threshold-based segmentation, (2) Bayesian segmentation and (3) statistical regression. Each approach contained two methods. Approach 1 used bulk density assignment of MRI voxels into air, soft tissue and bone based on logical masks and the transverse relaxation time T2 of the bone. Approach 2 used similar bulk density assignments with Bayesian statistics including or excluding additional spatial information. Approach 3 used a statistical regression correlating MRI voxels with their corresponding CT voxels. A similar photon and proton treatment plan was generated for a target positioned between the nasal cavity and the brainstem for all patients. The CT agreement with the pCT of each method was quantified and compared with the other methods geometrically and dosimetrically using both a number of reported metrics and introducing some novel metrics. The best geometrical agreement with CT was obtained with the statistical regression methods which performed significantly better than the threshold and Bayesian segmentation methods (excluding spatial information). All methods agreed significantly better with CT than a reference water MRI comparison. The mean dosimetric deviation for photons and protons compared to the CT was about 2% and highest in the gradient dose region of the brainstem. Both the threshold based method and the statistical regression methods showed the highest dosimetrical agreement. Generation of pCTs using statistical regression seems to be the most promising candidate for MRI-only RT of the brain. Further, the total amount of different tissues needs to be taken into account for dosimetric considerations regardless of their correct geometrical position.

A Modified Double Multiple Nonlinear Regression Constitutive Equation for Modeling and Prediction of High Temperature Flow Behavior of BFe10-1-2 Alloy

NASA Astrophysics Data System (ADS)

Cai, Jun; Wang, Kuaishe; Shi, Jiamin; Wang, Wen; Liu, Yingying

2018-01-01

Constitutive analysis for hot working of BFe10-1-2 alloy was carried out by using experimental stress-strain data from isothermal hot compression tests, in a wide range of temperature of 1,023 1,273 K, and strain rate range of 0.001 10 s-1. A constitutive equation based on modified double multiple nonlinear regression was proposed considering the independent effects of strain, strain rate, temperature and their interrelation. The predicted flow stress data calculated from the developed equation was compared with the experimental data. Correlation coefficient (R), average absolute relative error (AARE) and relative errors were introduced to verify the validity of the developed constitutive equation. Subsequently, a comparative study was made on the capability of strain-compensated Arrhenius-type constitutive model. The results showed that the developed constitutive equation based on modified double multiple nonlinear regression could predict flow stress of BFe10-1-2 alloy with good correlation and generalization.

TG study of the Li0.4Fe2.4Zn0.2O4 ferrite synthesis

NASA Astrophysics Data System (ADS)

Lysenko, E. N.; Nikolaev, E. V.; Surzhikov, A. P.

2016-02-01

In this paper, the kinetic analysis of Li-Zn ferrite synthesis was studied using thermogravimetry (TG) method through the simultaneous application of non-linear regression to several measurements run at different heating rates (multivariate non-linear regression). Using TG-curves obtained for the four heating rates and Netzsch Thermokinetics software package, the kinetic models with minimal adjustable parameters were selected to quantitatively describe the reaction of Li-Zn ferrite synthesis. It was shown that the experimental TG-curves clearly suggest a two-step process for the ferrite synthesis and therefore a model-fitting kinetic analysis based on multivariate non-linear regressions was conducted. The complex reaction was described by a two-step reaction scheme consisting of sequential reaction steps. It is established that the best results were obtained using the Yander three-dimensional diffusion model at the first stage and Ginstling-Bronstein model at the second step. The kinetic parameters for lithium-zinc ferrite synthesis reaction were found and discussed.

Sparsity-promoting and edge-preserving maximum a posteriori estimators in non-parametric Bayesian inverse problems

NASA Astrophysics Data System (ADS)

Agapiou, Sergios; Burger, Martin; Dashti, Masoumeh; Helin, Tapio

2018-04-01

We consider the inverse problem of recovering an unknown functional parameter u in a separable Banach space, from a noisy observation vector y of its image through a known possibly non-linear map {{\\mathcal G}} . We adopt a Bayesian approach to the problem and consider Besov space priors (see Lassas et al (2009 Inverse Problems Imaging 3 87-122)), which are well-known for their edge-preserving and sparsity-promoting properties and have recently attracted wide attention especially in the medical imaging community. Our key result is to show that in this non-parametric setup the maximum a posteriori (MAP) estimates are characterized by the minimizers of a generalized Onsager-Machlup functional of the posterior. This is done independently for the so-called weak and strong MAP estimates, which as we show coincide in our context. In addition, we prove a form of weak consistency for the MAP estimators in the infinitely informative data limit. Our results are remarkable for two reasons: first, the prior distribution is non-Gaussian and does not meet the smoothness conditions required in previous research on non-parametric MAP estimates. Second, the result analytically justifies existing uses of the MAP estimate in finite but high dimensional discretizations of Bayesian inverse problems with the considered Besov priors.

Quantifying temporal trends in fisheries abundance using Bayesian dynamic linear models: A case study of riverine Smallmouth Bass populations

USGS Publications Warehouse

Schall, Megan K.; Blazer, Vicki S.; Lorantas, Robert M.; Smith, Geoffrey; Mullican, John E.; Keplinger, Brandon J.; Wagner, Tyler

2018-01-01

Detecting temporal changes in fish abundance is an essential component of fisheries management. Because of the need to understand short‐term and nonlinear changes in fish abundance, traditional linear models may not provide adequate information for management decisions. This study highlights the utility of Bayesian dynamic linear models (DLMs) as a tool for quantifying temporal dynamics in fish abundance. To achieve this goal, we quantified temporal trends of Smallmouth Bass Micropterus dolomieu catch per effort (CPE) from rivers in the mid‐Atlantic states, and we calculated annual probabilities of decline from the posterior distributions of annual rates of change in CPE. We were interested in annual declines because of recent concerns about fish health in portions of the study area. In general, periods of decline were greatest within the Susquehanna River basin, Pennsylvania. The declines in CPE began in the late 1990s—prior to observations of fish health problems—and began to stabilize toward the end of the time series (2011). In contrast, many of the other rivers investigated did not have the same magnitude or duration of decline in CPE. Bayesian DLMs provide information about annual changes in abundance that can inform management and are easily communicated with managers and stakeholders.

Classical and Bayesian Seismic Yield Estimation: The 1998 Indian and Pakistani Tests

NASA Astrophysics Data System (ADS)

Shumway, R. H.

2001-10-01

- The nuclear tests in May, 1998, in India and Pakistan have stimulated a renewed interest in yield estimation, based on limited data from uncalibrated test sites. We study here the problem of estimating yields using classical and Bayesian methods developed by Shumway (1992), utilizing calibration data from the Semipalatinsk test site and measured magnitudes for the 1998 Indian and Pakistani tests given by Murphy (1998). Calibration is done using multivariate classical or Bayesian linear regression, depending on the availability of measured magnitude-yield data and prior information. Confidence intervals for the classical approach are derived applying an extension of Fieller's method suggested by Brown (1982). In the case where prior information is available, the posterior predictive magnitude densities are inverted to give posterior intervals for yield. Intervals obtained using the joint distribution of magnitudes are comparable to the single-magnitude estimates produced by Murphy (1998) and reinforce the conclusion that the announced yields of the Indian and Pakistani tests were too high.

Classical and Bayesian Seismic Yield Estimation: The 1998 Indian and Pakistani Tests

NASA Astrophysics Data System (ADS)

Shumway, R. H.

The nuclear tests in May, 1998, in India and Pakistan have stimulated a renewed interest in yield estimation, based on limited data from uncalibrated test sites. We study here the problem of estimating yields using classical and Bayesian methods developed by Shumway (1992), utilizing calibration data from the Semipalatinsk test site and measured magnitudes for the 1998 Indian and Pakistani tests given by Murphy (1998). Calibration is done using multivariate classical or Bayesian linear regression, depending on the availability of measured magnitude-yield data and prior information. Confidence intervals for the classical approach are derived applying an extension of Fieller's method suggested by Brown (1982). In the case where prior information is available, the posterior predictive magnitude densities are inverted to give posterior intervals for yield. Intervals obtained using the joint distribution of magnitudes are comparable to the single-magnitude estimates produced by Murphy (1998) and reinforce the conclusion that the announced yields of the Indian and Pakistani tests were too high.

The application of neural network model to the simulation nitrous oxide emission in the hydro-fluctuation belt of Three Gorges Reservoir

NASA Astrophysics Data System (ADS)

Song, Lanlan

2017-04-01

Nitrous oxide is much more potent greenhouse gas than carbon dioxide. However, the estimation of N2O flux is usually clouded with uncertainty, mainly due to high spatial and temporal variations. This hampers the development of general mechanistic models for N2O emission as well, as most previously developed models were empirical or exhibited low predictability with numerous assumptions. In this study, we tested General Regression Neural Networks (GRNN) as an alternative to classic empirical models for simulating N2O emission in riparian zones of Reservoirs. GRNN and nonlinear regression (NLR) were applied to estimate the N2O flux of 1-year observations in riparian zones of Three Gorge Reservoir. NLR resulted in lower prediction power and higher residuals compared to GRNN. Although nonlinear regression model estimated similar average values of N2O, it could not capture the fluctuation patterns accurately. In contrast, GRNN model achieved a fairly high predictability, with an R2 of 0.59 for model validation, 0.77 for model calibration (training), and a low root mean square error (RMSE), indicating a high capacity to simulate the dynamics of N2O flux. According to a sensitivity analysis of the GRNN, nonlinear relationships between input variables and N2O flux were well explained. Our results suggest that the GRNN developed in this study has a greater performance in simulating variations in N2O flux than nonlinear regressions.

How Much Can We Learn from a Single Chromatographic Experiment? A Bayesian Perspective.

PubMed

Wiczling, Paweł; Kaliszan, Roman

2016-01-05

In this work, we proposed and investigated a Bayesian inference procedure to find the desired chromatographic conditions based on known analyte properties (lipophilicity, pKa, and polar surface area) using one preliminary experiment. A previously developed nonlinear mixed effect model was used to specify the prior information about a new analyte with known physicochemical properties. Further, the prior (no preliminary data) and posterior predictive distribution (prior + one experiment) were determined sequentially to search towards the desired separation. The following isocratic high-performance reversed-phase liquid chromatographic conditions were sought: (1) retention time of a single analyte within the range of 4-6 min and (2) baseline separation of two analytes with retention times within the range of 4-10 min. The empirical posterior Bayesian distribution of parameters was estimated using the "slice sampling" Markov Chain Monte Carlo (MCMC) algorithm implemented in Matlab. The simulations with artificial analytes and experimental data of ketoprofen and papaverine were used to test the proposed methodology. The simulation experiment showed that for a single and two randomly selected analytes, there is 97% and 74% probability of obtaining a successful chromatogram using none or one preliminary experiment. The desired separation for ketoprofen and papaverine was established based on a single experiment. It was confirmed that the search for a desired separation rarely requires a large number of chromatographic analyses at least for a simple optimization problem. The proposed Bayesian-based optimization scheme is a powerful method of finding a desired chromatographic separation based on a small number of preliminary experiments.

Neuromusculoskeletal model self-calibration for on-line sequential bayesian moment estimation

NASA Astrophysics Data System (ADS)

Bueno, Diana R.; Montano, L.

2017-04-01

Objective. Neuromusculoskeletal models involve many subject-specific physiological parameters that need to be adjusted to adequately represent muscle properties. Traditionally, neuromusculoskeletal models have been calibrated with a forward-inverse dynamic optimization which is time-consuming and unfeasible for rehabilitation therapy. Non self-calibration algorithms have been applied to these models. To the best of our knowledge, the algorithm proposed in this work is the first on-line calibration algorithm for muscle models that allows a generic model to be adjusted to different subjects in a few steps. Approach. In this paper we propose a reformulation of the traditional muscle models that is able to sequentially estimate the kinetics (net joint moments), and also its full self-calibration (subject-specific internal parameters of the muscle from a set of arbitrary uncalibrated data), based on the unscented Kalman filter. The nonlinearity of the model as well as its calibration problem have obliged us to adopt the sum of Gaussians filter suitable for nonlinear systems. Main results. This sequential Bayesian self-calibration algorithm achieves a complete muscle model calibration using as input only a dataset of uncalibrated sEMG and kinematics data. The approach is validated experimentally using data from the upper limbs of 21 subjects. Significance. The results show the feasibility of neuromusculoskeletal model self-calibration. This study will contribute to a better understanding of the generalization of muscle models for subject-specific rehabilitation therapies. Moreover, this work is very promising for rehabilitation devices such as electromyography-driven exoskeletons or prostheses.

Social Influence on Information Technology Adoption and Sustained Use in Healthcare: A Hierarchical Bayesian Learning Method Analysis

ERIC Educational Resources Information Center

Hao, Haijing

2013-01-01

Information technology adoption and diffusion is currently a significant challenge in the healthcare delivery setting. This thesis includes three papers that explore social influence on information technology adoption and sustained use in the healthcare delivery environment using conventional regression models and novel hierarchical Bayesian…

Collection Fusion Using Bayesian Estimation of a Linear Regression Model in Image Databases on the Web.

ERIC Educational Resources Information Center

Kim, Deok-Hwan; Chung, Chin-Wan

2003-01-01

Discusses the collection fusion problem of image databases, concerned with retrieving relevant images by content based retrieval from image databases distributed on the Web. Focuses on a metaserver which selects image databases supporting similarity measures and proposes a new algorithm which exploits a probabilistic technique using Bayesian…

Weakly Informative Prior for Point Estimation of Covariance Matrices in Hierarchical Models

ERIC Educational Resources Information Center

Chung, Yeojin; Gelman, Andrew; Rabe-Hesketh, Sophia; Liu, Jingchen; Dorie, Vincent

2015-01-01

When fitting hierarchical regression models, maximum likelihood (ML) estimation has computational (and, for some users, philosophical) advantages compared to full Bayesian inference, but when the number of groups is small, estimates of the covariance matrix (S) of group-level varying coefficients are often degenerate. One can do better, even from…

Analyzing thresholds and efficiency with hierarchical Bayesian logistic regression.

PubMed

Houpt, Joseph W; Bittner, Jennifer L

2018-07-01

Ideal observer analysis is a fundamental tool used widely in vision science for analyzing the efficiency with which a cognitive or perceptual system uses available information. The performance of an ideal observer provides a formal measure of the amount of information in a given experiment. The ratio of human to ideal performance is then used to compute efficiency, a construct that can be directly compared across experimental conditions while controlling for the differences due to the stimuli and/or task specific demands. In previous research using ideal observer analysis, the effects of varying experimental conditions on efficiency have been tested using ANOVAs and pairwise comparisons. In this work, we present a model that combines Bayesian estimates of psychometric functions with hierarchical logistic regression for inference about both unadjusted human performance metrics and efficiencies. Our approach improves upon the existing methods by constraining the statistical analysis using a standard model connecting stimulus intensity to human observer accuracy and by accounting for variability in the estimates of human and ideal observer performance scores. This allows for both individual and group level inferences. Copyright © 2018 Elsevier Ltd. All rights reserved.

Model selection with multiple regression on distance matrices leads to incorrect inferences.

PubMed

Franckowiak, Ryan P; Panasci, Michael; Jarvis, Karl J; Acuña-Rodriguez, Ian S; Landguth, Erin L; Fortin, Marie-Josée; Wagner, Helene H

2017-01-01

In landscape genetics, model selection procedures based on Information Theoretic and Bayesian principles have been used with multiple regression on distance matrices (MRM) to test the relationship between multiple vectors of pairwise genetic, geographic, and environmental distance. Using Monte Carlo simulations, we examined the ability of model selection criteria based on Akaike's information criterion (AIC), its small-sample correction (AICc), and the Bayesian information criterion (BIC) to reliably rank candidate models when applied with MRM while varying the sample size. The results showed a serious problem: all three criteria exhibit a systematic bias toward selecting unnecessarily complex models containing spurious random variables and erroneously suggest a high level of support for the incorrectly ranked best model. These problems effectively increased with increasing sample size. The failure of AIC, AICc, and BIC was likely driven by the inflated sample size and different sum-of-squares partitioned by MRM, and the resulting effect on delta values. Based on these findings, we strongly discourage the continued application of AIC, AICc, and BIC for model selection with MRM.

Bayesian additive decision trees of biomarker by treatment interactions for predictive biomarker detection and subgroup identification.

PubMed

Zhao, Yang; Zheng, Wei; Zhuo, Daisy Y; Lu, Yuefeng; Ma, Xiwen; Liu, Hengchang; Zeng, Zhen; Laird, Glen

2017-10-11

Personalized medicine, or tailored therapy, has been an active and important topic in recent medical research. Many methods have been proposed in the literature for predictive biomarker detection and subgroup identification. In this article, we propose a novel decision tree-based approach applicable in randomized clinical trials. We model the prognostic effects of the biomarkers using additive regression trees and the biomarker-by-treatment effect using a single regression tree. Bayesian approach is utilized to periodically revise the split variables and the split rules of the decision trees, which provides a better overall fitting. Gibbs sampler is implemented in the MCMC procedure, which updates the prognostic trees and the interaction tree separately. We use the posterior distribution of the interaction tree to construct the predictive scores of the biomarkers and to identify the subgroup where the treatment is superior to the control. Numerical simulations show that our proposed method performs well under various settings comparing to existing methods. We also demonstrate an application of our method in a real clinical trial.

Revisiting crash spatial heterogeneity: A Bayesian spatially varying coefficients approach.

PubMed

Xu, Pengpeng; Huang, Helai; Dong, Ni; Wong, S C

2017-01-01

This study was performed to investigate the spatially varying relationships between crash frequency and related risk factors. A Bayesian spatially varying coefficients model was elaborately introduced as a methodological alternative to simultaneously account for the unstructured and spatially structured heterogeneity of the regression coefficients in predicting crash frequencies. The proposed method was appealing in that the parameters were modeled via a conditional autoregressive prior distribution, which involved a single set of random effects and a spatial correlation parameter with extreme values corresponding to pure unstructured or pure spatially correlated random effects. A case study using a three-year crash dataset from the Hillsborough County, Florida, was conducted to illustrate the proposed model. Empirical analysis confirmed the presence of both unstructured and spatially correlated variations in the effects of contributory factors on severe crash occurrences. The findings also suggested that ignoring spatially structured heterogeneity may result in biased parameter estimates and incorrect inferences, while assuming the regression coefficients to be spatially clustered only is probably subject to the issue of over-smoothness. Copyright © 2016 Elsevier Ltd. All rights reserved.

Spatial Bayesian Latent Factor Regression Modeling of Coordinate-based Meta-analysis Data

PubMed Central

Montagna, Silvia; Wager, Tor; Barrett, Lisa Feldman; Johnson, Timothy D.; Nichols, Thomas E.

2017-01-01

Summary Now over 20 years old, functional MRI (fMRI) has a large and growing literature that is best synthesised with meta-analytic tools. As most authors do not share image data, only the peak activation coordinates (foci) reported in the paper are available for Coordinate-Based Meta-Analysis (CBMA). Neuroimaging meta-analysis is used to 1) identify areas of consistent activation; and 2) build a predictive model of task type or cognitive process for new studies (reverse inference). To simultaneously address these aims, we propose a Bayesian point process hierarchical model for CBMA. We model the foci from each study as a doubly stochastic Poisson process, where the study-specific log intensity function is characterised as a linear combination of a high-dimensional basis set. A sparse representation of the intensities is guaranteed through latent factor modeling of the basis coefficients. Within our framework, it is also possible to account for the effect of study-level covariates (meta-regression), significantly expanding the capabilities of the current neuroimaging meta-analysis methods available. We apply our methodology to synthetic data and neuroimaging meta-analysis datasets. PMID:28498564

Logistic Mixed Models to Investigate Implicit and Explicit Belief Tracking

PubMed Central

Lages, Martin; Scheel, Anne

2016-01-01

We investigated the proposition of a two-systems Theory of Mind in adults’ belief tracking. A sample of N = 45 participants predicted the choice of one of two opponent players after observing several rounds in an animated card game. Three matches of this card game were played and initial gaze direction on target and subsequent choice predictions were recorded for each belief task and participant. We conducted logistic regressions with mixed effects on the binary data and developed Bayesian logistic mixed models to infer implicit and explicit mentalizing in true belief and false belief tasks. Although logistic regressions with mixed effects predicted the data well a Bayesian logistic mixed model with latent task- and subject-specific parameters gave a better account of the data. As expected explicit choice predictions suggested a clear understanding of true and false beliefs (TB/FB). Surprisingly, however, model parameters for initial gaze direction also indicated belief tracking. We discuss why task-specific parameters for initial gaze directions are different from choice predictions yet reflect second-order perspective taking. PMID:27853440

Bayesian networks in overlay recipe optimization

NASA Astrophysics Data System (ADS)

Binns, Lewis A.; Reynolds, Greg; Rigden, Timothy C.; Watkins, Stephen; Soroka, Andrew

2005-05-01

Currently, overlay measurements are characterized by "recipe", which defines both physical parameters such as focus, illumination et cetera, and also the software parameters such as algorithm to be used and regions of interest. Setting up these recipes requires both engineering time and wafer availability on an overlay tool, so reducing these requirements will result in higher tool productivity. One of the significant challenges to automating this process is that the parameters are highly and complexly correlated. At the same time, a high level of traceability and transparency is required in the recipe creation process, so a technique that maintains its decisions in terms of well defined physical parameters is desirable. Running time should be short, given the system (automatic recipe creation) is being implemented to reduce overheads. Finally, a failure of the system to determine acceptable parameters should be obvious, so a certainty metric is also desirable. The complex, nonlinear interactions make solution by an expert system difficult at best, especially in the verification of the resulting decision network. The transparency requirements tend to preclude classical neural networks and similar techniques. Genetic algorithms and other "global minimization" techniques require too much computational power (given system footprint and cost requirements). A Bayesian network, however, provides a solution to these requirements. Such a network, with appropriate priors, can be used during recipe creation / optimization not just to select a good set of parameters, but also to guide the direction of search, by evaluating the network state while only incomplete information is available. As a Bayesian network maintains an estimate of the probability distribution of nodal values, a maximum-entropy approach can be utilized to obtain a working recipe in a minimum or near-minimum number of steps. In this paper we discuss the potential use of a Bayesian network in such a capacity, reducing the amount of engineering intervention. We discuss the benefits of this approach, especially improved repeatability and traceability of the learning process, and quantification of uncertainty in decisions made. We also consider the problems associated with this approach, especially in detailed construction of network topology, validation of the Bayesian network and the recipes it generates, and issues arising from the integration of a Bayesian network with a complex multithreaded application; these primarily relate to maintaining Bayesian network and system architecture integrity.

How to interpret the results of medical time series data analysis: Classical statistical approaches versus dynamic Bayesian network modeling.

PubMed

Onisko, Agnieszka; Druzdzel, Marek J; Austin, R Marshall

2016-01-01

Classical statistics is a well-established approach in the analysis of medical data. While the medical community seems to be familiar with the concept of a statistical analysis and its interpretation, the Bayesian approach, argued by many of its proponents to be superior to the classical frequentist approach, is still not well-recognized in the analysis of medical data. The goal of this study is to encourage data analysts to use the Bayesian approach, such as modeling with graphical probabilistic networks, as an insightful alternative to classical statistical analysis of medical data. This paper offers a comparison of two approaches to analysis of medical time series data: (1) classical statistical approach, such as the Kaplan-Meier estimator and the Cox proportional hazards regression model, and (2) dynamic Bayesian network modeling. Our comparison is based on time series cervical cancer screening data collected at Magee-Womens Hospital, University of Pittsburgh Medical Center over 10 years. The main outcomes of our comparison are cervical cancer risk assessments produced by the three approaches. However, our analysis discusses also several aspects of the comparison, such as modeling assumptions, model building, dealing with incomplete data, individualized risk assessment, results interpretation, and model validation. Our study shows that the Bayesian approach is (1) much more flexible in terms of modeling effort, and (2) it offers an individualized risk assessment, which is more cumbersome for classical statistical approaches.

A regularization corrected score method for nonlinear regression models with covariate error.

PubMed

Zucker, David M; Gorfine, Malka; Li, Yi; Tadesse, Mahlet G; Spiegelman, Donna

2013-03-01

Many regression analyses involve explanatory variables that are measured with error, and failing to account for this error is well known to lead to biased point and interval estimates of the regression coefficients. We present here a new general method for adjusting for covariate error. Our method consists of an approximate version of the Stefanski-Nakamura corrected score approach, using the method of regularization to obtain an approximate solution of the relevant integral equation. We develop the theory in the setting of classical likelihood models; this setting covers, for example, linear regression, nonlinear regression, logistic regression, and Poisson regression. The method is extremely general in terms of the types of measurement error models covered, and is a functional method in the sense of not involving assumptions on the distribution of the true covariate. We discuss the theoretical properties of the method and present simulation results in the logistic regression setting (univariate and multivariate). For illustration, we apply the method to data from the Harvard Nurses' Health Study concerning the relationship between physical activity and breast cancer mortality in the period following a diagnosis of breast cancer. Copyright © 2013, The International Biometric Society.

An ensemble Kalman filter for statistical estimation of physics constrained nonlinear regression models

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

Harlim, John, E-mail: jharlim@psu.edu; Mahdi, Adam, E-mail: amahdi@ncsu.edu; Majda, Andrew J., E-mail: jonjon@cims.nyu.edu

2014-01-15

A central issue in contemporary science is the development of nonlinear data driven statistical–dynamical models for time series of noisy partial observations from nature or a complex model. It has been established recently that ad-hoc quadratic multi-level regression models can have finite-time blow-up of statistical solutions and/or pathological behavior of their invariant measure. Recently, a new class of physics constrained nonlinear regression models were developed to ameliorate this pathological behavior. Here a new finite ensemble Kalman filtering algorithm is developed for estimating the state, the linear and nonlinear model coefficients, the model and the observation noise covariances from available partialmore » noisy observations of the state. Several stringent tests and applications of the method are developed here. In the most complex application, the perfect model has 57 degrees of freedom involving a zonal (east–west) jet, two topographic Rossby waves, and 54 nonlinearly interacting Rossby waves; the perfect model has significant non-Gaussian statistics in the zonal jet with blocked and unblocked regimes and a non-Gaussian skewed distribution due to interaction with the other 56 modes. We only observe the zonal jet contaminated by noise and apply the ensemble filter algorithm for estimation. Numerically, we find that a three dimensional nonlinear stochastic model with one level of memory mimics the statistical effect of the other 56 modes on the zonal jet in an accurate fashion, including the skew non-Gaussian distribution and autocorrelation decay. On the other hand, a similar stochastic model with zero memory levels fails to capture the crucial non-Gaussian behavior of the zonal jet from the perfect 57-mode model.« less

Analog ensemble and Bayesian regression techniques to improve the wind speed prediction during extreme storms in the NE U.S.

NASA Astrophysics Data System (ADS)

Yang, J.; Astitha, M.; Delle Monache, L.; Alessandrini, S.

2016-12-01

Accuracy of weather forecasts in Northeast U.S. has become very important in recent years, given the serious and devastating effects of extreme weather events. Despite the use of evolved forecasting tools and techniques strengthened by increased super-computing resources, the weather forecasting systems still have their limitations in predicting extreme events. In this study, we examine the combination of analog ensemble and Bayesian regression techniques to improve the prediction of storms that have impacted NE U.S., mostly defined by the occurrence of high wind speeds (i.e. blizzards, winter storms, hurricanes and thunderstorms). The predicted wind speed, wind direction and temperature by two state-of-the-science atmospheric models (WRF and RAMS/ICLAMS) are combined using the mentioned techniques, exploring various ways that those variables influence the minimization of the prediction error (systematic and random). This study is focused on retrospective simulations of 146 storms that affected the NE U.S. in the period 2005-2016. In order to evaluate the techniques, leave-one-out cross validation procedure was implemented regarding 145 storms as the training dataset. The analog ensemble method selects a set of past observations that corresponded to the best analogs of the numerical weather prediction and provides a set of ensemble members of the selected observation dataset. The set of ensemble members can then be used in a deterministic or probabilistic way. In the Bayesian regression framework, optimal variances are estimated for the training partition by minimizing the root mean square error and are applied to the out-of-sample storm. The preliminary results indicate a significant improvement in the statistical metrics of 10-m wind speed for 146 storms using both techniques (20-30% bias and error reduction in all observation-model pairs). In this presentation, we discuss the various combinations of atmospheric predictors and techniques and illustrate how the long record of predicted storms is valuable in the improvement of wind speed prediction.

Predictability of extreme weather events for NE U.S.: improvement of the numerical prediction using a Bayesian regression approach

NASA Astrophysics Data System (ADS)

Yang, J.; Astitha, M.; Anagnostou, E. N.; Hartman, B.; Kallos, G. B.

2015-12-01

Weather prediction accuracy has become very important for the Northeast U.S. given the devastating effects of extreme weather events in the recent years. Weather forecasting systems are used towards building strategies to prevent catastrophic losses for human lives and the environment. Concurrently, weather forecast tools and techniques have evolved with improved forecast skill as numerical prediction techniques are strengthened by increased super-computing resources. In this study, we examine the combination of two state-of-the-science atmospheric models (WRF and RAMS/ICLAMS) by utilizing a Bayesian regression approach to improve the prediction of extreme weather events for NE U.S. The basic concept behind the Bayesian regression approach is to take advantage of the strengths of two atmospheric modeling systems and, similar to the multi-model ensemble approach, limit their weaknesses which are related to systematic and random errors in the numerical prediction of physical processes. The first part of this study is focused on retrospective simulations of seventeen storms that affected the region in the period 2004-2013. Optimal variances are estimated by minimizing the root mean square error and are applied to out-of-sample weather events. The applicability and usefulness of this approach are demonstrated by conducting an error analysis based on in-situ observations from meteorological stations of the National Weather Service (NWS) for wind speed and wind direction, and NCEP Stage IV radar data, mosaicked from the regional multi-sensor for precipitation. The preliminary results indicate a significant improvement in the statistical metrics of the modeled-observed pairs for meteorological variables using various combinations of the sixteen events as predictors of the seventeenth. This presentation will illustrate the implemented methodology and the obtained results for wind speed, wind direction and precipitation, as well as set the research steps that will be followed in the future.

Spatiotemporal Modeling of Ozone Levels in Quebec (Canada): A Comparison of Kriging, Land-Use Regression (LUR), and Combined Bayesian Maximum Entropy–LUR Approaches

PubMed Central

Adam-Poupart, Ariane; Brand, Allan; Fournier, Michel; Jerrett, Michael

2014-01-01

Background: Ambient air ozone (O3) is a pulmonary irritant that has been associated with respiratory health effects including increased lung inflammation and permeability, airway hyperreactivity, respiratory symptoms, and decreased lung function. Estimation of O3 exposure is a complex task because the pollutant exhibits complex spatiotemporal patterns. To refine the quality of exposure estimation, various spatiotemporal methods have been developed worldwide. Objectives: We sought to compare the accuracy of three spatiotemporal models to predict summer ground-level O3 in Quebec, Canada. Methods: We developed a land-use mixed-effects regression (LUR) model based on readily available data (air quality and meteorological monitoring data, road networks information, latitude), a Bayesian maximum entropy (BME) model incorporating both O3 monitoring station data and the land-use mixed model outputs (BME-LUR), and a kriging method model based only on available O3 monitoring station data (BME kriging). We performed leave-one-station-out cross-validation and visually assessed the predictive capability of each model by examining the mean temporal and spatial distributions of the average estimated errors. Results: The BME-LUR was the best predictive model (R2 = 0.653) with the lowest root mean-square error (RMSE ;7.06 ppb), followed by the LUR model (R2 = 0.466, RMSE = 8.747) and the BME kriging model (R2 = 0.414, RMSE = 9.164). Conclusions: Our findings suggest that errors of estimation in the interpolation of O3 concentrations with BME can be greatly reduced by incorporating outputs from a LUR model developed with readily available data. Citation: Adam-Poupart A, Brand A, Fournier M, Jerrett M, Smargiassi A. 2014. Spatiotemporal modeling of ozone levels in Quebec (Canada): a comparison of kriging, land-use regression (LUR), and combined Bayesian maximum entropy–LUR approaches. Environ Health Perspect 122:970–976; http://dx.doi.org/10.1289/ehp.1306566 PMID:24879650

Extensions and applications of ensemble-of-trees methods in machine learning

NASA Astrophysics Data System (ADS)

Bleich, Justin

Ensemble-of-trees algorithms have emerged to the forefront of machine learning due to their ability to generate high forecasting accuracy for a wide array of regression and classification problems. Classic ensemble methodologies such as random forests (RF) and stochastic gradient boosting (SGB) rely on algorithmic procedures to generate fits to data. In contrast, more recent ensemble techniques such as Bayesian Additive Regression Trees (BART) and Dynamic Trees (DT) focus on an underlying Bayesian probability model to generate the fits. These new probability model-based approaches show much promise versus their algorithmic counterparts, but also offer substantial room for improvement. The first part of this thesis focuses on methodological advances for ensemble-of-trees techniques with an emphasis on the more recent Bayesian approaches. In particular, we focus on extensions of BART in four distinct ways. First, we develop a more robust implementation of BART for both research and application. We then develop a principled approach to variable selection for BART as well as the ability to naturally incorporate prior information on important covariates into the algorithm. Next, we propose a method for handling missing data that relies on the recursive structure of decision trees and does not require imputation. Last, we relax the assumption of homoskedasticity in the BART model to allow for parametric modeling of heteroskedasticity. The second part of this thesis returns to the classic algorithmic approaches in the context of classification problems with asymmetric costs of forecasting errors. First we consider the performance of RF and SGB more broadly and demonstrate its superiority to logistic regression for applications in criminology with asymmetric costs. Next, we use RF to forecast unplanned hospital readmissions upon patient discharge with asymmetric costs taken into account. Finally, we explore the construction of stable decision trees for forecasts of violence during probation hearings in court systems.

Bayesian Design of Superiority Clinical Trials for Recurrent Events Data with Applications to Bleeding and Transfusion Events in Myelodyplastic Syndrome

PubMed Central

Chen, Ming-Hui; Zeng, Donglin; Hu, Kuolung; Jia, Catherine

2014-01-01

Summary In many biomedical studies, patients may experience the same type of recurrent event repeatedly over time, such as bleeding, multiple infections and disease. In this article, we propose a Bayesian design to a pivotal clinical trial in which lower risk myelodysplastic syndromes (MDS) patients are treated with MDS disease modifying therapies. One of the key study objectives is to demonstrate the investigational product (treatment) effect on reduction of platelet transfusion and bleeding events while receiving MDS therapies. In this context, we propose a new Bayesian approach for the design of superiority clinical trials using recurrent events frailty regression models. Historical recurrent events data from an already completed phase 2 trial are incorporated into the Bayesian design via the partial borrowing power prior of Ibrahim et al. (2012, Biometrics 68, 578–586). An efficient Gibbs sampling algorithm, a predictive data generation algorithm, and a simulation-based algorithm are developed for sampling from the fitting posterior distribution, generating the predictive recurrent events data, and computing various design quantities such as the type I error rate and power, respectively. An extensive simulation study is conducted to compare the proposed method to the existing frequentist methods and to investigate various operating characteristics of the proposed design. PMID:25041037

Hierarchical Adaptive Regression Kernels for Regression with Functional Predictors.

PubMed

Woodard, Dawn B; Crainiceanu, Ciprian; Ruppert, David

2013-01-01

We propose a new method for regression using a parsimonious and scientifically interpretable representation of functional predictors. Our approach is designed for data that exhibit features such as spikes, dips, and plateaus whose frequency, location, size, and shape varies stochastically across subjects. We propose Bayesian inference of the joint functional and exposure models, and give a method for efficient computation. We contrast our approach with existing state-of-the-art methods for regression with functional predictors, and show that our method is more effective and efficient for data that include features occurring at varying locations. We apply our methodology to a large and complex dataset from the Sleep Heart Health Study, to quantify the association between sleep characteristics and health outcomes. Software and technical appendices are provided in online supplemental materials.

A Bayesian network model for predicting type 2 diabetes risk based on electronic health records

NASA Astrophysics Data System (ADS)

Xie, Jiang; Liu, Yan; Zeng, Xu; Zhang, Wu; Mei, Zhen

2017-07-01

An extensive, in-depth study of diabetes risk factors (DBRF) is of crucial importance to prevent (or reduce) the chance of suffering from type 2 diabetes (T2D). Accumulation of electronic health records (EHRs) makes it possible to build nonlinear relationships between risk factors and diabetes. However, the current DBRF researches mainly focus on qualitative analyses, and the inconformity of physical examination items makes the risk factors likely to be lost, which drives us to study the novel machine learning approach for risk model development. In this paper, we use Bayesian networks (BNs) to analyze the relationship between physical examination information and T2D, and to quantify the link between risk factors and T2D. Furthermore, with the quantitative analyses of DBRF, we adopt EHR and propose a machine learning approach based on BNs to predict the risk of T2D. The experiments demonstrate that our approach can lead to better predictive performance than the classical risk model.

Bayesian inference of physiologically meaningful parameters from body sway measurements.

PubMed

Tietäväinen, A; Gutmann, M U; Keski-Vakkuri, E; Corander, J; Hæggström, E

2017-06-19

The control of the human body sway by the central nervous system, muscles, and conscious brain is of interest since body sway carries information about the physiological status of a person. Several models have been proposed to describe body sway in an upright standing position, however, due to the statistical intractability of the more realistic models, no formal parameter inference has previously been conducted and the expressive power of such models for real human subjects remains unknown. Using the latest advances in Bayesian statistical inference for intractable models, we fitted a nonlinear control model to posturographic measurements, and we showed that it can accurately predict the sway characteristics of both simulated and real subjects. Our method provides a full statistical characterization of the uncertainty related to all model parameters as quantified by posterior probability density functions, which is useful for comparisons across subjects and test settings. The ability to infer intractable control models from sensor data opens new possibilities for monitoring and predicting body status in health applications.

Hybrid ICA-Bayesian network approach reveals distinct effective connectivity differences in schizophrenia.

PubMed

Kim, D; Burge, J; Lane, T; Pearlson, G D; Kiehl, K A; Calhoun, V D

2008-10-01

We utilized a discrete dynamic Bayesian network (dDBN) approach (Burge, J., Lane, T., Link, H., Qiu, S., Clark, V.P., 2007. Discrete dynamic Bayesian network analysis of fMRI data. Hum Brain Mapp.) to determine differences in brain regions between patients with schizophrenia and healthy controls on a measure of effective connectivity, termed the approximate conditional likelihood score (ACL) (Burge, J., Lane, T., 2005. Learning Class-Discriminative Dynamic Bayesian Networks. Proceedings of the International Conference on Machine Learning, Bonn, Germany, pp. 97-104.). The ACL score represents a class-discriminative measure of effective connectivity by measuring the relative likelihood of the correlation between brain regions in one group versus another. The algorithm is capable of finding non-linear relationships between brain regions because it uses discrete rather than continuous values and attempts to model temporal relationships with a first-order Markov and stationary assumption constraint (Papoulis, A., 1991. Probability, random variables, and stochastic processes. McGraw-Hill, New York.). Since Bayesian networks are overly sensitive to noisy data, we introduced an independent component analysis (ICA) filtering approach that attempted to reduce the noise found in fMRI data by unmixing the raw datasets into a set of independent spatial component maps. Components that represented noise were removed and the remaining components reconstructed into the dimensions of the original fMRI datasets. We applied the dDBN algorithm to a group of 35 patients with schizophrenia and 35 matched healthy controls using an ICA filtered and unfiltered approach. We determined that filtering the data significantly improved the magnitude of the ACL score. Patients showed the greatest ACL scores in several regions, most markedly the cerebellar vermis and hemispheres. Our findings suggest that schizophrenia patients exhibit weaker connectivity than healthy controls in multiple regions, including bilateral temporal, frontal, and cerebellar regions during an auditory paradigm.

A data driven nonlinear stochastic model for blood glucose dynamics.

PubMed

Zhang, Yan; Holt, Tim A; Khovanova, Natalia

2016-03-01

The development of adequate mathematical models for blood glucose dynamics may improve early diagnosis and control of diabetes mellitus (DM). We have developed a stochastic nonlinear second order differential equation to describe the response of blood glucose concentration to food intake using continuous glucose monitoring (CGM) data. A variational Bayesian learning scheme was applied to define the number and values of the system's parameters by iterative optimisation of free energy. The model has the minimal order and number of parameters to successfully describe blood glucose dynamics in people with and without DM. The model accounts for the nonlinearity and stochasticity of the underlying glucose-insulin dynamic process. Being data-driven, it takes full advantage of available CGM data and, at the same time, reflects the intrinsic characteristics of the glucose-insulin system without detailed knowledge of the physiological mechanisms. We have shown that the dynamics of some postprandial blood glucose excursions can be described by a reduced (linear) model, previously seen in the literature. A comprehensive analysis demonstrates that deterministic system parameters belong to different ranges for diabetes and controls. Implications for clinical practice are discussed. This is the first study introducing a continuous data-driven nonlinear stochastic model capable of describing both DM and non-DM profiles. Copyright © 2015 The Authors. Published by Elsevier Ireland Ltd.. All rights reserved.

The mechanical properties of high speed GTAW weld and factors of nonlinear multiple regression model under external transverse magnetic field

NASA Astrophysics Data System (ADS)

Lu, Lin; Chang, Yunlong; Li, Yingmin; He, Youyou

2013-05-01

A transverse magnetic field was introduced to the arc plasma in the process of welding stainless steel tubes by high-speed Tungsten Inert Gas Arc Welding (TIG for short) without filler wire. The influence of external magnetic field on welding quality was investigated. 9 sets of parameters were designed by the means of orthogonal experiment. The welding joint tensile strength and form factor of weld were regarded as the main standards of welding quality. A binary quadratic nonlinear regression equation was established with the conditions of magnetic induction and flow rate of Ar gas. The residual standard deviation was calculated to adjust the accuracy of regression model. The results showed that, the regression model was correct and effective in calculating the tensile strength and aspect ratio of weld. Two 3D regression models were designed respectively, and then the impact law of magnetic induction on welding quality was researched.

Nonlinear multivariate and time series analysis by neural network methods

NASA Astrophysics Data System (ADS)

Hsieh, William W.

2004-03-01

Methods in multivariate statistical analysis are essential for working with large amounts of geophysical data, data from observational arrays, from satellites, or from numerical model output. In classical multivariate statistical analysis, there is a hierarchy of methods, starting with linear regression at the base, followed by principal component analysis (PCA) and finally canonical correlation analysis (CCA). A multivariate time series method, the singular spectrum analysis (SSA), has been a fruitful extension of the PCA technique. The common drawback of these classical methods is that only linear structures can be correctly extracted from the data. Since the late 1980s, neural network methods have become popular for performing nonlinear regression and classification. More recently, neural network methods have been extended to perform nonlinear PCA (NLPCA), nonlinear CCA (NLCCA), and nonlinear SSA (NLSSA). This paper presents a unified view of the NLPCA, NLCCA, and NLSSA techniques and their applications to various data sets of the atmosphere and the ocean (especially for the El Niño-Southern Oscillation and the stratospheric quasi-biennial oscillation). These data sets reveal that the linear methods are often too simplistic to describe real-world systems, with a tendency to scatter a single oscillatory phenomenon into numerous unphysical modes or higher harmonics, which can be largely alleviated in the new nonlinear paradigm.

Evidence for Legacy Contamination of Nitrate in Groundwater of North Carolina Using Monitoring and Private Well Data Models

NASA Astrophysics Data System (ADS)

Messier, K. P.; Kane, E.; Bolich, R.; Serre, M. L.

2014-12-01

Nitrate (NO3-) is a widespread contaminant of groundwater and surface water across the United States that has deleterious effects to human and ecological health. Legacy contamination, or past releases of NO3-, is thought to be impacting current groundwater and surface water of North Carolina. This study develops a model for predicting point-level groundwater NO3- at a state scale for monitoring wells and private wells of North Carolina. A land use regression (LUR) model selection procedure known as constrained forward nonlinear regression and hyperparameter optimization (CFN-RHO) is developed for determining nonlinear model explanatory variables when they are known to be correlated. Bayesian Maximum Entropy (BME) is then used to integrate the LUR model to create a LUR-BME model of spatial/temporal varying groundwater NO3- concentrations. LUR-BME results in a leave-one-out cross-validation r2 of 0.74 and 0.33 for monitoring and private wells, effectively predicting within spatial covariance ranges. The major finding regarding legacy sources NO3- in this study is that the LUR-BME models show the geographical extent of low-level contamination of deeper drinking-water aquifers is beyond that of the shallower monitoring well. Groundwater NO3- in monitoring wells is highly variable with many areas predicted above the current Environmental Protection Agency standard of 10 mg/L. Contrarily, the private well results depict widespread, low-level NO3-concentrations. This evidence supports that in addition to downward transport, there is also a significant outward transport of groundwater NO3- in the drinking water aquifer to areas outside the range of sources. Results indicate that the deeper aquifers are potentially acting as a reservoir that is not only deeper, but also covers a larger geographical area, than the reservoir formed by the shallow aquifers. Results are of interest to agencies that regulate surface water and drinking water sources impacted by the effects of legacy NO3- sources. Additionally, the results can provide guidance on factors affecting the point-level variability of groundwater NO3- and areas where monitoring is needed to reduce uncertainty. Lastly, LUR-BME predictions can be integrated into surface water models for more accurate management of non-point sources of nitrogen.

Breaking Computational Barriers: Real-time Analysis and Optimization with Large-scale Nonlinear Models via Model Reduction

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

Carlberg, Kevin Thomas; Drohmann, Martin; Tuminaro, Raymond S.

2014-10-01

Model reduction for dynamical systems is a promising approach for reducing the computational cost of large-scale physics-based simulations to enable high-fidelity models to be used in many- query (e.g., Bayesian inference) and near-real-time (e.g., fast-turnaround simulation) contexts. While model reduction works well for specialized problems such as linear time-invariant systems, it is much more difficult to obtain accurate, stable, and efficient reduced-order models (ROMs) for systems with general nonlinearities. This report describes several advances that enable nonlinear reduced-order models (ROMs) to be deployed in a variety of time-critical settings. First, we present an error bound for the Gauss-Newton with Approximatedmore » Tensors (GNAT) nonlinear model reduction technique. This bound allows the state-space error for the GNAT method to be quantified when applied with the backward Euler time-integration scheme. Second, we present a methodology for preserving classical Lagrangian structure in nonlinear model reduction. This technique guarantees that important properties--such as energy conservation and symplectic time-evolution maps--are preserved when performing model reduction for models described by a Lagrangian formalism (e.g., molecular dynamics, structural dynamics). Third, we present a novel technique for decreasing the temporal complexity --defined as the number of Newton-like iterations performed over the course of the simulation--by exploiting time-domain data. Fourth, we describe a novel method for refining projection-based reduced-order models a posteriori using a goal-oriented framework similar to mesh-adaptive h -refinement in finite elements. The technique allows the ROM to generate arbitrarily accurate solutions, thereby providing the ROM with a 'failsafe' mechanism in the event of insufficient training data. Finally, we present the reduced-order model error surrogate (ROMES) method for statistically quantifying reduced- order-model errors. This enables ROMs to be rigorously incorporated in uncertainty-quantification settings, as the error model can be treated as a source of epistemic uncertainty. This work was completed as part of a Truman Fellowship appointment. We note that much additional work was performed as part of the Fellowship. One salient project is the development of the Trilinos-based model-reduction software module Razor , which is currently bundled with the Albany PDE code and currently allows nonlinear reduced-order models to be constructed for any application supported in Albany. Other important projects include the following: 1. ROMES-equipped ROMs for Bayesian inference: K. Carlberg, M. Drohmann, F. Lu (Lawrence Berkeley National Laboratory), M. Morzfeld (Lawrence Berkeley National Laboratory). 2. ROM-enabled Krylov-subspace recycling: K. Carlberg, V. Forstall (University of Maryland), P. Tsuji, R. Tuminaro. 3. A pseudo balanced POD method using only dual snapshots: K. Carlberg, M. Sarovar. 4. An analysis of discrete v. continuous optimality in nonlinear model reduction: K. Carlberg, M. Barone, H. Antil (George Mason University). Journal articles for these projects are in progress at the time of this writing.« less

A spectral-spatial-dynamic hierarchical Bayesian (SSD-HB) model for estimating soybean yield

NASA Astrophysics Data System (ADS)

Kazama, Yoriko; Kujirai, Toshihiro

2014-10-01

A method called a "spectral-spatial-dynamic hierarchical-Bayesian (SSD-HB) model," which can deal with many parameters (such as spectral and weather information all together) by reducing the occurrence of multicollinearity, is proposed. Experiments conducted on soybean yields in Brazil fields with a RapidEye satellite image indicate that the proposed SSD-HB model can predict soybean yield with a higher degree of accuracy than other estimation methods commonly used in remote-sensing applications. In the case of the SSD-HB model, the mean absolute error between estimated yield of the target area and actual yield is 0.28 t/ha, compared to 0.34 t/ha when conventional PLS regression was applied, showing the potential effectiveness of the proposed model.

Data-driven Modelling for decision making under uncertainty

NASA Astrophysics Data System (ADS)

Angria S, Layla; Dwi Sari, Yunita; Zarlis, Muhammad; Tulus

2018-01-01

The rise of the issues with the uncertainty of decision making has become a very warm conversation in operation research. Many models have been presented, one of which is with data-driven modelling (DDM). The purpose of this paper is to extract and recognize patterns in data, and find the best model in decision-making problem under uncertainty by using data-driven modeling approach with linear programming, linear and nonlinear differential equation, bayesian approach. Model criteria tested to determine the smallest error, and it will be the best model that can be used.

Uncertainty quantification for PZT bimorph actuators

NASA Astrophysics Data System (ADS)

Bravo, Nikolas; Smith, Ralph C.; Crews, John

2018-03-01

In this paper, we discuss the development of a high fidelity model for a PZT bimorph actuator used for micro-air vehicles, which includes the Robobee. We developed a high-fidelity model for the actuator using the homogenized energy model (HEM) framework, which quantifies the nonlinear, hysteretic, and rate-dependent behavior inherent to PZT in dynamic operating regimes. We then discussed an inverse problem on the model. We included local and global sensitivity analysis of the parameters in the high-fidelity model. Finally, we will discuss the results of Bayesian inference and uncertainty quantification on the HEM.

Construction cost estimation of spherical storage tanks: artificial neural networks and hybrid regression—GA algorithms

NASA Astrophysics Data System (ADS)

Arabzadeh, Vida; Niaki, S. T. A.; Arabzadeh, Vahid

2017-10-01

One of the most important processes in the early stages of construction projects is to estimate the cost involved. This process involves a wide range of uncertainties, which make it a challenging task. Because of unknown issues, using the experience of the experts or looking for similar cases are the conventional methods to deal with cost estimation. The current study presents data-driven methods for cost estimation based on the application of artificial neural network (ANN) and regression models. The learning algorithms of the ANN are the Levenberg-Marquardt and the Bayesian regulated. Moreover, regression models are hybridized with a genetic algorithm to obtain better estimates of the coefficients. The methods are applied in a real case, where the input parameters of the models are assigned based on the key issues involved in a spherical tank construction. The results reveal that while a high correlation between the estimated cost and the real cost exists; both ANNs could perform better than the hybridized regression models. In addition, the ANN with the Levenberg-Marquardt learning algorithm (LMNN) obtains a better estimation than the ANN with the Bayesian-regulated learning algorithm (BRNN). The correlation between real data and estimated values is over 90%, while the mean square error is achieved around 0.4. The proposed LMNN model can be effective to reduce uncertainty and complexity in the early stages of the construction project.

Classification of mislabelled microarrays using robust sparse logistic regression.

PubMed

Bootkrajang, Jakramate; Kabán, Ata

2013-04-01

Previous studies reported that labelling errors are not uncommon in microarray datasets. In such cases, the training set may become misleading, and the ability of classifiers to make reliable inferences from the data is compromised. Yet, few methods are currently available in the bioinformatics literature to deal with this problem. The few existing methods focus on data cleansing alone, without reference to classification, and their performance crucially depends on some tuning parameters. In this article, we develop a new method to detect mislabelled arrays simultaneously with learning a sparse logistic regression classifier. Our method may be seen as a label-noise robust extension of the well-known and successful Bayesian logistic regression classifier. To account for possible mislabelling, we formulate a label-flipping process as part of the classifier. The regularization parameter is automatically set using Bayesian regularization, which not only saves the computation time that cross-validation would take, but also eliminates any unwanted effects of label noise when setting the regularization parameter. Extensive experiments with both synthetic data and real microarray datasets demonstrate that our approach is able to counter the bad effects of labelling errors in terms of predictive performance, it is effective at identifying marker genes and simultaneously it detects mislabelled arrays to high accuracy. The code is available from http://cs.bham.ac.uk/∼jxb008. Supplementary data are available at Bioinformatics online.

Intelligent fault recognition strategy based on adaptive optimized multiple centers

NASA Astrophysics Data System (ADS)

Zheng, Bo; Li, Yan-Feng; Huang, Hong-Zhong

2018-06-01

For the recognition principle based optimized single center, one important issue is that the data with nonlinear separatrix cannot be recognized accurately. In order to solve this problem, a novel recognition strategy based on adaptive optimized multiple centers is proposed in this paper. This strategy recognizes the data sets with nonlinear separatrix by the multiple centers. Meanwhile, the priority levels are introduced into the multi-objective optimization, including recognition accuracy, the quantity of optimized centers, and distance relationship. According to the characteristics of various data, the priority levels are adjusted to ensure the quantity of optimized centers adaptively and to keep the original accuracy. The proposed method is compared with other methods, including support vector machine (SVM), neural network, and Bayesian classifier. The results demonstrate that the proposed strategy has the same or even better recognition ability on different distribution characteristics of data.

Comparison of two non-convex mixed-integer nonlinear programming algorithms applied to autoregressive moving average model structure and parameter estimation

NASA Astrophysics Data System (ADS)

Uilhoorn, F. E.

2016-10-01

In this article, the stochastic modelling approach proposed by Box and Jenkins is treated as a mixed-integer nonlinear programming (MINLP) problem solved with a mesh adaptive direct search and a real-coded genetic class of algorithms. The aim is to estimate the real-valued parameters and non-negative integer, correlated structure of stationary autoregressive moving average (ARMA) processes. The maximum likelihood function of the stationary ARMA process is embedded in Akaike's information criterion and the Bayesian information criterion, whereas the estimation procedure is based on Kalman filter recursions. The constraints imposed on the objective function enforce stability and invertibility. The best ARMA model is regarded as the global minimum of the non-convex MINLP problem. The robustness and computational performance of the MINLP solvers are compared with brute-force enumeration. Numerical experiments are done for existing time series and one new data set.

Accounting for Slipping and Other False Negatives in Logistic Models of Student Learning

ERIC Educational Resources Information Center

MacLellan, Christopher J.; Liu, Ran; Koedinger, Kenneth R.

2015-01-01

Additive Factors Model (AFM) and Performance Factors Analysis (PFA) are two popular models of student learning that employ logistic regression to estimate parameters and predict performance. This is in contrast to Bayesian Knowledge Tracing (BKT) which uses a Hidden Markov Model formalism. While all three models tend to make similar predictions,…

Bayesian Optimization for Neuroimaging Pre-processing in Brain Age Classification and Prediction

PubMed Central

Lancaster, Jenessa; Lorenz, Romy; Leech, Rob; Cole, James H.

2018-01-01

Neuroimaging-based age prediction using machine learning is proposed as a biomarker of brain aging, relating to cognitive performance, health outcomes and progression of neurodegenerative disease. However, even leading age-prediction algorithms contain measurement error, motivating efforts to improve experimental pipelines. T1-weighted MRI is commonly used for age prediction, and the pre-processing of these scans involves normalization to a common template and resampling to a common voxel size, followed by spatial smoothing. Resampling parameters are often selected arbitrarily. Here, we sought to improve brain-age prediction accuracy by optimizing resampling parameters using Bayesian optimization. Using data on N = 2003 healthy individuals (aged 16–90 years) we trained support vector machines to (i) distinguish between young (<22 years) and old (>50 years) brains (classification) and (ii) predict chronological age (regression). We also evaluated generalisability of the age-regression model to an independent dataset (CamCAN, N = 648, aged 18–88 years). Bayesian optimization was used to identify optimal voxel size and smoothing kernel size for each task. This procedure adaptively samples the parameter space to evaluate accuracy across a range of possible parameters, using independent sub-samples to iteratively assess different parameter combinations to arrive at optimal values. When distinguishing between young and old brains a classification accuracy of 88.1% was achieved, (optimal voxel size = 11.5 mm3, smoothing kernel = 2.3 mm). For predicting chronological age, a mean absolute error (MAE) of 5.08 years was achieved, (optimal voxel size = 3.73 mm3, smoothing kernel = 3.68 mm). This was compared to performance using default values of 1.5 mm3 and 4mm respectively, resulting in MAE = 5.48 years, though this 7.3% improvement was not statistically significant. When assessing generalisability, best performance was achieved when applying the entire Bayesian optimization framework to the new dataset, out-performing the parameters optimized for the initial training dataset. Our study outlines the proof-of-principle that neuroimaging models for brain-age prediction can use Bayesian optimization to derive case-specific pre-processing parameters. Our results suggest that different pre-processing parameters are selected when optimization is conducted in specific contexts. This potentially motivates use of optimization techniques at many different points during the experimental process, which may improve statistical sensitivity and reduce opportunities for experimenter-led bias. PMID:29483870

Developing and Testing a Model to Predict Outcomes of Organizational Change

PubMed Central

Gustafson, David H; Sainfort, François; Eichler, Mary; Adams, Laura; Bisognano, Maureen; Steudel, Harold

2003-01-01

Objective To test the effectiveness of a Bayesian model employing subjective probability estimates for predicting success and failure of health care improvement projects. Data Sources Experts' subjective assessment data for model development and independent retrospective data on 221 healthcare improvement projects in the United States, Canada, and the Netherlands collected between 1996 and 2000 for validation. Methods A panel of theoretical and practical experts and literature in organizational change were used to identify factors predicting the outcome of improvement efforts. A Bayesian model was developed to estimate probability of successful change using subjective estimates of likelihood ratios and prior odds elicited from the panel of experts. A subsequent retrospective empirical analysis of change efforts in 198 health care organizations was performed to validate the model. Logistic regression and ROC analysis were used to evaluate the model's performance using three alternative definitions of success. Data Collection For the model development, experts' subjective assessments were elicited using an integrative group process. For the validation study, a staff person intimately involved in each improvement project responded to a written survey asking questions about model factors and project outcomes. Results Logistic regression chi-square statistics and areas under the ROC curve demonstrated a high level of model performance in predicting success. Chi-square statistics were significant at the 0.001 level and areas under the ROC curve were greater than 0.84. Conclusions A subjective Bayesian model was effective in predicting the outcome of actual improvement projects. Additional prospective evaluations as well as testing the impact of this model as an intervention are warranted. PMID:12785571

Health state utility instruments compared: inquiring into nonlinearity across EQ-5D-5L, SF-6D, HUI-3 and 15D.

PubMed

Gamst-Klaussen, Thor; Chen, Gang; Lamu, Admassu N; Olsen, Jan Abel

2016-07-01

Different health state utility (HSU) instruments produce different utilities for the same individuals, thereby compromising the intended comparability of economic evaluations of health care interventions. When developing crosswalks, previous studies have indicated nonlinear relationships. This paper inquires into the degree of nonlinearity across the four most widely used HSU-instruments and proposes exchange rates that differ depending on the severity levels of the health state utility scale. Overall, 7933 respondents from six countries, 1760 in a non-diagnosed healthy group and 6173 in seven disease groups, reported their health states using four different instruments: EQ-5D-5L, SF-6D, HUI-3 and 15D. Quantile regressions investigate the degree of nonlinear relationships between these instruments. To compare the instruments across different disease severities, we split the health state utility scale into utility intervals with 0.2 successive decrements in utility starting from perfect health at 1.00. Exchange rates (ERs) are calculated as the mean utility difference between two utility intervals on one HSU-instrument divided by the difference in mean utility on another HSU-instrument. Quantile regressions reveal significant nonlinear relationships across all four HSU-instruments. The degrees of nonlinearities differ, with a maximum degree of difference in the coefficients along the health state utility scale of 3.34 when SF-6D is regressed on EQ-5D. At the lower end of the health state utility scale, the exchange rate from SF-6D to EQ-5D is 2.11, whilst at the upper end it is 0.38. Comparisons at different utility levels illustrate the fallacy of using linear functions as crosswalks between HSU-instruments. The existence of nonlinear relationships between different HSU-instruments suggests that level-specific exchange rates should be used when converting a change in utility on the instrument used, onto a corresponding utility change had another instrument been used. Accounting for nonlinearities will increase the validity of the comparison for decision makers when faced with a choice between interventions whose calculations of QALY gains have been based on different HSU-instruments.

Massive-training support vector regression and Gaussian process for false-positive reduction in computer-aided detection of polyps in CT colonography

PubMed Central

Xu, Jian-Wu; Suzuki, Kenji

2011-01-01

Purpose: A massive-training artificial neural network (MTANN) has been developed for the reduction of false positives (FPs) in computer-aided detection (CADe) of polyps in CT colonography (CTC). A major limitation of the MTANN is the long training time. To address this issue, the authors investigated the feasibility of two state-of-the-art regression models, namely, support vector regression (SVR) and Gaussian process regression (GPR) models, in the massive-training framework and developed massive-training SVR (MTSVR) and massive-training GPR (MTGPR) for the reduction of FPs in CADe of polyps. Methods: The authors applied SVR and GPR as volume-processing techniques in the distinction of polyps from FP detections in a CTC CADe scheme. Unlike artificial neural networks (ANNs), both SVR and GPR are memory-based methods that store a part of or the entire training data for testing. Therefore, their training is generally fast and they are able to improve the efficiency of the massive-training methodology. Rooted in a maximum margin property, SVR offers excellent generalization ability and robustness to outliers. On the other hand, GPR approaches nonlinear regression from a Bayesian perspective, which produces both the optimal estimated function and the covariance associated with the estimation. Therefore, both SVR and GPR, as the state-of-the-art nonlinear regression models, are able to offer a performance comparable or potentially superior to that of ANN, with highly efficient training. Both MTSVR and MTGPR were trained directly with voxel values from CTC images. A 3D scoring method based on a 3D Gaussian weighting function was applied to the outputs of MTSVR and MTGPR for distinction between polyps and nonpolyps. To test the performance of the proposed models, the authors compared them to the original MTANN in the distinction between actual polyps and various types of FPs in terms of training time reduction and FP reduction performance. The authors’ CTC database consisted of 240 CTC data sets obtained from 120 patients in the supine and prone positions. The training set consisted of 27 patients, 10 of which had 10 polyps. The authors selected 10 nonpolyps (i.e., FP sources) from the training set. These ten polyps and ten nonpolyps were used for training the proposed models. The testing set consisted of 93 patients, including 19 polyps in 7 patients and 86 negative patients with 474 FPs produced by an original CADe scheme. Results: With the MTSVR, the training time was reduced by a factor of 190, while a FP reduction performance [by-polyp sensitivity of 94.7% (18∕19) with 2.5 (230∕93) FPs∕patient] comparable to that of the original MTANN [the same sensitivity with 2.6 (244∕93) FPs∕patient] was achieved. The classification performance in terms of the area under the receiver-operating-characteristic curve value of the MTGPR (0.82) was statistically significantly higher than that of the original MTANN (0.77), with a two-sided p-value of 0.03. The MTGPR yielded a 94.7% (18∕19) by-polyp sensitivity at a FP rate of 2.5 (235∕93) per patient and reduced the training time by a factor of 1.3. Conclusions: Both MTSVR and MTGPR improve the efficiency of the training in the massive-training framework while maintaining a comparable performance. PMID:21626922

Population-level differences in disease transmission: A Bayesian analysis of multiple smallpox epidemics

PubMed Central

Elderd, Bret D.; Dwyer, Greg; Dukic, Vanja

2013-01-01

Estimates of a disease’s basic reproductive rate R0 play a central role in understanding outbreaks and planning intervention strategies. In many calculations of R0, a simplifying assumption is that different host populations have effectively identical transmission rates. This assumption can lead to an underestimate of the overall uncertainty associated with R0, which, due to the non-linearity of epidemic processes, may result in a mis-estimate of epidemic intensity and miscalculated expenditures associated with public-health interventions. In this paper, we utilize a Bayesian method for quantifying the overall uncertainty arising from differences in population-specific basic reproductive rates. Using this method, we fit spatial and non-spatial susceptible-exposed-infected-recovered (SEIR) models to a series of 13 smallpox outbreaks. Five outbreaks occurred in populations that had been previously exposed to smallpox, while the remaining eight occurred in Native-American populations that were naïve to the disease at the time. The Native-American outbreaks were close in a spatial and temporal sense. Using Bayesian Information Criterion (BIC), we show that the best model includes population-specific R0 values. These differences in R0 values may, in part, be due to differences in genetic background, social structure, or food and water availability. As a result of these inter-population differences, the overall uncertainty associated with the “population average” value of smallpox R0 is larger, a finding that can have important consequences for controlling epidemics. In general, Bayesian hierarchical models are able to properly account for the uncertainty associated with multiple epidemics, provide a clearer understanding of variability in epidemic dynamics, and yield a better assessment of the range of potential risks and consequences that decision makers face. PMID:24021521

Population pharmacokinetics and maximum a posteriori probability Bayesian estimator of abacavir: application of individualized therapy in HIV-infected infants and toddlers

PubMed Central

Zhao, Wei; Cella, Massimo; Della Pasqua, Oscar; Burger, David; Jacqz-Aigrain, Evelyne

2012-01-01

AIMS To develop a population pharmacokinetic model for abacavir in HIV-infected infants and toddlers, which will be used to describe both once and twice daily pharmacokinetic profiles, identify covariates that explain variability and propose optimal time points to optimize the area under the concentration–time curve (AUC) targeted dosage and individualize therapy. METHODS The pharmacokinetics of abacavir was described with plasma concentrations from 23 patients using nonlinear mixed-effects modelling (NONMEM) software. A two-compartment model with first-order absorption and elimination was developed. The final model was validated using bootstrap, visual predictive check and normalized prediction distribution errors. The Bayesian estimator was validated using the cross-validation and simulation–estimation method. RESULTS The typical population pharmacokinetic parameters and relative standard errors (RSE) were apparent systemic clearance (CL) 13.4 l h−1 (RSE 6.3%), apparent central volume of distribution 4.94 l (RSE 28.7%), apparent peripheral volume of distribution 8.12 l (RSE14.2%), apparent intercompartment clearance 1.25 l h−1 (RSE 16.9%) and absorption rate constant 0.758 h−1 (RSE 5.8%). The covariate analysis identified weight as the individual factor influencing the apparent oral clearance: CL = 13.4 × (weight/12)1.14. The maximum a posteriori probability Bayesian estimator, based on three concentrations measured at 0, 1 or 2, and 3 h after drug intake allowed predicting individual AUC0–t. CONCLUSIONS The population pharmacokinetic model developed for abacavir in HIV-infected infants and toddlers accurately described both once and twice daily pharmacokinetic profiles. The maximum a posteriori probability Bayesian estimator of AUC0–t was developed from the final model and can be used routinely to optimize individual dosing. PMID:21988586

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.

Capturing Ecosystem Services, Stakeholders' Preferences and Trade-Offs in Coastal Aquaculture Decisions: A Bayesian Belief Network Application

PubMed Central

Schmitt, Laetitia Helene Marie; Brugere, Cecile

2013-01-01

Aquaculture activities are embedded in complex social-ecological systems. However, aquaculture development decisions have tended to be driven by revenue generation, failing to account for interactions with the environment and the full value of the benefits derived from services provided by local ecosystems. Trade-offs resulting from changes in ecosystem services provision and associated impacts on livelihoods are also often overlooked. This paper proposes an innovative application of Bayesian belief networks - influence diagrams - as a decision support system for mediating trade-offs arising from the development of shrimp aquaculture in Thailand. Senior experts were consulted (n = 12) and primary farm data on the economics of shrimp farming (n = 20) were collected alongside secondary information on ecosystem services, in order to construct and populate the network. Trade-offs were quantitatively assessed through the generation of a probabilistic impact matrix. This matrix captures nonlinearity and uncertainty and describes the relative performance and impacts of shrimp farming management scenarios on local livelihoods. It also incorporates export revenues and provision and value of ecosystem services such as coastal protection and biodiversity. This research shows that Bayesian belief modeling can support complex decision-making on pathways for sustainable coastal aquaculture development and thus contributes to the debate on the role of aquaculture in social-ecological resilience and economic development. PMID:24155876

Bayesian shrinkage approach for a joint model of longitudinal and survival outcomes assuming different association structures.

PubMed

Andrinopoulou, Eleni-Rosalina; Rizopoulos, Dimitris

2016-11-20

The joint modeling of longitudinal and survival data has recently received much attention. Several extensions of the standard joint model that consists of one longitudinal and one survival outcome have been proposed including the use of different association structures between the longitudinal and the survival outcomes. However, in general, relatively little attention has been given to the selection of the most appropriate functional form to link the two outcomes. In common practice, it is assumed that the underlying value of the longitudinal outcome is associated with the survival outcome. However, it could be that different characteristics of the patients' longitudinal profiles influence the hazard. For example, not only the current value but also the slope or the area under the curve of the longitudinal outcome. The choice of which functional form to use is an important decision that needs to be investigated because it could influence the results. In this paper, we use a Bayesian shrinkage approach in order to determine the most appropriate functional forms. We propose a joint model that includes different association structures of different biomarkers and assume informative priors for the regression coefficients that correspond to the terms of the longitudinal process. Specifically, we assume Bayesian lasso, Bayesian ridge, Bayesian elastic net, and horseshoe. These methods are applied to a dataset consisting of patients with a chronic liver disease, where it is important to investigate which characteristics of the biomarkers have an influence on survival. Copyright © 2016 John Wiley & Sons, Ltd. Copyright © 2016 John Wiley & Sons, Ltd.

Bayesian Inference on Malignant Breast Cancer in Nigeria: A Diagnosis of MCMC Convergence

PubMed Central

Ogunsakin, Ropo Ebenezer; Siaka, Lougue

2017-01-01

Background: There has been no previous study to classify malignant breast tumor in details based on Markov Chain Monte Carlo (MCMC) convergence in Western, Nigeria. This study therefore aims to profile patients living with benign and malignant breast tumor in two different hospitals among women of Western Nigeria, with a focus on prognostic factors and MCMC convergence. Materials and Methods: A hospital-based record was used to identify prognostic factors for malignant breast cancer among women of Western Nigeria. This paper describes Bayesian inference and demonstrates its usage to estimation of parameters of the logistic regression via Markov Chain Monte Carlo (MCMC) algorithm. The result of the Bayesian approach is compared with the classical statistics. Results: The mean age of the respondents was 42.2 ±16.6 years with 52% of the women aged between 35-49 years. The results of both techniques suggest that age and women with at least high school education have a significantly higher risk of being diagnosed with malignant breast tumors than benign breast tumors. The results also indicate a reduction of standard errors is associated with the coefficients obtained from the Bayesian approach. In addition, simulation result reveal that women with at least high school are 1.3 times more at risk of having malignant breast lesion in western Nigeria compared to benign breast lesion. Conclusion: We concluded that more efforts are required towards creating awareness and advocacy campaigns on how the prevalence of malignant breast lesions can be reduced, especially among women. The application of Bayesian produces precise estimates for modeling malignant breast cancer. PMID:29072396

Deriving the Regression Equation without Using Calculus

ERIC Educational Resources Information Center

Gordon, Sheldon P.; Gordon, Florence S.

2004-01-01

Probably the one "new" mathematical topic that is most responsible for modernizing courses in college algebra and precalculus over the last few years is the idea of fitting a function to a set of data in the sense of a least squares fit. Whether it be simple linear regression or nonlinear regression, this topic opens the door to applying the…

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.

Model inversion via multi-fidelity Bayesian optimization: a new paradigm for parameter estimation in haemodynamics, and beyond.

PubMed

Perdikaris, Paris; Karniadakis, George Em

2016-05-01

We present a computational framework for model inversion based on multi-fidelity information fusion and Bayesian optimization. The proposed methodology targets the accurate construction of response surfaces in parameter space, and the efficient pursuit to identify global optima while keeping the number of expensive function evaluations at a minimum. We train families of correlated surrogates on available data using Gaussian processes and auto-regressive stochastic schemes, and exploit the resulting predictive posterior distributions within a Bayesian optimization setting. This enables a smart adaptive sampling procedure that uses the predictive posterior variance to balance the exploration versus exploitation trade-off, and is a key enabler for practical computations under limited budgets. The effectiveness of the proposed framework is tested on three parameter estimation problems. The first two involve the calibration of outflow boundary conditions of blood flow simulations in arterial bifurcations using multi-fidelity realizations of one- and three-dimensional models, whereas the last one aims to identify the forcing term that generated a particular solution to an elliptic partial differential equation. © 2016 The Author(s).

Model inversion via multi-fidelity Bayesian optimization: a new paradigm for parameter estimation in haemodynamics, and beyond

PubMed Central

Perdikaris, Paris; Karniadakis, George Em

2016-01-01

We present a computational framework for model inversion based on multi-fidelity information fusion and Bayesian optimization. The proposed methodology targets the accurate construction of response surfaces in parameter space, and the efficient pursuit to identify global optima while keeping the number of expensive function evaluations at a minimum. We train families of correlated surrogates on available data using Gaussian processes and auto-regressive stochastic schemes, and exploit the resulting predictive posterior distributions within a Bayesian optimization setting. This enables a smart adaptive sampling procedure that uses the predictive posterior variance to balance the exploration versus exploitation trade-off, and is a key enabler for practical computations under limited budgets. The effectiveness of the proposed framework is tested on three parameter estimation problems. The first two involve the calibration of outflow boundary conditions of blood flow simulations in arterial bifurcations using multi-fidelity realizations of one- and three-dimensional models, whereas the last one aims to identify the forcing term that generated a particular solution to an elliptic partial differential equation. PMID:27194481

Boosted Regression Tree Models to Explain Watershed Nutrient Concentrations and Biological Condition

EPA Science Inventory

Boosted regression tree (BRT) models were developed to quantify the nonlinear relationships between landscape variables and nutrient concentrations in a mesoscale mixed land cover watershed during base-flow conditions. Factors that affect instream biological components, based on ...

CO2 flux determination by closed-chamber methods can be seriously biased by inappropriate application of linear regression

NASA Astrophysics Data System (ADS)

Kutzbach, L.; Schneider, J.; Sachs, T.; Giebels, M.; Nykänen, H.; Shurpali, N. J.; Martikainen, P. J.; Alm, J.; Wilmking, M.

2007-07-01

Closed (non-steady state) chambers are widely used for quantifying carbon dioxide (CO2) fluxes between soils or low-stature canopies and the atmosphere. It is well recognised that covering a soil or vegetation by a closed chamber inherently disturbs the natural CO2 fluxes by altering the concentration gradients between the soil, the vegetation and the overlying air. Thus, the driving factors of CO2 fluxes are not constant during the closed chamber experiment, and no linear increase or decrease of CO2 concentration over time within the chamber headspace can be expected. Nevertheless, linear regression has been applied for calculating CO2 fluxes in many recent, partly influential, studies. This approach was justified by keeping the closure time short and assuming the concentration change over time to be in the linear range. Here, we test if the application of linear regression is really appropriate for estimating CO2 fluxes using closed chambers over short closure times and if the application of nonlinear regression is necessary. We developed a nonlinear exponential regression model from diffusion and photosynthesis theory. This exponential model was tested with four different datasets of CO2 flux measurements (total number: 1764) conducted at three peatland sites in Finland and a tundra site in Siberia. The flux measurements were performed using transparent chambers on vegetated surfaces and opaque chambers on bare peat surfaces. Thorough analyses of residuals demonstrated that linear regression was frequently not appropriate for the determination of CO2 fluxes by closed-chamber methods, even if closure times were kept short. The developed exponential model was well suited for nonlinear regression of the concentration over time c(t) evolution in the chamber headspace and estimation of the initial CO2 fluxes at closure time for the majority of experiments. CO2 flux estimates by linear regression can be as low as 40% of the flux estimates of exponential regression for closure times of only two minutes and even lower for longer closure times. The degree of underestimation increased with increasing CO2 flux strength and is dependent on soil and vegetation conditions which can disturb not only the quantitative but also the qualitative evaluation of CO2 flux dynamics. The underestimation effect by linear regression was observed to be different for CO2 uptake and release situations which can lead to stronger bias in the daily, seasonal and annual CO2 balances than in the individual fluxes. To avoid serious bias of CO2 flux estimates based on closed chamber experiments, we suggest further tests using published datasets and recommend the use of nonlinear regression models for future closed chamber studies.

Comparison of Linear and Non-linear Regression Analysis to Determine Pulmonary Pressure in Hyperthyroidism.

PubMed

Scarneciu, Camelia C; Sangeorzan, Livia; Rus, Horatiu; Scarneciu, Vlad D; Varciu, Mihai S; Andreescu, Oana; Scarneciu, Ioan

2017-01-01

This study aimed at assessing the incidence of pulmonary hypertension (PH) at newly diagnosed hyperthyroid patients and at finding a simple model showing the complex functional relation between pulmonary hypertension in hyperthyroidism and the factors causing it. The 53 hyperthyroid patients (H-group) were evaluated mainly by using an echocardiographical method and compared with 35 euthyroid (E-group) and 25 healthy people (C-group). In order to identify the factors causing pulmonary hypertension the statistical method of comparing the values of arithmetical means is used. The functional relation between the two random variables (PAPs and each of the factors determining it within our research study) can be expressed by linear or non-linear function. By applying the linear regression method described by a first-degree equation the line of regression (linear model) has been determined; by applying the non-linear regression method described by a second degree equation, a parabola-type curve of regression (non-linear or polynomial model) has been determined. We made the comparison and the validation of these two models by calculating the determination coefficient (criterion 1), the comparison of residuals (criterion 2), application of AIC criterion (criterion 3) and use of F-test (criterion 4). From the H-group, 47% have pulmonary hypertension completely reversible when obtaining euthyroidism. The factors causing pulmonary hypertension were identified: previously known- level of free thyroxin, pulmonary vascular resistance, cardiac output; new factors identified in this study- pretreatment period, age, systolic blood pressure. According to the four criteria and to the clinical judgment, we consider that the polynomial model (graphically parabola- type) is better than the linear one. The better model showing the functional relation between the pulmonary hypertension in hyperthyroidism and the factors identified in this study is given by a polynomial equation of second degree where the parabola is its graphical representation.

Logistic random effects regression models: a comparison of statistical packages for binary and ordinal outcomes.

PubMed

Li, Baoyue; Lingsma, Hester F; Steyerberg, Ewout W; Lesaffre, Emmanuel

2011-05-23

Logistic random effects models are a popular tool to analyze multilevel also called hierarchical data with a binary or ordinal outcome. Here, we aim to compare different statistical software implementations of these models. We used individual patient data from 8509 patients in 231 centers with moderate and severe Traumatic Brain Injury (TBI) enrolled in eight Randomized Controlled Trials (RCTs) and three observational studies. We fitted logistic random effects regression models with the 5-point Glasgow Outcome Scale (GOS) as outcome, both dichotomized as well as ordinal, with center and/or trial as random effects, and as covariates age, motor score, pupil reactivity or trial. We then compared the implementations of frequentist and Bayesian methods to estimate the fixed and random effects. Frequentist approaches included R (lme4), Stata (GLLAMM), SAS (GLIMMIX and NLMIXED), MLwiN ([R]IGLS) and MIXOR, Bayesian approaches included WinBUGS, MLwiN (MCMC), R package MCMCglmm and SAS experimental procedure MCMC.Three data sets (the full data set and two sub-datasets) were analysed using basically two logistic random effects models with either one random effect for the center or two random effects for center and trial. For the ordinal outcome in the full data set also a proportional odds model with a random center effect was fitted. The packages gave similar parameter estimates for both the fixed and random effects and for the binary (and ordinal) models for the main study and when based on a relatively large number of level-1 (patient level) data compared to the number of level-2 (hospital level) data. However, when based on relatively sparse data set, i.e. when the numbers of level-1 and level-2 data units were about the same, the frequentist and Bayesian approaches showed somewhat different results. The software implementations differ considerably in flexibility, computation time, and usability. There are also differences in the availability of additional tools for model evaluation, such as diagnostic plots. The experimental SAS (version 9.2) procedure MCMC appeared to be inefficient. On relatively large data sets, the different software implementations of logistic random effects regression models produced similar results. Thus, for a large data set there seems to be no explicit preference (of course if there is no preference from a philosophical point of view) for either a frequentist or Bayesian approach (if based on vague priors). The choice for a particular implementation may largely depend on the desired flexibility, and the usability of the package. For small data sets the random effects variances are difficult to estimate. In the frequentist approaches the MLE of this variance was often estimated zero with a standard error that is either zero or could not be determined, while for Bayesian methods the estimates could depend on the chosen "non-informative" prior of the variance parameter. The starting value for the variance parameter may be also critical for the convergence of the Markov chain.

Nonlinear Constitutive Modeling of Piezoelectric Ceramics

NASA Astrophysics Data System (ADS)

Xu, Jia; Li, Chao; Wang, Haibo; Zhu, Zhiwen

2017-12-01

Nonlinear constitutive modeling of piezoelectric ceramics is discussed in this paper. Van der Pol item is introduced to explain the simple hysteretic curve. Improved nonlinear difference items are used to interpret the hysteresis phenomena of piezoelectric ceramics. The fitting effect of the model on experimental data is proved by the partial least-square regression method. The results show that this method can describe the real curve well. The results of this paper are helpful to piezoelectric ceramics constitutive modeling.

Validity of the reduced-sample insulin modified frequently-sampled intravenous glucose tolerance test using the nonlinear regression approach.

PubMed

Sumner, Anne E; Luercio, Marcella F; Frempong, Barbara A; Ricks, Madia; Sen, Sabyasachi; Kushner, Harvey; Tulloch-Reid, Marshall K

2009-02-01

The disposition index, the product of the insulin sensitivity index (S(I)) and the acute insulin response to glucose, is linked in African Americans to chromosome 11q. This link was determined with S(I) calculated with the nonlinear regression approach to the minimal model and data from the reduced-sample insulin-modified frequently-sampled intravenous glucose tolerance test (Reduced-Sample-IM-FSIGT). However, the application of the nonlinear regression approach to calculate S(I) using data from the Reduced-Sample-IM-FSIGT has been challenged as being not only inaccurate but also having a high failure rate in insulin-resistant subjects. Our goal was to determine the accuracy and failure rate of the Reduced-Sample-IM-FSIGT using the nonlinear regression approach to the minimal model. With S(I) from the Full-Sample-IM-FSIGT considered the standard and using the nonlinear regression approach to the minimal model, we compared the agreement between S(I) from the Full- and Reduced-Sample-IM-FSIGT protocols. One hundred African Americans (body mass index, 31.3 +/- 7.6 kg/m(2) [mean +/- SD]; range, 19.0-56.9 kg/m(2)) had FSIGTs. Glucose (0.3 g/kg) was given at baseline. Insulin was infused from 20 to 25 minutes (total insulin dose, 0.02 U/kg). For the Full-Sample-IM-FSIGT, S(I) was calculated based on the glucose and insulin samples taken at -1, 1, 2, 3, 4, 5, 6, 7, 8,10, 12, 14, 16, 19, 22, 23, 24, 25, 27, 30, 40, 50, 60, 70, 80, 90, 100, 120, 150, and 180 minutes. For the Reduced-Sample-FSIGT, S(I) was calculated based on the time points that appear in bold. Agreement was determined by Spearman correlation, concordance, and the Bland-Altman method. In addition, for both protocols, the population was divided into tertiles of S(I). Insulin resistance was defined by the lowest tertile of S(I) from the Full-Sample-IM-FSIGT. The distribution of subjects across tertiles was compared by rank order and kappa statistic. We found that the rate of failure of resolution of S(I) by the Reduced-Sample-IM-FSIGT was 3% (3/100). For the remaining 97 subjects, S(I) for the Full- and Reduced-Sample-IM-FSIGTs were as follows: 3.76 +/- 2.41 L mU(-1) min(-1) (range, 0.58-14.50) and 4.29 +/- 2.89 L mU(-1) min(-1) (range, 0.52-14.42); relative error, 21% +/- 18%; Spearman r = 0.97; and concordance, 0.94 (both P < .001). After log transformation, the Bland-Altman limits of agreement were -0.29 and 0.53. The exact agreement for distribution of the population in the insulin-resistant tertile vs the insulin-sensitive tertiles was 92%, kappa of 0.82 +/- 0.06. Using the nonlinear regression approach and data from the Reduced-Sample-IM-FSIGT in subjects with a wide range of insulin sensitivity, failure to resolve S(I) occurred in only 3% of subjects. The agreement and maintenance of rank order of S(I) between protocols support the use of the nonlinear regression approach to the minimal model and the Reduced-Sample-IM-FSIGT in clinical studies.

Two-Stage Bayesian Model Averaging in Endogenous Variable Models*

PubMed Central

Lenkoski, Alex; Eicher, Theo S.; Raftery, Adrian E.

2013-01-01

Economic modeling in the presence of endogeneity is subject to model uncertainty at both the instrument and covariate level. We propose a Two-Stage Bayesian Model Averaging (2SBMA) methodology that extends the Two-Stage Least Squares (2SLS) estimator. By constructing a Two-Stage Unit Information Prior in the endogenous variable model, we are able to efficiently combine established methods for addressing model uncertainty in regression models with the classic technique of 2SLS. To assess the validity of instruments in the 2SBMA context, we develop Bayesian tests of the identification restriction that are based on model averaged posterior predictive p-values. A simulation study showed that 2SBMA has the ability to recover structure in both the instrument and covariate set, and substantially improves the sharpness of resulting coefficient estimates in comparison to 2SLS using the full specification in an automatic fashion. Due to the increased parsimony of the 2SBMA estimate, the Bayesian Sargan test had a power of 50 percent in detecting a violation of the exogeneity assumption, while the method based on 2SLS using the full specification had negligible power. We apply our approach to the problem of development accounting, and find support not only for institutions, but also for geography and integration as development determinants, once both model uncertainty and endogeneity have been jointly addressed. PMID:24223471

Hierarchical Bayesian inference on genetic and non-genetic components of partial efficiencies determining feed efficiency in dairy cattle

USDA-ARS?s Scientific Manuscript database

Dairy cattle feed efficiency (FE) can be defined as the ability to convert DMI into milk energy (MILKE) and maintenance or metabolic body weight (MBW). In other words, DMI is conditional on MILKE and MBW (DMI|MILKE,MBW). These partial regressions or partial efficiencies (PE) of DMI on MILKE and MBW ...

LiDAR based prediction of forest biomass using hierarchical models with spatially varying coefficients

Treesearch

Chad Babcock; Andrew O. Finley; John B. Bradford; Randy Kolka; Richard Birdsey; Michael G. Ryan

2015-01-01

Many studies and production inventory systems have shown the utility of coupling covariates derived from Light Detection and Ranging (LiDAR) data with forest variables measured on georeferenced inventory plots through regression models. The objective of this study was to propose and assess the use of a Bayesian hierarchical modeling framework that accommodates both...

Impact of trucking network flow on preferred biorefinery locations in the southern United States

Treesearch

Timothy M. Young; Lee D. Han; James H. Perdue; Stephanie R. Hargrove; Frank M. Guess; Xia Huang; Chung-Hao Chen

2017-01-01

The impact of the trucking transportation network flow was modeled for the southern United States. The study addresses a gap in existing research by applying a Bayesian logistic regression and Geographic Information System (GIS) geospatial analysis to predict biorefinery site locations. A one-way trucking cost assuming a 128.8 km (80-mile) haul distance was estimated...

Curriculum-Based Measurement of Reading: An Evaluation of Frequentist and Bayesian Methods to Model Progress Monitoring Data

ERIC Educational Resources Information Center

Christ, Theodore J.; Desjardins, Christopher David

2018-01-01

Curriculum-Based Measurement of Oral Reading (CBM-R) is often used to monitor student progress and guide educational decisions. Ordinary least squares regression (OLSR) is the most widely used method to estimate the slope, or rate of improvement (ROI), even though published research demonstrates OLSR's lack of validity and reliability, and…

Information-Decay Pursuit of Dynamic Parameters in Student Models

DTIC Science & Technology

1994-04-01

simple worked-through example). Commercially available computer programs for structuring and using Bayesian inference include ERGO ( Noetic Systems...Tukey, J.W. (1977). Data analysis and Regression: A second course in statistics. Reading, MA: Addison-Wesley. Noetic Systems, Inc. (1991). ERGO...Naval Academy Division of Educational Studies Annapolis MD 21402-5002 Elmory Univerity Dr Janice Gifford 210 Fiabburne Bldg University of

Comparison of various error functions in predicting the optimum isotherm by linear and non-linear regression analysis for the sorption of basic red 9 by activated carbon.

PubMed

Kumar, K Vasanth; Porkodi, K; Rocha, F

2008-01-15

A comparison of linear and non-linear regression method in selecting the optimum isotherm was made to the experimental equilibrium data of basic red 9 sorption by activated carbon. The r(2) was used to select the best fit linear theoretical isotherm. In the case of non-linear regression method, six error functions namely coefficient of determination (r(2)), hybrid fractional error function (HYBRID), Marquardt's percent standard deviation (MPSD), the average relative error (ARE), sum of the errors squared (ERRSQ) and sum of the absolute errors (EABS) were used to predict the parameters involved in the two and three parameter isotherms and also to predict the optimum isotherm. Non-linear regression was found to be a better way to obtain the parameters involved in the isotherms and also the optimum isotherm. For two parameter isotherm, MPSD was found to be the best error function in minimizing the error distribution between the experimental equilibrium data and predicted isotherms. In the case of three parameter isotherm, r(2) was found to be the best error function to minimize the error distribution structure between experimental equilibrium data and theoretical isotherms. The present study showed that the size of the error function alone is not a deciding factor to choose the optimum isotherm. In addition to the size of error function, the theory behind the predicted isotherm should be verified with the help of experimental data while selecting the optimum isotherm. A coefficient of non-determination, K(2) was explained and was found to be very useful in identifying the best error function while selecting the optimum isotherm.

Spatiotemporal modeling of PM2.5 concentrations at the national scale combining land use regression and Bayesian maximum entropy in China.

PubMed

Chen, Li; Gao, Shuang; Zhang, Hui; Sun, Yanling; Ma, Zhenxing; Vedal, Sverre; Mao, Jian; Bai, Zhipeng

2018-05-03

Concentrations of particulate matter with aerodynamic diameter <2.5 μm (PM 2.5 ) are relatively high in China. Estimation of PM 2.5 exposure is complex because PM 2.5 exhibits complex spatiotemporal patterns. To improve the validity of exposure predictions, several methods have been developed and applied worldwide. A hybrid approach combining a land use regression (LUR) model and Bayesian Maximum Entropy (BME) interpolation of the LUR space-time residuals were developed to estimate the PM 2.5 concentrations on a national scale in China. This hybrid model could potentially provide more valid predictions than a commonly-used LUR model. The LUR/BME model had good performance characteristics, with R 2  = 0.82 and root mean square error (RMSE) of 4.6 μg/m 3 . Prediction errors of the LUR/BME model were reduced by incorporating soft data accounting for data uncertainty, with the R 2 increasing by 6%. The performance of LUR/BME is better than OK/BME. The LUR/BME model is the most accurate fine spatial scale PM 2.5 model developed to date for China. Copyright © 2018. Published by Elsevier Ltd.

Brief and precarious lives: infant mortality in contrasting sites from medieval and post-medieval England (AD 850-1859).

PubMed

Lewis, Mary E; Gowland, Rebecca

2007-09-01

This study compares the infant mortality profiles of 128 infants from two urban and two rural cemetery sites in medieval England. The aim of this paper is to assess the impact of urbanization and industrialization in terms of endogenous or exogenous causes of death. In order to undertake this analysis, two different methods of estimating gestational age from long bone lengths were used: a traditional regression method and a Bayesian method. The regression method tended to produce more marked peaks at 38 weeks, while the Bayesian method produced a broader range of ages and were more comparable with the expected "natural" mortality profiles.At all the sites, neonatal mortality (28-40 weeks) outweighed post-neonatal mortality (41-48 weeks) with rural Raunds Furnells in Northamptonshire, showing the highest number of neonatal deaths and post-medieval Spitalfields, London, showing a greater proportion of deaths due to exogenous or environmental factors. Of the four sites under study, Wharram Percy in Yorkshire showed the most convincing "natural" infant mortality profile, suggesting the inclusion of all births at the site (i.e., stillbirths and unbaptised infants). (c) 2007 Wiley-Liss, Inc.

Hierarchical Bayesian Markov switching models with application to predicting spawning success of shovelnose sturgeon

USGS Publications Warehouse

Holan, S.H.; Davis, G.M.; Wildhaber, M.L.; DeLonay, A.J.; Papoulias, D.M.

2009-01-01

The timing of spawning in fish is tightly linked to environmental factors; however, these factors are not very well understood for many species. Specifically, little information is available to guide recruitment efforts for endangered species such as the sturgeon. Therefore, we propose a Bayesian hierarchical model for predicting the success of spawning of the shovelnose sturgeon which uses both biological and behavioural (longitudinal) data. In particular, we use data that were produced from a tracking study that was conducted in the Lower Missouri River. The data that were produced from this study consist of biological variables associated with readiness to spawn along with longitudinal behavioural data collected by using telemetry and archival data storage tags. These high frequency data are complex both biologically and in the underlying behavioural process. To accommodate such complexity we developed a hierarchical linear regression model that uses an eigenvalue predictor, derived from the transition probability matrix of a two-state Markov switching model with generalized auto-regressive conditional heteroscedastic dynamics. Finally, to minimize the computational burden that is associated with estimation of this model, a parallel computing approach is proposed. ?? Journal compilation 2009 Royal Statistical Society.

Spatial Bayesian latent factor regression modeling of coordinate-based meta-analysis data.

PubMed

Montagna, Silvia; Wager, Tor; Barrett, Lisa Feldman; Johnson, Timothy D; Nichols, Thomas E

2018-03-01

Now over 20 years old, functional MRI (fMRI) has a large and growing literature that is best synthesised with meta-analytic tools. As most authors do not share image data, only the peak activation coordinates (foci) reported in the article are available for Coordinate-Based Meta-Analysis (CBMA). Neuroimaging meta-analysis is used to (i) identify areas of consistent activation; and (ii) build a predictive model of task type or cognitive process for new studies (reverse inference). To simultaneously address these aims, we propose a Bayesian point process hierarchical model for CBMA. We model the foci from each study as a doubly stochastic Poisson process, where the study-specific log intensity function is characterized as a linear combination of a high-dimensional basis set. A sparse representation of the intensities is guaranteed through latent factor modeling of the basis coefficients. Within our framework, it is also possible to account for the effect of study-level covariates (meta-regression), significantly expanding the capabilities of the current neuroimaging meta-analysis methods available. We apply our methodology to synthetic data and neuroimaging meta-analysis datasets. © 2017, The International Biometric Society.

Bayesian semiparametric estimation of covariate-dependent ROC curves

PubMed Central

Rodríguez, Abel; Martínez, Julissa C.

2014-01-01

Receiver operating characteristic (ROC) curves are widely used to measure the discriminating power of medical tests and other classification procedures. In many practical applications, the performance of these procedures can depend on covariates such as age, naturally leading to a collection of curves associated with different covariate levels. This paper develops a Bayesian heteroscedastic semiparametric regression model and applies it to the estimation of covariate-dependent ROC curves. More specifically, our approach uses Gaussian process priors to model the conditional mean and conditional variance of the biomarker of interest for each of the populations under study. The model is illustrated through an application to the evaluation of prostate-specific antigen for the diagnosis of prostate cancer, which contrasts the performance of our model against alternative models. PMID:24174579

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

Trust from the past: Bayesian Personalized Ranking based Link Prediction in Knowledge Graphs

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

Zhang, Baichuan; Choudhury, Sutanay; Al-Hasan, Mohammad

2016-02-01

Estimating the confidence for a link is a critical task for Knowledge Graph construction. Link prediction, or predicting the likelihood of a link in a knowledge graph based on prior state is a key research direction within this area. We propose a Latent Feature Embedding based link recommendation model for prediction task and utilize Bayesian Personalized Ranking based optimization technique for learning models for each predicate. Experimental results on large-scale knowledge bases such as YAGO2 show that our approach achieves substantially higher performance than several state-of-art approaches. Furthermore, we also study the performance of the link prediction algorithm in termsmore » of topological properties of the Knowledge Graph and present a linear regression model to reason about its expected level of accuracy.« less

QSRR modeling for diverse drugs using different feature selection methods coupled with linear and nonlinear regressions.

PubMed

Goodarzi, Mohammad; Jensen, Richard; Vander Heyden, Yvan

2012-12-01

A Quantitative Structure-Retention Relationship (QSRR) is proposed to estimate the chromatographic retention of 83 diverse drugs on a Unisphere poly butadiene (PBD) column, using isocratic elutions at pH 11.7. Previous work has generated QSRR models for them using Classification And Regression Trees (CART). In this work, Ant Colony Optimization is used as a feature selection method to find the best molecular descriptors from a large pool. In addition, several other selection methods have been applied, such as Genetic Algorithms, Stepwise Regression and the Relief method, not only to evaluate Ant Colony Optimization as a feature selection method but also to investigate its ability to find the important descriptors in QSRR. Multiple Linear Regression (MLR) and Support Vector Machines (SVMs) were applied as linear and nonlinear regression methods, respectively, giving excellent correlation between the experimental, i.e. extrapolated to a mobile phase consisting of pure water, and predicted logarithms of the retention factors of the drugs (logk(w)). The overall best model was the SVM one built using descriptors selected by ACO. Copyright © 2012 Elsevier B.V. All rights reserved.

Visualizing Confidence Bands for Semiparametrically Estimated Nonlinear Relations among Latent Variables

ERIC Educational Resources Information Center

Pek, Jolynn; Chalmers, R. Philip; Kok, Bethany E.; Losardo, Diane

2015-01-01

Structural equation mixture models (SEMMs), when applied as a semiparametric model (SPM), can adequately recover potentially nonlinear latent relationships without their specification. This SPM is useful for exploratory analysis when the form of the latent regression is unknown. The purpose of this article is to help users familiar with structural…

INNOVATIVE INSTRUMENTATION AND ANALYSIS OF THE TEMPERATURE MEASUREMENT FOR HIGH TEMPERATURE GASIFICATION

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

Seong W. Lee

2004-10-01

The systematic tests of the gasifier simulator on the clean thermocouple were completed in this reporting period. Within the systematic tests on the clean thermocouple, five (5) factors were considered as the experimental parameters including air flow rate, water flow rate, fine dust particle amount, ammonia addition and high/low frequency device (electric motor). The fractional factorial design method was used in the experiment design with sixteen (16) data sets of readings. Analysis of Variances (ANOVA) was applied to the results from systematic tests. The ANOVA results show that the un-balanced motor vibration frequency did not have the significant impact onmore » the temperature changes in the gasifier simulator. For the fine dust particles testing, the amount of fine dust particles has significant impact to the temperature measurements in the gasifier simulator. The effects of the air and water on the temperature measurements show the same results as reported in the previous report. The ammonia concentration was included as an experimental parameter for the reducing environment in this reporting period. The ammonia concentration does not seem to be a significant factor on the temperature changes. The linear regression analysis was applied to the temperature reading with five (5) factors. The accuracy of the linear regression is relatively low, which is less than 10% accuracy. Nonlinear regression was also conducted to the temperature reading with the same factors. Since the experiments were designed in two (2) levels, the nonlinear regression is not very effective with the dataset (16 readings). An extra central point test was conducted. With the data of the center point testing, the accuracy of the nonlinear regression is much better than the linear regression.« less

Non-Linear Relationship between Economic Growth and CO2 Emissions in China: An Empirical Study Based on Panel Smooth Transition Regression Models

PubMed Central

Wang, Zheng-Xin; Hao, Peng; Yao, Pei-Yi

2017-01-01

The non-linear relationship between provincial economic growth and carbon emissions is investigated by using panel smooth transition regression (PSTR) models. The research indicates that, on the condition of separately taking Gross Domestic Product per capita (GDPpc), energy structure (Es), and urbanisation level (Ul) as transition variables, three models all reject the null hypothesis of a linear relationship, i.e., a non-linear relationship exists. The results show that the three models all contain only one transition function but different numbers of location parameters. The model taking GDPpc as the transition variable has two location parameters, while the other two models separately considering Es and Ul as the transition variables both contain one location parameter. The three models applied in the study all favourably describe the non-linear relationship between economic growth and CO2 emissions in China. It also can be seen that the conversion rate of the influence of Ul on per capita CO2 emissions is significantly higher than those of GDPpc and Es on per capita CO2 emissions. PMID:29236083

Analysis of nonlinear relationships in dual epidemics, and its application to the management of grapevine downy and powdery mildews.

PubMed

Savary, Serge; Delbac, Lionel; Rochas, Amélie; Taisant, Guillaume; Willocquet, Laetitia

2009-08-01

Dual epidemics are defined as epidemics developing on two or several plant organs in the course of a cropping season. Agricultural pathosystems where such epidemics develop are often very important, because the harvestable part is one of the organs affected. These epidemics also are often difficult to manage, because the linkage between epidemiological components occurring on different organs is poorly understood, and because prediction of the risk toward the harvestable organs is difficult. In the case of downy mildew (DM) and powdery mildew (PM) of grapevine, nonlinear modeling and logistic regression indicated nonlinearity in the foliage-cluster relationships. Nonlinear modeling enabled the parameterization of a transmission coefficient that numerically links the two components, leaves and clusters, in DM and PM epidemics. Logistic regression analysis yielded a series of probabilistic models that enabled predicting preset levels of cluster infection risks based on DM and PM severities on the foliage at successive crop stages. The usefulness of this framework for tactical decision-making for disease control is discussed.

Non-Linear Relationship between Economic Growth and CO₂ Emissions in China: An Empirical Study Based on Panel Smooth Transition Regression Models.

PubMed

Wang, Zheng-Xin; Hao, Peng; Yao, Pei-Yi

2017-12-13

The non-linear relationship between provincial economic growth and carbon emissions is investigated by using panel smooth transition regression (PSTR) models. The research indicates that, on the condition of separately taking Gross Domestic Product per capita (GDPpc), energy structure (Es), and urbanisation level (Ul) as transition variables, three models all reject the null hypothesis of a linear relationship, i.e., a non-linear relationship exists. The results show that the three models all contain only one transition function but different numbers of location parameters. The model taking GDPpc as the transition variable has two location parameters, while the other two models separately considering Es and Ul as the transition variables both contain one location parameter. The three models applied in the study all favourably describe the non-linear relationship between economic growth and CO₂ emissions in China. It also can be seen that the conversion rate of the influence of Ul on per capita CO₂ emissions is significantly higher than those of GDPpc and Es on per capita CO₂ emissions.

Appraisal of jump distributions in ensemble-based sampling algorithms

NASA Astrophysics Data System (ADS)

Dejanic, Sanda; Scheidegger, Andreas; Rieckermann, Jörg; Albert, Carlo

2017-04-01

Sampling Bayesian posteriors of model parameters is often required for making model-based probabilistic predictions. For complex environmental models, standard Monte Carlo Markov Chain (MCMC) methods are often infeasible because they require too many sequential model runs. Therefore, we focused on ensemble methods that use many Markov chains in parallel, since they can be run on modern cluster architectures. Little is known about how to choose the best performing sampler, for a given application. A poor choice can lead to an inappropriate representation of posterior knowledge. We assessed two different jump moves, the stretch and the differential evolution move, underlying, respectively, the software packages EMCEE and DREAM, which are popular in different scientific communities. For the assessment, we used analytical posteriors with features as they often occur in real posteriors, namely high dimensionality, strong non-linear correlations or multimodality. For posteriors with non-linear features, standard convergence diagnostics based on sample means can be insufficient. Therefore, we resorted to an entropy-based convergence measure. We assessed the samplers by means of their convergence speed, robustness and effective sample sizes. For posteriors with strongly non-linear features, we found that the stretch move outperforms the differential evolution move, w.r.t. all three aspects.

Model-based optimal design of experiments - semidefinite and nonlinear programming formulations

PubMed Central

Duarte, Belmiro P.M.; Wong, Weng Kee; Oliveira, Nuno M.C.

2015-01-01

We use mathematical programming tools, such as Semidefinite Programming (SDP) and Nonlinear Programming (NLP)-based formulations to find optimal designs for models used in chemistry and chemical engineering. In particular, we employ local design-based setups in linear models and a Bayesian setup in nonlinear models to find optimal designs. In the latter case, Gaussian Quadrature Formulas (GQFs) are used to evaluate the optimality criterion averaged over the prior distribution for the model parameters. Mathematical programming techniques are then applied to solve the optimization problems. Because such methods require the design space be discretized, we also evaluate the impact of the discretization scheme on the generated design. We demonstrate the techniques for finding D–, A– and E–optimal designs using design problems in biochemical engineering and show the method can also be directly applied to tackle additional issues, such as heteroscedasticity in the model. Our results show that the NLP formulation produces highly efficient D–optimal designs but is computationally less efficient than that required for the SDP formulation. The efficiencies of the generated designs from the two methods are generally very close and so we recommend the SDP formulation in practice. PMID:26949279

Model-based optimal design of experiments - semidefinite and nonlinear programming formulations.

PubMed

Duarte, Belmiro P M; Wong, Weng Kee; Oliveira, Nuno M C

2016-02-15

We use mathematical programming tools, such as Semidefinite Programming (SDP) and Nonlinear Programming (NLP)-based formulations to find optimal designs for models used in chemistry and chemical engineering. In particular, we employ local design-based setups in linear models and a Bayesian setup in nonlinear models to find optimal designs. In the latter case, Gaussian Quadrature Formulas (GQFs) are used to evaluate the optimality criterion averaged over the prior distribution for the model parameters. Mathematical programming techniques are then applied to solve the optimization problems. Because such methods require the design space be discretized, we also evaluate the impact of the discretization scheme on the generated design. We demonstrate the techniques for finding D -, A - and E -optimal designs using design problems in biochemical engineering and show the method can also be directly applied to tackle additional issues, such as heteroscedasticity in the model. Our results show that the NLP formulation produces highly efficient D -optimal designs but is computationally less efficient than that required for the SDP formulation. The efficiencies of the generated designs from the two methods are generally very close and so we recommend the SDP formulation in practice.

Equilibrium, kinetics and process design of acid yellow 132 adsorption onto red pine sawdust.

PubMed

Can, Mustafa

2015-01-01

Linear and non-linear regression procedures have been applied to the Langmuir, Freundlich, Tempkin, Dubinin-Radushkevich, and Redlich-Peterson isotherms for adsorption of acid yellow 132 (AY132) dye onto red pine (Pinus resinosa) sawdust. The effects of parameters such as particle size, stirring rate, contact time, dye concentration, adsorption dose, pH, and temperature were investigated, and interaction was characterized by Fourier transform infrared spectroscopy and field emission scanning electron microscope. The non-linear method of the Langmuir isotherm equation was found to be the best fitting model to the equilibrium data. The maximum monolayer adsorption capacity was found as 79.5 mg/g. The calculated thermodynamic results suggested that AY132 adsorption onto red pine sawdust was an exothermic, physisorption, and spontaneous process. Kinetics was analyzed by four different kinetic equations using non-linear regression analysis. The pseudo-second-order equation provides the best fit with experimental data.

Temporal Changes in Mortality Related to Extreme Temperatures for 15 Cities in Northeast Asia: Adaptation to Heat and Maladaptation to Cold.

PubMed

Chung, Yeonseung; Noh, Heesang; Honda, Yasushi; Hashizume, Masahiro; Bell, Michelle L; Guo, Yue-Liang Leon; Kim, Ho

2017-05-15

Understanding how the temperature-mortality association worldwide changes over time is crucial to addressing questions of human adaptation under climate change. Previous studies investigated the temporal changes in the association over a few discrete time frames or assumed a linear change. Also, most studies focused on attenuation of heat-related mortality and studied the United States or Europe. This research examined continuous temporal changes (potentially nonlinear) in mortality related to extreme temperature (both heat and cold) for 15 cities in Northeast Asia (1972-2009). We used a generalized linear model with splines to simultaneously capture 2 types of nonlinearity: nonlinear association between temperature and mortality and nonlinear change over time in the association. We combined city-specific results to generate country-specific results using Bayesian hierarchical modeling. Cold-related mortality remained roughly constant over decades and slightly increased in the late 2000s, with a larger increase for cardiorespiratory deaths than for deaths from other causes. Heat-related mortality rates have decreased continuously over time, with more substantial decrease in earlier decades, for older populations and for cardiorespiratory deaths. Our findings suggest that future assessment of health effects of climate change should account for the continuous changes in temperature-related health risk and variations by factors such as age, cause of death, and location. © Crown copyright 2017.

Enhanced damping for bridge cables using a self-sensing MR damper

NASA Astrophysics Data System (ADS)

Chen, Z. H.; Lam, K. H.; Ni, Y. Q.

2016-08-01

This paper investigates enhanced damping for protecting bridge stay cables from excessive vibration using a newly developed self-sensing magnetorheological (MR) damper. The semi-active control strategy for effectively operating the self-sensing MR damper is formulated based on the linear-quadratic-Gaussian (LQG) control by further considering a collocated control configuration, limited measurements and nonlinear damper dynamics. Due to its attractive feature of sensing-while-damping, the self-sensing MR damper facilitates the collocated control. On the other hand, only the sensor measurements from the self-sensing device are employed in the feedback control. The nonlinear dynamics of the self-sensing MR damper, represented by a validated Bayesian NARX network technique, are further accommodated in the control formulation to compensate for its nonlinearities. Numerical and experimental investigations are conducted on stay cables equipped with the self-sensing MR damper operated in passive and semi-active control modes. The results verify that the collocated self-sensing MR damper facilitates smart damping for inclined cables employing energy-dissipative LQG control with only force and displacement measurements at the damper. It is also demonstrated that the synthesis of nonlinear damper dynamics in the LQG control enhances damping force tracking efficiently, explores the features of the self-sensing MR damper, and achieves better control performance over the passive MR damping control and the Heaviside step function-based LQG control that ignores the damper dynamics.

Comparison of Sub-Pixel Classification Approaches for Crop-Specific Mapping

EPA Science Inventory

This paper examined two non-linear models, Multilayer Perceptron (MLP) regression and Regression Tree (RT), for estimating sub-pixel crop proportions using time-series MODIS-NDVI data. The sub-pixel proportions were estimated for three major crop types including corn, soybean, a...

Probabilistic mapping of descriptive health status responses onto health state utilities using Bayesian networks: an empirical analysis converting SF-12 into EQ-5D utility index in a national US sample.

PubMed

Le, Quang A; Doctor, Jason N

2011-05-01

As quality-adjusted life years have become the standard metric in health economic evaluations, mapping health-profile or disease-specific measures onto preference-based measures to obtain quality-adjusted life years has become a solution when health utilities are not directly available. However, current mapping methods are limited due to their predictive validity, reliability, and/or other methodological issues. We employ probability theory together with a graphical model, called a Bayesian network, to convert health-profile measures into preference-based measures and to compare the results to those estimated with current mapping methods. A sample of 19,678 adults who completed both the 12-item Short Form Health Survey (SF-12v2) and EuroQoL 5D (EQ-5D) questionnaires from the 2003 Medical Expenditure Panel Survey was split into training and validation sets. Bayesian networks were constructed to explore the probabilistic relationships between each EQ-5D domain and 12 items of the SF-12v2. The EQ-5D utility scores were estimated on the basis of the predicted probability of each response level of the 5 EQ-5D domains obtained from the Bayesian inference process using the following methods: Monte Carlo simulation, expected utility, and most-likely probability. Results were then compared with current mapping methods including multinomial logistic regression, ordinary least squares, and censored least absolute deviations. The Bayesian networks consistently outperformed other mapping models in the overall sample (mean absolute error=0.077, mean square error=0.013, and R overall=0.802), in different age groups, number of chronic conditions, and ranges of the EQ-5D index. Bayesian networks provide a new robust and natural approach to map health status responses into health utility measures for health economic evaluations.

CO2 flux determination by closed-chamber methods can be seriously biased by inappropriate application of linear regression

NASA Astrophysics Data System (ADS)

Kutzbach, L.; Schneider, J.; Sachs, T.; Giebels, M.; Nykänen, H.; Shurpali, N. J.; Martikainen, P. J.; Alm, J.; Wilmking, M.

2007-11-01

Closed (non-steady state) chambers are widely used for quantifying carbon dioxide (CO2) fluxes between soils or low-stature canopies and the atmosphere. It is well recognised that covering a soil or vegetation by a closed chamber inherently disturbs the natural CO2 fluxes by altering the concentration gradients between the soil, the vegetation and the overlying air. Thus, the driving factors of CO2 fluxes are not constant during the closed chamber experiment, and no linear increase or decrease of CO2 concentration over time within the chamber headspace can be expected. Nevertheless, linear regression has been applied for calculating CO2 fluxes in many recent, partly influential, studies. This approach has been justified by keeping the closure time short and assuming the concentration change over time to be in the linear range. Here, we test if the application of linear regression is really appropriate for estimating CO2 fluxes using closed chambers over short closure times and if the application of nonlinear regression is necessary. We developed a nonlinear exponential regression model from diffusion and photosynthesis theory. This exponential model was tested with four different datasets of CO2 flux measurements (total number: 1764) conducted at three peatlands sites in Finland and a tundra site in Siberia. Thorough analyses of residuals demonstrated that linear regression was frequently not appropriate for the determination of CO2 fluxes by closed-chamber methods, even if closure times were kept short. The developed exponential model was well suited for nonlinear regression of the concentration over time c(t) evolution in the chamber headspace and estimation of the initial CO2 fluxes at closure time for the majority of experiments. However, a rather large percentage of the exponential regression functions showed curvatures not consistent with the theoretical model which is considered to be caused by violations of the underlying model assumptions. Especially the effects of turbulence and pressure disturbances by the chamber deployment are suspected to have caused unexplainable curvatures. CO2 flux estimates by linear regression can be as low as 40% of the flux estimates of exponential regression for closure times of only two minutes. The degree of underestimation increased with increasing CO2 flux strength and was dependent on soil and vegetation conditions which can disturb not only the quantitative but also the qualitative evaluation of CO2 flux dynamics. The underestimation effect by linear regression was observed to be different for CO2 uptake and release situations which can lead to stronger bias in the daily, seasonal and annual CO2 balances than in the individual fluxes. To avoid serious bias of CO2 flux estimates based on closed chamber experiments, we suggest further tests using published datasets and recommend the use of nonlinear regression models for future closed chamber studies.

Exploring unobserved heterogeneity in bicyclists' red-light running behaviors at different crossing facilities.

PubMed

Guo, Yanyong; Li, Zhibin; Wu, Yao; Xu, Chengcheng

2018-06-01

Bicyclists running the red light at crossing facilities increase the potential of colliding with motor vehicles. Exploring the contributing factors could improve the prediction of running red-light probability and develop countermeasures to reduce such behaviors. However, individuals could have unobserved heterogeneities in running a red light, which make the accurate prediction more challenging. Traditional models assume that factor parameters are fixed and cannot capture the varying impacts on red-light running behaviors. In this study, we employed the full Bayesian random parameters logistic regression approach to account for the unobserved heterogeneous effects. Two types of crossing facilities were considered which were the signalized intersection crosswalks and the road segment crosswalks. Electric and conventional bikes were distinguished in the modeling. Data were collected from 16 crosswalks in urban area of Nanjing, China. Factors such as individual characteristics, road geometric design, environmental features, and traffic variables were examined. Model comparison indicates that the full Bayesian random parameters logistic regression approach is statistically superior to the standard logistic regression model. More red-light runners are predicted at signalized intersection crosswalks than at road segment crosswalks. Factors affecting red-light running behaviors are gender, age, bike type, road width, presence of raised median, separation width, signal type, green ratio, bike and vehicle volume, and average vehicle speed. Factors associated with the unobserved heterogeneity are gender, bike type, signal type, separation width, and bike volume. Copyright © 2018 Elsevier Ltd. All rights reserved.

A General Bayesian Network Approach to Analyzing Online Game Item Values and Its Influence on Consumer Satisfaction and Purchase Intention

NASA Astrophysics Data System (ADS)

Lee, Kun Chang; Park, Bong-Won

Many online game users purchase game items with which to play free-to-play games. Because of a lack of research into which there is no specified framework for categorizing the values of game items, this study proposes four types of online game item values based on an analysis of literature regarding online game characteristics. It then proposes to investigate how online game users perceive satisfaction and purchase intention from the proposed four types of online game item values. Though regression analysis has been used frequently to answer this kind of research question, we propose a new approach, a General Bayesian Network (GBN), which can be performed in an understandable way without sacrificing predictive accuracy. Conventional techniques, such as regression analysis, do not provide significant explanation for this kind of problem because they are fixed to a linear structure and are limited in explaining why customers are likely to purchase game items and if they are satisfied with their purchases. In contrast, the proposed GBN provides a flexible underlying structure based on questionnaire survey data and offers robust decision support on this kind of research question by identifying its causal relationships. To illustrate the validity of GBN in solving the research question in this study, 327 valid questionnaires were analyzed using GBN with what-if and goal-seeking approaches. The experimental results were promising and meaningful in comparison with regression analysis results.

Development of a Bayesian model to estimate health care outcomes in the severely wounded

PubMed Central

Stojadinovic, Alexander; Eberhardt, John; Brown, Trevor S; Hawksworth, Jason S; Gage, Frederick; Tadaki, Douglas K; Forsberg, Jonathan A; Davis, Thomas A; Potter, Benjamin K; Dunne, James R; Elster, E A

2010-01-01

Background: Graphical probabilistic models have the ability to provide insights as to how clinical factors are conditionally related. These models can be used to help us understand factors influencing health care outcomes and resource utilization, and to estimate morbidity and clinical outcomes in trauma patient populations. Study design: Thirty-two combat casualties with severe extremity injuries enrolled in a prospective observational study were analyzed using step-wise machine-learned Bayesian belief network (BBN) and step-wise logistic regression (LR). Models were evaluated using 10-fold cross-validation to calculate area-under-the-curve (AUC) from receiver operating characteristics (ROC) curves. Results: Our BBN showed important associations between various factors in our data set that could not be developed using standard regression methods. Cross-validated ROC curve analysis showed that our BBN model was a robust representation of our data domain and that LR models trained on these findings were also robust: hospital-acquired infection (AUC: LR, 0.81; BBN, 0.79), intensive care unit length of stay (AUC: LR, 0.97; BBN, 0.81), and wound healing (AUC: LR, 0.91; BBN, 0.72) showed strong AUC. Conclusions: A BBN model can effectively represent clinical outcomes and biomarkers in patients hospitalized after severe wounding, and is confirmed by 10-fold cross-validation and further confirmed through logistic regression modeling. The method warrants further development and independent validation in other, more diverse patient populations. PMID:21197361

Applications of Support Vector Machines In Chemo And Bioinformatics

NASA Astrophysics Data System (ADS)

Jayaraman, V. K.; Sundararajan, V.

2010-10-01

Conventional linear & nonlinear tools for classification, regression & data driven modeling are being replaced on a rapid scale by newer techniques & tools based on artificial intelligence and machine learning. While the linear techniques are not applicable for inherently nonlinear problems, newer methods serve as attractive alternatives for solving real life problems. Support Vector Machine (SVM) classifiers are a set of universal feed-forward network based classification algorithms that have been formulated from statistical learning theory and structural risk minimization principle. SVM regression closely follows the classification methodology. In this work recent applications of SVM in Chemo & Bioinformatics will be described with suitable illustrative examples.

Improved spatial regression analysis of diffusion tensor imaging for lesion detection during longitudinal progression of multiple sclerosis in individual subjects

NASA Astrophysics Data System (ADS)

Liu, Bilan; Qiu, Xing; Zhu, Tong; Tian, Wei; Hu, Rui; Ekholm, Sven; Schifitto, Giovanni; Zhong, Jianhui

2016-03-01

Subject-specific longitudinal DTI study is vital for investigation of pathological changes of lesions and disease evolution. Spatial Regression Analysis of Diffusion tensor imaging (SPREAD) is a non-parametric permutation-based statistical framework that combines spatial regression and resampling techniques to achieve effective detection of localized longitudinal diffusion changes within the whole brain at individual level without a priori hypotheses. However, boundary blurring and dislocation limit its sensitivity, especially towards detecting lesions of irregular shapes. In the present study, we propose an improved SPREAD (dubbed improved SPREAD, or iSPREAD) method by incorporating a three-dimensional (3D) nonlinear anisotropic diffusion filtering method, which provides edge-preserving image smoothing through a nonlinear scale space approach. The statistical inference based on iSPREAD was evaluated and compared with the original SPREAD method using both simulated and in vivo human brain data. Results demonstrated that the sensitivity and accuracy of the SPREAD method has been improved substantially by adapting nonlinear anisotropic filtering. iSPREAD identifies subject-specific longitudinal changes in the brain with improved sensitivity, accuracy, and enhanced statistical power, especially when the spatial correlation is heterogeneous among neighboring image pixels in DTI.