Statistical limitations in functional neuroimaging. I. Non-inferential methods and statistical models.

PubMed Central

Petersson, K M; Nichols, T E; Poline, J B; Holmes, A P

1999-01-01

Functional neuroimaging (FNI) provides experimental access to the intact living brain making it possible to study higher cognitive functions in humans. In this review and in a companion paper in this issue, we discuss some common methods used to analyse FNI data. The emphasis in both papers is on assumptions and limitations of the methods reviewed. There are several methods available to analyse FNI data indicating that none is optimal for all purposes. In order to make optimal use of the methods available it is important to know the limits of applicability. For the interpretation of FNI results it is also important to take into account the assumptions, approximations and inherent limitations of the methods used. This paper gives a brief overview over some non-inferential descriptive methods and common statistical models used in FNI. Issues relating to the complex problem of model selection are discussed. In general, proper model selection is a necessary prerequisite for the validity of the subsequent statistical inference. The non-inferential section describes methods that, combined with inspection of parameter estimates and other simple measures, can aid in the process of model selection and verification of assumptions. The section on statistical models covers approaches to global normalization and some aspects of univariate, multivariate, and Bayesian models. Finally, approaches to functional connectivity and effective connectivity are discussed. In the companion paper we review issues related to signal detection and statistical inference. PMID:10466149

Distributed Sensing and Processing for Multi-Camera Networks

NASA Astrophysics Data System (ADS)

Sankaranarayanan, Aswin C.; Chellappa, Rama; Baraniuk, Richard G.

Sensor networks with large numbers of cameras are becoming increasingly prevalent in a wide range of applications, including video conferencing, motion capture, surveillance, and clinical diagnostics. In this chapter, we identify some of the fundamental challenges in designing such systems: robust statistical inference, computationally efficiency, and opportunistic and parsimonious sensing. We show that the geometric constraints induced by the imaging process are extremely useful for identifying and designing optimal estimators for object detection and tracking tasks. We also derive pipelined and parallelized implementations of popular tools used for statistical inference in non-linear systems, of which multi-camera systems are examples. Finally, we highlight the use of the emerging theory of compressive sensing in reducing the amount of data sensed and communicated by a camera network.

Selecting the right statistical model for analysis of insect count data by using information theoretic measures.

PubMed

Sileshi, G

2006-10-01

Researchers and regulatory agencies often make statistical inferences from insect count data using modelling approaches that assume homogeneous variance. Such models do not allow for formal appraisal of variability which in its different forms is the subject of interest in ecology. Therefore, the objectives of this paper were to (i) compare models suitable for handling variance heterogeneity and (ii) select optimal models to ensure valid statistical inferences from insect count data. The log-normal, standard Poisson, Poisson corrected for overdispersion, zero-inflated Poisson, the negative binomial distribution and zero-inflated negative binomial models were compared using six count datasets on foliage-dwelling insects and five families of soil-dwelling insects. Akaike's and Schwarz Bayesian information criteria were used for comparing the various models. Over 50% of the counts were zeros even in locally abundant species such as Ootheca bennigseni Weise, Mesoplatys ochroptera Stål and Diaecoderus spp. The Poisson model after correction for overdispersion and the standard negative binomial distribution model provided better description of the probability distribution of seven out of the 11 insects than the log-normal, standard Poisson, zero-inflated Poisson or zero-inflated negative binomial models. It is concluded that excess zeros and variance heterogeneity are common data phenomena in insect counts. If not properly modelled, these properties can invalidate the normal distribution assumptions resulting in biased estimation of ecological effects and jeopardizing the integrity of the scientific inferences. Therefore, it is recommended that statistical models appropriate for handling these data properties be selected using objective criteria to ensure efficient statistical inference.

Experimental validation of the RATE tool for inferring HLA restrictions of T cell epitopes.

PubMed

Paul, Sinu; Arlehamn, Cecilia S Lindestam; Schulten, Veronique; Westernberg, Luise; Sidney, John; Peters, Bjoern; Sette, Alessandro

2017-06-21

The RATE tool was recently developed to computationally infer the HLA restriction of given epitopes from immune response data of HLA typed subjects without additional cumbersome experimentation. Here, RATE was validated using experimentally defined restriction data from a set of 191 tuberculosis-derived epitopes and 63 healthy individuals with MTB infection from the Western Cape Region of South Africa. Using this experimental dataset, the parameters utilized by the RATE tool to infer restriction were optimized, which included relative frequency (RF) of the subjects responding to a given epitope and expressing a given allele as compared to the general test population and the associated p-value in a Fisher's exact test. We also examined the potential for further optimization based on the predicted binding affinity of epitopes to potential restricting HLA alleles, and the absolute number of individuals expressing a given allele and responding to the specific epitope. Different statistical measures, including Matthew's correlation coefficient, accuracy, sensitivity and specificity were used to evaluate performance of RATE as a function of these criteria. Based on our results we recommend selection of HLA restrictions with cutoffs of p-value < 0.01 and RF ≥ 1.3. The usefulness of the tool was demonstrated by inferring new HLA restrictions for epitope sets where restrictions could not be experimentally determined due to lack of necessary cell lines and for an additional data set related to recognition of pollen derived epitopes from allergic patients. Experimental data sets were used to validate RATE tool and the parameters used by the RATE tool to infer restriction were optimized. New HLA restrictions were identified using the optimized RATE tool.

Decision-theoretic saliency: computational principles, biological plausibility, and implications for neurophysiology and psychophysics.

PubMed

Gao, Dashan; Vasconcelos, Nuno

2009-01-01

A decision-theoretic formulation of visual saliency, first proposed for top-down processing (object recognition) (Gao & Vasconcelos, 2005a), is extended to the problem of bottom-up saliency. Under this formulation, optimality is defined in the minimum probability of error sense, under a constraint of computational parsimony. The saliency of the visual features at a given location of the visual field is defined as the power of those features to discriminate between the stimulus at the location and a null hypothesis. For bottom-up saliency, this is the set of visual features that surround the location under consideration. Discrimination is defined in an information-theoretic sense and the optimal saliency detector derived for a class of stimuli that complies with known statistical properties of natural images. It is shown that under the assumption that saliency is driven by linear filtering, the optimal detector consists of what is usually referred to as the standard architecture of V1: a cascade of linear filtering, divisive normalization, rectification, and spatial pooling. The optimal detector is also shown to replicate the fundamental properties of the psychophysics of saliency: stimulus pop-out, saliency asymmetries for stimulus presence versus absence, disregard of feature conjunctions, and Weber's law. Finally, it is shown that the optimal saliency architecture can be applied to the solution of generic inference problems. In particular, for the class of stimuli studied, it performs the three fundamental operations of statistical inference: assessment of probabilities, implementation of Bayes decision rule, and feature selection.

Learning planar Ising models

DOE PAGES

Johnson, Jason K.; Oyen, Diane Adele; Chertkov, Michael; ...

2016-12-01

Inference and learning of graphical models are both well-studied problems in statistics and machine learning that have found many applications in science and engineering. However, exact inference is intractable in general graphical models, which suggests the problem of seeking the best approximation to a collection of random variables within some tractable family of graphical models. In this paper, we focus on the class of planar Ising models, for which exact inference is tractable using techniques of statistical physics. Based on these techniques and recent methods for planarity testing and planar embedding, we propose a greedy algorithm for learning the bestmore » planar Ising model to approximate an arbitrary collection of binary random variables (possibly from sample data). Given the set of all pairwise correlations among variables, we select a planar graph and optimal planar Ising model defined on this graph to best approximate that set of correlations. Finally, we demonstrate our method in simulations and for two applications: modeling senate voting records and identifying geo-chemical depth trends from Mars rover data.« less

Learning planar Ising models

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

Johnson, Jason K.; Oyen, Diane Adele; Chertkov, Michael

Inference and learning of graphical models are both well-studied problems in statistics and machine learning that have found many applications in science and engineering. However, exact inference is intractable in general graphical models, which suggests the problem of seeking the best approximation to a collection of random variables within some tractable family of graphical models. In this paper, we focus on the class of planar Ising models, for which exact inference is tractable using techniques of statistical physics. Based on these techniques and recent methods for planarity testing and planar embedding, we propose a greedy algorithm for learning the bestmore » planar Ising model to approximate an arbitrary collection of binary random variables (possibly from sample data). Given the set of all pairwise correlations among variables, we select a planar graph and optimal planar Ising model defined on this graph to best approximate that set of correlations. Finally, we demonstrate our method in simulations and for two applications: modeling senate voting records and identifying geo-chemical depth trends from Mars rover data.« less

Unbiased split variable selection for random survival forests using maximally selected rank statistics.

PubMed

Wright, Marvin N; Dankowski, Theresa; Ziegler, Andreas

2017-04-15

The most popular approach for analyzing survival data is the Cox regression model. The Cox model may, however, be misspecified, and its proportionality assumption may not always be fulfilled. An alternative approach for survival prediction is random forests for survival outcomes. The standard split criterion for random survival forests is the log-rank test statistic, which favors splitting variables with many possible split points. Conditional inference forests avoid this split variable selection bias. However, linear rank statistics are utilized by default in conditional inference forests to select the optimal splitting variable, which cannot detect non-linear effects in the independent variables. An alternative is to use maximally selected rank statistics for the split point selection. As in conditional inference forests, splitting variables are compared on the p-value scale. However, instead of the conditional Monte-Carlo approach used in conditional inference forests, p-value approximations are employed. We describe several p-value approximations and the implementation of the proposed random forest approach. A simulation study demonstrates that unbiased split variable selection is possible. However, there is a trade-off between unbiased split variable selection and runtime. In benchmark studies of prediction performance on simulated and real datasets, the new method performs better than random survival forests if informative dichotomous variables are combined with uninformative variables with more categories and better than conditional inference forests if non-linear covariate effects are included. In a runtime comparison, the method proves to be computationally faster than both alternatives, if a simple p-value approximation is used. Copyright © 2017 John Wiley & Sons, Ltd. Copyright © 2017 John Wiley & Sons, Ltd.

Data Acquisition and Preprocessing in Studies on Humans: What Is Not Taught in Statistics Classes?

PubMed

Zhu, Yeyi; Hernandez, Ladia M; Mueller, Peter; Dong, Yongquan; Forman, Michele R

2013-01-01

The aim of this paper is to address issues in research that may be missing from statistics classes and important for (bio-)statistics students. In the context of a case study, we discuss data acquisition and preprocessing steps that fill the gap between research questions posed by subject matter scientists and statistical methodology for formal inference. Issues include participant recruitment, data collection training and standardization, variable coding, data review and verification, data cleaning and editing, and documentation. Despite the critical importance of these details in research, most of these issues are rarely discussed in an applied statistics program. One reason for the lack of more formal training is the difficulty in addressing the many challenges that can possibly arise in the course of a study in a systematic way. This article can help to bridge this gap between research questions and formal statistical inference by using an illustrative case study for a discussion. We hope that reading and discussing this paper and practicing data preprocessing exercises will sensitize statistics students to these important issues and achieve optimal conduct, quality control, analysis, and interpretation of a study.

Role of sufficient statistics in stochastic thermodynamics and its implication to sensory adaptation

NASA Astrophysics Data System (ADS)

Matsumoto, Takumi; Sagawa, Takahiro

2018-04-01

A sufficient statistic is a significant concept in statistics, which means a probability variable that has sufficient information required for an inference task. We investigate the roles of sufficient statistics and related quantities in stochastic thermodynamics. Specifically, we prove that for general continuous-time bipartite networks, the existence of a sufficient statistic implies that an informational quantity called the sensory capacity takes the maximum. Since the maximal sensory capacity imposes a constraint that the energetic efficiency cannot exceed one-half, our result implies that the existence of a sufficient statistic is inevitably accompanied by energetic dissipation. We also show that, in a particular parameter region of linear Langevin systems there exists the optimal noise intensity at which the sensory capacity, the information-thermodynamic efficiency, and the total entropy production are optimized at the same time. We apply our general result to a model of sensory adaptation of E. coli and find that the sensory capacity is nearly maximal with experimentally realistic parameters.

Rage against the Machine: Evaluation Metrics in the 21st Century

ERIC Educational Resources Information Center

Yang, Charles

2017-01-01

I review the classic literature in generative grammar and Marr's three-level program for cognitive science to defend the Evaluation Metric as a psychological theory of language learning. Focusing on well-established facts of language variation, change, and use, I argue that optimal statistical principles embodied in Bayesian inference models are…

[Applications of mathematical statistics methods on compatibility researches of traditional Chinese medicines formulae].

PubMed

Mai, Lan-Yin; Li, Yi-Xuan; Chen, Yong; Xie, Zhen; Li, Jie; Zhong, Ming-Yu

2014-05-01

The compatibility of traditional Chinese medicines (TCMs) formulae containing enormous information, is a complex component system. Applications of mathematical statistics methods on the compatibility researches of traditional Chinese medicines formulae have great significance for promoting the modernization of traditional Chinese medicines and improving clinical efficacies and optimizations of formulae. As a tool for quantitative analysis, data inference and exploring inherent rules of substances, the mathematical statistics method can be used to reveal the working mechanisms of the compatibility of traditional Chinese medicines formulae in qualitatively and quantitatively. By reviewing studies based on the applications of mathematical statistics methods, this paper were summarized from perspective of dosages optimization, efficacies and changes of chemical components as well as the rules of incompatibility and contraindication of formulae, will provide the references for further studying and revealing the working mechanisms and the connotations of traditional Chinese medicines.

Rational approximations to rational models: alternative algorithms for category learning.

PubMed

Sanborn, Adam N; Griffiths, Thomas L; Navarro, Daniel J

2010-10-01

Rational models of cognition typically consider the abstract computational problems posed by the environment, assuming that people are capable of optimally solving those problems. This differs from more traditional formal models of cognition, which focus on the psychological processes responsible for behavior. A basic challenge for rational models is thus explaining how optimal solutions can be approximated by psychological processes. We outline a general strategy for answering this question, namely to explore the psychological plausibility of approximation algorithms developed in computer science and statistics. In particular, we argue that Monte Carlo methods provide a source of rational process models that connect optimal solutions to psychological processes. We support this argument through a detailed example, applying this approach to Anderson's (1990, 1991) rational model of categorization (RMC), which involves a particularly challenging computational problem. Drawing on a connection between the RMC and ideas from nonparametric Bayesian statistics, we propose 2 alternative algorithms for approximate inference in this model. The algorithms we consider include Gibbs sampling, a procedure appropriate when all stimuli are presented simultaneously, and particle filters, which sequentially approximate the posterior distribution with a small number of samples that are updated as new data become available. Applying these algorithms to several existing datasets shows that a particle filter with a single particle provides a good description of human inferences.

Statistical Inference at Work: Statistical Process Control as an Example

ERIC Educational Resources Information Center

Bakker, Arthur; Kent, Phillip; Derry, Jan; Noss, Richard; Hoyles, Celia

2008-01-01

To characterise statistical inference in the workplace this paper compares a prototypical type of statistical inference at work, statistical process control (SPC), with a type of statistical inference that is better known in educational settings, hypothesis testing. Although there are some similarities between the reasoning structure involved in…

Reading biological processes from nucleotide sequences

NASA Astrophysics Data System (ADS)

Murugan, Anand

Cellular processes have traditionally been investigated by techniques of imaging and biochemical analysis of the molecules involved. The recent rapid progress in our ability to manipulate and read nucleic acid sequences gives us direct access to the genetic information that directs and constrains biological processes. While sequence data is being used widely to investigate genotype-phenotype relationships and population structure, here we use sequencing to understand biophysical mechanisms. We present work on two different systems. First, in chapter 2, we characterize the stochastic genetic editing mechanism that produces diverse T-cell receptors in the human immune system. We do this by inferring statistical distributions of the underlying biochemical events that generate T-cell receptor coding sequences from the statistics of the observed sequences. This inferred model quantitatively describes the potential repertoire of T-cell receptors that can be produced by an individual, providing insight into its potential diversity and the probability of generation of any specific T-cell receptor. Then in chapter 3, we present work on understanding the functioning of regulatory DNA sequences in both prokaryotes and eukaryotes. Here we use experiments that measure the transcriptional activity of large libraries of mutagenized promoters and enhancers and infer models of the sequence-function relationship from this data. For the bacterial promoter, we infer a physically motivated 'thermodynamic' model of the interaction of DNA-binding proteins and RNA polymerase determining the transcription rate of the downstream gene. For the eukaryotic enhancers, we infer heuristic models of the sequence-function relationship and use these models to find synthetic enhancer sequences that optimize inducibility of expression. Both projects demonstrate the utility of sequence information in conjunction with sophisticated statistical inference techniques for dissecting underlying biophysical mechanisms.

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

NASA Astrophysics Data System (ADS)

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

2017-03-01

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

A normative inference approach for optimal sample sizes in decisions from experience

PubMed Central

Ostwald, Dirk; Starke, Ludger; Hertwig, Ralph

2015-01-01

“Decisions from experience” (DFE) refers to a body of work that emerged in research on behavioral decision making over the last decade. One of the major experimental paradigms employed to study experience-based choice is the “sampling paradigm,” which serves as a model of decision making under limited knowledge about the statistical structure of the world. In this paradigm respondents are presented with two payoff distributions, which, in contrast to standard approaches in behavioral economics, are specified not in terms of explicit outcome-probability information, but by the opportunity to sample outcomes from each distribution without economic consequences. Participants are encouraged to explore the distributions until they feel confident enough to decide from which they would prefer to draw from in a final trial involving real monetary payoffs. One commonly employed measure to characterize the behavior of participants in the sampling paradigm is the sample size, that is, the number of outcome draws which participants choose to obtain from each distribution prior to terminating sampling. A natural question that arises in this context concerns the “optimal” sample size, which could be used as a normative benchmark to evaluate human sampling behavior in DFE. In this theoretical study, we relate the DFE sampling paradigm to the classical statistical decision theoretic literature and, under a probabilistic inference assumption, evaluate optimal sample sizes for DFE. In our treatment we go beyond analytically established results by showing how the classical statistical decision theoretic framework can be used to derive optimal sample sizes under arbitrary, but numerically evaluable, constraints. Finally, we critically evaluate the value of deriving optimal sample sizes under this framework as testable predictions for the experimental study of sampling behavior in DFE. PMID:26441720

Assessing risk factors for dental caries: a statistical modeling approach.

PubMed

Trottini, Mario; Bossù, Maurizio; Corridore, Denise; Ierardo, Gaetano; Luzzi, Valeria; Saccucci, Matteo; Polimeni, Antonella

2015-01-01

The problem of identifying potential determinants and predictors of dental caries is of key importance in caries research and it has received considerable attention in the scientific literature. From the methodological side, a broad range of statistical models is currently available to analyze dental caries indices (DMFT, dmfs, etc.). These models have been applied in several studies to investigate the impact of different risk factors on the cumulative severity of dental caries experience. However, in most of the cases (i) these studies focus on a very specific subset of risk factors; and (ii) in the statistical modeling only few candidate models are considered and model selection is at best only marginally addressed. As a result, our understanding of the robustness of the statistical inferences with respect to the choice of the model is very limited; the richness of the set of statistical models available for analysis in only marginally exploited; and inferences could be biased due the omission of potentially important confounding variables in the model's specification. In this paper we argue that these limitations can be overcome considering a general class of candidate models and carefully exploring the model space using standard model selection criteria and measures of global fit and predictive performance of the candidate models. Strengths and limitations of the proposed approach are illustrated with a real data set. In our illustration the model space contains more than 2.6 million models, which require inferences to be adjusted for 'optimism'.

The potential for increased power from combining P-values testing the same hypothesis.

PubMed

Ganju, Jitendra; Julie Ma, Guoguang

2017-02-01

The conventional approach to hypothesis testing for formal inference is to prespecify a single test statistic thought to be optimal. However, we usually have more than one test statistic in mind for testing the null hypothesis of no treatment effect but we do not know which one is the most powerful. Rather than relying on a single p-value, combining p-values from prespecified multiple test statistics can be used for inference. Combining functions include Fisher's combination test and the minimum p-value. Using randomization-based tests, the increase in power can be remarkable when compared with a single test and Simes's method. The versatility of the method is that it also applies when the number of covariates exceeds the number of observations. The increase in power is large enough to prefer combined p-values over a single p-value. The limitation is that the method does not provide an unbiased estimator of the treatment effect and does not apply to situations when the model includes treatment by covariate interaction.

Applying a multiobjective metaheuristic inspired by honey bees to phylogenetic inference.

PubMed

Santander-Jiménez, Sergio; Vega-Rodríguez, Miguel A

2013-10-01

The development of increasingly popular multiobjective metaheuristics has allowed bioinformaticians to deal with optimization problems in computational biology where multiple objective functions must be taken into account. One of the most relevant research topics that can benefit from these techniques is phylogenetic inference. Throughout the years, different researchers have proposed their own view about the reconstruction of ancestral evolutionary relationships among species. As a result, biologists often report different phylogenetic trees from a same dataset when considering distinct optimality principles. In this work, we detail a multiobjective swarm intelligence approach based on the novel Artificial Bee Colony algorithm for inferring phylogenies. The aim of this paper is to propose a complementary view of phylogenetics according to the maximum parsimony and maximum likelihood criteria, in order to generate a set of phylogenetic trees that represent a compromise between these principles. Experimental results on a variety of nucleotide data sets and statistical studies highlight the relevance of the proposal with regard to other multiobjective algorithms and state-of-the-art biological methods. Copyright © 2013 Elsevier Ireland Ltd. All rights reserved.

Decision-making when data and inferences are not conclusive: risk-benefit and acceptable regret approach.

PubMed

Hozo, Iztok; Schell, Michael J; Djulbegovic, Benjamin

2008-07-01

The absolute truth in research is unobtainable, as no evidence or research hypothesis is ever 100% conclusive. Therefore, all data and inferences can in principle be considered as "inconclusive." Scientific inference and decision-making need to take into account errors, which are unavoidable in the research enterprise. The errors can occur at the level of conclusions that aim to discern the truthfulness of research hypothesis based on the accuracy of research evidence and hypothesis, and decisions, the goal of which is to enable optimal decision-making under present and specific circumstances. To optimize the chance of both correct conclusions and correct decisions, the synthesis of all major statistical approaches to clinical research is needed. The integration of these approaches (frequentist, Bayesian, and decision-analytic) can be accomplished through formal risk:benefit (R:B) analysis. This chapter illustrates the rational choice of a research hypothesis using R:B analysis based on decision-theoretic expected utility theory framework and the concept of "acceptable regret" to calculate the threshold probability of the "truth" above which the benefit of accepting a research hypothesis outweighs its risks.

Outcome-Dependent Sampling Design and Inference for Cox's Proportional Hazards Model.

PubMed

Yu, Jichang; Liu, Yanyan; Cai, Jianwen; Sandler, Dale P; Zhou, Haibo

2016-11-01

We propose a cost-effective outcome-dependent sampling design for the failure time data and develop an efficient inference procedure for data collected with this design. To account for the biased sampling scheme, we derive estimators from a weighted partial likelihood estimating equation. The proposed estimators for regression parameters are shown to be consistent and asymptotically normally distributed. A criteria that can be used to optimally implement the ODS design in practice is proposed and studied. The small sample performance of the proposed method is evaluated by simulation studies. The proposed design and inference procedure is shown to be statistically more powerful than existing alternative designs with the same sample sizes. We illustrate the proposed method with an existing real data from the Cancer Incidence and Mortality of Uranium Miners Study.

Investigation of Statistical Inference Methodologies Through Scale Model Propagation Experiments

DTIC Science & Technology

2015-09-30

statistical inference methodologies for ocean- acoustic problems by investigating and applying statistical methods to data collected from scale-model...to begin planning experiments for statistical inference applications. APPROACH In the ocean acoustics community over the past two decades...solutions for waveguide parameters. With the introduction of statistical inference to the field of ocean acoustics came the desire to interpret marginal

Forward and backward inference in spatial cognition.

PubMed

Penny, Will D; Zeidman, Peter; Burgess, Neil

2013-01-01

This paper shows that the various computations underlying spatial cognition can be implemented using statistical inference in a single probabilistic model. Inference is implemented using a common set of 'lower-level' computations involving forward and backward inference over time. For example, to estimate where you are in a known environment, forward inference is used to optimally combine location estimates from path integration with those from sensory input. To decide which way to turn to reach a goal, forward inference is used to compute the likelihood of reaching that goal under each option. To work out which environment you are in, forward inference is used to compute the likelihood of sensory observations under the different hypotheses. For reaching sensory goals that require a chaining together of decisions, forward inference can be used to compute a state trajectory that will lead to that goal, and backward inference to refine the route and estimate control signals that produce the required trajectory. We propose that these computations are reflected in recent findings of pattern replay in the mammalian brain. Specifically, that theta sequences reflect decision making, theta flickering reflects model selection, and remote replay reflects route and motor planning. We also propose a mapping of the above computational processes onto lateral and medial entorhinal cortex and hippocampus.

Forward and Backward Inference in Spatial Cognition

PubMed Central

Penny, Will D.; Zeidman, Peter; Burgess, Neil

2013-01-01

This paper shows that the various computations underlying spatial cognition can be implemented using statistical inference in a single probabilistic model. Inference is implemented using a common set of ‘lower-level’ computations involving forward and backward inference over time. For example, to estimate where you are in a known environment, forward inference is used to optimally combine location estimates from path integration with those from sensory input. To decide which way to turn to reach a goal, forward inference is used to compute the likelihood of reaching that goal under each option. To work out which environment you are in, forward inference is used to compute the likelihood of sensory observations under the different hypotheses. For reaching sensory goals that require a chaining together of decisions, forward inference can be used to compute a state trajectory that will lead to that goal, and backward inference to refine the route and estimate control signals that produce the required trajectory. We propose that these computations are reflected in recent findings of pattern replay in the mammalian brain. Specifically, that theta sequences reflect decision making, theta flickering reflects model selection, and remote replay reflects route and motor planning. We also propose a mapping of the above computational processes onto lateral and medial entorhinal cortex and hippocampus. PMID:24348230

Robust inference for group sequential trials.

PubMed

Ganju, Jitendra; Lin, Yunzhi; Zhou, Kefei

2017-03-01

For ethical reasons, group sequential trials were introduced to allow trials to stop early in the event of extreme results. Endpoints in such trials are usually mortality or irreversible morbidity. For a given endpoint, the norm is to use a single test statistic and to use that same statistic for each analysis. This approach is risky because the test statistic has to be specified before the study is unblinded, and there is loss in power if the assumptions that ensure optimality for each analysis are not met. To minimize the risk of moderate to substantial loss in power due to a suboptimal choice of a statistic, a robust method was developed for nonsequential trials. The concept is analogous to diversification of financial investments to minimize risk. The method is based on combining P values from multiple test statistics for formal inference while controlling the type I error rate at its designated value.This article evaluates the performance of 2 P value combining methods for group sequential trials. The emphasis is on time to event trials although results from less complex trials are also included. The gain or loss in power with the combination method relative to a single statistic is asymmetric in its favor. Depending on the power of each individual test, the combination method can give more power than any single test or give power that is closer to the test with the most power. The versatility of the method is that it can combine P values from different test statistics for analysis at different times. The robustness of results suggests that inference from group sequential trials can be strengthened with the use of combined tests. Copyright © 2017 John Wiley & Sons, Ltd.

Context-Aware Generative Adversarial Privacy

NASA Astrophysics Data System (ADS)

Huang, Chong; Kairouz, Peter; Chen, Xiao; Sankar, Lalitha; Rajagopal, Ram

2017-12-01

Preserving the utility of published datasets while simultaneously providing provable privacy guarantees is a well-known challenge. On the one hand, context-free privacy solutions, such as differential privacy, provide strong privacy guarantees, but often lead to a significant reduction in utility. On the other hand, context-aware privacy solutions, such as information theoretic privacy, achieve an improved privacy-utility tradeoff, but assume that the data holder has access to dataset statistics. We circumvent these limitations by introducing a novel context-aware privacy framework called generative adversarial privacy (GAP). GAP leverages recent advancements in generative adversarial networks (GANs) to allow the data holder to learn privatization schemes from the dataset itself. Under GAP, learning the privacy mechanism is formulated as a constrained minimax game between two players: a privatizer that sanitizes the dataset in a way that limits the risk of inference attacks on the individuals' private variables, and an adversary that tries to infer the private variables from the sanitized dataset. To evaluate GAP's performance, we investigate two simple (yet canonical) statistical dataset models: (a) the binary data model, and (b) the binary Gaussian mixture model. For both models, we derive game-theoretically optimal minimax privacy mechanisms, and show that the privacy mechanisms learned from data (in a generative adversarial fashion) match the theoretically optimal ones. This demonstrates that our framework can be easily applied in practice, even in the absence of dataset statistics.

Optimally designing games for behavioural research

PubMed Central

Rafferty, Anna N.; Zaharia, Matei; Griffiths, Thomas L.

2014-01-01

Computer games can be motivating and engaging experiences that facilitate learning, leading to their increasing use in education and behavioural experiments. For these applications, it is often important to make inferences about the knowledge and cognitive processes of players based on their behaviour. However, designing games that provide useful behavioural data are a difficult task that typically requires significant trial and error. We address this issue by creating a new formal framework that extends optimal experiment design, used in statistics, to apply to game design. In this framework, we use Markov decision processes to model players' actions within a game, and then make inferences about the parameters of a cognitive model from these actions. Using a variety of concept learning games, we show that in practice, this method can predict which games will result in better estimates of the parameters of interest. The best games require only half as many players to attain the same level of precision. PMID:25002821

Cardinal rules: Visual orientation perception reflects knowledge of environmental statistics

PubMed Central

Girshick, Ahna R.; Landy, Michael S.; Simoncelli, Eero P.

2011-01-01

Humans are remarkably good at performing visual tasks, but experimental measurements reveal substantial biases in the perception of basic visual attributes. An appealing hypothesis is that these biases arise through a process of statistical inference, in which information from noisy measurements is fused with a probabilistic model of the environment. But such inference is optimal only if the observer’s internal model matches the environment. Here, we provide evidence that this is the case. We measured performance in an orientation-estimation task, demonstrating the well-known fact that orientation judgements are more accurate at cardinal (horizontal and vertical) orientations, along with a new observation that judgements made under conditions of uncertainty are strongly biased toward cardinal orientations. We estimate observers’ internal models for orientation and find that they match the local orientation distribution measured in photographs. We also show how a neural population could embed probabilistic information responsible for such biases. PMID:21642976

Clustering Genes of Common Evolutionary History

PubMed Central

Gori, Kevin; Suchan, Tomasz; Alvarez, Nadir; Goldman, Nick; Dessimoz, Christophe

2016-01-01

Phylogenetic inference can potentially result in a more accurate tree using data from multiple loci. However, if the loci are incongruent—due to events such as incomplete lineage sorting or horizontal gene transfer—it can be misleading to infer a single tree. To address this, many previous contributions have taken a mechanistic approach, by modeling specific processes. Alternatively, one can cluster loci without assuming how these incongruencies might arise. Such “process-agnostic” approaches typically infer a tree for each locus and cluster these. There are, however, many possible combinations of tree distance and clustering methods; their comparative performance in the context of tree incongruence is largely unknown. Furthermore, because standard model selection criteria such as AIC cannot be applied to problems with a variable number of topologies, the issue of inferring the optimal number of clusters is poorly understood. Here, we perform a large-scale simulation study of phylogenetic distances and clustering methods to infer loci of common evolutionary history. We observe that the best-performing combinations are distances accounting for branch lengths followed by spectral clustering or Ward’s method. We also introduce two statistical tests to infer the optimal number of clusters and show that they strongly outperform the silhouette criterion, a general-purpose heuristic. We illustrate the usefulness of the approach by 1) identifying errors in a previous phylogenetic analysis of yeast species and 2) identifying topological incongruence among newly sequenced loci of the globeflower fly genus Chiastocheta. We release treeCl, a new program to cluster genes of common evolutionary history (http://git.io/treeCl). PMID:26893301

Stan: Statistical inference

NASA Astrophysics Data System (ADS)

Stan Development Team

2018-01-01

Stan facilitates statistical inference at the frontiers of applied statistics and provides both a modeling language for specifying complex statistical models and a library of statistical algorithms for computing inferences with those models. These components are exposed through interfaces in environments such as R, Python, and the command line.

The Development of Introductory Statistics Students' Informal Inferential Reasoning and Its Relationship to Formal Inferential Reasoning

ERIC Educational Resources Information Center

Jacob, Bridgette L.

2013-01-01

The difficulties introductory statistics students have with formal statistical inference are well known in the field of statistics education. "Informal" statistical inference has been studied as a means to introduce inferential reasoning well before and without the formalities of formal statistical inference. This mixed methods study…

Students' Emergent Articulations of Statistical Models and Modeling in Making Informal Statistical Inferences

ERIC Educational Resources Information Center

Braham, Hana Manor; Ben-Zvi, Dani

2017-01-01

A fundamental aspect of statistical inference is representation of real-world data using statistical models. This article analyzes students' articulations of statistical models and modeling during their first steps in making informal statistical inferences. An integrated modeling approach (IMA) was designed and implemented to help students…

Outcome-Dependent Sampling Design and Inference for Cox’s Proportional Hazards Model

PubMed Central

Yu, Jichang; Liu, Yanyan; Cai, Jianwen; Sandler, Dale P.; Zhou, Haibo

2016-01-01

We propose a cost-effective outcome-dependent sampling design for the failure time data and develop an efficient inference procedure for data collected with this design. To account for the biased sampling scheme, we derive estimators from a weighted partial likelihood estimating equation. The proposed estimators for regression parameters are shown to be consistent and asymptotically normally distributed. A criteria that can be used to optimally implement the ODS design in practice is proposed and studied. The small sample performance of the proposed method is evaluated by simulation studies. The proposed design and inference procedure is shown to be statistically more powerful than existing alternative designs with the same sample sizes. We illustrate the proposed method with an existing real data from the Cancer Incidence and Mortality of Uranium Miners Study. PMID:28090134

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

Human vision is determined based on information theory.

PubMed

Delgado-Bonal, Alfonso; Martín-Torres, Javier

2016-11-03

It is commonly accepted that the evolution of the human eye has been driven by the maximum intensity of the radiation emitted by the Sun. However, the interpretation of the surrounding environment is constrained not only by the amount of energy received but also by the information content of the radiation. Information is related to entropy rather than energy. The human brain follows Bayesian statistical inference for the interpretation of visual space. The maximization of information occurs in the process of maximizing the entropy. Here, we show that the photopic and scotopic vision absorption peaks in humans are determined not only by the intensity but also by the entropy of radiation. We suggest that through the course of evolution, the human eye has not adapted only to the maximum intensity or to the maximum information but to the optimal wavelength for obtaining information. On Earth, the optimal wavelengths for photopic and scotopic vision are 555 nm and 508 nm, respectively, as inferred experimentally. These optimal wavelengths are determined by the temperature of the star (in this case, the Sun) and by the atmospheric composition.

Human vision is determined based on information theory

NASA Astrophysics Data System (ADS)

Delgado-Bonal, Alfonso; Martín-Torres, Javier

2016-11-01

It is commonly accepted that the evolution of the human eye has been driven by the maximum intensity of the radiation emitted by the Sun. However, the interpretation of the surrounding environment is constrained not only by the amount of energy received but also by the information content of the radiation. Information is related to entropy rather than energy. The human brain follows Bayesian statistical inference for the interpretation of visual space. The maximization of information occurs in the process of maximizing the entropy. Here, we show that the photopic and scotopic vision absorption peaks in humans are determined not only by the intensity but also by the entropy of radiation. We suggest that through the course of evolution, the human eye has not adapted only to the maximum intensity or to the maximum information but to the optimal wavelength for obtaining information. On Earth, the optimal wavelengths for photopic and scotopic vision are 555 nm and 508 nm, respectively, as inferred experimentally. These optimal wavelengths are determined by the temperature of the star (in this case, the Sun) and by the atmospheric composition.

Human vision is determined based on information theory

PubMed Central

Delgado-Bonal, Alfonso; Martín-Torres, Javier

2016-01-01

It is commonly accepted that the evolution of the human eye has been driven by the maximum intensity of the radiation emitted by the Sun. However, the interpretation of the surrounding environment is constrained not only by the amount of energy received but also by the information content of the radiation. Information is related to entropy rather than energy. The human brain follows Bayesian statistical inference for the interpretation of visual space. The maximization of information occurs in the process of maximizing the entropy. Here, we show that the photopic and scotopic vision absorption peaks in humans are determined not only by the intensity but also by the entropy of radiation. We suggest that through the course of evolution, the human eye has not adapted only to the maximum intensity or to the maximum information but to the optimal wavelength for obtaining information. On Earth, the optimal wavelengths for photopic and scotopic vision are 555 nm and 508 nm, respectively, as inferred experimentally. These optimal wavelengths are determined by the temperature of the star (in this case, the Sun) and by the atmospheric composition. PMID:27808236

Stan : A Probabilistic Programming Language

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

Carpenter, Bob; Gelman, Andrew; Hoffman, Matthew D.

Stan is a probabilistic programming language for specifying statistical models. A Stan program imperatively defines a log probability function over parameters conditioned on specified data and constants. As of version 2.14.0, Stan provides full Bayesian inference for continuous-variable models through Markov chain Monte Carlo methods such as the No-U-Turn sampler, an adaptive form of Hamiltonian Monte Carlo sampling. Penalized maximum likelihood estimates are calculated using optimization methods such as the limited memory Broyden-Fletcher-Goldfarb-Shanno algorithm. Stan is also a platform for computing log densities and their gradients and Hessians, which can be used in alternative algorithms such as variational Bayes, expectationmore » propagation, and marginal inference using approximate integration. To this end, Stan is set up so that the densities, gradients, and Hessians, along with intermediate quantities of the algorithm such as acceptance probabilities, are easily accessible. Stan can also be called from the command line using the cmdstan package, through R using the rstan package, and through Python using the pystan package. All three interfaces support sampling and optimization-based inference with diagnostics and posterior analysis. rstan and pystan also provide access to log probabilities, gradients, Hessians, parameter transforms, and specialized plotting.« less

Stan : A Probabilistic Programming Language

DOE PAGES

Carpenter, Bob; Gelman, Andrew; Hoffman, Matthew D.; ...

2017-01-01

Stan is a probabilistic programming language for specifying statistical models. A Stan program imperatively defines a log probability function over parameters conditioned on specified data and constants. As of version 2.14.0, Stan provides full Bayesian inference for continuous-variable models through Markov chain Monte Carlo methods such as the No-U-Turn sampler, an adaptive form of Hamiltonian Monte Carlo sampling. Penalized maximum likelihood estimates are calculated using optimization methods such as the limited memory Broyden-Fletcher-Goldfarb-Shanno algorithm. Stan is also a platform for computing log densities and their gradients and Hessians, which can be used in alternative algorithms such as variational Bayes, expectationmore » propagation, and marginal inference using approximate integration. To this end, Stan is set up so that the densities, gradients, and Hessians, along with intermediate quantities of the algorithm such as acceptance probabilities, are easily accessible. Stan can also be called from the command line using the cmdstan package, through R using the rstan package, and through Python using the pystan package. All three interfaces support sampling and optimization-based inference with diagnostics and posterior analysis. rstan and pystan also provide access to log probabilities, gradients, Hessians, parameter transforms, and specialized plotting.« less

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.

Astrophysical data analysis with information field theory

NASA Astrophysics Data System (ADS)

Enßlin, Torsten

2014-12-01

Non-parametric imaging and data analysis in astrophysics and cosmology can be addressed by information field theory (IFT), a means of Bayesian, data based inference on spatially distributed signal fields. IFT is a statistical field theory, which permits the construction of optimal signal recovery algorithms. It exploits spatial correlations of the signal fields even for nonlinear and non-Gaussian signal inference problems. The alleviation of a perception threshold for recovering signals of unknown correlation structure by using IFT will be discussed in particular as well as a novel improvement on instrumental self-calibration schemes. IFT can be applied to many areas. Here, applications in in cosmology (cosmic microwave background, large-scale structure) and astrophysics (galactic magnetism, radio interferometry) are presented.

The Reasoning behind Informal Statistical Inference

ERIC Educational Resources Information Center

Makar, Katie; Bakker, Arthur; Ben-Zvi, Dani

2011-01-01

Informal statistical inference (ISI) has been a frequent focus of recent research in statistics education. Considering the role that context plays in developing ISI calls into question the need to be more explicit about the reasoning that underpins ISI. This paper uses educational literature on informal statistical inference and philosophical…

Optimization of analytical parameters for inferring relationships among Escherichia coli isolates from repetitive-element PCR by maximizing correspondence with multilocus sequence typing data.

PubMed

Goldberg, Tony L; Gillespie, Thomas R; Singer, Randall S

2006-09-01

Repetitive-element PCR (rep-PCR) is a method for genotyping bacteria based on the selective amplification of repetitive genetic elements dispersed throughout bacterial chromosomes. The method has great potential for large-scale epidemiological studies because of its speed and simplicity; however, objective guidelines for inferring relationships among bacterial isolates from rep-PCR data are lacking. We used multilocus sequence typing (MLST) as a "gold standard" to optimize the analytical parameters for inferring relationships among Escherichia coli isolates from rep-PCR data. We chose 12 isolates from a large database to represent a wide range of pairwise genetic distances, based on the initial evaluation of their rep-PCR fingerprints. We conducted MLST with these same isolates and systematically varied the analytical parameters to maximize the correspondence between the relationships inferred from rep-PCR and those inferred from MLST. Methods that compared the shapes of densitometric profiles ("curve-based" methods) yielded consistently higher correspondence values between data types than did methods that calculated indices of similarity based on shared and different bands (maximum correspondences of 84.5% and 80.3%, respectively). Curve-based methods were also markedly more robust in accommodating variations in user-specified analytical parameter values than were "band-sharing coefficient" methods, and they enhanced the reproducibility of rep-PCR. Phylogenetic analyses of rep-PCR data yielded trees with high topological correspondence to trees based on MLST and high statistical support for major clades. These results indicate that rep-PCR yields accurate information for inferring relationships among E. coli isolates and that accuracy can be enhanced with the use of analytical methods that consider the shapes of densitometric profiles.

Bayesian Monte Carlo and Maximum Likelihood Approach for ...

EPA Pesticide Factsheets

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

Optimal inference with suboptimal models: Addiction and active Bayesian inference

PubMed Central

Schwartenbeck, Philipp; FitzGerald, Thomas H.B.; Mathys, Christoph; Dolan, Ray; Wurst, Friedrich; Kronbichler, Martin; Friston, Karl

2015-01-01

When casting behaviour as active (Bayesian) inference, optimal inference is defined with respect to an agent’s beliefs – based on its generative model of the world. This contrasts with normative accounts of choice behaviour, in which optimal actions are considered in relation to the true structure of the environment – as opposed to the agent’s beliefs about worldly states (or the task). This distinction shifts an understanding of suboptimal or pathological behaviour away from aberrant inference as such, to understanding the prior beliefs of a subject that cause them to behave less ‘optimally’ than our prior beliefs suggest they should behave. Put simply, suboptimal or pathological behaviour does not speak against understanding behaviour in terms of (Bayes optimal) inference, but rather calls for a more refined understanding of the subject’s generative model upon which their (optimal) Bayesian inference is based. Here, we discuss this fundamental distinction and its implications for understanding optimality, bounded rationality and pathological (choice) behaviour. We illustrate our argument using addictive choice behaviour in a recently described ‘limited offer’ task. Our simulations of pathological choices and addictive behaviour also generate some clear hypotheses, which we hope to pursue in ongoing empirical work. PMID:25561321

The anatomy of choice: dopamine and decision-making

PubMed Central

Friston, Karl; Schwartenbeck, Philipp; FitzGerald, Thomas; Moutoussis, Michael; Behrens, Timothy; Dolan, Raymond J.

2014-01-01

This paper considers goal-directed decision-making in terms of embodied or active inference. We associate bounded rationality with approximate Bayesian inference that optimizes a free energy bound on model evidence. Several constructs such as expected utility, exploration or novelty bonuses, softmax choice rules and optimism bias emerge as natural consequences of free energy minimization. Previous accounts of active inference have focused on predictive coding. In this paper, we consider variational Bayes as a scheme that the brain might use for approximate Bayesian inference. This scheme provides formal constraints on the computational anatomy of inference and action, which appear to be remarkably consistent with neuroanatomy. Active inference contextualizes optimal decision theory within embodied inference, where goals become prior beliefs. For example, expected utility theory emerges as a special case of free energy minimization, where the sensitivity or inverse temperature (associated with softmax functions and quantal response equilibria) has a unique and Bayes-optimal solution. Crucially, this sensitivity corresponds to the precision of beliefs about behaviour. The changes in precision during variational updates are remarkably reminiscent of empirical dopaminergic responses—and they may provide a new perspective on the role of dopamine in assimilating reward prediction errors to optimize decision-making. PMID:25267823

The anatomy of choice: dopamine and decision-making.

PubMed

Friston, Karl; Schwartenbeck, Philipp; FitzGerald, Thomas; Moutoussis, Michael; Behrens, Timothy; Dolan, Raymond J

2014-11-05

This paper considers goal-directed decision-making in terms of embodied or active inference. We associate bounded rationality with approximate Bayesian inference that optimizes a free energy bound on model evidence. Several constructs such as expected utility, exploration or novelty bonuses, softmax choice rules and optimism bias emerge as natural consequences of free energy minimization. Previous accounts of active inference have focused on predictive coding. In this paper, we consider variational Bayes as a scheme that the brain might use for approximate Bayesian inference. This scheme provides formal constraints on the computational anatomy of inference and action, which appear to be remarkably consistent with neuroanatomy. Active inference contextualizes optimal decision theory within embodied inference, where goals become prior beliefs. For example, expected utility theory emerges as a special case of free energy minimization, where the sensitivity or inverse temperature (associated with softmax functions and quantal response equilibria) has a unique and Bayes-optimal solution. Crucially, this sensitivity corresponds to the precision of beliefs about behaviour. The changes in precision during variational updates are remarkably reminiscent of empirical dopaminergic responses-and they may provide a new perspective on the role of dopamine in assimilating reward prediction errors to optimize decision-making.

Automatic physical inference with information maximizing neural networks

NASA Astrophysics Data System (ADS)

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

2018-04-01

Compressing large data sets to a manageable number of summaries that are informative about the underlying parameters vastly simplifies both frequentist and Bayesian inference. When only simulations are available, these summaries are typically chosen heuristically, so they may inadvertently miss important information. We introduce a simulation-based machine learning technique that trains artificial neural networks to find nonlinear functionals of data that maximize Fisher information: information maximizing neural networks (IMNNs). In test cases where the posterior can be derived exactly, likelihood-free inference based on automatically derived IMNN summaries produces nearly exact posteriors, showing that these summaries are good approximations to sufficient statistics. In a series of numerical examples of increasing complexity and astrophysical relevance we show that IMNNs are robustly capable of automatically finding optimal, nonlinear 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. We anticipate that the automatic physical inference method described in this paper will be essential to obtain both accurate and precise cosmological parameter estimates from complex and large astronomical data sets, including those from LSST and Euclid.

Computational approaches to protein inference in shotgun proteomics

PubMed Central

2012-01-01

Shotgun proteomics has recently emerged as a powerful approach to characterizing proteomes in biological samples. Its overall objective is to identify the form and quantity of each protein in a high-throughput manner by coupling liquid chromatography with tandem mass spectrometry. As a consequence of its high throughput nature, shotgun proteomics faces challenges with respect to the analysis and interpretation of experimental data. Among such challenges, the identification of proteins present in a sample has been recognized as an important computational task. This task generally consists of (1) assigning experimental tandem mass spectra to peptides derived from a protein database, and (2) mapping assigned peptides to proteins and quantifying the confidence of identified proteins. Protein identification is fundamentally a statistical inference problem with a number of methods proposed to address its challenges. In this review we categorize current approaches into rule-based, combinatorial optimization and probabilistic inference techniques, and present them using integer programing and Bayesian inference frameworks. We also discuss the main challenges of protein identification and propose potential solutions with the goal of spurring innovative research in this area. PMID:23176300

The Role of Working Memory in the Probabilistic Inference of Future Sensory Events.

PubMed

Cashdollar, Nathan; Ruhnau, Philipp; Weisz, Nathan; Hasson, Uri

2017-05-01

The ability to represent the emerging regularity of sensory information from the external environment has been thought to allow one to probabilistically infer future sensory occurrences and thus optimize behavior. However, the underlying neural implementation of this process is still not comprehensively understood. Through a convergence of behavioral and neurophysiological evidence, we establish that the probabilistic inference of future events is critically linked to people's ability to maintain the recent past in working memory. Magnetoencephalography recordings demonstrated that when visual stimuli occurring over an extended time series had a greater statistical regularity, individuals with higher working-memory capacity (WMC) displayed enhanced slow-wave neural oscillations in the θ frequency band (4-8 Hz.) prior to, but not during stimulus appearance. This prestimulus neural activity was specifically linked to contexts where information could be anticipated and influenced the preferential sensory processing for this visual information after its appearance. A separate behavioral study demonstrated that this process intrinsically emerges during continuous perception and underpins a realistic advantage for efficient behavioral responses. In this way, WMC optimizes the anticipation of higher level semantic concepts expected to occur in the near future. © The Author 2016. Published by Oxford University Press. All rights reserved. For Permissions, please e-mail: journals.permissions@oup.com.

RESOLVE: A new algorithm for aperture synthesis imaging of extended emission in radio astronomy

NASA Astrophysics Data System (ADS)

Junklewitz, H.; Bell, M. R.; Selig, M.; Enßlin, T. A.

2016-02-01

We present resolve, a new algorithm for radio aperture synthesis imaging of extended and diffuse emission in total intensity. The algorithm is derived using Bayesian statistical inference techniques, estimating the surface brightness in the sky assuming a priori log-normal statistics. resolve estimates the measured sky brightness in total intensity, and the spatial correlation structure in the sky, which is used to guide the algorithm to an optimal reconstruction of extended and diffuse sources. During this process, the algorithm succeeds in deconvolving the effects of the radio interferometric point spread function. Additionally, resolve provides a map with an uncertainty estimate of the reconstructed surface brightness. Furthermore, with resolve we introduce a new, optimal visibility weighting scheme that can be viewed as an extension to robust weighting. In tests using simulated observations, the algorithm shows improved performance against two standard imaging approaches for extended sources, Multiscale-CLEAN and the Maximum Entropy Method.

Efficient Moment-Based Inference of Admixture Parameters and Sources of Gene Flow

PubMed Central

Levin, Alex; Reich, David; Patterson, Nick; Berger, Bonnie

2013-01-01

The recent explosion in available genetic data has led to significant advances in understanding the demographic histories of and relationships among human populations. It is still a challenge, however, to infer reliable parameter values for complicated models involving many populations. Here, we present MixMapper, an efficient, interactive method for constructing phylogenetic trees including admixture events using single nucleotide polymorphism (SNP) genotype data. MixMapper implements a novel two-phase approach to admixture inference using moment statistics, first building an unadmixed scaffold tree and then adding admixed populations by solving systems of equations that express allele frequency divergences in terms of mixture parameters. Importantly, all features of the model, including topology, sources of gene flow, branch lengths, and mixture proportions, are optimized automatically from the data and include estimates of statistical uncertainty. MixMapper also uses a new method to express branch lengths in easily interpretable drift units. We apply MixMapper to recently published data for Human Genome Diversity Cell Line Panel individuals genotyped on a SNP array designed especially for use in population genetics studies, obtaining confident results for 30 populations, 20 of them admixed. Notably, we confirm a signal of ancient admixture in European populations—including previously undetected admixture in Sardinians and Basques—involving a proportion of 20–40% ancient northern Eurasian ancestry. PMID:23709261

Design-based Sample and Probability Law-Assumed Sample: Their Role in Scientific Investigation.

ERIC Educational Resources Information Center

Ojeda, Mario Miguel; Sahai, Hardeo

2002-01-01

Discusses some key statistical concepts in probabilistic and non-probabilistic sampling to provide an overview for understanding the inference process. Suggests a statistical model constituting the basis of statistical inference and provides a brief review of the finite population descriptive inference and a quota sampling inferential theory.…

The Importance of Statistical Modeling in Data Analysis and Inference

ERIC Educational Resources Information Center

Rollins, Derrick, Sr.

2017-01-01

Statistical inference simply means to draw a conclusion based on information that comes from data. Error bars are the most commonly used tool for data analysis and inference in chemical engineering data studies. This work demonstrates, using common types of data collection studies, the importance of specifying the statistical model for sound…

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

Bennett, Janine Camille; Thompson, David; Pebay, Philippe Pierre

Statistical analysis is typically used to reduce the dimensionality of and infer meaning from data. A key challenge of any statistical analysis package aimed at large-scale, distributed data is to address the orthogonal issues of parallel scalability and numerical stability. Many statistical techniques, e.g., descriptive statistics or principal component analysis, are based on moments and co-moments and, using robust online update formulas, can be computed in an embarrassingly parallel manner, amenable to a map-reduce style implementation. In this paper we focus on contingency tables, through which numerous derived statistics such as joint and marginal probability, point-wise mutual information, information entropy,more » and {chi}{sup 2} independence statistics can be directly obtained. However, contingency tables can become large as data size increases, requiring a correspondingly large amount of communication between processors. This potential increase in communication prevents optimal parallel speedup and is the main difference with moment-based statistics (which we discussed in [1]) where the amount of inter-processor communication is independent of data size. Here we present the design trade-offs which we made to implement the computation of contingency tables in parallel. We also study the parallel speedup and scalability properties of our open source implementation. In particular, we observe optimal speed-up and scalability when the contingency statistics are used in their appropriate context, namely, when the data input is not quasi-diffuse.« less

Inferring Demographic History Using Two-Locus Statistics.

PubMed

Ragsdale, Aaron P; Gutenkunst, Ryan N

2017-06-01

Population demographic history may be learned from contemporary genetic variation data. Methods based on aggregating the statistics of many single loci into an allele frequency spectrum (AFS) have proven powerful, but such methods ignore potentially informative patterns of linkage disequilibrium (LD) between neighboring loci. To leverage such patterns, we developed a composite-likelihood framework for inferring demographic history from aggregated statistics of pairs of loci. Using this framework, we show that two-locus statistics are more sensitive to demographic history than single-locus statistics such as the AFS. In particular, two-locus statistics escape the notorious confounding of depth and duration of a bottleneck, and they provide a means to estimate effective population size based on the recombination rather than mutation rate. We applied our approach to a Zambian population of Drosophila melanogaster Notably, using both single- and two-locus statistics, we inferred a substantially lower ancestral effective population size than previous works and did not infer a bottleneck history. Together, our results demonstrate the broad potential for two-locus statistics to enable powerful population genetic inference. Copyright © 2017 by the Genetics Society of America.

Fast maximum likelihood estimation using continuous-time neural point process models.

PubMed

Lepage, Kyle Q; MacDonald, Christopher J

2015-06-01

A recent report estimates that the number of simultaneously recorded neurons is growing exponentially. A commonly employed statistical paradigm using discrete-time point process models of neural activity involves the computation of a maximum-likelihood estimate. The time to computate this estimate, per neuron, is proportional to the number of bins in a finely spaced discretization of time. By using continuous-time models of neural activity and the optimally efficient Gaussian quadrature, memory requirements and computation times are dramatically decreased in the commonly encountered situation where the number of parameters p is much less than the number of time-bins n. In this regime, with q equal to the quadrature order, memory requirements are decreased from O(np) to O(qp), and the number of floating-point operations are decreased from O(np(2)) to O(qp(2)). Accuracy of the proposed estimates is assessed based upon physiological consideration, error bounds, and mathematical results describing the relation between numerical integration error and numerical error affecting both parameter estimates and the observed Fisher information. A check is provided which is used to adapt the order of numerical integration. The procedure is verified in simulation and for hippocampal recordings. It is found that in 95 % of hippocampal recordings a q of 60 yields numerical error negligible with respect to parameter estimate standard error. Statistical inference using the proposed methodology is a fast and convenient alternative to statistical inference performed using a discrete-time point process model of neural activity. It enables the employment of the statistical methodology available with discrete-time inference, but is faster, uses less memory, and avoids any error due to discretization.

Approximation of epidemic models by diffusion processes and their statistical inference.

PubMed

Guy, Romain; Larédo, Catherine; Vergu, Elisabeta

2015-02-01

Multidimensional continuous-time Markov jump processes [Formula: see text] on [Formula: see text] form a usual set-up for modeling [Formula: see text]-like epidemics. However, when facing incomplete epidemic data, inference based on [Formula: see text] is not easy to be achieved. Here, we start building a new framework for the estimation of key parameters of epidemic models based on statistics of diffusion processes approximating [Formula: see text]. First, previous results on the approximation of density-dependent [Formula: see text]-like models by diffusion processes with small diffusion coefficient [Formula: see text], where [Formula: see text] is the population size, are generalized to non-autonomous systems. Second, our previous inference results on discretely observed diffusion processes with small diffusion coefficient are extended to time-dependent diffusions. Consistent and asymptotically Gaussian estimates are obtained for a fixed number [Formula: see text] of observations, which corresponds to the epidemic context, and for [Formula: see text]. A correction term, which yields better estimates non asymptotically, is also included. Finally, performances and robustness of our estimators with respect to various parameters such as [Formula: see text] (the basic reproduction number), [Formula: see text], [Formula: see text] are investigated on simulations. Two models, [Formula: see text] and [Formula: see text], corresponding to single and recurrent outbreaks, respectively, are used to simulate data. The findings indicate that our estimators have good asymptotic properties and behave noticeably well for realistic numbers of observations and population sizes. This study lays the foundations of a generic inference method currently under extension to incompletely observed epidemic data. Indeed, contrary to the majority of current inference techniques for partially observed processes, which necessitates computer intensive simulations, our method being mostly an analytical approach requires only the classical optimization steps.

Teaching Statistical Inference for Causal Effects in Experiments and Observational Studies

ERIC Educational Resources Information Center

Rubin, Donald B.

2004-01-01

Inference for causal effects is a critical activity in many branches of science and public policy. The field of statistics is the one field most suited to address such problems, whether from designed experiments or observational studies. Consequently, it is arguably essential that departments of statistics teach courses in causal inference to both…

A Robust Adaptive Autonomous Approach to Optimal Experimental Design

NASA Astrophysics Data System (ADS)

Gu, Hairong

Experimentation is the fundamental tool of scientific inquiries to understand the laws governing the nature and human behaviors. Many complex real-world experimental scenarios, particularly in quest of prediction accuracy, often encounter difficulties to conduct experiments using an existing experimental procedure for the following two reasons. First, the existing experimental procedures require a parametric model to serve as the proxy of the latent data structure or data-generating mechanism at the beginning of an experiment. However, for those experimental scenarios of concern, a sound model is often unavailable before an experiment. Second, those experimental scenarios usually contain a large number of design variables, which potentially leads to a lengthy and costly data collection cycle. Incompetently, the existing experimental procedures are unable to optimize large-scale experiments so as to minimize the experimental length and cost. Facing the two challenges in those experimental scenarios, the aim of the present study is to develop a new experimental procedure that allows an experiment to be conducted without the assumption of a parametric model while still achieving satisfactory prediction, and performs optimization of experimental designs to improve the efficiency of an experiment. The new experimental procedure developed in the present study is named robust adaptive autonomous system (RAAS). RAAS is a procedure for sequential experiments composed of multiple experimental trials, which performs function estimation, variable selection, reverse prediction and design optimization on each trial. Directly addressing the challenges in those experimental scenarios of concern, function estimation and variable selection are performed by data-driven modeling methods to generate a predictive model from data collected during the course of an experiment, thus exempting the requirement of a parametric model at the beginning of an experiment; design optimization is performed to select experimental designs on the fly of an experiment based on their usefulness so that fewest designs are needed to reach useful inferential conclusions. Technically, function estimation is realized by Bayesian P-splines, variable selection is realized by Bayesian spike-and-slab prior, reverse prediction is realized by grid-search and design optimization is realized by the concepts of active learning. The present study demonstrated that RAAS achieves statistical robustness by making accurate predictions without the assumption of a parametric model serving as the proxy of latent data structure while the existing procedures can draw poor statistical inferences if a misspecified model is assumed; RAAS also achieves inferential efficiency by taking fewer designs to acquire useful statistical inferences than non-optimal procedures. Thus, RAAS is expected to be a principled solution to real-world experimental scenarios pursuing robust prediction and efficient experimentation.

Optimal design of gene knockout experiments for gene regulatory network inference

PubMed Central

Ud-Dean, S. M. Minhaz; Gunawan, Rudiyanto

2016-01-01

Motivation: We addressed the problem of inferring gene regulatory network (GRN) from gene expression data of knockout (KO) experiments. This inference is known to be underdetermined and the GRN is not identifiable from data. Past studies have shown that suboptimal design of experiments (DOE) contributes significantly to the identifiability issue of biological networks, including GRNs. However, optimizing DOE has received much less attention than developing methods for GRN inference. Results: We developed REDuction of UnCertain Edges (REDUCE) algorithm for finding the optimal gene KO experiment for inferring directed graphs (digraphs) of GRNs. REDUCE employed ensemble inference to define uncertain gene interactions that could not be verified by prior data. The optimal experiment corresponds to the maximum number of uncertain interactions that could be verified by the resulting data. For this purpose, we introduced the concept of edge separatoid which gave a list of nodes (genes) that upon their removal would allow the verification of a particular gene interaction. Finally, we proposed a procedure that iterates over performing KO experiments, ensemble update and optimal DOE. The case studies including the inference of Escherichia coli GRN and DREAM 4 100-gene GRNs, demonstrated the efficacy of the iterative GRN inference. In comparison to systematic KOs, REDUCE could provide much higher information return per gene KO experiment and consequently more accurate GRN estimates. Conclusions: REDUCE represents an enabling tool for tackling the underdetermined GRN inference. Along with advances in gene deletion and automation technology, the iterative procedure brings an efficient and fully automated GRN inference closer to reality. Availability and implementation: MATLAB and Python scripts of REDUCE are available on www.cabsel.ethz.ch/tools/REDUCE. Contact: rudi.gunawan@chem.ethz.ch Supplementary information: Supplementary data are available at Bioinformatics online. PMID:26568633

Adaptive design optimization: a mutual information-based approach to model discrimination in cognitive science.

PubMed

Cavagnaro, Daniel R; Myung, Jay I; Pitt, Mark A; Kujala, Janne V

2010-04-01

Discriminating among competing statistical models is a pressing issue for many experimentalists in the field of cognitive science. Resolving this issue begins with designing maximally informative experiments. To this end, the problem to be solved in adaptive design optimization is identifying experimental designs under which one can infer the underlying model in the fewest possible steps. When the models under consideration are nonlinear, as is often the case in cognitive science, this problem can be impossible to solve analytically without simplifying assumptions. However, as we show in this letter, a full solution can be found numerically with the help of a Bayesian computational trick derived from the statistics literature, which recasts the problem as a probability density simulation in which the optimal design is the mode of the density. We use a utility function based on mutual information and give three intuitive interpretations of the utility function in terms of Bayesian posterior estimates. As a proof of concept, we offer a simple example application to an experiment on memory retention.

Reasoning about Informal Statistical Inference: One Statistician's View

ERIC Educational Resources Information Center

Rossman, Allan J.

2008-01-01

This paper identifies key concepts and issues associated with the reasoning of informal statistical inference. I focus on key ideas of inference that I think all students should learn, including at secondary level as well as tertiary. I argue that a fundamental component of inference is to go beyond the data at hand, and I propose that statistical…

Data-driven inference for the spatial scan statistic.

PubMed

Almeida, Alexandre C L; Duarte, Anderson R; Duczmal, Luiz H; Oliveira, Fernando L P; Takahashi, Ricardo H C

2011-08-02

Kulldorff's spatial scan statistic for aggregated area maps searches for clusters of cases without specifying their size (number of areas) or geographic location in advance. Their statistical significance is tested while adjusting for the multiple testing inherent in such a procedure. However, as is shown in this work, this adjustment is not done in an even manner for all possible cluster sizes. A modification is proposed to the usual inference test of the spatial scan statistic, incorporating additional information about the size of the most likely cluster found. A new interpretation of the results of the spatial scan statistic is done, posing a modified inference question: what is the probability that the null hypothesis is rejected for the original observed cases map with a most likely cluster of size k, taking into account only those most likely clusters of size k found under null hypothesis for comparison? This question is especially important when the p-value computed by the usual inference process is near the alpha significance level, regarding the correctness of the decision based in this inference. A practical procedure is provided to make more accurate inferences about the most likely cluster found by the spatial scan statistic.

Assessment of statistical education in Indonesia: Preliminary results and initiation to simulation-based inference

NASA Astrophysics Data System (ADS)

Saputra, K. V. I.; Cahyadi, L.; Sembiring, U. A.

2018-01-01

Start in this paper, we assess our traditional elementary statistics education and also we introduce elementary statistics with simulation-based inference. To assess our statistical class, we adapt the well-known CAOS (Comprehensive Assessment of Outcomes in Statistics) test that serves as an external measure to assess the student’s basic statistical literacy. This test generally represents as an accepted measure of statistical literacy. We also introduce a new teaching method on elementary statistics class. Different from the traditional elementary statistics course, we will introduce a simulation-based inference method to conduct hypothesis testing. From the literature, it has shown that this new teaching method works very well in increasing student’s understanding of statistics.

Apes are intuitive statisticians.

PubMed

Rakoczy, Hannes; Clüver, Annette; Saucke, Liane; Stoffregen, Nicole; Gräbener, Alice; Migura, Judith; Call, Josep

2014-04-01

Inductive learning and reasoning, as we use it both in everyday life and in science, is characterized by flexible inferences based on statistical information: inferences from populations to samples and vice versa. Many forms of such statistical reasoning have been found to develop late in human ontogeny, depending on formal education and language, and to be fragile even in adults. New revolutionary research, however, suggests that even preverbal human infants make use of intuitive statistics. Here, we conducted the first investigation of such intuitive statistical reasoning with non-human primates. In a series of 7 experiments, Bonobos, Chimpanzees, Gorillas and Orangutans drew flexible statistical inferences from populations to samples. These inferences, furthermore, were truly based on statistical information regarding the relative frequency distributions in a population, and not on absolute frequencies. Intuitive statistics in its most basic form is thus an evolutionarily more ancient rather than a uniquely human capacity. Copyright © 2014 Elsevier B.V. All rights reserved.

Cortical Hierarchies Perform Bayesian Causal Inference in Multisensory Perception

PubMed Central

Rohe, Tim; Noppeney, Uta

2015-01-01

To form a veridical percept of the environment, the brain needs to integrate sensory signals from a common source but segregate those from independent sources. Thus, perception inherently relies on solving the “causal inference problem.” Behaviorally, humans solve this problem optimally as predicted by Bayesian Causal Inference; yet, the underlying neural mechanisms are unexplored. Combining psychophysics, Bayesian modeling, functional magnetic resonance imaging (fMRI), and multivariate decoding in an audiovisual spatial localization task, we demonstrate that Bayesian Causal Inference is performed by a hierarchy of multisensory processes in the human brain. At the bottom of the hierarchy, in auditory and visual areas, location is represented on the basis that the two signals are generated by independent sources (= segregation). At the next stage, in posterior intraparietal sulcus, location is estimated under the assumption that the two signals are from a common source (= forced fusion). Only at the top of the hierarchy, in anterior intraparietal sulcus, the uncertainty about the causal structure of the world is taken into account and sensory signals are combined as predicted by Bayesian Causal Inference. Characterizing the computational operations of signal interactions reveals the hierarchical nature of multisensory perception in human neocortex. It unravels how the brain accomplishes Bayesian Causal Inference, a statistical computation fundamental for perception and cognition. Our results demonstrate how the brain combines information in the face of uncertainty about the underlying causal structure of the world. PMID:25710328

Cluster mass inference via random field theory.

PubMed

Zhang, Hui; Nichols, Thomas E; Johnson, Timothy D

2009-01-01

Cluster extent and voxel intensity are two widely used statistics in neuroimaging inference. Cluster extent is sensitive to spatially extended signals while voxel intensity is better for intense but focal signals. In order to leverage strength from both statistics, several nonparametric permutation methods have been proposed to combine the two methods. Simulation studies have shown that of the different cluster permutation methods, the cluster mass statistic is generally the best. However, to date, there is no parametric cluster mass inference available. In this paper, we propose a cluster mass inference method based on random field theory (RFT). We develop this method for Gaussian images, evaluate it on Gaussian and Gaussianized t-statistic images and investigate its statistical properties via simulation studies and real data. Simulation results show that the method is valid under the null hypothesis and demonstrate that it can be more powerful than the cluster extent inference method. Further, analyses with a single subject and a group fMRI dataset demonstrate better power than traditional cluster size inference, and good accuracy relative to a gold-standard permutation test.

A Test by Any Other Name: P Values, Bayes Factors, and Statistical Inference.

PubMed

Stern, Hal S

2016-01-01

Procedures used for statistical inference are receiving increased scrutiny as the scientific community studies the factors associated with insuring reproducible research. This note addresses recent negative attention directed at p values, the relationship of confidence intervals and tests, and the role of Bayesian inference and Bayes factors, with an eye toward better understanding these different strategies for statistical inference. We argue that researchers and data analysts too often resort to binary decisions (e.g., whether to reject or accept the null hypothesis) in settings where this may not be required.

Specificity and timescales of cortical adaptation as inferences about natural movie statistics.

PubMed

Snow, Michoel; Coen-Cagli, Ruben; Schwartz, Odelia

2016-10-01

Adaptation is a phenomenological umbrella term under which a variety of temporal contextual effects are grouped. Previous models have shown that some aspects of visual adaptation reflect optimal processing of dynamic visual inputs, suggesting that adaptation should be tuned to the properties of natural visual inputs. However, the link between natural dynamic inputs and adaptation is poorly understood. Here, we extend a previously developed Bayesian modeling framework for spatial contextual effects to the temporal domain. The model learns temporal statistical regularities of natural movies and links these statistics to adaptation in primary visual cortex via divisive normalization, a ubiquitous neural computation. In particular, the model divisively normalizes the present visual input by the past visual inputs only to the degree that these are inferred to be statistically dependent. We show that this flexible form of normalization reproduces classical findings on how brief adaptation affects neuronal selectivity. Furthermore, prior knowledge acquired by the Bayesian model from natural movies can be modified by prolonged exposure to novel visual stimuli. We show that this updating can explain classical results on contrast adaptation. We also simulate the recent finding that adaptation maintains population homeostasis, namely, a balanced level of activity across a population of neurons with different orientation preferences. Consistent with previous disparate observations, our work further clarifies the influence of stimulus-specific and neuronal-specific normalization signals in adaptation.

Specificity and timescales of cortical adaptation as inferences about natural movie statistics

PubMed Central

Snow, Michoel; Coen-Cagli, Ruben; Schwartz, Odelia

2016-01-01

Adaptation is a phenomenological umbrella term under which a variety of temporal contextual effects are grouped. Previous models have shown that some aspects of visual adaptation reflect optimal processing of dynamic visual inputs, suggesting that adaptation should be tuned to the properties of natural visual inputs. However, the link between natural dynamic inputs and adaptation is poorly understood. Here, we extend a previously developed Bayesian modeling framework for spatial contextual effects to the temporal domain. The model learns temporal statistical regularities of natural movies and links these statistics to adaptation in primary visual cortex via divisive normalization, a ubiquitous neural computation. In particular, the model divisively normalizes the present visual input by the past visual inputs only to the degree that these are inferred to be statistically dependent. We show that this flexible form of normalization reproduces classical findings on how brief adaptation affects neuronal selectivity. Furthermore, prior knowledge acquired by the Bayesian model from natural movies can be modified by prolonged exposure to novel visual stimuli. We show that this updating can explain classical results on contrast adaptation. We also simulate the recent finding that adaptation maintains population homeostasis, namely, a balanced level of activity across a population of neurons with different orientation preferences. Consistent with previous disparate observations, our work further clarifies the influence of stimulus-specific and neuronal-specific normalization signals in adaptation. PMID:27699416

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.

The anatomy of choice: active inference and agency.

PubMed

Friston, Karl; Schwartenbeck, Philipp; Fitzgerald, Thomas; Moutoussis, Michael; Behrens, Timothy; Dolan, Raymond J

2013-01-01

This paper considers agency in the setting of embodied or active inference. In brief, we associate a sense of agency with prior beliefs about action and ask what sorts of beliefs underlie optimal behavior. In particular, we consider prior beliefs that action minimizes the Kullback-Leibler (KL) divergence between desired states and attainable states in the future. This allows one to formulate bounded rationality as approximate Bayesian inference that optimizes a free energy bound on model evidence. We show that constructs like expected utility, exploration bonuses, softmax choice rules and optimism bias emerge as natural consequences of this formulation. Previous accounts of active inference have focused on predictive coding and Bayesian filtering schemes for minimizing free energy. Here, we consider variational Bayes as an alternative scheme that provides formal constraints on the computational anatomy of inference and action-constraints that are remarkably consistent with neuroanatomy. Furthermore, this scheme contextualizes optimal decision theory and economic (utilitarian) formulations as pure inference problems. For example, expected utility theory emerges as a special case of free energy minimization, where the sensitivity or inverse temperature (of softmax functions and quantal response equilibria) has a unique and Bayes-optimal solution-that minimizes free energy. This sensitivity corresponds to the precision of beliefs about behavior, such that attainable goals are afforded a higher precision or confidence. In turn, this means that optimal behavior entails a representation of confidence about outcomes that are under an agent's control.

Statistical inference methods for sparse biological time series data.

PubMed

Ndukum, Juliet; Fonseca, Luís L; Santos, Helena; Voit, Eberhard O; Datta, Susmita

2011-04-25

Comparing metabolic profiles under different biological perturbations has become a powerful approach to investigating the functioning of cells. The profiles can be taken as single snapshots of a system, but more information is gained if they are measured longitudinally over time. The results are short time series consisting of relatively sparse data that cannot be analyzed effectively with standard time series techniques, such as autocorrelation and frequency domain methods. In this work, we study longitudinal time series profiles of glucose consumption in the yeast Saccharomyces cerevisiae under different temperatures and preconditioning regimens, which we obtained with methods of in vivo nuclear magnetic resonance (NMR) spectroscopy. For the statistical analysis we first fit several nonlinear mixed effect regression models to the longitudinal profiles and then used an ANOVA likelihood ratio method in order to test for significant differences between the profiles. The proposed methods are capable of distinguishing metabolic time trends resulting from different treatments and associate significance levels to these differences. Among several nonlinear mixed-effects regression models tested, a three-parameter logistic function represents the data with highest accuracy. ANOVA and likelihood ratio tests suggest that there are significant differences between the glucose consumption rate profiles for cells that had been--or had not been--preconditioned by heat during growth. Furthermore, pair-wise t-tests reveal significant differences in the longitudinal profiles for glucose consumption rates between optimal conditions and heat stress, optimal and recovery conditions, and heat stress and recovery conditions (p-values <0.0001). We have developed a nonlinear mixed effects model that is appropriate for the analysis of sparse metabolic and physiological time profiles. The model permits sound statistical inference procedures, based on ANOVA likelihood ratio tests, for testing the significance of differences between short time course data under different biological perturbations.

Performance evaluation of the machine learning algorithms used in inference mechanism of a medical decision support system.

PubMed

Bal, Mert; Amasyali, M Fatih; Sever, Hayri; Kose, Guven; Demirhan, Ayse

2014-01-01

The importance of the decision support systems is increasingly supporting the decision making process in cases of uncertainty and the lack of information and they are widely used in various fields like engineering, finance, medicine, and so forth, Medical decision support systems help the healthcare personnel to select optimal method during the treatment of the patients. Decision support systems are intelligent software systems that support decision makers on their decisions. The design of decision support systems consists of four main subjects called inference mechanism, knowledge-base, explanation module, and active memory. Inference mechanism constitutes the basis of decision support systems. There are various methods that can be used in these mechanisms approaches. Some of these methods are decision trees, artificial neural networks, statistical methods, rule-based methods, and so forth. In decision support systems, those methods can be used separately or a hybrid system, and also combination of those methods. In this study, synthetic data with 10, 100, 1000, and 2000 records have been produced to reflect the probabilities on the ALARM network. The accuracy of 11 machine learning methods for the inference mechanism of medical decision support system is compared on various data sets.

Using Guided Reinvention to Develop Teachers' Understanding of Hypothesis Testing Concepts

ERIC Educational Resources Information Center

Dolor, Jason; Noll, Jennifer

2015-01-01

Statistics education reform efforts emphasize the importance of informal inference in the learning of statistics. Research suggests statistics teachers experience similar difficulties understanding statistical inference concepts as students and how teacher knowledge can impact student learning. This study investigates how teachers reinvented an…

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.

Mutual Information in Frequency and Its Application to Measure Cross-Frequency Coupling in Epilepsy

NASA Astrophysics Data System (ADS)

Malladi, Rakesh; Johnson, Don H.; Kalamangalam, Giridhar P.; Tandon, Nitin; Aazhang, Behnaam

2018-06-01

We define a metric, mutual information in frequency (MI-in-frequency), to detect and quantify the statistical dependence between different frequency components in the data, referred to as cross-frequency coupling and apply it to electrophysiological recordings from the brain to infer cross-frequency coupling. The current metrics used to quantify the cross-frequency coupling in neuroscience cannot detect if two frequency components in non-Gaussian brain recordings are statistically independent or not. Our MI-in-frequency metric, based on Shannon's mutual information between the Cramer's representation of stochastic processes, overcomes this shortcoming and can detect statistical dependence in frequency between non-Gaussian signals. We then describe two data-driven estimators of MI-in-frequency: one based on kernel density estimation and the other based on the nearest neighbor algorithm and validate their performance on simulated data. We then use MI-in-frequency to estimate mutual information between two data streams that are dependent across time, without making any parametric model assumptions. Finally, we use the MI-in- frequency metric to investigate the cross-frequency coupling in seizure onset zone from electrocorticographic recordings during seizures. The inferred cross-frequency coupling characteristics are essential to optimize the spatial and spectral parameters of electrical stimulation based treatments of epilepsy.

Evaluating the Use of Random Distribution Theory to Introduce Statistical Inference Concepts to Business Students

ERIC Educational Resources Information Center

Larwin, Karen H.; Larwin, David A.

2011-01-01

Bootstrapping methods and random distribution methods are increasingly recommended as better approaches for teaching students about statistical inference in introductory-level statistics courses. The authors examined the effect of teaching undergraduate business statistics students using random distribution and bootstrapping simulations. It is the…

Application of Transformations in Parametric Inference

ERIC Educational Resources Information Center

Brownstein, Naomi; Pensky, Marianna

2008-01-01

The objective of the present paper is to provide a simple approach to statistical inference using the method of transformations of variables. We demonstrate performance of this powerful tool on examples of constructions of various estimation procedures, hypothesis testing, Bayes analysis and statistical inference for the stress-strength systems.…

Targeted estimation of nuisance parameters to obtain valid statistical inference.

PubMed

van der Laan, Mark J

2014-01-01

In order to obtain concrete results, we focus on estimation of the treatment specific mean, controlling for all measured baseline covariates, based on observing independent and identically distributed copies of a random variable consisting of baseline covariates, a subsequently assigned binary treatment, and a final outcome. The statistical model only assumes possible restrictions on the conditional distribution of treatment, given the covariates, the so-called propensity score. Estimators of the treatment specific mean involve estimation of the propensity score and/or estimation of the conditional mean of the outcome, given the treatment and covariates. In order to make these estimators asymptotically unbiased at any data distribution in the statistical model, it is essential to use data-adaptive estimators of these nuisance parameters such as ensemble learning, and specifically super-learning. Because such estimators involve optimal trade-off of bias and variance w.r.t. the infinite dimensional nuisance parameter itself, they result in a sub-optimal bias/variance trade-off for the resulting real-valued estimator of the estimand. We demonstrate that additional targeting of the estimators of these nuisance parameters guarantees that this bias for the estimand is second order and thereby allows us to prove theorems that establish asymptotic linearity of the estimator of the treatment specific mean under regularity conditions. These insights result in novel targeted minimum loss-based estimators (TMLEs) that use ensemble learning with additional targeted bias reduction to construct estimators of the nuisance parameters. In particular, we construct collaborative TMLEs (C-TMLEs) with known influence curve allowing for statistical inference, even though these C-TMLEs involve variable selection for the propensity score based on a criterion that measures how effective the resulting fit of the propensity score is in removing bias for the estimand. As a particular special case, we also demonstrate the required targeting of the propensity score for the inverse probability of treatment weighted estimator using super-learning to fit the propensity score.

The lawful imprecision of human surface tilt estimation in natural scenes

PubMed Central

2018-01-01

Estimating local surface orientation (slant and tilt) is fundamental to recovering the three-dimensional structure of the environment. It is unknown how well humans perform this task in natural scenes. Here, with a database of natural stereo-images having groundtruth surface orientation at each pixel, we find dramatic differences in human tilt estimation with natural and artificial stimuli. Estimates are precise and unbiased with artificial stimuli and imprecise and strongly biased with natural stimuli. An image-computable Bayes optimal model grounded in natural scene statistics predicts human bias, precision, and trial-by-trial errors without fitting parameters to the human data. The similarities between human and model performance suggest that the complex human performance patterns with natural stimuli are lawful, and that human visual systems have internalized local image and scene statistics to optimally infer the three-dimensional structure of the environment. These results generalize our understanding of vision from the lab to the real world. PMID:29384477

The lawful imprecision of human surface tilt estimation in natural scenes.

PubMed

Kim, Seha; Burge, Johannes

2018-01-31

Estimating local surface orientation (slant and tilt) is fundamental to recovering the three-dimensional structure of the environment. It is unknown how well humans perform this task in natural scenes. Here, with a database of natural stereo-images having groundtruth surface orientation at each pixel, we find dramatic differences in human tilt estimation with natural and artificial stimuli. Estimates are precise and unbiased with artificial stimuli and imprecise and strongly biased with natural stimuli. An image-computable Bayes optimal model grounded in natural scene statistics predicts human bias, precision, and trial-by-trial errors without fitting parameters to the human data. The similarities between human and model performance suggest that the complex human performance patterns with natural stimuli are lawful, and that human visual systems have internalized local image and scene statistics to optimally infer the three-dimensional structure of the environment. These results generalize our understanding of vision from the lab to the real world. © 2018, Kim et al.

The anatomy of choice: active inference and agency

PubMed Central

Friston, Karl; Schwartenbeck, Philipp; FitzGerald, Thomas; Moutoussis, Michael; Behrens, Timothy; Dolan, Raymond J.

2013-01-01

This paper considers agency in the setting of embodied or active inference. In brief, we associate a sense of agency with prior beliefs about action and ask what sorts of beliefs underlie optimal behavior. In particular, we consider prior beliefs that action minimizes the Kullback–Leibler (KL) divergence between desired states and attainable states in the future. This allows one to formulate bounded rationality as approximate Bayesian inference that optimizes a free energy bound on model evidence. We show that constructs like expected utility, exploration bonuses, softmax choice rules and optimism bias emerge as natural consequences of this formulation. Previous accounts of active inference have focused on predictive coding and Bayesian filtering schemes for minimizing free energy. Here, we consider variational Bayes as an alternative scheme that provides formal constraints on the computational anatomy of inference and action—constraints that are remarkably consistent with neuroanatomy. Furthermore, this scheme contextualizes optimal decision theory and economic (utilitarian) formulations as pure inference problems. For example, expected utility theory emerges as a special case of free energy minimization, where the sensitivity or inverse temperature (of softmax functions and quantal response equilibria) has a unique and Bayes-optimal solution—that minimizes free energy. This sensitivity corresponds to the precision of beliefs about behavior, such that attainable goals are afforded a higher precision or confidence. In turn, this means that optimal behavior entails a representation of confidence about outcomes that are under an agent's control. PMID:24093015

Statistical inference for tumor growth inhibition T/C ratio.

PubMed

Wu, Jianrong

2010-09-01

The tumor growth inhibition T/C ratio is commonly used to quantify treatment effects in drug screening tumor xenograft experiments. The T/C ratio is converted to an antitumor activity rating using an arbitrary cutoff point and often without any formal statistical inference. Here, we applied a nonparametric bootstrap method and a small sample likelihood ratio statistic to make a statistical inference of the T/C ratio, including both hypothesis testing and a confidence interval estimate. Furthermore, sample size and power are also discussed for statistical design of tumor xenograft experiments. Tumor xenograft data from an actual experiment were analyzed to illustrate the application.

Species tree inference by minimizing deep coalescences.

PubMed

Than, Cuong; Nakhleh, Luay

2009-09-01

In a 1997 seminal paper, W. Maddison proposed minimizing deep coalescences, or MDC, as an optimization criterion for inferring the species tree from a set of incongruent gene trees, assuming the incongruence is exclusively due to lineage sorting. In a subsequent paper, Maddison and Knowles provided and implemented a search heuristic for optimizing the MDC criterion, given a set of gene trees. However, the heuristic is not guaranteed to compute optimal solutions, and its hill-climbing search makes it slow in practice. In this paper, we provide two exact solutions to the problem of inferring the species tree from a set of gene trees under the MDC criterion. In other words, our solutions are guaranteed to find the tree that minimizes the total number of deep coalescences from a set of gene trees. One solution is based on a novel integer linear programming (ILP) formulation, and another is based on a simple dynamic programming (DP) approach. Powerful ILP solvers, such as CPLEX, make the first solution appealing, particularly for very large-scale instances of the problem, whereas the DP-based solution eliminates dependence on proprietary tools, and its simplicity makes it easy to integrate with other genomic events that may cause gene tree incongruence. Using the exact solutions, we analyze a data set of 106 loci from eight yeast species, a data set of 268 loci from eight Apicomplexan species, and several simulated data sets. We show that the MDC criterion provides very accurate estimates of the species tree topologies, and that our solutions are very fast, thus allowing for the accurate analysis of genome-scale data sets. Further, the efficiency of the solutions allow for quick exploration of sub-optimal solutions, which is important for a parsimony-based criterion such as MDC, as we show. We show that searching for the species tree in the compatibility graph of the clusters induced by the gene trees may be sufficient in practice, a finding that helps ameliorate the computational requirements of optimization solutions. Further, we study the statistical consistency and convergence rate of the MDC criterion, as well as its optimality in inferring the species tree. Finally, we show how our solutions can be used to identify potential horizontal gene transfer events that may have caused some of the incongruence in the data, thus augmenting Maddison's original framework. We have implemented our solutions in the PhyloNet software package, which is freely available at: http://bioinfo.cs.rice.edu/phylonet.

Investigating Mathematics Teachers' Thoughts of Statistical Inference

ERIC Educational Resources Information Center

Yang, Kai-Lin

2012-01-01

Research on statistical cognition and application suggests that statistical inference concepts are commonly misunderstood by students and even misinterpreted by researchers. Although some research has been done on students' misunderstanding or misconceptions of confidence intervals (CIs), few studies explore either students' or mathematics…

Lessons from Inferentialism for Statistics Education

ERIC Educational Resources Information Center

Bakker, Arthur; Derry, Jan

2011-01-01

This theoretical paper relates recent interest in informal statistical inference (ISI) to the semantic theory termed inferentialism, a significant development in contemporary philosophy, which places inference at the heart of human knowing. This theory assists epistemological reflection on challenges in statistics education encountered when…

Statistical Inference and Patterns of Inequality in the Global North

ERIC Educational Resources Information Center

Moran, Timothy Patrick

2006-01-01

Cross-national inequality trends have historically been a crucial field of inquiry across the social sciences, and new methodological techniques of statistical inference have recently improved the ability to analyze these trends over time. This paper applies Monte Carlo, bootstrap inference methods to the income surveys of the Luxembourg Income…

Statistical inference and Aristotle's Rhetoric.

PubMed

Macdonald, Ranald R

2004-11-01

Formal logic operates in a closed system where all the information relevant to any conclusion is present, whereas this is not the case when one reasons about events and states of the world. Pollard and Richardson drew attention to the fact that the reasoning behind statistical tests does not lead to logically justifiable conclusions. In this paper statistical inferences are defended not by logic but by the standards of everyday reasoning. Aristotle invented formal logic, but argued that people mostly get at the truth with the aid of enthymemes--incomplete syllogisms which include arguing from examples, analogies and signs. It is proposed that statistical tests work in the same way--in that they are based on examples, invoke the analogy of a model and use the size of the effect under test as a sign that the chance hypothesis is unlikely. Of existing theories of statistical inference only a weak version of Fisher's takes this into account. Aristotle anticipated Fisher by producing an argument of the form that there were too many cases in which an outcome went in a particular direction for that direction to be plausibly attributed to chance. We can therefore conclude that Aristotle would have approved of statistical inference and there is a good reason for calling this form of statistical inference classical.

Frequentist Model Averaging in Structural Equation Modelling.

PubMed

Jin, Shaobo; Ankargren, Sebastian

2018-06-04

Model selection from a set of candidate models plays an important role in many structural equation modelling applications. However, traditional model selection methods introduce extra randomness that is not accounted for by post-model selection inference. In the current study, we propose a model averaging technique within the frequentist statistical framework. Instead of selecting an optimal model, the contributions of all candidate models are acknowledged. Valid confidence intervals and a [Formula: see text] test statistic are proposed. A simulation study shows that the proposed method is able to produce a robust mean-squared error, a better coverage probability, and a better goodness-of-fit test compared to model selection. It is an interesting compromise between model selection and the full model.

Discovering time-lagged rules from microarray data using gene profile classifiers

PubMed Central

2011-01-01

Background Gene regulatory networks have an essential role in every process of life. In this regard, the amount of genome-wide time series data is becoming increasingly available, providing the opportunity to discover the time-delayed gene regulatory networks that govern the majority of these molecular processes. Results This paper aims at reconstructing gene regulatory networks from multiple genome-wide microarray time series datasets. In this sense, a new model-free algorithm called GRNCOP2 (Gene Regulatory Network inference by Combinatorial OPtimization 2), which is a significant evolution of the GRNCOP algorithm, was developed using combinatorial optimization of gene profile classifiers. The method is capable of inferring potential time-delay relationships with any span of time between genes from various time series datasets given as input. The proposed algorithm was applied to time series data composed of twenty yeast genes that are highly relevant for the cell-cycle study, and the results were compared against several related approaches. The outcomes have shown that GRNCOP2 outperforms the contrasted methods in terms of the proposed metrics, and that the results are consistent with previous biological knowledge. Additionally, a genome-wide study on multiple publicly available time series data was performed. In this case, the experimentation has exhibited the soundness and scalability of the new method which inferred highly-related statistically-significant gene associations. Conclusions A novel method for inferring time-delayed gene regulatory networks from genome-wide time series datasets is proposed in this paper. The method was carefully validated with several publicly available data sets. The results have demonstrated that the algorithm constitutes a usable model-free approach capable of predicting meaningful relationships between genes, revealing the time-trends of gene regulation. PMID:21524308

Efficient statistical tests to compare Youden index: accounting for contingency correlation.

PubMed

Chen, Fangyao; Xue, Yuqiang; Tan, Ming T; Chen, Pingyan

2015-04-30

Youden index is widely utilized in studies evaluating accuracy of diagnostic tests and performance of predictive, prognostic, or risk models. However, both one and two independent sample tests on Youden index have been derived ignoring the dependence (association) between sensitivity and specificity, resulting in potentially misleading findings. Besides, paired sample test on Youden index is currently unavailable. This article develops efficient statistical inference procedures for one sample, independent, and paired sample tests on Youden index by accounting for contingency correlation, namely associations between sensitivity and specificity and paired samples typically represented in contingency tables. For one and two independent sample tests, the variances are estimated by Delta method, and the statistical inference is based on the central limit theory, which are then verified by bootstrap estimates. For paired samples test, we show that the estimated covariance of the two sensitivities and specificities can be represented as a function of kappa statistic so the test can be readily carried out. We then show the remarkable accuracy of the estimated variance using a constrained optimization approach. Simulation is performed to evaluate the statistical properties of the derived tests. The proposed approaches yield more stable type I errors at the nominal level and substantially higher power (efficiency) than does the original Youden's approach. Therefore, the simple explicit large sample solution performs very well. Because we can readily implement the asymptotic and exact bootstrap computation with common software like R, the method is broadly applicable to the evaluation of diagnostic tests and model performance. Copyright © 2015 John Wiley & Sons, Ltd.

CADDIS Volume 4. Data Analysis: Biological and Environmental Data Requirements

EPA Pesticide Factsheets

Overview of PECBO Module, using scripts to infer environmental conditions from biological observations, statistically estimating species-environment relationships, methods for inferring environmental conditions, statistical scripts in module.

Modularity-like objective function in annotated networks

NASA Astrophysics Data System (ADS)

Xie, Jia-Rong; Wang, Bing-Hong

2017-12-01

We ascertain the modularity-like objective function whose optimization is equivalent to the maximum likelihood in annotated networks. We demonstrate that the modularity-like objective function is a linear combination of modularity and conditional entropy. In contrast with statistical inference methods, in our method, the influence of the metadata is adjustable; when its influence is strong enough, the metadata can be recovered. Conversely, when it is weak, the detection may correspond to another partition. Between the two, there is a transition. This paper provides a concept for expanding the scope of modularity methods.

Influence of study goals on study design and execution.

PubMed

Kirklin, J W; Blackstone, E H; Naftel, D C; Turner, M E

1997-12-01

From the viewpoint of a clinician who makes recommendations to patients about choosing from the multiple possible management schemes, quantitative information derived from statistical analyses of observational studies is useful. Although random assignment of therapy is optimal, appropriately performed studies in which therapy has been nonrandomly "assigned" are considered acceptable, albeit occasionally with limitations in inferences. The analyses are considered most useful when they generate multivariable equations suitable for predicting time-related outcomes in individual patients. Graphic presentations improve communication with patients and facilitate truly informed consent.

Statistical methods for the beta-binomial model in teratology.

PubMed Central

Yamamoto, E; Yanagimoto, T

1994-01-01

The beta-binomial model is widely used for analyzing teratological data involving littermates. Recent developments in statistical analyses of teratological data are briefly reviewed with emphasis on the model. For statistical inference of the parameters in the beta-binomial distribution, separation of the likelihood introduces an likelihood inference. This leads to reducing biases of estimators and also to improving accuracy of empirical significance levels of tests. Separate inference of the parameters can be conducted in a unified way. PMID:8187716

Algorithm Optimally Orders Forward-Chaining Inference Rules

NASA Technical Reports Server (NTRS)

James, Mark

2008-01-01

People typically develop knowledge bases in a somewhat ad hoc manner by incrementally adding rules with no specific organization. This often results in a very inefficient execution of those rules since they are so often order sensitive. This is relevant to tasks like Deep Space Network in that it allows the knowledge base to be incrementally developed and have it automatically ordered for efficiency. Although data flow analysis was first developed for use in compilers for producing optimal code sequences, its usefulness is now recognized in many software systems including knowledge-based systems. However, this approach for exhaustively computing data-flow information cannot directly be applied to inference systems because of the ubiquitous execution of the rules. An algorithm is presented that efficiently performs a complete producer/consumer analysis for each antecedent and consequence clause in a knowledge base to optimally order the rules to minimize inference cycles. An algorithm was developed that optimally orders a knowledge base composed of forwarding chaining inference rules such that independent inference cycle executions are minimized, thus, resulting in significantly faster execution. This algorithm was integrated into the JPL tool Spacecraft Health Inference Engine (SHINE) for verification and it resulted in a significant reduction in inference cycles for what was previously considered an ordered knowledge base. For a knowledge base that is completely unordered, then the improvement is much greater.

On Some Assumptions of the Null Hypothesis Statistical Testing

ERIC Educational Resources Information Center

Patriota, Alexandre Galvão

2017-01-01

Bayesian and classical statistical approaches are based on different types of logical principles. In order to avoid mistaken inferences and misguided interpretations, the practitioner must respect the inference rules embedded into each statistical method. Ignoring these principles leads to the paradoxical conclusions that the hypothesis…

Physics-based statistical learning approach to mesoscopic model selection.

PubMed

Taverniers, Søren; Haut, Terry S; Barros, Kipton; Alexander, Francis J; Lookman, Turab

2015-11-01

In materials science and many other research areas, models are frequently inferred without considering their generalization to unseen data. We apply statistical learning using cross-validation to obtain an optimally predictive coarse-grained description of a two-dimensional kinetic nearest-neighbor Ising model with Glauber dynamics (GD) based on the stochastic Ginzburg-Landau equation (sGLE). The latter is learned from GD "training" data using a log-likelihood analysis, and its predictive ability for various complexities of the model is tested on GD "test" data independent of the data used to train the model on. Using two different error metrics, we perform a detailed analysis of the error between magnetization time trajectories simulated using the learned sGLE coarse-grained description and those obtained using the GD model. We show that both for equilibrium and out-of-equilibrium GD training trajectories, the standard phenomenological description using a quartic free energy does not always yield the most predictive coarse-grained model. Moreover, increasing the amount of training data can shift the optimal model complexity to higher values. Our results are promising in that they pave the way for the use of statistical learning as a general tool for materials modeling and discovery.

Direct evidence for a dual process model of deductive inference.

PubMed

Markovits, Henry; Brunet, Marie-Laurence; Thompson, Valerie; Brisson, Janie

2013-07-01

In 2 experiments, we tested a strong version of a dual process theory of conditional inference (cf. Verschueren et al., 2005a, 2005b) that assumes that most reasoners have 2 strategies available, the choice of which is determined by situational variables, cognitive capacity, and metacognitive control. The statistical strategy evaluates inferences probabilistically, accepting those with high conditional probability. The counterexample strategy rejects inferences when a counterexample shows the inference to be invalid. To discriminate strategy use, we presented reasoners with conditional statements (if p, then q) and explicit statistical information about the relative frequency of the probability of p/q (50% vs. 90%). A statistical strategy would accept the more probable inferences more frequently, whereas the counterexample one would reject both. In Experiment 1, reasoners under time pressure used the statistical strategy more, but switched to the counterexample strategy when time constraints were removed; the former took less time than the latter. These data are consistent with the hypothesis that the statistical strategy is the default heuristic. Under a free-time condition, reasoners preferred the counterexample strategy and kept it when put under time pressure. Thus, it is not simply a lack of capacity that produces a statistical strategy; instead, it seems that time pressure disrupts the ability to make good metacognitive choices. In line with this conclusion, in a 2nd experiment, we measured reasoners' confidence in their performance; those under time pressure were less confident in the statistical than the counterexample strategy and more likely to switch strategies under free-time conditions. PsycINFO Database Record (c) 2013 APA, all rights reserved.

The APA Task Force on Statistical Inference (TFSI) Report as a Framework for Teaching and Evaluating Students' Understandings of Study Validity.

ERIC Educational Resources Information Center

Thompson, Bruce

Web-based statistical instruction, like all statistical instruction, ought to focus on teaching the essence of the research endeavor: the exercise of reflective judgment. Using the framework of the recent report of the American Psychological Association (APA) Task Force on Statistical Inference (Wilkinson and the APA Task Force on Statistical…

CADDIS Volume 4. Data Analysis: Predicting Environmental Conditions from Biological Observations (PECBO Appendix)

EPA Pesticide Factsheets

Overview of PECBO Module, using scripts to infer environmental conditions from biological observations, statistically estimating species-environment relationships, methods for inferring environmental conditions, statistical scripts in module.

Maximum profile likelihood estimation of differential equation parameters through model based smoothing state estimates.

PubMed

Campbell, D A; Chkrebtii, O

2013-12-01

Statistical inference for biochemical models often faces a variety of characteristic challenges. In this paper we examine state and parameter estimation for the JAK-STAT intracellular signalling mechanism, which exemplifies the implementation intricacies common in many biochemical inference problems. We introduce an extension to the Generalized Smoothing approach for estimating delay differential equation models, addressing selection of complexity parameters, choice of the basis system, and appropriate optimization strategies. Motivated by the JAK-STAT system, we further extend the generalized smoothing approach to consider a nonlinear observation process with additional unknown parameters, and highlight how the approach handles unobserved states and unevenly spaced observations. The methodology developed is generally applicable to problems of estimation for differential equation models with delays, unobserved states, nonlinear observation processes, and partially observed histories. Crown Copyright © 2013. Published by Elsevier Inc. All rights reserved.

The effects of spatial autoregressive dependencies on inference in ordinary least squares: a geometric approach

NASA Astrophysics Data System (ADS)

Smith, Tony E.; Lee, Ka Lok

2012-01-01

There is a common belief that the presence of residual spatial autocorrelation in ordinary least squares (OLS) regression leads to inflated significance levels in beta coefficients and, in particular, inflated levels relative to the more efficient spatial error model (SEM). However, our simulations show that this is not always the case. Hence, the purpose of this paper is to examine this question from a geometric viewpoint. The key idea is to characterize the OLS test statistic in terms of angle cosines and examine the geometric implications of this characterization. Our first result is to show that if the explanatory variables in the regression exhibit no spatial autocorrelation, then the distribution of test statistics for individual beta coefficients in OLS is independent of any spatial autocorrelation in the error term. Hence, inferences about betas exhibit all the optimality properties of the classic uncorrelated error case. However, a second more important series of results show that if spatial autocorrelation is present in both the dependent and explanatory variables, then the conventional wisdom is correct. In particular, even when an explanatory variable is statistically independent of the dependent variable, such joint spatial dependencies tend to produce "spurious correlation" that results in over-rejection of the null hypothesis. The underlying geometric nature of this problem is clarified by illustrative examples. The paper concludes with a brief discussion of some possible remedies for this problem.

Statistical Inferences from Formaldehyde Dna-Protein Cross-Link Data

EPA Science Inventory

Physiologically-based pharmacokinetic (PBPK) modeling has reached considerable sophistication in its application in the pharmacological and environmental health areas. Yet, mature methodologies for making statistical inferences have not been routinely incorporated in these applic...

Statistics for nuclear engineers and scientists. Part 1. Basic statistical inference

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

Beggs, W.J.

1981-02-01

This report is intended for the use of engineers and scientists working in the nuclear industry, especially at the Bettis Atomic Power Laboratory. It serves as the basis for several Bettis in-house statistics courses. The objectives of the report are to introduce the reader to the language and concepts of statistics and to provide a basic set of techniques to apply to problems of the collection and analysis of data. Part 1 covers subjects of basic inference. The subjects include: descriptive statistics; probability; simple inference for normally distributed populations, and for non-normal populations as well; comparison of two populations; themore » analysis of variance; quality control procedures; and linear regression analysis.« less

Introducing Statistical Inference to Biology Students through Bootstrapping and Randomization

ERIC Educational Resources Information Center

Lock, Robin H.; Lock, Patti Frazer

2008-01-01

Bootstrap methods and randomization tests are increasingly being used as alternatives to standard statistical procedures in biology. They also serve as an effective introduction to the key ideas of statistical inference in introductory courses for biology students. We discuss the use of such simulation based procedures in an integrated curriculum…

Developing Young Children's Emergent Inferential Practices in Statistics

ERIC Educational Resources Information Center

Makar, Katie

2016-01-01

Informal statistical inference has now been researched at all levels of schooling and initial tertiary study. Work in informal statistical inference is least understood in the early years, where children have had little if any exposure to data handling. A qualitative study in Australia was carried out through a series of teaching experiments with…

Spiking neuron network Helmholtz machine.

PubMed

Sountsov, Pavel; Miller, Paul

2015-01-01

An increasing amount of behavioral and neurophysiological data suggests that the brain performs optimal (or near-optimal) probabilistic inference and learning during perception and other tasks. Although many machine learning algorithms exist that perform inference and learning in an optimal way, the complete description of how one of those algorithms (or a novel algorithm) can be implemented in the brain is currently incomplete. There have been many proposed solutions that address how neurons can perform optimal inference but the question of how synaptic plasticity can implement optimal learning is rarely addressed. This paper aims to unify the two fields of probabilistic inference and synaptic plasticity by using a neuronal network of realistic model spiking neurons to implement a well-studied computational model called the Helmholtz Machine. The Helmholtz Machine is amenable to neural implementation as the algorithm it uses to learn its parameters, called the wake-sleep algorithm, uses a local delta learning rule. Our spiking-neuron network implements both the delta rule and a small example of a Helmholtz machine. This neuronal network can learn an internal model of continuous-valued training data sets without supervision. The network can also perform inference on the learned internal models. We show how various biophysical features of the neural implementation constrain the parameters of the wake-sleep algorithm, such as the duration of the wake and sleep phases of learning and the minimal sample duration. We examine the deviations from optimal performance and tie them to the properties of the synaptic plasticity rule.

Spiking neuron network Helmholtz machine

PubMed Central

Sountsov, Pavel; Miller, Paul

2015-01-01

An increasing amount of behavioral and neurophysiological data suggests that the brain performs optimal (or near-optimal) probabilistic inference and learning during perception and other tasks. Although many machine learning algorithms exist that perform inference and learning in an optimal way, the complete description of how one of those algorithms (or a novel algorithm) can be implemented in the brain is currently incomplete. There have been many proposed solutions that address how neurons can perform optimal inference but the question of how synaptic plasticity can implement optimal learning is rarely addressed. This paper aims to unify the two fields of probabilistic inference and synaptic plasticity by using a neuronal network of realistic model spiking neurons to implement a well-studied computational model called the Helmholtz Machine. The Helmholtz Machine is amenable to neural implementation as the algorithm it uses to learn its parameters, called the wake-sleep algorithm, uses a local delta learning rule. Our spiking-neuron network implements both the delta rule and a small example of a Helmholtz machine. This neuronal network can learn an internal model of continuous-valued training data sets without supervision. The network can also perform inference on the learned internal models. We show how various biophysical features of the neural implementation constrain the parameters of the wake-sleep algorithm, such as the duration of the wake and sleep phases of learning and the minimal sample duration. We examine the deviations from optimal performance and tie them to the properties of the synaptic plasticity rule. PMID:25954191

Use of the wavelet transform to investigate differences in brain PET images between patient groups

NASA Astrophysics Data System (ADS)

Ruttimann, Urs E.; Unser, Michael A.; Rio, Daniel E.; Rawlings, Robert R.

1993-06-01

Suitability of the wavelet transform was studied for the analysis of glucose utilization differences between subject groups as displayed in PET images. To strengthen statistical inference, it was of particular interest investigating the tradeoff between signal localization and image decomposition into uncorrelated components. This tradeoff is shown to be controlled by wavelet regularity, with the optimal compromise attained by third-order orthogonal spline wavelets. Testing of the ensuing wavelet coefficients identified only about 1.5% as statistically different (p < .05) from noise, which then served to resynthesize the difference images by the inverse wavelet transform. The resulting images displayed relatively uniform, noise-free regions of significant differences with, due to the good localization maintained by the wavelets, very little reconstruction artifacts.

Students' Expressions of Uncertainty in Making Informal Inference When Engaged in a Statistical Investigation Using TinkerPlots

ERIC Educational Resources Information Center

Henriques, Ana; Oliveira, Hélia

2016-01-01

This paper reports on the results of a study investigating the potential to embed Informal Statistical Inference in statistical investigations, using TinkerPlots, for assisting 8th grade students' informal inferential reasoning to emerge, particularly their articulations of uncertainty. Data collection included students' written work on a…

Statistical atlas based extrapolation of CT data

NASA Astrophysics Data System (ADS)

Chintalapani, Gouthami; Murphy, Ryan; Armiger, Robert S.; Lepisto, Jyri; Otake, Yoshito; Sugano, Nobuhiko; Taylor, Russell H.; Armand, Mehran

2010-02-01

We present a framework to estimate the missing anatomical details from a partial CT scan with the help of statistical shape models. The motivating application is periacetabular osteotomy (PAO), a technique for treating developmental hip dysplasia, an abnormal condition of the hip socket that, if untreated, may lead to osteoarthritis. The common goals of PAO are to reduce pain, joint subluxation and improve contact pressure distribution by increasing the coverage of the femoral head by the hip socket. While current diagnosis and planning is based on radiological measurements, because of significant structural variations in dysplastic hips, a computer-assisted geometrical and biomechanical planning based on CT data is desirable to help the surgeon achieve optimal joint realignments. Most of the patients undergoing PAO are young females, hence it is usually desirable to minimize the radiation dose by scanning only the joint portion of the hip anatomy. These partial scans, however, do not provide enough information for biomechanical analysis due to missing iliac region. A statistical shape model of full pelvis anatomy is constructed from a database of CT scans. The partial volume is first aligned with the statistical atlas using an iterative affine registration, followed by a deformable registration step and the missing information is inferred from the atlas. The atlas inferences are further enhanced by the use of X-ray images of the patient, which are very common in an osteotomy procedure. The proposed method is validated with a leave-one-out analysis method. Osteotomy cuts are simulated and the effect of atlas predicted models on the actual procedure is evaluated.

Exploring complex dynamics in multi agent-based intelligent systems: Theoretical and experimental approaches using the Multi Agent-based Behavioral Economic Landscape (MABEL) model

NASA Astrophysics Data System (ADS)

Alexandridis, Konstantinos T.

This dissertation adopts a holistic and detailed approach to modeling spatially explicit agent-based artificial intelligent systems, using the Multi Agent-based Behavioral Economic Landscape (MABEL) model. The research questions that addresses stem from the need to understand and analyze the real-world patterns and dynamics of land use change from a coupled human-environmental systems perspective. Describes the systemic, mathematical, statistical, socio-economic and spatial dynamics of the MABEL modeling framework, and provides a wide array of cross-disciplinary modeling applications within the research, decision-making and policy domains. Establishes the symbolic properties of the MABEL model as a Markov decision process, analyzes the decision-theoretic utility and optimization attributes of agents towards comprising statistically and spatially optimal policies and actions, and explores the probabilogic character of the agents' decision-making and inference mechanisms via the use of Bayesian belief and decision networks. Develops and describes a Monte Carlo methodology for experimental replications of agent's decisions regarding complex spatial parcel acquisition and learning. Recognizes the gap on spatially-explicit accuracy assessment techniques for complex spatial models, and proposes an ensemble of statistical tools designed to address this problem. Advanced information assessment techniques such as the Receiver-Operator Characteristic curve, the impurity entropy and Gini functions, and the Bayesian classification functions are proposed. The theoretical foundation for modular Bayesian inference in spatially-explicit multi-agent artificial intelligent systems, and the ensembles of cognitive and scenario assessment modular tools build for the MABEL model are provided. Emphasizes the modularity and robustness as valuable qualitative modeling attributes, and examines the role of robust intelligent modeling as a tool for improving policy-decisions related to land use change. Finally, the major contributions to the science are presented along with valuable directions for future research.

Faster Mass Spectrometry-based Protein Inference: Junction Trees are More Efficient than Sampling and Marginalization by Enumeration

PubMed Central

Serang, Oliver; Noble, William Stafford

2012-01-01

The problem of identifying the proteins in a complex mixture using tandem mass spectrometry can be framed as an inference problem on a graph that connects peptides to proteins. Several existing protein identification methods make use of statistical inference methods for graphical models, including expectation maximization, Markov chain Monte Carlo, and full marginalization coupled with approximation heuristics. We show that, for this problem, the majority of the cost of inference usually comes from a few highly connected subgraphs. Furthermore, we evaluate three different statistical inference methods using a common graphical model, and we demonstrate that junction tree inference substantially improves rates of convergence compared to existing methods. The python code used for this paper is available at http://noble.gs.washington.edu/proj/fido. PMID:22331862

Using genetic data to strengthen causal inference in observational research.

PubMed

Pingault, Jean-Baptiste; O'Reilly, Paul F; Schoeler, Tabea; Ploubidis, George B; Rijsdijk, Frühling; Dudbridge, Frank

2018-06-05

Causal inference is essential across the biomedical, behavioural and social sciences.By progressing from confounded statistical associations to evidence of causal relationships, causal inference can reveal complex pathways underlying traits and diseases and help to prioritize targets for intervention. Recent progress in genetic epidemiology - including statistical innovation, massive genotyped data sets and novel computational tools for deep data mining - has fostered the intense development of methods exploiting genetic data and relatedness to strengthen causal inference in observational research. In this Review, we describe how such genetically informed methods differ in their rationale, applicability and inherent limitations and outline how they should be integrated in the future to offer a rich causal inference toolbox.

Risk, statistical inference, and the law of evidence: the use of epidemiological data in toxic tort cases.

PubMed

Brannigan, V M; Bier, V M; Berg, C

1992-09-01

Toxic torts are product liability cases dealing with alleged injuries due to chemical or biological hazards such as radiation, thalidomide, or Agent Orange. Toxic tort cases typically rely more heavily than other product liability cases on indirect or statistical proof of injury. There have been numerous theoretical analyses of statistical proof of injury in toxic tort cases. However, there have been only a handful of actual legal decisions regarding the use of such statistical evidence, and most of those decisions have been inconclusive. Recently, a major case from the Fifth Circuit, involving allegations that Benedectin (a morning sickness drug) caused birth defects, was decided entirely on the basis of statistical inference. This paper examines both the conceptual basis of that decision, and also the relationships among statistical inference, scientific evidence, and the rules of product liability in general.

Inference of Vohradský's Models of Genetic Networks by Solving Two-Dimensional Function Optimization Problems

PubMed Central

Kimura, Shuhei; Sato, Masanao; Okada-Hatakeyama, Mariko

2013-01-01

The inference of a genetic network is a problem in which mutual interactions among genes are inferred from time-series of gene expression levels. While a number of models have been proposed to describe genetic networks, this study focuses on a mathematical model proposed by Vohradský. Because of its advantageous features, several researchers have proposed the inference methods based on Vohradský's model. When trying to analyze large-scale networks consisting of dozens of genes, however, these methods must solve high-dimensional non-linear function optimization problems. In order to resolve the difficulty of estimating the parameters of the Vohradský's model, this study proposes a new method that defines the problem as several two-dimensional function optimization problems. Through numerical experiments on artificial genetic network inference problems, we showed that, although the computation time of the proposed method is not the shortest, the method has the ability to estimate parameters of Vohradský's models more effectively with sufficiently short computation times. This study then applied the proposed method to an actual inference problem of the bacterial SOS DNA repair system, and succeeded in finding several reasonable regulations. PMID:24386175

Making statistical inferences about software reliability

NASA Technical Reports Server (NTRS)

Miller, Douglas R.

1988-01-01

Failure times of software undergoing random debugging can be modelled as order statistics of independent but nonidentically distributed exponential random variables. Using this model inferences can be made about current reliability and, if debugging continues, future reliability. This model also shows the difficulty inherent in statistical verification of very highly reliable software such as that used by digital avionics in commercial aircraft.

Comparing Trend and Gap Statistics across Tests: Distributional Change Using Ordinal Methods and Bayesian Inference

ERIC Educational Resources Information Center

Denbleyker, John Nickolas

2012-01-01

The shortcomings of the proportion above cut (PAC) statistic used so prominently in the educational landscape renders it a very problematic measure for making correct inferences with student test data. The limitations of PAC-based statistics are more pronounced with cross-test comparisons due to their dependency on cut-score locations. A better…

Aspects of First Year Statistics Students' Reasoning When Performing Intuitive Analysis of Variance: Effects of Within- and Between-Group Variability

ERIC Educational Resources Information Center

Trumpower, David L.

2015-01-01

Making inferences about population differences based on samples of data, that is, performing intuitive analysis of variance (IANOVA), is common in everyday life. However, the intuitive reasoning of individuals when making such inferences (even following statistics instruction), often differs from the normative logic of formal statistics. The…

Difference to Inference: teaching logical and statistical reasoning through on-line interactivity.

PubMed

Malloy, T E

2001-05-01

Difference to Inference is an on-line JAVA program that simulates theory testing and falsification through research design and data collection in a game format. The program, based on cognitive and epistemological principles, is designed to support learning of the thinking skills underlying deductive and inductive logic and statistical reasoning. Difference to Inference has database connectivity so that game scores can be counted as part of course grades.

Likelihood-based inference for discretely observed birth-death-shift processes, with applications to evolution of mobile genetic elements.

PubMed

Xu, Jason; Guttorp, Peter; Kato-Maeda, Midori; Minin, Vladimir N

2015-12-01

Continuous-time birth-death-shift (BDS) processes are frequently used in stochastic modeling, with many applications in ecology and epidemiology. In particular, such processes can model evolutionary dynamics of transposable elements-important genetic markers in molecular epidemiology. Estimation of the effects of individual covariates on the birth, death, and shift rates of the process can be accomplished by analyzing patient data, but inferring these rates in a discretely and unevenly observed setting presents computational challenges. We propose a multi-type branching process approximation to BDS processes and develop a corresponding expectation maximization algorithm, where we use spectral techniques to reduce calculation of expected sufficient statistics to low-dimensional integration. These techniques yield an efficient and robust optimization routine for inferring the rates of the BDS process, and apply broadly to multi-type branching processes whose rates can depend on many covariates. After rigorously testing our methodology in simulation studies, we apply our method to study intrapatient time evolution of IS6110 transposable element, a genetic marker frequently used during estimation of epidemiological clusters of Mycobacterium tuberculosis infections. © 2015, The International Biometric Society.

Bayesian Inference for Generalized Linear Models for Spiking Neurons

PubMed Central

Gerwinn, Sebastian; Macke, Jakob H.; Bethge, Matthias

2010-01-01

Generalized Linear Models (GLMs) are commonly used statistical methods for modelling the relationship between neural population activity and presented stimuli. When the dimension of the parameter space is large, strong regularization has to be used in order to fit GLMs to datasets of realistic size without overfitting. By imposing properly chosen priors over parameters, Bayesian inference provides an effective and principled approach for achieving regularization. Here we show how the posterior distribution over model parameters of GLMs can be approximated by a Gaussian using the Expectation Propagation algorithm. In this way, we obtain an estimate of the posterior mean and posterior covariance, allowing us to calculate Bayesian confidence intervals that characterize the uncertainty about the optimal solution. From the posterior we also obtain a different point estimate, namely the posterior mean as opposed to the commonly used maximum a posteriori estimate. We systematically compare the different inference techniques on simulated as well as on multi-electrode recordings of retinal ganglion cells, and explore the effects of the chosen prior and the performance measure used. We find that good performance can be achieved by choosing an Laplace prior together with the posterior mean estimate. PMID:20577627

SEX-DETector: A Probabilistic Approach to Study Sex Chromosomes in Non-Model Organisms

PubMed Central

Muyle, Aline; Käfer, Jos; Zemp, Niklaus; Mousset, Sylvain; Picard, Franck; Marais, Gabriel AB

2016-01-01

We propose a probabilistic framework to infer autosomal and sex-linked genes from RNA-seq data of a cross for any sex chromosome type (XY, ZW, and UV). Sex chromosomes (especially the non-recombining and repeat-dense Y, W, U, and V) are notoriously difficult to sequence. Strategies have been developed to obtain partially assembled sex chromosome sequences. Most of them remain difficult to apply to numerous non-model organisms, either because they require a reference genome, or because they are designed for evolutionarily old systems. Sequencing a cross (parents and progeny) by RNA-seq to study the segregation of alleles and infer sex-linked genes is a cost-efficient strategy, which also provides expression level estimates. However, the lack of a proper statistical framework has limited a broader application of this approach. Tests on empirical Silene data show that our method identifies 20–35% more sex-linked genes than existing pipelines, while making reliable inferences for downstream analyses. Approximately 12 individuals are needed for optimal results based on simulations. For species with an unknown sex-determination system, the method can assess the presence and type (XY vs. ZW) of sex chromosomes through a model comparison strategy. The method is particularly well optimized for sex chromosomes of young or intermediate age, which are expected in thousands of yet unstudied lineages. Any organisms, including non-model ones for which nothing is known a priori, that can be bred in the lab, are suitable for our method. SEX-DETector and its implementation in a Galaxy workflow are made freely available. PMID:27492231

Inference as Prediction

ERIC Educational Resources Information Center

Watson, Jane

2007-01-01

Inference, or decision making, is seen in curriculum documents as the final step in a statistical investigation. For a formal statistical enquiry this may be associated with sophisticated tests involving probability distributions. For young students without the mathematical background to perform such tests, it is still possible to draw informal…

A Framework for Thinking about Informal Statistical Inference

ERIC Educational Resources Information Center

Makar, Katie; Rubin, Andee

2009-01-01

Informal inferential reasoning has shown some promise in developing students' deeper understanding of statistical processes. This paper presents a framework to think about three key principles of informal inference--generalizations "beyond the data," probabilistic language, and data as evidence. The authors use primary school classroom…

Sensitivity to the Sampling Process Emerges From the Principle of Efficiency.

PubMed

Jara-Ettinger, Julian; Sun, Felix; Schulz, Laura; Tenenbaum, Joshua B

2018-05-01

Humans can seamlessly infer other people's preferences, based on what they do. Broadly, two types of accounts have been proposed to explain different aspects of this ability. The first account focuses on spatial information: Agents' efficient navigation in space reveals what they like. The second account focuses on statistical information: Uncommon choices reveal stronger preferences. Together, these two lines of research suggest that we have two distinct capacities for inferring preferences. Here we propose that this is not the case, and that spatial-based and statistical-based preference inferences can be explained by the assumption that agents are efficient alone. We show that people's sensitivity to spatial and statistical information when they infer preferences is best predicted by a computational model of the principle of efficiency, and that this model outperforms dual-system models, even when the latter are fit to participant judgments. Our results suggest that, as adults, a unified understanding of agency under the principle of efficiency underlies our ability to infer preferences. Copyright © 2018 Cognitive Science Society, Inc.

Graph rigidity, cyclic belief propagation, and point pattern matching.

PubMed

McAuley, Julian J; Caetano, Tibério S; Barbosa, Marconi S

2008-11-01

A recent paper [1] proposed a provably optimal polynomial time method for performing near-isometric point pattern matching by means of exact probabilistic inference in a chordal graphical model. Its fundamental result is that the chordal graph in question is shown to be globally rigid, implying that exact inference provides the same matching solution as exact inference in a complete graphical model. This implies that the algorithm is optimal when there is no noise in the point patterns. In this paper, we present a new graph that is also globally rigid but has an advantage over the graph proposed in [1]: Its maximal clique size is smaller, rendering inference significantly more efficient. However, this graph is not chordal, and thus, standard Junction Tree algorithms cannot be directly applied. Nevertheless, we show that loopy belief propagation in such a graph converges to the optimal solution. This allows us to retain the optimality guarantee in the noiseless case, while substantially reducing both memory requirements and processing time. Our experimental results show that the accuracy of the proposed solution is indistinguishable from that in [1] when there is noise in the point patterns.

Statistical inference for extended or shortened phase II studies based on Simon's two-stage designs.

PubMed

Zhao, Junjun; Yu, Menggang; Feng, Xi-Ping

2015-06-07

Simon's two-stage designs are popular choices for conducting phase II clinical trials, especially in the oncology trials to reduce the number of patients placed on ineffective experimental therapies. Recently Koyama and Chen (2008) discussed how to conduct proper inference for such studies because they found that inference procedures used with Simon's designs almost always ignore the actual sampling plan used. In particular, they proposed an inference method for studies when the actual second stage sample sizes differ from planned ones. We consider an alternative inference method based on likelihood ratio. In particular, we order permissible sample paths under Simon's two-stage designs using their corresponding conditional likelihood. In this way, we can calculate p-values using the common definition: the probability of obtaining a test statistic value at least as extreme as that observed under the null hypothesis. In addition to providing inference for a couple of scenarios where Koyama and Chen's method can be difficult to apply, the resulting estimate based on our method appears to have certain advantage in terms of inference properties in many numerical simulations. It generally led to smaller biases and narrower confidence intervals while maintaining similar coverages. We also illustrated the two methods in a real data setting. Inference procedures used with Simon's designs almost always ignore the actual sampling plan. Reported P-values, point estimates and confidence intervals for the response rate are not usually adjusted for the design's adaptiveness. Proper statistical inference procedures should be used.

Maximum likelihood inference implies a high, not a low, ancestral haploid chromosome number in Araceae, with a critique of the bias introduced by ‘x’

PubMed Central

Cusimano, Natalie; Sousa, Aretuza; Renner, Susanne S.

2012-01-01

Background and Aims For 84 years, botanists have relied on calculating the highest common factor for series of haploid chromosome numbers to arrive at a so-called basic number, x. This was done without consistent (reproducible) reference to species relationships and frequencies of different numbers in a clade. Likelihood models that treat polyploidy, chromosome fusion and fission as events with particular probabilities now allow reconstruction of ancestral chromosome numbers in an explicit framework. We have used a modelling approach to reconstruct chromosome number change in the large monocot family Araceae and to test earlier hypotheses about basic numbers in the family. Methods Using a maximum likelihood approach and chromosome counts for 26 % of the 3300 species of Araceae and representative numbers for each of the other 13 families of Alismatales, polyploidization events and single chromosome changes were inferred on a genus-level phylogenetic tree for 113 of the 117 genera of Araceae. Key Results The previously inferred basic numbers x = 14 and x = 7 are rejected. Instead, maximum likelihood optimization revealed an ancestral haploid chromosome number of n = 16, Bayesian inference of n = 18. Chromosome fusion (loss) is the predominant inferred event, whereas polyploidization events occurred less frequently and mainly towards the tips of the tree. Conclusions The bias towards low basic numbers (x) introduced by the algebraic approach to inferring chromosome number changes, prevalent among botanists, may have contributed to an unrealistic picture of ancestral chromosome numbers in many plant clades. The availability of robust quantitative methods for reconstructing ancestral chromosome numbers on molecular phylogenetic trees (with or without branch length information), with confidence statistics, makes the calculation of x an obsolete approach, at least when applied to large clades. PMID:22210850

A Coalitional Game for Distributed Inference in Sensor Networks With Dependent Observations

NASA Astrophysics Data System (ADS)

He, Hao; Varshney, Pramod K.

2016-04-01

We consider the problem of collaborative inference in a sensor network with heterogeneous and statistically dependent sensor observations. Each sensor aims to maximize its inference performance by forming a coalition with other sensors and sharing information within the coalition. It is proved that the inference performance is a nondecreasing function of the coalition size. However, in an energy constrained network, the energy consumption of inter-sensor communication also increases with increasing coalition size, which discourages the formation of the grand coalition (the set of all sensors). In this paper, the formation of non-overlapping coalitions with statistically dependent sensors is investigated under a specific communication constraint. We apply a game theoretical approach to fully explore and utilize the information contained in the spatial dependence among sensors to maximize individual sensor performance. Before formulating the distributed inference problem as a coalition formation game, we first quantify the gain and loss in forming a coalition by introducing the concepts of diversity gain and redundancy loss for both estimation and detection problems. These definitions, enabled by the statistical theory of copulas, allow us to characterize the influence of statistical dependence among sensor observations on inference performance. An iterative algorithm based on merge-and-split operations is proposed for the solution and the stability of the proposed algorithm is analyzed. Numerical results are provided to demonstrate the superiority of our proposed game theoretical approach.

A Simulation Optimization Approach to Epidemic Forecasting

PubMed Central

Nsoesie, Elaine O.; Beckman, Richard J.; Shashaani, Sara; Nagaraj, Kalyani S.; Marathe, Madhav V.

2013-01-01

Reliable forecasts of influenza can aid in the control of both seasonal and pandemic outbreaks. We introduce a simulation optimization (SIMOP) approach for forecasting the influenza epidemic curve. This study represents the final step of a project aimed at using a combination of simulation, classification, statistical and optimization techniques to forecast the epidemic curve and infer underlying model parameters during an influenza outbreak. The SIMOP procedure combines an individual-based model and the Nelder-Mead simplex optimization method. The method is used to forecast epidemics simulated over synthetic social networks representing Montgomery County in Virginia, Miami, Seattle and surrounding metropolitan regions. The results are presented for the first four weeks. Depending on the synthetic network, the peak time could be predicted within a 95% CI as early as seven weeks before the actual peak. The peak infected and total infected were also accurately forecasted for Montgomery County in Virginia within the forecasting period. Forecasting of the epidemic curve for both seasonal and pandemic influenza outbreaks is a complex problem, however this is a preliminary step and the results suggest that more can be achieved in this area. PMID:23826222

A Simulation Optimization Approach to Epidemic Forecasting.

PubMed

Nsoesie, Elaine O; Beckman, Richard J; Shashaani, Sara; Nagaraj, Kalyani S; Marathe, Madhav V

2013-01-01

Reliable forecasts of influenza can aid in the control of both seasonal and pandemic outbreaks. We introduce a simulation optimization (SIMOP) approach for forecasting the influenza epidemic curve. This study represents the final step of a project aimed at using a combination of simulation, classification, statistical and optimization techniques to forecast the epidemic curve and infer underlying model parameters during an influenza outbreak. The SIMOP procedure combines an individual-based model and the Nelder-Mead simplex optimization method. The method is used to forecast epidemics simulated over synthetic social networks representing Montgomery County in Virginia, Miami, Seattle and surrounding metropolitan regions. The results are presented for the first four weeks. Depending on the synthetic network, the peak time could be predicted within a 95% CI as early as seven weeks before the actual peak. The peak infected and total infected were also accurately forecasted for Montgomery County in Virginia within the forecasting period. Forecasting of the epidemic curve for both seasonal and pandemic influenza outbreaks is a complex problem, however this is a preliminary step and the results suggest that more can be achieved in this area.

Statistical detection of EEG synchrony using empirical bayesian inference.

PubMed

Singh, Archana K; Asoh, Hideki; Takeda, Yuji; Phillips, Steven

2015-01-01

There is growing interest in understanding how the brain utilizes synchronized oscillatory activity to integrate information across functionally connected regions. Computing phase-locking values (PLV) between EEG signals is a popular method for quantifying such synchronizations and elucidating their role in cognitive tasks. However, high-dimensionality in PLV data incurs a serious multiple testing problem. Standard multiple testing methods in neuroimaging research (e.g., false discovery rate, FDR) suffer severe loss of power, because they fail to exploit complex dependence structure between hypotheses that vary in spectral, temporal and spatial dimension. Previously, we showed that a hierarchical FDR and optimal discovery procedures could be effectively applied for PLV analysis to provide better power than FDR. In this article, we revisit the multiple comparison problem from a new Empirical Bayes perspective and propose the application of the local FDR method (locFDR; Efron, 2001) for PLV synchrony analysis to compute FDR as a posterior probability that an observed statistic belongs to a null hypothesis. We demonstrate the application of Efron's Empirical Bayes approach for PLV synchrony analysis for the first time. We use simulations to validate the specificity and sensitivity of locFDR and a real EEG dataset from a visual search study for experimental validation. We also compare locFDR with hierarchical FDR and optimal discovery procedures in both simulation and experimental analyses. Our simulation results showed that the locFDR can effectively control false positives without compromising on the power of PLV synchrony inference. Our results from the application locFDR on experiment data detected more significant discoveries than our previously proposed methods whereas the standard FDR method failed to detect any significant discoveries.

The prevalence of terraced treescapes in analyses of phylogenetic data sets.

PubMed

Dobrin, Barbara H; Zwickl, Derrick J; Sanderson, Michael J

2018-04-04

The pattern of data availability in a phylogenetic data set may lead to the formation of terraces, collections of equally optimal trees. Terraces can arise in tree space if trees are scored with parsimony or with partitioned, edge-unlinked maximum likelihood. Theory predicts that terraces can be large, but their prevalence in contemporary data sets has never been surveyed. We selected 26 data sets and phylogenetic trees reported in recent literature and investigated the terraces to which the trees would belong, under a common set of inference assumptions. We examined terrace size as a function of the sampling properties of the data sets, including taxon coverage density (the proportion of taxon-by-gene positions with any data present) and a measure of gene sampling "sufficiency". We evaluated each data set in relation to the theoretical minimum gene sampling depth needed to reduce terrace size to a single tree, and explored the impact of the terraces found in replicate trees in bootstrap methods. Terraces were identified in nearly all data sets with taxon coverage densities < 0.90. They were not found, however, in high-coverage-density (i.e., ≥ 0.94) transcriptomic and genomic data sets. The terraces could be very large, and size varied inversely with taxon coverage density and with gene sampling sufficiency. Few data sets achieved a theoretical minimum gene sampling depth needed to reduce terrace size to a single tree. Terraces found during bootstrap resampling reduced overall support. If certain inference assumptions apply, trees estimated from empirical data sets often belong to large terraces of equally optimal trees. Terrace size correlates to data set sampling properties. Data sets seldom include enough genes to reduce terrace size to one tree. When bootstrap replicate trees lie on a terrace, statistical support for phylogenetic hypotheses may be reduced. Although some of the published analyses surveyed were conducted with edge-linked inference models (which do not induce terraces), unlinked models have been used and advocated. The present study describes the potential impact of that inference assumption on phylogenetic inference in the context of the kinds of multigene data sets now widely assembled for large-scale tree construction.

Using a genetic algorithm to optimize a water-monitoring network for accuracy and cost effectiveness

NASA Astrophysics Data System (ADS)

Julich, R. J.

2004-05-01

The purpose of this project is to determine the optimal spatial distribution of water-monitoring wells to maximize important data collection and to minimize the cost of managing the network. We have employed a genetic algorithm (GA) towards this goal. The GA uses a simple fitness measure with two parts: the first part awards a maximal score to those combinations of hydraulic head observations whose net uncertainty is closest to the value representing all observations present, thereby maximizing accuracy; the second part applies a penalty function to minimize the number of observations, thereby minimizing the overall cost of the monitoring network. We used the linear statistical inference equation to calculate standard deviations on predictions from a numerical model generated for the 501-observation Death Valley Regional Flow System as the basis for our uncertainty calculations. We have organized the results to address the following three questions: 1) what is the optimal design strategy for a genetic algorithm to optimize this problem domain; 2) what is the consistency of solutions over several optimization runs; and 3) how do these results compare to what is known about the conceptual hydrogeology? Our results indicate the genetic algorithms are a more efficient and robust method for solving this class of optimization problems than have been traditional optimization approaches.

Spurious correlations and inference in landscape genetics

Treesearch

Samuel A. Cushman; Erin L. Landguth

2010-01-01

Reliable interpretation of landscape genetic analyses depends on statistical methods that have high power to identify the correct process driving gene flow while rejecting incorrect alternative hypotheses. Little is known about statistical power and inference in individual-based landscape genetics. Our objective was to evaluate the power of causalmodelling with partial...

The Philosophical Foundations of Prescriptive Statements and Statistical Inference

ERIC Educational Resources Information Center

Sun, Shuyan; Pan, Wei

2011-01-01

From the perspectives of the philosophy of science and statistical inference, we discuss the challenges of making prescriptive statements in quantitative research articles. We first consider the prescriptive nature of educational research and argue that prescriptive statements are a necessity in educational research. The logic of deduction,…

Inference and the Introductory Statistics Course

ERIC Educational Resources Information Center

Pfannkuch, Maxine; Regan, Matt; Wild, Chris; Budgett, Stephanie; Forbes, Sharleen; Harraway, John; Parsonage, Ross

2011-01-01

This article sets out some of the rationale and arguments for making major changes to the teaching and learning of statistical inference in introductory courses at our universities by changing from a norm-based, mathematical approach to more conceptually accessible computer-based approaches. The core problem of the inferential argument with its…

"Magnitude-based inference": a statistical review.

PubMed

Welsh, Alan H; Knight, Emma J

2015-04-01

We consider "magnitude-based inference" and its interpretation by examining in detail its use in the problem of comparing two means. We extract from the spreadsheets, which are provided to users of the analysis (http://www.sportsci.org/), a precise description of how "magnitude-based inference" is implemented. We compare the implemented version of the method with general descriptions of it and interpret the method in familiar statistical terms. We show that "magnitude-based inference" is not a progressive improvement on modern statistics. The additional probabilities introduced are not directly related to the confidence interval but, rather, are interpretable either as P values for two different nonstandard tests (for different null hypotheses) or as approximate Bayesian calculations, which also lead to a type of test. We also discuss sample size calculations associated with "magnitude-based inference" and show that the substantial reduction in sample sizes claimed for the method (30% of the sample size obtained from standard frequentist calculations) is not justifiable so the sample size calculations should not be used. Rather than using "magnitude-based inference," a better solution is to be realistic about the limitations of the data and use either confidence intervals or a fully Bayesian analysis.

Load Balancing Using Time Series Analysis for Soft Real Time Systems with Statistically Periodic Loads

NASA Technical Reports Server (NTRS)

Hailperin, Max

1993-01-01

This thesis provides design and analysis of techniques for global load balancing on ensemble architectures running soft-real-time object-oriented applications with statistically periodic loads. It focuses on estimating the instantaneous average load over all the processing elements. The major contribution is the use of explicit stochastic process models for both the loading and the averaging itself. These models are exploited via statistical time-series analysis and Bayesian inference to provide improved average load estimates, and thus to facilitate global load balancing. This thesis explains the distributed algorithms used and provides some optimality results. It also describes the algorithms' implementation and gives performance results from simulation. These results show that our techniques allow more accurate estimation of the global system load ing, resulting in fewer object migration than local methods. Our method is shown to provide superior performance, relative not only to static load-balancing schemes but also to many adaptive methods.

A statistical inference for concentrations of benzo[a]pyrene partially measured in the ambient air of an industrial city in Korea

NASA Astrophysics Data System (ADS)

Kim, Yongku; Seo, Young-Kyo; Baek, Sung-Ok

2013-12-01

Although large quantities of air pollutants are released into the atmosphere, they are partially monitored and routinely assessed for their health implications. This paper proposes a statistical model describing the temporal behavior of hazardous air pollutants (HAPs), which can have negative effects on human health. Benzo[a]pyrene (BaP) is selected for statistical modeling. The proposed model incorporates the linkage between BaP and meteorology and is specifically formulated to identify meteorological effects and allow for seasonal trends. The model is used to estimate and forecast temporal fields of BaP conditional on observed (or forecasted) meteorological conditions, including temperature, precipitation, wind speed, and air quality. The effects of BaP on human health are examined by characterizing health indicators, namely the cancer risk and the hazard quotient. The model provides useful information for the optimal monitoring period and projection of future BaP concentrations for both industrial and residential areas in Korea.

Statistical inference for the additive hazards model under outcome-dependent sampling.

PubMed

Yu, Jichang; Liu, Yanyan; Sandler, Dale P; Zhou, Haibo

2015-09-01

Cost-effective study design and proper inference procedures for data from such designs are always of particular interests to study investigators. In this article, we propose a biased sampling scheme, an outcome-dependent sampling (ODS) design for survival data with right censoring under the additive hazards model. We develop a weighted pseudo-score estimator for the regression parameters for the proposed design and derive the asymptotic properties of the proposed estimator. We also provide some suggestions for using the proposed method by evaluating the relative efficiency of the proposed method against simple random sampling design and derive the optimal allocation of the subsamples for the proposed design. Simulation studies show that the proposed ODS design is more powerful than other existing designs and the proposed estimator is more efficient than other estimators. We apply our method to analyze a cancer study conducted at NIEHS, the Cancer Incidence and Mortality of Uranium Miners Study, to study the risk of radon exposure to cancer.

Statistical inference for the additive hazards model under outcome-dependent sampling

PubMed Central

Yu, Jichang; Liu, Yanyan; Sandler, Dale P.; Zhou, Haibo

2015-01-01

Cost-effective study design and proper inference procedures for data from such designs are always of particular interests to study investigators. In this article, we propose a biased sampling scheme, an outcome-dependent sampling (ODS) design for survival data with right censoring under the additive hazards model. We develop a weighted pseudo-score estimator for the regression parameters for the proposed design and derive the asymptotic properties of the proposed estimator. We also provide some suggestions for using the proposed method by evaluating the relative efficiency of the proposed method against simple random sampling design and derive the optimal allocation of the subsamples for the proposed design. Simulation studies show that the proposed ODS design is more powerful than other existing designs and the proposed estimator is more efficient than other estimators. We apply our method to analyze a cancer study conducted at NIEHS, the Cancer Incidence and Mortality of Uranium Miners Study, to study the risk of radon exposure to cancer. PMID:26379363

Multi-Agent Inference in Social Networks: A Finite Population Learning Approach.

PubMed

Fan, Jianqing; Tong, Xin; Zeng, Yao

When people in a society want to make inference about some parameter, each person may want to use data collected by other people. Information (data) exchange in social networks is usually costly, so to make reliable statistical decisions, people need to trade off the benefits and costs of information acquisition. Conflicts of interests and coordination problems will arise in the process. Classical statistics does not consider people's incentives and interactions in the data collection process. To address this imperfection, this work explores multi-agent Bayesian inference problems with a game theoretic social network model. Motivated by our interest in aggregate inference at the societal level, we propose a new concept, finite population learning , to address whether with high probability, a large fraction of people in a given finite population network can make "good" inference. Serving as a foundation, this concept enables us to study the long run trend of aggregate inference quality as population grows.

Intuitive statistics by 8-month-old infants

PubMed Central

Xu, Fei; Garcia, Vashti

2008-01-01

Human learners make inductive inferences based on small amounts of data: we generalize from samples to populations and vice versa. The academic discipline of statistics formalizes these intuitive statistical inferences. What is the origin of this ability? We report six experiments investigating whether 8-month-old infants are “intuitive statisticians.” Our results showed that, given a sample, the infants were able to make inferences about the population from which the sample had been drawn. Conversely, given information about the entire population of relatively small size, the infants were able to make predictions about the sample. Our findings provide evidence that infants possess a powerful mechanism for inductive learning, either using heuristics or basic principles of probability. This ability to make inferences based on samples or information about the population develops early and in the absence of schooling or explicit teaching. Human infants may be rational learners from very early in development. PMID:18378901

Assessing colour-dependent occupation statistics inferred from galaxy group catalogues

NASA Astrophysics Data System (ADS)

Campbell, Duncan; van den Bosch, Frank C.; Hearin, Andrew; Padmanabhan, Nikhil; Berlind, Andreas; Mo, H. J.; Tinker, Jeremy; Yang, Xiaohu

2015-09-01

We investigate the ability of current implementations of galaxy group finders to recover colour-dependent halo occupation statistics. To test the fidelity of group catalogue inferred statistics, we run three different group finders used in the literature over a mock that includes galaxy colours in a realistic manner. Overall, the resulting mock group catalogues are remarkably similar, and most colour-dependent statistics are recovered with reasonable accuracy. However, it is also clear that certain systematic errors arise as a consequence of correlated errors in group membership determination, central/satellite designation, and halo mass assignment. We introduce a new statistic, the halo transition probability (HTP), which captures the combined impact of all these errors. As a rule of thumb, errors tend to equalize the properties of distinct galaxy populations (i.e. red versus blue galaxies or centrals versus satellites), and to result in inferred occupation statistics that are more accurate for red galaxies than for blue galaxies. A statistic that is particularly poorly recovered from the group catalogues is the red fraction of central galaxies as a function of halo mass. Group finders do a good job in recovering galactic conformity, but also have a tendency to introduce weak conformity when none is present. We conclude that proper inference of colour-dependent statistics from group catalogues is best achieved using forward modelling (i.e. running group finders over mock data) or by implementing a correction scheme based on the HTP, as long as the latter is not too strongly model dependent.

Statistical learning and selective inference.

PubMed

Taylor, Jonathan; Tibshirani, Robert J

2015-06-23

We describe the problem of "selective inference." This addresses the following challenge: Having mined a set of data to find potential associations, how do we properly assess the strength of these associations? The fact that we have "cherry-picked"--searched for the strongest associations--means that we must set a higher bar for declaring significant the associations that we see. This challenge becomes more important in the era of big data and complex statistical modeling. The cherry tree (dataset) can be very large and the tools for cherry picking (statistical learning methods) are now very sophisticated. We describe some recent new developments in selective inference and illustrate their use in forward stepwise regression, the lasso, and principal components analysis.

Variations on Bayesian Prediction and Inference

DTIC Science & Technology

2016-05-09

inference 2.2.1 Background There are a number of statistical inference problems that are not generally formulated via a full probability model...problem of inference about an unknown parameter, the Bayesian approach requires a full probability 1. REPORT DATE (DD-MM-YYYY) 4. TITLE AND...the problem of inference about an unknown parameter, the Bayesian approach requires a full probability model/likelihood which can be an obstacle

Computational Precision of Mental Inference as Critical Source of Human Choice Suboptimality.

PubMed

Drugowitsch, Jan; Wyart, Valentin; Devauchelle, Anne-Dominique; Koechlin, Etienne

2016-12-21

Making decisions in uncertain environments often requires combining multiple pieces of ambiguous information from external cues. In such conditions, human choices resemble optimal Bayesian inference, but typically show a large suboptimal variability whose origin remains poorly understood. In particular, this choice suboptimality might arise from imperfections in mental inference rather than in peripheral stages, such as sensory processing and response selection. Here, we dissociate these three sources of suboptimality in human choices based on combining multiple ambiguous cues. Using a novel quantitative approach for identifying the origin and structure of choice variability, we show that imperfections in inference alone cause a dominant fraction of suboptimal choices. Furthermore, two-thirds of this suboptimality appear to derive from the limited precision of neural computations implementing inference rather than from systematic deviations from Bayes-optimal inference. These findings set an upper bound on the accuracy and ultimate predictability of human choices in uncertain environments. Copyright © 2016 Elsevier Inc. All rights reserved.

Inferring causal relationships between phenotypes using summary statistics from genome-wide association studies.

PubMed

Meng, Xiang-He; Shen, Hui; Chen, Xiang-Ding; Xiao, Hong-Mei; Deng, Hong-Wen

2018-03-01

Genome-wide association studies (GWAS) have successfully identified numerous genetic variants associated with diverse complex phenotypes and diseases, and provided tremendous opportunities for further analyses using summary association statistics. Recently, Pickrell et al. developed a robust method for causal inference using independent putative causal SNPs. However, this method may fail to infer the causal relationship between two phenotypes when only a limited number of independent putative causal SNPs identified. Here, we extended Pickrell's method to make it more applicable for the general situations. We extended the causal inference method by replacing the putative causal SNPs with the lead SNPs (the set of the most significant SNPs in each independent locus) and tested the performance of our extended method using both simulation and empirical data. Simulations suggested that when the same number of genetic variants is used, our extended method had similar distribution of test statistic under the null model as well as comparable power under the causal model compared with the original method by Pickrell et al. But in practice, our extended method would generally be more powerful because the number of independent lead SNPs was often larger than the number of independent putative causal SNPs. And including more SNPs, on the other hand, would not cause more false positives. By applying our extended method to summary statistics from GWAS for blood metabolites and femoral neck bone mineral density (FN-BMD), we successfully identified ten blood metabolites that may causally influence FN-BMD. We extended a causal inference method for inferring putative causal relationship between two phenotypes using summary statistics from GWAS, and identified a number of potential causal metabolites for FN-BMD, which may provide novel insights into the pathophysiological mechanisms underlying osteoporosis.

Optimal estimation of the optomechanical coupling strength

NASA Astrophysics Data System (ADS)

Bernád, József Zsolt; Sanavio, Claudio; Xuereb, André

2018-06-01

We apply the formalism of quantum estimation theory to obtain information about the value of the nonlinear optomechanical coupling strength. In particular, we discuss the minimum mean-square error estimator and a quantum Cramér-Rao-type inequality for the estimation of the coupling strength. Our estimation strategy reveals some cases where quantum statistical inference is inconclusive and merely results in the reinforcement of prior expectations. We show that these situations also involve the highest expected information losses. We demonstrate that interaction times on the order of one time period of mechanical oscillations are the most suitable for our estimation scenario, and compare situations involving different photon and phonon excitations.

In defence of model-based inference in phylogeography

PubMed Central

Beaumont, Mark A.; Nielsen, Rasmus; Robert, Christian; Hey, Jody; Gaggiotti, Oscar; Knowles, Lacey; Estoup, Arnaud; Panchal, Mahesh; Corander, Jukka; Hickerson, Mike; Sisson, Scott A.; Fagundes, Nelson; Chikhi, Lounès; Beerli, Peter; Vitalis, Renaud; Cornuet, Jean-Marie; Huelsenbeck, John; Foll, Matthieu; Yang, Ziheng; Rousset, Francois; Balding, David; Excoffier, Laurent

2017-01-01

Recent papers have promoted the view that model-based methods in general, and those based on Approximate Bayesian Computation (ABC) in particular, are flawed in a number of ways, and are therefore inappropriate for the analysis of phylogeographic data. These papers further argue that Nested Clade Phylogeographic Analysis (NCPA) offers the best approach in statistical phylogeography. In order to remove the confusion and misconceptions introduced by these papers, we justify and explain the reasoning behind model-based inference. We argue that ABC is a statistically valid approach, alongside other computational statistical techniques that have been successfully used to infer parameters and compare models in population genetics. We also examine the NCPA method and highlight numerous deficiencies, either when used with single or multiple loci. We further show that the ages of clades are carelessly used to infer ages of demographic events, that these ages are estimated under a simple model of panmixia and population stationarity but are then used under different and unspecified models to test hypotheses, a usage the invalidates these testing procedures. We conclude by encouraging researchers to study and use model-based inference in population genetics. PMID:29284924

Statistical inference for remote sensing-based estimates of net deforestation

Treesearch

Ronald E. McRoberts; Brian F. Walters

2012-01-01

Statistical inference requires expression of an estimate in probabilistic terms, usually in the form of a confidence interval. An approach to constructing confidence intervals for remote sensing-based estimates of net deforestation is illustrated. The approach is based on post-classification methods using two independent forest/non-forest classifications because...

Ecological statistics of Gestalt laws for the perceptual organization of contours.

PubMed

Elder, James H; Goldberg, Richard M

2002-01-01

Although numerous studies have measured the strength of visual grouping cues for controlled psychophysical stimuli, little is known about the statistical utility of these various cues for natural images. In this study, we conducted experiments in which human participants trace perceived contours in natural images. These contours are automatically mapped to sequences of discrete tangent elements detected in the image. By examining relational properties between pairs of successive tangents on these traced curves, and between randomly selected pairs of tangents, we are able to estimate the likelihood distributions required to construct an optimal Bayesian model for contour grouping. We employed this novel methodology to investigate the inferential power of three classical Gestalt cues for contour grouping: proximity, good continuation, and luminance similarity. The study yielded a number of important results: (1) these cues, when appropriately defined, are approximately uncorrelated, suggesting a simple factorial model for statistical inference; (2) moderate image-to-image variation of the statistics indicates the utility of general probabilistic models for perceptual organization; (3) these cues differ greatly in their inferential power, proximity being by far the most powerful; and (4) statistical modeling of the proximity cue indicates a scale-invariant power law in close agreement with prior psychophysics.

Goal-oriented Site Characterization in Hydrogeological Applications: An Overview

NASA Astrophysics Data System (ADS)

Nowak, W.; de Barros, F.; Rubin, Y.

2011-12-01

In this study, we address the importance of goal-oriented site characterization. Given the multiple sources of uncertainty in hydrogeological applications, information needs of modeling, prediction and decision support should be satisfied with efficient and rational field campaigns. In this work, we provide an overview of an optimal sampling design framework based on Bayesian decision theory, statistical parameter inference and Bayesian model averaging. It optimizes the field sampling campaign around decisions on environmental performance metrics (e.g., risk, arrival times, etc.) while accounting for parametric and model uncertainty in the geostatistical characterization, in forcing terms, and measurement error. The appealing aspects of the framework lie on its goal-oriented character and that it is directly linked to the confidence in a specified decision. We illustrate how these concepts could be applied in a human health risk problem where uncertainty from both hydrogeological and health parameters are accounted.

Optimal region of latching activity in an adaptive Potts model for networks of neurons

NASA Astrophysics Data System (ADS)

Abdollah-nia, Mohammad-Farshad; Saeedghalati, Mohammadkarim; Abbassian, Abdolhossein

2012-02-01

In statistical mechanics, the Potts model is a model for interacting spins with more than two discrete states. Neural networks which exhibit features of learning and associative memory can also be modeled by a system of Potts spins. A spontaneous behavior of hopping from one discrete attractor state to another (referred to as latching) has been proposed to be associated with higher cognitive functions. Here we propose a model in which both the stochastic dynamics of Potts models and an adaptive potential function are present. A latching dynamics is observed in a limited region of the noise(temperature)-adaptation parameter space. We hence suggest noise as a fundamental factor in such alternations alongside adaptation. From a dynamical systems point of view, the noise-adaptation alternations may be the underlying mechanism for multi-stability in attractor-based models. An optimality criterion for realistic models is finally inferred.

Minimax Rate-optimal Estimation of High-dimensional Covariance Matrices with Incomplete Data*

PubMed Central

Cai, T. Tony; Zhang, Anru

2016-01-01

Missing data occur frequently in a wide range of applications. In this paper, we consider estimation of high-dimensional covariance matrices in the presence of missing observations under a general missing completely at random model in the sense that the missingness is not dependent on the values of the data. Based on incomplete data, estimators for bandable and sparse covariance matrices are proposed and their theoretical and numerical properties are investigated. Minimax rates of convergence are established under the spectral norm loss and the proposed estimators are shown to be rate-optimal under mild regularity conditions. Simulation studies demonstrate that the estimators perform well numerically. The methods are also illustrated through an application to data from four ovarian cancer studies. The key technical tools developed in this paper are of independent interest and potentially useful for a range of related problems in high-dimensional statistical inference with missing data. PMID:27777471

Minimax Rate-optimal Estimation of High-dimensional Covariance Matrices with Incomplete Data.

PubMed

Cai, T Tony; Zhang, Anru

2016-09-01

Missing data occur frequently in a wide range of applications. In this paper, we consider estimation of high-dimensional covariance matrices in the presence of missing observations under a general missing completely at random model in the sense that the missingness is not dependent on the values of the data. Based on incomplete data, estimators for bandable and sparse covariance matrices are proposed and their theoretical and numerical properties are investigated. Minimax rates of convergence are established under the spectral norm loss and the proposed estimators are shown to be rate-optimal under mild regularity conditions. Simulation studies demonstrate that the estimators perform well numerically. The methods are also illustrated through an application to data from four ovarian cancer studies. The key technical tools developed in this paper are of independent interest and potentially useful for a range of related problems in high-dimensional statistical inference with missing data.

Applications of spatial statistical network models to stream data

USGS Publications Warehouse

Isaak, Daniel J.; Peterson, Erin E.; Ver Hoef, Jay M.; Wenger, Seth J.; Falke, Jeffrey A.; Torgersen, Christian E.; Sowder, Colin; Steel, E. Ashley; Fortin, Marie-Josée; Jordan, Chris E.; Ruesch, Aaron S.; Som, Nicholas; Monestiez, Pascal

2014-01-01

Streams and rivers host a significant portion of Earth's biodiversity and provide important ecosystem services for human populations. Accurate information regarding the status and trends of stream resources is vital for their effective conservation and management. Most statistical techniques applied to data measured on stream networks were developed for terrestrial applications and are not optimized for streams. A new class of spatial statistical model, based on valid covariance structures for stream networks, can be used with many common types of stream data (e.g., water quality attributes, habitat conditions, biological surveys) through application of appropriate distributions (e.g., Gaussian, binomial, Poisson). The spatial statistical network models account for spatial autocorrelation (i.e., nonindependence) among measurements, which allows their application to databases with clustered measurement locations. Large amounts of stream data exist in many areas where spatial statistical analyses could be used to develop novel insights, improve predictions at unsampled sites, and aid in the design of efficient monitoring strategies at relatively low cost. We review the topic of spatial autocorrelation and its effects on statistical inference, demonstrate the use of spatial statistics with stream datasets relevant to common research and management questions, and discuss additional applications and development potential for spatial statistics on stream networks. Free software for implementing the spatial statistical network models has been developed that enables custom applications with many stream databases.

Mechanistic analysis of challenge-response experiments.

PubMed

Shotwell, M S; Drake, K J; Sidorov, V Y; Wikswo, J P

2013-09-01

We present an application of mechanistic modeling and nonlinear longitudinal regression in the context of biomedical response-to-challenge experiments, a field where these methods are underutilized. In this type of experiment, a system is studied by imposing an experimental challenge, and then observing its response. The combination of mechanistic modeling and nonlinear longitudinal regression has brought new insight, and revealed an unexpected opportunity for optimal design. Specifically, the mechanistic aspect of our approach enables the optimal design of experimental challenge characteristics (e.g., intensity, duration). This article lays some groundwork for this approach. We consider a series of experiments wherein an isolated rabbit heart is challenged with intermittent anoxia. The heart responds to the challenge onset, and recovers when the challenge ends. The mean response is modeled by a system of differential equations that describe a candidate mechanism for cardiac response to anoxia challenge. The cardiac system behaves more variably when challenged than when at rest. Hence, observations arising from this experiment exhibit complex heteroscedasticity and sharp changes in central tendency. We present evidence that an asymptotic statistical inference strategy may fail to adequately account for statistical uncertainty. Two alternative methods are critiqued qualitatively (i.e., for utility in the current context), and quantitatively using an innovative Monte-Carlo method. We conclude with a discussion of the exciting opportunities in optimal design of response-to-challenge experiments. © 2013, The International Biometric Society.

Generic comparison of protein inference engines.

PubMed

Claassen, Manfred; Reiter, Lukas; Hengartner, Michael O; Buhmann, Joachim M; Aebersold, Ruedi

2012-04-01

Protein identifications, instead of peptide-spectrum matches, constitute the biologically relevant result of shotgun proteomics studies. How to appropriately infer and report protein identifications has triggered a still ongoing debate. This debate has so far suffered from the lack of appropriate performance measures that allow us to objectively assess protein inference approaches. This study describes an intuitive, generic and yet formal performance measure and demonstrates how it enables experimentalists to select an optimal protein inference strategy for a given collection of fragment ion spectra. We applied the performance measure to systematically explore the benefit of excluding possibly unreliable protein identifications, such as single-hit wonders. Therefore, we defined a family of protein inference engines by extending a simple inference engine by thousands of pruning variants, each excluding a different specified set of possibly unreliable identifications. We benchmarked these protein inference engines on several data sets representing different proteomes and mass spectrometry platforms. Optimally performing inference engines retained all high confidence spectral evidence, without posterior exclusion of any type of protein identifications. Despite the diversity of studied data sets consistently supporting this rule, other data sets might behave differently. In order to ensure maximal reliable proteome coverage for data sets arising in other studies we advocate abstaining from rigid protein inference rules, such as exclusion of single-hit wonders, and instead consider several protein inference approaches and assess these with respect to the presented performance measure in the specific application context.

Brain networks for confidence weighting and hierarchical inference during probabilistic learning.

PubMed

Meyniel, Florent; Dehaene, Stanislas

2017-05-09

Learning is difficult when the world fluctuates randomly and ceaselessly. Classical learning algorithms, such as the delta rule with constant learning rate, are not optimal. Mathematically, the optimal learning rule requires weighting prior knowledge and incoming evidence according to their respective reliabilities. This "confidence weighting" implies the maintenance of an accurate estimate of the reliability of what has been learned. Here, using fMRI and an ideal-observer analysis, we demonstrate that the brain's learning algorithm relies on confidence weighting. While in the fMRI scanner, human adults attempted to learn the transition probabilities underlying an auditory or visual sequence, and reported their confidence in those estimates. They knew that these transition probabilities could change simultaneously at unpredicted moments, and therefore that the learning problem was inherently hierarchical. Subjective confidence reports tightly followed the predictions derived from the ideal observer. In particular, subjects managed to attach distinct levels of confidence to each learned transition probability, as required by Bayes-optimal inference. Distinct brain areas tracked the likelihood of new observations given current predictions, and the confidence in those predictions. Both signals were combined in the right inferior frontal gyrus, where they operated in agreement with the confidence-weighting model. This brain region also presented signatures of a hierarchical process that disentangles distinct sources of uncertainty. Together, our results provide evidence that the sense of confidence is an essential ingredient of probabilistic learning in the human brain, and that the right inferior frontal gyrus hosts a confidence-based statistical learning algorithm for auditory and visual sequences.

Brain networks for confidence weighting and hierarchical inference during probabilistic learning

PubMed Central

Meyniel, Florent; Dehaene, Stanislas

2017-01-01

Learning is difficult when the world fluctuates randomly and ceaselessly. Classical learning algorithms, such as the delta rule with constant learning rate, are not optimal. Mathematically, the optimal learning rule requires weighting prior knowledge and incoming evidence according to their respective reliabilities. This “confidence weighting” implies the maintenance of an accurate estimate of the reliability of what has been learned. Here, using fMRI and an ideal-observer analysis, we demonstrate that the brain’s learning algorithm relies on confidence weighting. While in the fMRI scanner, human adults attempted to learn the transition probabilities underlying an auditory or visual sequence, and reported their confidence in those estimates. They knew that these transition probabilities could change simultaneously at unpredicted moments, and therefore that the learning problem was inherently hierarchical. Subjective confidence reports tightly followed the predictions derived from the ideal observer. In particular, subjects managed to attach distinct levels of confidence to each learned transition probability, as required by Bayes-optimal inference. Distinct brain areas tracked the likelihood of new observations given current predictions, and the confidence in those predictions. Both signals were combined in the right inferior frontal gyrus, where they operated in agreement with the confidence-weighting model. This brain region also presented signatures of a hierarchical process that disentangles distinct sources of uncertainty. Together, our results provide evidence that the sense of confidence is an essential ingredient of probabilistic learning in the human brain, and that the right inferior frontal gyrus hosts a confidence-based statistical learning algorithm for auditory and visual sequences. PMID:28439014

Thermodynamics of statistical inference by cells.

PubMed

Lang, Alex H; Fisher, Charles K; Mora, Thierry; Mehta, Pankaj

2014-10-03

The deep connection between thermodynamics, computation, and information is now well established both theoretically and experimentally. Here, we extend these ideas to show that thermodynamics also places fundamental constraints on statistical estimation and learning. To do so, we investigate the constraints placed by (nonequilibrium) thermodynamics on the ability of biochemical signaling networks to estimate the concentration of an external signal. We show that accuracy is limited by energy consumption, suggesting that there are fundamental thermodynamic constraints on statistical inference.

Multi-objective calibration and uncertainty analysis of hydrologic models; A comparative study between formal and informal methods

NASA Astrophysics Data System (ADS)

Shafii, M.; Tolson, B.; Matott, L. S.

2012-04-01

Hydrologic modeling has benefited from significant developments over the past two decades. This has resulted in building of higher levels of complexity into hydrologic models, which eventually makes the model evaluation process (parameter estimation via calibration and uncertainty analysis) more challenging. In order to avoid unreasonable parameter estimates, many researchers have suggested implementation of multi-criteria calibration schemes. Furthermore, for predictive hydrologic models to be useful, proper consideration of uncertainty is essential. Consequently, recent research has emphasized comprehensive model assessment procedures in which multi-criteria parameter estimation is combined with statistically-based uncertainty analysis routines such as Bayesian inference using Markov Chain Monte Carlo (MCMC) sampling. Such a procedure relies on the use of formal likelihood functions based on statistical assumptions, and moreover, the Bayesian inference structured on MCMC samplers requires a considerably large number of simulations. Due to these issues, especially in complex non-linear hydrological models, a variety of alternative informal approaches have been proposed for uncertainty analysis in the multi-criteria context. This study aims at exploring a number of such informal uncertainty analysis techniques in multi-criteria calibration of hydrological models. The informal methods addressed in this study are (i) Pareto optimality which quantifies the parameter uncertainty using the Pareto solutions, (ii) DDS-AU which uses the weighted sum of objective functions to derive the prediction limits, and (iii) GLUE which describes the total uncertainty through identification of behavioral solutions. The main objective is to compare such methods with MCMC-based Bayesian inference with respect to factors such as computational burden, and predictive capacity, which are evaluated based on multiple comparative measures. The measures for comparison are calculated both for calibration and evaluation periods. The uncertainty analysis methodologies are applied to a simple 5-parameter rainfall-runoff model, called HYMOD.

Optimization of Sinter Plant Operating Conditions Using Advanced Multivariate Statistics: Intelligent Data Processing

NASA Astrophysics Data System (ADS)

Fernández-González, Daniel; Martín-Duarte, Ramón; Ruiz-Bustinza, Íñigo; Mochón, Javier; González-Gasca, Carmen; Verdeja, Luis Felipe

2016-08-01

Blast furnace operators expect to get sinter with homogenous and regular properties (chemical and mechanical), necessary to ensure regular blast furnace operation. Blends for sintering also include several iron by-products and other wastes that are obtained in different processes inside the steelworks. Due to their source, the availability of such materials is not always consistent, but their total production should be consumed in the sintering process, to both save money and recycle wastes. The main scope of this paper is to obtain the least expensive iron ore blend for the sintering process, which will provide suitable chemical and mechanical features for the homogeneous and regular operation of the blast furnace. The systematic use of statistical tools was employed to analyze historical data, including linear and partial correlations applied to the data and fuzzy clustering based on the Sugeno Fuzzy Inference System to establish relationships among the available variables.

Constructing networks with correlation maximization methods.

PubMed

Mellor, Joseph C; Wu, Jie; Delisi, Charles

2004-01-01

Problems of inference in systems biology are ideally reduced to formulations which can efficiently represent the features of interest. In the case of predicting gene regulation and pathway networks, an important feature which describes connected genes and proteins is the relationship between active and inactive forms, i.e. between the "on" and "off" states of the components. While not optimal at the limits of resolution, these logical relationships between discrete states can often yield good approximations of the behavior in larger complex systems, where exact representation of measurement relationships may be intractable. We explore techniques for extracting binary state variables from measurement of gene expression, and go on to describe robust measures for statistical significance and information that can be applied to many such types of data. We show how statistical strength and information are equivalent criteria in limiting cases, and demonstrate the application of these measures to simple systems of gene regulation.

Massive parallelization of serial inference algorithms for a complex generalized linear model

PubMed Central

Suchard, Marc A.; Simpson, Shawn E.; Zorych, Ivan; Ryan, Patrick; Madigan, David

2014-01-01

Following a series of high-profile drug safety disasters in recent years, many countries are redoubling their efforts to ensure the safety of licensed medical products. Large-scale observational databases such as claims databases or electronic health record systems are attracting particular attention in this regard, but present significant methodological and computational concerns. In this paper we show how high-performance statistical computation, including graphics processing units, relatively inexpensive highly parallel computing devices, can enable complex methods in large databases. We focus on optimization and massive parallelization of cyclic coordinate descent approaches to fit a conditioned generalized linear model involving tens of millions of observations and thousands of predictors in a Bayesian context. We find orders-of-magnitude improvement in overall run-time. Coordinate descent approaches are ubiquitous in high-dimensional statistics and the algorithms we propose open up exciting new methodological possibilities with the potential to significantly improve drug safety. PMID:25328363

Proper and Paradigmatic Metonymy as a Lens for Characterizing Student Conceptions of Distributions and Sampling

ERIC Educational Resources Information Center

Noll, Jennifer; Hancock, Stacey

2015-01-01

This research investigates what students' use of statistical language can tell us about their conceptions of distribution and sampling in relation to informal inference. Prior research documents students' challenges in understanding ideas of distribution and sampling as tools for making informal statistical inferences. We know that these…

Multi-Agent Inference in Social Networks: A Finite Population Learning Approach

PubMed Central

Tong, Xin; Zeng, Yao

2016-01-01

When people in a society want to make inference about some parameter, each person may want to use data collected by other people. Information (data) exchange in social networks is usually costly, so to make reliable statistical decisions, people need to trade off the benefits and costs of information acquisition. Conflicts of interests and coordination problems will arise in the process. Classical statistics does not consider people’s incentives and interactions in the data collection process. To address this imperfection, this work explores multi-agent Bayesian inference problems with a game theoretic social network model. Motivated by our interest in aggregate inference at the societal level, we propose a new concept, finite population learning, to address whether with high probability, a large fraction of people in a given finite population network can make “good” inference. Serving as a foundation, this concept enables us to study the long run trend of aggregate inference quality as population grows. PMID:27076691

Robust inference from multiple test statistics via permutations: a better alternative to the single test statistic approach for randomized trials.

PubMed

Ganju, Jitendra; Yu, Xinxin; Ma, Guoguang Julie

2013-01-01

Formal inference in randomized clinical trials is based on controlling the type I error rate associated with a single pre-specified statistic. The deficiency of using just one method of analysis is that it depends on assumptions that may not be met. For robust inference, we propose pre-specifying multiple test statistics and relying on the minimum p-value for testing the null hypothesis of no treatment effect. The null hypothesis associated with the various test statistics is that the treatment groups are indistinguishable. The critical value for hypothesis testing comes from permutation distributions. Rejection of the null hypothesis when the smallest p-value is less than the critical value controls the type I error rate at its designated value. Even if one of the candidate test statistics has low power, the adverse effect on the power of the minimum p-value statistic is not much. Its use is illustrated with examples. We conclude that it is better to rely on the minimum p-value rather than a single statistic particularly when that single statistic is the logrank test, because of the cost and complexity of many survival trials. Copyright © 2013 John Wiley & Sons, Ltd.

Ensemble stacking mitigates biases in inference of synaptic connectivity.

PubMed

Chambers, Brendan; Levy, Maayan; Dechery, Joseph B; MacLean, Jason N

2018-01-01

A promising alternative to directly measuring the anatomical connections in a neuronal population is inferring the connections from the activity. We employ simulated spiking neuronal networks to compare and contrast commonly used inference methods that identify likely excitatory synaptic connections using statistical regularities in spike timing. We find that simple adjustments to standard algorithms improve inference accuracy: A signing procedure improves the power of unsigned mutual-information-based approaches and a correction that accounts for differences in mean and variance of background timing relationships, such as those expected to be induced by heterogeneous firing rates, increases the sensitivity of frequency-based methods. We also find that different inference methods reveal distinct subsets of the synaptic network and each method exhibits different biases in the accurate detection of reciprocity and local clustering. To correct for errors and biases specific to single inference algorithms, we combine methods into an ensemble. Ensemble predictions, generated as a linear combination of multiple inference algorithms, are more sensitive than the best individual measures alone, and are more faithful to ground-truth statistics of connectivity, mitigating biases specific to single inference methods. These weightings generalize across simulated datasets, emphasizing the potential for the broad utility of ensemble-based approaches.

Performance Optimization Control of ECH using Fuzzy Inference Application

NASA Astrophysics Data System (ADS)

Dubey, Abhay Kumar

Electro-chemical honing (ECH) is a hybrid electrolytic precision micro-finishing technology that, by combining physico-chemical actions of electro-chemical machining and conventional honing processes, provides the controlled functional surfaces-generation and fast material removal capabilities in a single operation. Process multi-performance optimization has become vital for utilizing full potential of manufacturing processes to meet the challenging requirements being placed on the surface quality, size, tolerances and production rate of engineering components in this globally competitive scenario. This paper presents an strategy that integrates the Taguchi matrix experimental design, analysis of variances and fuzzy inference system (FIS) to formulate a robust practical multi-performance optimization methodology for complex manufacturing processes like ECH, which involve several control variables. Two methodologies one using a genetic algorithm tuning of FIS (GA-tuned FIS) and another using an adaptive network based fuzzy inference system (ANFIS) have been evaluated for a multi-performance optimization case study of ECH. The actual experimental results confirm their potential for a wide range of machining conditions employed in ECH.

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.

Image-Data Compression Using Edge-Optimizing Algorithm for WFA Inference.

ERIC Educational Resources Information Center

Culik, Karel II; Kari, Jarkko

1994-01-01

Presents an inference algorithm that produces a weighted finite automata (WFA), in particular, the grayness functions of graytone images. Image-data compression results based on the new inference algorithm produces a WFA with a relatively small number of edges. Image-data compression results alone and in combination with wavelets are discussed.…

Potential sources of variability in mesocosm experiments on the response of phytoplankton to ocean acidification

NASA Astrophysics Data System (ADS)

Moreno de Castro, Maria; Schartau, Markus; Wirtz, Kai

2017-04-01

Mesocosm experiments on phytoplankton dynamics under high CO2 concentrations mimic the response of marine primary producers to future ocean acidification. However, potential acidification effects can be hindered by the high standard deviation typically found in the replicates of the same CO2 treatment level. In experiments with multiple unresolved factors and a sub-optimal number of replicates, post-processing statistical inference tools might fail to detect an effect that is present. We propose that in such cases, data-based model analyses might be suitable tools to unearth potential responses to the treatment and identify the uncertainties that could produce the observed variability. As test cases, we used data from two independent mesocosm experiments. Both experiments showed high standard deviations and, according to statistical inference tools, biomass appeared insensitive to changing CO2 conditions. Conversely, our simulations showed earlier and more intense phytoplankton blooms in modeled replicates at high CO2 concentrations and suggested that uncertainties in average cell size, phytoplankton biomass losses, and initial nutrient concentration potentially outweigh acidification effects by triggering strong variability during the bloom phase. We also estimated the thresholds below which uncertainties do not escalate to high variability. This information might help in designing future mesocosm experiments and interpreting controversial results on the effect of acidification or other pressures on ecosystem functions.

Basics of Bayesian methods.

PubMed

Ghosh, Sujit K

2010-01-01

Bayesian methods are rapidly becoming popular tools for making statistical inference in various fields of science including biology, engineering, finance, and genetics. One of the key aspects of Bayesian inferential method is its logical foundation that provides a coherent framework to utilize not only empirical but also scientific information available to a researcher. Prior knowledge arising from scientific background, expert judgment, or previously collected data is used to build a prior distribution which is then combined with current data via the likelihood function to characterize the current state of knowledge using the so-called posterior distribution. Bayesian methods allow the use of models of complex physical phenomena that were previously too difficult to estimate (e.g., using asymptotic approximations). Bayesian methods offer a means of more fully understanding issues that are central to many practical problems by allowing researchers to build integrated models based on hierarchical conditional distributions that can be estimated even with limited amounts of data. Furthermore, advances in numerical integration methods, particularly those based on Monte Carlo methods, have made it possible to compute the optimal Bayes estimators. However, there is a reasonably wide gap between the background of the empirically trained scientists and the full weight of Bayesian statistical inference. Hence, one of the goals of this chapter is to bridge the gap by offering elementary to advanced concepts that emphasize linkages between standard approaches and full probability modeling via Bayesian methods.

Research participant compensation: A matter of statistical inference as well as ethics.

PubMed

Swanson, David M; Betensky, Rebecca A

2015-11-01

The ethics of compensation of research subjects for participation in clinical trials has been debated for years. One ethical issue of concern is variation among subjects in the level of compensation for identical treatments. Surprisingly, the impact of variation on the statistical inferences made from trial results has not been examined. We seek to identify how variation in compensation may influence any existing dependent censoring in clinical trials, thereby also influencing inference about the survival curve, hazard ratio, or other measures of treatment efficacy. In simulation studies, we consider a model for how compensation structure may influence the censoring model. Under existing dependent censoring, we estimate survival curves under different compensation structures and observe how these structures induce variability in the estimates. We show through this model that if the compensation structure affects the censoring model and dependent censoring is present, then variation in that structure induces variation in the estimates and affects the accuracy of estimation and inference on treatment efficacy. From the perspectives of both ethics and statistical inference, standardization and transparency in the compensation of participants in clinical trials are warranted. Copyright © 2015 Elsevier Inc. All rights reserved.

Pre-Service Mathematics Teachers' Use of Probability Models in Making Informal Inferences about a Chance Game

ERIC Educational Resources Information Center

Kazak, Sibel; Pratt, Dave

2017-01-01

This study considers probability models as tools for both making informal statistical inferences and building stronger conceptual connections between data and chance topics in teaching statistics. In this paper, we aim to explore pre-service mathematics teachers' use of probability models for a chance game, where the sum of two dice matters in…

Phylogeography Takes a Relaxed Random Walk in Continuous Space and Time

PubMed Central

Lemey, Philippe; Rambaut, Andrew; Welch, John J.; Suchard, Marc A.

2010-01-01

Research aimed at understanding the geographic context of evolutionary histories is burgeoning across biological disciplines. Recent endeavors attempt to interpret contemporaneous genetic variation in the light of increasingly detailed geographical and environmental observations. Such interest has promoted the development of phylogeographic inference techniques that explicitly aim to integrate such heterogeneous data. One promising development involves reconstructing phylogeographic history on a continuous landscape. Here, we present a Bayesian statistical approach to infer continuous phylogeographic diffusion using random walk models while simultaneously reconstructing the evolutionary history in time from molecular sequence data. Moreover, by accommodating branch-specific variation in dispersal rates, we relax the most restrictive assumption of the standard Brownian diffusion process and demonstrate increased statistical efficiency in spatial reconstructions of overdispersed random walks by analyzing both simulated and real viral genetic data. We further illustrate how drawing inference about summary statistics from a fully specified stochastic process over both sequence evolution and spatial movement reveals important characteristics of a rabies epidemic. Together with recent advances in discrete phylogeographic inference, the continuous model developments furnish a flexible statistical framework for biogeographical reconstructions that is easily expanded upon to accommodate various landscape genetic features. PMID:20203288

Variation in reaction norms: Statistical considerations and biological interpretation.

PubMed

Morrissey, Michael B; Liefting, Maartje

2016-09-01

Analysis of reaction norms, the functions by which the phenotype produced by a given genotype depends on the environment, is critical to studying many aspects of phenotypic evolution. Different techniques are available for quantifying different aspects of reaction norm variation. We examine what biological inferences can be drawn from some of the more readily applicable analyses for studying reaction norms. We adopt a strongly biologically motivated view, but draw on statistical theory to highlight strengths and drawbacks of different techniques. In particular, consideration of some formal statistical theory leads to revision of some recently, and forcefully, advocated opinions on reaction norm analysis. We clarify what simple analysis of the slope between mean phenotype in two environments can tell us about reaction norms, explore the conditions under which polynomial regression can provide robust inferences about reaction norm shape, and explore how different existing approaches may be used to draw inferences about variation in reaction norm shape. We show how mixed model-based approaches can provide more robust inferences than more commonly used multistep statistical approaches, and derive new metrics of the relative importance of variation in reaction norm intercepts, slopes, and curvatures. © 2016 The Author(s). Evolution © 2016 The Society for the Study of Evolution.

Connectivity-based fixel enhancement: Whole-brain statistical analysis of diffusion MRI measures in the presence of crossing fibres

PubMed Central

Raffelt, David A.; Smith, Robert E.; Ridgway, Gerard R.; Tournier, J-Donald; Vaughan, David N.; Rose, Stephen; Henderson, Robert; Connelly, Alan

2015-01-01

In brain regions containing crossing fibre bundles, voxel-average diffusion MRI measures such as fractional anisotropy (FA) are difficult to interpret, and lack within-voxel single fibre population specificity. Recent work has focused on the development of more interpretable quantitative measures that can be associated with a specific fibre population within a voxel containing crossing fibres (herein we use fixel to refer to a specific fibre population within a single voxel). Unfortunately, traditional 3D methods for smoothing and cluster-based statistical inference cannot be used for voxel-based analysis of these measures, since the local neighbourhood for smoothing and cluster formation can be ambiguous when adjacent voxels may have different numbers of fixels, or ill-defined when they belong to different tracts. Here we introduce a novel statistical method to perform whole-brain fixel-based analysis called connectivity-based fixel enhancement (CFE). CFE uses probabilistic tractography to identify structurally connected fixels that are likely to share underlying anatomy and pathology. Probabilistic connectivity information is then used for tract-specific smoothing (prior to the statistical analysis) and enhancement of the statistical map (using a threshold-free cluster enhancement-like approach). To investigate the characteristics of the CFE method, we assessed sensitivity and specificity using a large number of combinations of CFE enhancement parameters and smoothing extents, using simulated pathology generated with a range of test-statistic signal-to-noise ratios in five different white matter regions (chosen to cover a broad range of fibre bundle features). The results suggest that CFE input parameters are relatively insensitive to the characteristics of the simulated pathology. We therefore recommend a single set of CFE parameters that should give near optimal results in future studies where the group effect is unknown. We then demonstrate the proposed method by comparing apparent fibre density between motor neurone disease (MND) patients with control subjects. The MND results illustrate the benefit of fixel-specific statistical inference in white matter regions that contain crossing fibres. PMID:26004503

Inference of the sparse kinetic Ising model using the decimation method

NASA Astrophysics Data System (ADS)

Decelle, Aurélien; Zhang, Pan

2015-05-01

In this paper we study the inference of the kinetic Ising model on sparse graphs by the decimation method. The decimation method, which was first proposed in Decelle and Ricci-Tersenghi [Phys. Rev. Lett. 112, 070603 (2014), 10.1103/PhysRevLett.112.070603] for the static inverse Ising problem, tries to recover the topology of the inferred system by setting the weakest couplings to zero iteratively. During the decimation process the likelihood function is maximized over the remaining couplings. Unlike the ℓ1-optimization-based methods, the decimation method does not use the Laplace distribution as a heuristic choice of prior to select a sparse solution. In our case, the whole process can be done auto-matically without fixing any parameters by hand. We show that in the dynamical inference problem, where the task is to reconstruct the couplings of an Ising model given the data, the decimation process can be applied naturally into a maximum-likelihood optimization algorithm, as opposed to the static case where pseudolikelihood method needs to be adopted. We also use extensive numerical studies to validate the accuracy of our methods in dynamical inference problems. Our results illustrate that, on various topologies and with different distribution of couplings, the decimation method outperforms the widely used ℓ1-optimization-based methods.

Model averaging, optimal inference, and habit formation

PubMed Central

FitzGerald, Thomas H. B.; Dolan, Raymond J.; Friston, Karl J.

2014-01-01

Postulating that the brain performs approximate Bayesian inference generates principled and empirically testable models of neuronal function—the subject of much current interest in neuroscience and related disciplines. Current formulations address inference and learning under some assumed and particular model. In reality, organisms are often faced with an additional challenge—that of determining which model or models of their environment are the best for guiding behavior. Bayesian model averaging—which says that an agent should weight the predictions of different models according to their evidence—provides a principled way to solve this problem. Importantly, because model evidence is determined by both the accuracy and complexity of the model, optimal inference requires that these be traded off against one another. This means an agent's behavior should show an equivalent balance. We hypothesize that Bayesian model averaging plays an important role in cognition, given that it is both optimal and realizable within a plausible neuronal architecture. We outline model averaging and how it might be implemented, and then explore a number of implications for brain and behavior. In particular, we propose that model averaging can explain a number of apparently suboptimal phenomena within the framework of approximate (bounded) Bayesian inference, focusing particularly upon the relationship between goal-directed and habitual behavior. PMID:25018724

The Role of Probability-Based Inference in an Intelligent Tutoring System.

ERIC Educational Resources Information Center

Mislevy, Robert J.; Gitomer, Drew H.

Probability-based inference in complex networks of interdependent variables is an active topic in statistical research, spurred by such diverse applications as forecasting, pedigree analysis, troubleshooting, and medical diagnosis. This paper concerns the role of Bayesian inference networks for updating student models in intelligent tutoring…

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.

An inferentialist perspective on the coordination of actions and reasons involved in making a statistical inference

NASA Astrophysics Data System (ADS)

Bakker, Arthur; Ben-Zvi, Dani; Makar, Katie

2017-12-01

To understand how statistical and other types of reasoning are coordinated with actions to reduce uncertainty, we conducted a case study in vocational education that involved statistical hypothesis testing. We analyzed an intern's research project in a hospital laboratory in which reducing uncertainties was crucial to make a valid statistical inference. In his project, the intern, Sam, investigated whether patients' blood could be sent through pneumatic post without influencing the measurement of particular blood components. We asked, in the process of making a statistical inference, how are reasons and actions coordinated to reduce uncertainty? For the analysis, we used the semantic theory of inferentialism, specifically, the concept of webs of reasons and actions—complexes of interconnected reasons for facts and actions; these reasons include premises and conclusions, inferential relations, implications, motives for action, and utility of tools for specific purposes in a particular context. Analysis of interviews with Sam, his supervisor and teacher as well as video data of Sam in the classroom showed that many of Sam's actions aimed to reduce variability, rule out errors, and thus reduce uncertainties so as to arrive at a valid inference. Interestingly, the decisive factor was not the outcome of a t test but of the reference change value, a clinical chemical measure of analytic and biological variability. With insights from this case study, we expect that students can be better supported in connecting statistics with context and in dealing with uncertainty.

Statistical Inference on Optimal Points to Evaluate Multi-State Classification Systems

DTIC Science & Technology

2014-09-18

vs2+ ( dbcm3 ˆ 2 ) *vm3+( dbcs3 ˆ 2 ) * vs3 80 VETA <−VBCA+VBC EETA<−EBCA−EBC 82 W<− (EETA−TV) / s q r t ( VETA ) # T e s t p−v a l u e − t o compare t o a...event set, E = (ε1, ε2, ..., εk) to k distinct elements of a label set, L = (l1, l2, ..., lk) . These partitions may be referred to as classes. For...set of features, F = ( f1, f2, ..., fm) . These features are then used to assign the different elements from E to the respective labels, L , (A : E → F

Optimal Contrast: Competition between Two Referents Improves Word Learning

ERIC Educational Resources Information Center

Zosh, Jennifer M.; Brinster, Meredith; Halberda, Justin

2013-01-01

Does making an inference lead to better learning than being instructed directly? Two experiments evaluated preschoolers' ability to learn new words, comparing their memory for words learned via inference or instruction. On Inference trials, one familiar and one novel object was presented and children were asked to "Point at the [object name (i.e.,…

PyClone: statistical inference of clonal population structure in cancer.

PubMed

Roth, Andrew; Khattra, Jaswinder; Yap, Damian; Wan, Adrian; Laks, Emma; Biele, Justina; Ha, Gavin; Aparicio, Samuel; Bouchard-Côté, Alexandre; Shah, Sohrab P

2014-04-01

We introduce PyClone, a statistical model for inference of clonal population structures in cancers. PyClone is a Bayesian clustering method for grouping sets of deeply sequenced somatic mutations into putative clonal clusters while estimating their cellular prevalences and accounting for allelic imbalances introduced by segmental copy-number changes and normal-cell contamination. Single-cell sequencing validation demonstrates PyClone's accuracy.

Statistical Signal Models and Algorithms for Image Analysis

DTIC Science & Technology

1984-10-25

In this report, two-dimensional stochastic linear models are used in developing algorithms for image analysis such as classification, segmentation, and object detection in images characterized by textured backgrounds. These models generate two-dimensional random processes as outputs to which statistical inference procedures can naturally be applied. A common thread throughout our algorithms is the interpretation of the inference procedures in terms of linear prediction

P values are only an index to evidence: 20th- vs. 21st-century statistical science.

PubMed

Burnham, K P; Anderson, D R

2014-03-01

Early statistical methods focused on pre-data probability statements (i.e., data as random variables) such as P values; these are not really inferences nor are P values evidential. Statistical science clung to these principles throughout much of the 20th century as a wide variety of methods were developed for special cases. Looking back, it is clear that the underlying paradigm (i.e., testing and P values) was weak. As Kuhn (1970) suggests, new paradigms have taken the place of earlier ones: this is a goal of good science. New methods have been developed and older methods extended and these allow proper measures of strength of evidence and multimodel inference. It is time to move forward with sound theory and practice for the difficult practical problems that lie ahead. Given data the useful foundation shifts to post-data probability statements such as model probabilities (Akaike weights) or related quantities such as odds ratios and likelihood intervals. These new methods allow formal inference from multiple models in the a prior set. These quantities are properly evidential. The past century was aimed at finding the "best" model and making inferences from it. The goal in the 21st century is to base inference on all the models weighted by their model probabilities (model averaging). Estimates of precision can include model selection uncertainty leading to variances conditional on the model set. The 21st century will be about the quantification of information, proper measures of evidence, and multi-model inference. Nelder (1999:261) concludes, "The most important task before us in developing statistical science is to demolish the P-value culture, which has taken root to a frightening extent in many areas of both pure and applied science and technology".

Statistical inference of the generation probability of T-cell receptors from sequence repertoires.

PubMed

Murugan, Anand; Mora, Thierry; Walczak, Aleksandra M; Callan, Curtis G

2012-10-02

Stochastic rearrangement of germline V-, D-, and J-genes to create variable coding sequence for certain cell surface receptors is at the origin of immune system diversity. This process, known as "VDJ recombination", is implemented via a series of stochastic molecular events involving gene choices and random nucleotide insertions between, and deletions from, genes. We use large sequence repertoires of the variable CDR3 region of human CD4+ T-cell receptor beta chains to infer the statistical properties of these basic biochemical events. Because any given CDR3 sequence can be produced in multiple ways, the probability distribution of hidden recombination events cannot be inferred directly from the observed sequences; we therefore develop a maximum likelihood inference method to achieve this end. To separate the properties of the molecular rearrangement mechanism from the effects of selection, we focus on nonproductive CDR3 sequences in T-cell DNA. We infer the joint distribution of the various generative events that occur when a new T-cell receptor gene is created. We find a rich picture of correlation (and absence thereof), providing insight into the molecular mechanisms involved. The generative event statistics are consistent between individuals, suggesting a universal biochemical process. Our probabilistic model predicts the generation probability of any specific CDR3 sequence by the primitive recombination process, allowing us to quantify the potential diversity of the T-cell repertoire and to understand why some sequences are shared between individuals. We argue that the use of formal statistical inference methods, of the kind presented in this paper, will be essential for quantitative understanding of the generation and evolution of diversity in the adaptive immune system.

Load Balancing Using Time Series Analysis for Soft Real Time Systems with Statistically Periodic Loads

NASA Technical Reports Server (NTRS)

Hailperin, M.

1993-01-01

This thesis provides design and analysis of techniques for global load balancing on ensemble architectures running soft-real-time object-oriented applications with statistically periodic loads. It focuses on estimating the instantaneous average load over all the processing elements. The major contribution is the use of explicit stochastic process models for both the loading and the averaging itself. These models are exploited via statistical time-series analysis and Bayesian inference to provide improved average load estimates, and thus to facilitate global load balancing. This thesis explains the distributed algorithms used and provides some optimality results. It also describes the algorithms' implementation and gives performance results from simulation. These results show that the authors' techniques allow more accurate estimation of the global system loading, resulting in fewer object migrations than local methods. The authors' method is shown to provide superior performance, relative not only to static load-balancing schemes but also to many adaptive load-balancing methods. Results from a preliminary analysis of another system and from simulation with a synthetic load provide some evidence of more general applicability.

Statistical Inference and Reverse Engineering of Gene Regulatory Networks from Observational Expression Data

PubMed Central

Emmert-Streib, Frank; Glazko, Galina V.; Altay, Gökmen; de Matos Simoes, Ricardo

2012-01-01

In this paper, we present a systematic and conceptual overview of methods for inferring gene regulatory networks from observational gene expression data. Further, we discuss two classic approaches to infer causal structures and compare them with contemporary methods by providing a conceptual categorization thereof. We complement the above by surveying global and local evaluation measures for assessing the performance of inference algorithms. PMID:22408642

Inferring Master Painters' Esthetic Biases from the Statistics of Portraits

PubMed Central

Aleem, Hassan; Correa-Herran, Ivan; Grzywacz, Norberto M.

2017-01-01

The Processing Fluency Theory posits that the ease of sensory information processing in the brain facilitates esthetic pleasure. Accordingly, the theory would predict that master painters should display biases toward visual properties such as symmetry, balance, and moderate complexity. Have these biases been occurring and if so, have painters been optimizing these properties (fluency variables)? Here, we address these questions with statistics of portrait paintings from the Early Renaissance period. To do this, we first developed different computational measures for each of the aforementioned fluency variables. Then, we measured their statistics in 153 portraits from 26 master painters, in 27 photographs of people in three controlled poses, and in 38 quickly snapped photographs of individual persons. A statistical comparison between Early Renaissance portraits and quickly snapped photographs revealed that painters showed a bias toward balance, symmetry, and moderate complexity. However, a comparison between portraits and controlled-pose photographs showed that painters did not optimize each of these properties. Instead, different painters presented biases toward different, narrow ranges of fluency variables. Further analysis suggested that the painters' individuality stemmed in part from having to resolve the tension between complexity vs. symmetry and balance. We additionally found that constraints on the use of different painting materials by distinct painters modulated these fluency variables systematically. In conclusion, the Processing Fluency Theory of Esthetic Pleasure would need expansion if we were to apply it to the history of visual art since it cannot explain the lack of optimization of each fluency variables. To expand the theory, we propose the existence of a Neuroesthetic Space, which encompasses the possible values that each of the fluency variables can reach in any given art period. We discuss the neural mechanisms of this Space and propose that it has a distributed representation in the human brain. We further propose that different artists reside in different, small sub-regions of the Space. This Neuroesthetic-Space hypothesis raises the question of how painters and their paintings evolve across art periods. PMID:28337133

Information Entropy Production of Maximum Entropy Markov Chains from Spike Trains

NASA Astrophysics Data System (ADS)

Cofré, Rodrigo; Maldonado, Cesar

2018-01-01

We consider the maximum entropy Markov chain inference approach to characterize the collective statistics of neuronal spike trains, focusing on the statistical properties of the inferred model. We review large deviations techniques useful in this context to describe properties of accuracy and convergence in terms of sampling size. We use these results to study the statistical fluctuation of correlations, distinguishability and irreversibility of maximum entropy Markov chains. We illustrate these applications using simple examples where the large deviation rate function is explicitly obtained for maximum entropy models of relevance in this field.

Efficient probabilistic inference in generic neural networks trained with non-probabilistic feedback.

PubMed

Orhan, A Emin; Ma, Wei Ji

2017-07-26

Animals perform near-optimal probabilistic inference in a wide range of psychophysical tasks. Probabilistic inference requires trial-to-trial representation of the uncertainties associated with task variables and subsequent use of this representation. Previous work has implemented such computations using neural networks with hand-crafted and task-dependent operations. We show that generic neural networks trained with a simple error-based learning rule perform near-optimal probabilistic inference in nine common psychophysical tasks. In a probabilistic categorization task, error-based learning in a generic network simultaneously explains a monkey's learning curve and the evolution of qualitative aspects of its choice behavior. In all tasks, the number of neurons required for a given level of performance grows sublinearly with the input population size, a substantial improvement on previous implementations of probabilistic inference. The trained networks develop a novel sparsity-based probabilistic population code. Our results suggest that probabilistic inference emerges naturally in generic neural networks trained with error-based learning rules.Behavioural tasks often require probability distributions to be inferred about task specific variables. Here, the authors demonstrate that generic neural networks can be trained using a simple error-based learning rule to perform such probabilistic computations efficiently without any need for task specific operations.

The Probabilistic Structure of Quantum Theory as Originating from Optimal Observation in the Face of the Observer's Lack of Knowledge of his Own State

NASA Astrophysics Data System (ADS)

Aerts, Sven

2014-03-01

One of the problems facing any attempt to understand quantum theory is that the theory does not seem to offer an explanation of the way the probabilities arise. Moreover, it is a commonly held view that no such explanation is compatible with the mathematical structure of quantum theory, i.e. that the theory is inherently indeterministic, simply because nature is like that. We propose an abstract formalisation of the observation of a system in which the interaction between the system and the observer deterministically produces one of n possible outcomes. If the observer consistently manages to realize the outcome which maximizes the likelihood ratio that the outcome was inferred from the state of the system under study (and not from his own state), he will be called optimal. The probability for a repeated measurement on an ensemble of identical system states, is then derived as a measure over observer states. If the state of the system is a statistical mixture, the optimal observer produces an unbiased estimate of the components of the mixture. In case the state space is a complex Hilbert space, the resulting probability is equal to the one given by the Born rule. The proposal offers a concise interpretation for the meaning of the occurrence of a specific outcome as the unique outcome that, relative to the state of the system, is least dependent on the state of the observer. We note that a similar paradigm is used in the literature of perception to explain optical illusions in human visual perception. We argue that the result strengthens Helmholtz's view that all observation, is in fact a form a inference.

Statistical inference based on the nonparametric maximum likelihood estimator under double-truncation.

PubMed

Emura, Takeshi; Konno, Yoshihiko; Michimae, Hirofumi

2015-07-01

Doubly truncated data consist of samples whose observed values fall between the right- and left- truncation limits. With such samples, the distribution function of interest is estimated using the nonparametric maximum likelihood estimator (NPMLE) that is obtained through a self-consistency algorithm. Owing to the complicated asymptotic distribution of the NPMLE, the bootstrap method has been suggested for statistical inference. This paper proposes a closed-form estimator for the asymptotic covariance function of the NPMLE, which is computationally attractive alternative to bootstrapping. Furthermore, we develop various statistical inference procedures, such as confidence interval, goodness-of-fit tests, and confidence bands to demonstrate the usefulness of the proposed covariance estimator. Simulations are performed to compare the proposed method with both the bootstrap and jackknife methods. The methods are illustrated using the childhood cancer dataset.

Structured statistical models of inductive reasoning.

PubMed

Kemp, Charles; Tenenbaum, Joshua B

2009-01-01

Everyday inductive inferences are often guided by rich background knowledge. Formal models of induction should aim to incorporate this knowledge and should explain how different kinds of knowledge lead to the distinctive patterns of reasoning found in different inductive contexts. This article presents a Bayesian framework that attempts to meet both goals and describes [corrected] 4 applications of the framework: a taxonomic model, a spatial model, a threshold model, and a causal model. Each model makes probabilistic inferences about the extensions of novel properties, but the priors for the 4 models are defined over different kinds of structures that capture different relationships between the categories in a domain. The framework therefore shows how statistical inference can operate over structured background knowledge, and the authors argue that this interaction between structure and statistics is critical for explaining the power and flexibility of human reasoning.

Inference on network statistics by restricting to the network space: applications to sexual history data.

PubMed

Goyal, Ravi; De Gruttola, Victor

2018-01-30

Analysis of sexual history data intended to describe sexual networks presents many challenges arising from the fact that most surveys collect information on only a very small fraction of the population of interest. In addition, partners are rarely identified and responses are subject to reporting biases. Typically, each network statistic of interest, such as mean number of sexual partners for men or women, is estimated independently of other network statistics. There is, however, a complex relationship among networks statistics; and knowledge of these relationships can aid in addressing concerns mentioned earlier. We develop a novel method that constrains a posterior predictive distribution of a collection of network statistics in order to leverage the relationships among network statistics in making inference about network properties of interest. The method ensures that inference on network properties is compatible with an actual network. Through extensive simulation studies, we also demonstrate that use of this method can improve estimates in settings where there is uncertainty that arises both from sampling and from systematic reporting bias compared with currently available approaches to estimation. To illustrate the method, we apply it to estimate network statistics using data from the Chicago Health and Social Life Survey. Copyright © 2017 John Wiley & Sons, Ltd. Copyright © 2017 John Wiley & Sons, Ltd.

Statistical comparison of a hybrid approach with approximate and exact inference models for Fusion 2+

NASA Astrophysics Data System (ADS)

Lee, K. David; Wiesenfeld, Eric; Gelfand, Andrew

2007-04-01

One of the greatest challenges in modern combat is maintaining a high level of timely Situational Awareness (SA). In many situations, computational complexity and accuracy considerations make the development and deployment of real-time, high-level inference tools very difficult. An innovative hybrid framework that combines Bayesian inference, in the form of Bayesian Networks, and Possibility Theory, in the form of Fuzzy Logic systems, has recently been introduced to provide a rigorous framework for high-level inference. In previous research, the theoretical basis and benefits of the hybrid approach have been developed. However, lacking is a concrete experimental comparison of the hybrid framework with traditional fusion methods, to demonstrate and quantify this benefit. The goal of this research, therefore, is to provide a statistical analysis on the comparison of the accuracy and performance of hybrid network theory, with pure Bayesian and Fuzzy systems and an inexact Bayesian system approximated using Particle Filtering. To accomplish this task, domain specific models will be developed under these different theoretical approaches and then evaluated, via Monte Carlo Simulation, in comparison to situational ground truth to measure accuracy and fidelity. Following this, a rigorous statistical analysis of the performance results will be performed, to quantify the benefit of hybrid inference to other fusion tools.

MORE: mixed optimization for reverse engineering--an application to modeling biological networks response via sparse systems of nonlinear differential equations.

PubMed

Sambo, Francesco; de Oca, Marco A Montes; Di Camillo, Barbara; Toffolo, Gianna; Stützle, Thomas

2012-01-01

Reverse engineering is the problem of inferring the structure of a network of interactions between biological variables from a set of observations. In this paper, we propose an optimization algorithm, called MORE, for the reverse engineering of biological networks from time series data. The model inferred by MORE is a sparse system of nonlinear differential equations, complex enough to realistically describe the dynamics of a biological system. MORE tackles separately the discrete component of the problem, the determination of the biological network topology, and the continuous component of the problem, the strength of the interactions. This approach allows us both to enforce system sparsity, by globally constraining the number of edges, and to integrate a priori information about the structure of the underlying interaction network. Experimental results on simulated and real-world networks show that the mixed discrete/continuous optimization approach of MORE significantly outperforms standard continuous optimization and that MORE is competitive with the state of the art in terms of accuracy of the inferred networks.

Estimation of parameter uncertainty for an activated sludge model using Bayesian inference: a comparison with the frequentist method.

PubMed

Zonta, Zivko J; Flotats, Xavier; Magrí, Albert

2014-08-01

The procedure commonly used for the assessment of the parameters included in activated sludge models (ASMs) relies on the estimation of their optimal value within a confidence region (i.e. frequentist inference). Once optimal values are estimated, parameter uncertainty is computed through the covariance matrix. However, alternative approaches based on the consideration of the model parameters as probability distributions (i.e. Bayesian inference), may be of interest. The aim of this work is to apply (and compare) both Bayesian and frequentist inference methods when assessing uncertainty for an ASM-type model, which considers intracellular storage and biomass growth, simultaneously. Practical identifiability was addressed exclusively considering respirometric profiles based on the oxygen uptake rate and with the aid of probabilistic global sensitivity analysis. Parameter uncertainty was thus estimated according to both the Bayesian and frequentist inferential procedures. Results were compared in order to evidence the strengths and weaknesses of both approaches. Since it was demonstrated that Bayesian inference could be reduced to a frequentist approach under particular hypotheses, the former can be considered as a more generalist methodology. Hence, the use of Bayesian inference is encouraged for tackling inferential issues in ASM environments.

On the analysis of very small samples of Gaussian repeated measurements: an alternative approach.

PubMed

Westgate, Philip M; Burchett, Woodrow W

2017-03-15

The analysis of very small samples of Gaussian repeated measurements can be challenging. First, due to a very small number of independent subjects contributing outcomes over time, statistical power can be quite small. Second, nuisance covariance parameters must be appropriately accounted for in the analysis in order to maintain the nominal test size. However, available statistical strategies that ensure valid statistical inference may lack power, whereas more powerful methods may have the potential for inflated test sizes. Therefore, we explore an alternative approach to the analysis of very small samples of Gaussian repeated measurements, with the goal of maintaining valid inference while also improving statistical power relative to other valid methods. This approach uses generalized estimating equations with a bias-corrected empirical covariance matrix that accounts for all small-sample aspects of nuisance correlation parameter estimation in order to maintain valid inference. Furthermore, the approach utilizes correlation selection strategies with the goal of choosing the working structure that will result in the greatest power. In our study, we show that when accurate modeling of the nuisance correlation structure impacts the efficiency of regression parameter estimation, this method can improve power relative to existing methods that yield valid inference. Copyright © 2017 John Wiley & Sons, Ltd. Copyright © 2017 John Wiley & Sons, Ltd.

Statistical inference for noisy nonlinear ecological dynamic systems.

PubMed

Wood, Simon N

2010-08-26

Chaotic ecological dynamic systems defy conventional statistical analysis. Systems with near-chaotic dynamics are little better. Such systems are almost invariably driven by endogenous dynamic processes plus demographic and environmental process noise, and are only observable with error. Their sensitivity to history means that minute changes in the driving noise realization, or the system parameters, will cause drastic changes in the system trajectory. This sensitivity is inherited and amplified by the joint probability density of the observable data and the process noise, rendering it useless as the basis for obtaining measures of statistical fit. Because the joint density is the basis for the fit measures used by all conventional statistical methods, this is a major theoretical shortcoming. The inability to make well-founded statistical inferences about biological dynamic models in the chaotic and near-chaotic regimes, other than on an ad hoc basis, leaves dynamic theory without the methods of quantitative validation that are essential tools in the rest of biological science. Here I show that this impasse can be resolved in a simple and general manner, using a method that requires only the ability to simulate the observed data on a system from the dynamic model about which inferences are required. The raw data series are reduced to phase-insensitive summary statistics, quantifying local dynamic structure and the distribution of observations. Simulation is used to obtain the mean and the covariance matrix of the statistics, given model parameters, allowing the construction of a 'synthetic likelihood' that assesses model fit. This likelihood can be explored using a straightforward Markov chain Monte Carlo sampler, but one further post-processing step returns pure likelihood-based inference. I apply the method to establish the dynamic nature of the fluctuations in Nicholson's classic blowfly experiments.

Summary of hydrologic modeling for the Delaware River Basin using the Water Availability Tool for Environmental Resources (WATER)

USGS Publications Warehouse

Williamson, Tanja N.; Lant, Jeremiah G.; Claggett, Peter; Nystrom, Elizabeth A.; Milly, Paul C.D.; Nelson, Hugh L.; Hoffman, Scott A.; Colarullo, Susan J.; Fischer, Jeffrey M.

2015-11-18

The Water Availability Tool for Environmental Resources (WATER) is a decision support system for the nontidal part of the Delaware River Basin that provides a consistent and objective method of simulating streamflow under historical, forecasted, and managed conditions. In order to quantify the uncertainty associated with these simulations, however, streamflow and the associated hydroclimatic variables of potential evapotranspiration, actual evapotranspiration, and snow accumulation and snowmelt must be simulated and compared to long-term, daily observations from sites. This report details model development and optimization, statistical evaluation of simulations for 57 basins ranging from 2 to 930 km2 and 11.0 to 99.5 percent forested cover, and how this statistical evaluation of daily streamflow relates to simulating environmental changes and management decisions that are best examined at monthly time steps normalized over multiple decades. The decision support system provides a database of historical spatial and climatic data for simulating streamflow for 2001–11, in addition to land-cover and general circulation model forecasts that focus on 2030 and 2060. WATER integrates geospatial sampling of landscape characteristics, including topographic and soil properties, with a regionally calibrated hillslope-hydrology model, an impervious-surface model, and hydroclimatic models that were parameterized by using three hydrologic response units: forested, agricultural, and developed land cover. This integration enables the regional hydrologic modeling approach used in WATER without requiring site-specific optimization or those stationary conditions inferred when using a statistical model.

Probabilistic Graphical Model Representation in Phylogenetics

PubMed Central

Höhna, Sebastian; Heath, Tracy A.; Boussau, Bastien; Landis, Michael J.; Ronquist, Fredrik; Huelsenbeck, John P.

2014-01-01

Recent years have seen a rapid expansion of the model space explored in statistical phylogenetics, emphasizing the need for new approaches to statistical model representation and software development. Clear communication and representation of the chosen model is crucial for: (i) reproducibility of an analysis, (ii) model development, and (iii) software design. Moreover, a unified, clear and understandable framework for model representation lowers the barrier for beginners and nonspecialists to grasp complex phylogenetic models, including their assumptions and parameter/variable dependencies. Graphical modeling is a unifying framework that has gained in popularity in the statistical literature in recent years. The core idea is to break complex models into conditionally independent distributions. The strength lies in the comprehensibility, flexibility, and adaptability of this formalism, and the large body of computational work based on it. Graphical models are well-suited to teach statistical models, to facilitate communication among phylogeneticists and in the development of generic software for simulation and statistical inference. Here, we provide an introduction to graphical models for phylogeneticists and extend the standard graphical model representation to the realm of phylogenetics. We introduce a new graphical model component, tree plates, to capture the changing structure of the subgraph corresponding to a phylogenetic tree. We describe a range of phylogenetic models using the graphical model framework and introduce modules to simplify the representation of standard components in large and complex models. Phylogenetic model graphs can be readily used in simulation, maximum likelihood inference, and Bayesian inference using, for example, Metropolis–Hastings or Gibbs sampling of the posterior distribution. [Computation; graphical models; inference; modularization; statistical phylogenetics; tree plate.] PMID:24951559

Protein and gene model inference based on statistical modeling in k-partite graphs.

PubMed

Gerster, Sarah; Qeli, Ermir; Ahrens, Christian H; Bühlmann, Peter

2010-07-06

One of the major goals of proteomics is the comprehensive and accurate description of a proteome. Shotgun proteomics, the method of choice for the analysis of complex protein mixtures, requires that experimentally observed peptides are mapped back to the proteins they were derived from. This process is also known as protein inference. We present Markovian Inference of Proteins and Gene Models (MIPGEM), a statistical model based on clearly stated assumptions to address the problem of protein and gene model inference for shotgun proteomics data. In particular, we are dealing with dependencies among peptides and proteins using a Markovian assumption on k-partite graphs. We are also addressing the problems of shared peptides and ambiguous proteins by scoring the encoding gene models. Empirical results on two control datasets with synthetic mixtures of proteins and on complex protein samples of Saccharomyces cerevisiae, Drosophila melanogaster, and Arabidopsis thaliana suggest that the results with MIPGEM are competitive with existing tools for protein inference.

minet: A R/Bioconductor package for inferring large transcriptional networks using mutual information.

PubMed

Meyer, Patrick E; Lafitte, Frédéric; Bontempi, Gianluca

2008-10-29

This paper presents the R/Bioconductor package minet (version 1.1.6) which provides a set of functions to infer mutual information networks from a dataset. Once fed with a microarray dataset, the package returns a network where nodes denote genes, edges model statistical dependencies between genes and the weight of an edge quantifies the statistical evidence of a specific (e.g transcriptional) gene-to-gene interaction. Four different entropy estimators are made available in the package minet (empirical, Miller-Madow, Schurmann-Grassberger and shrink) as well as four different inference methods, namely relevance networks, ARACNE, CLR and MRNET. Also, the package integrates accuracy assessment tools, like F-scores, PR-curves and ROC-curves in order to compare the inferred network with a reference one. The package minet provides a series of tools for inferring transcriptional networks from microarray data. It is freely available from the Comprehensive R Archive Network (CRAN) as well as from the Bioconductor website.

Infinite von Mises-Fisher Mixture Modeling of Whole Brain fMRI Data.

PubMed

Røge, Rasmus E; Madsen, Kristoffer H; Schmidt, Mikkel N; Mørup, Morten

2017-10-01

Cluster analysis of functional magnetic resonance imaging (fMRI) data is often performed using gaussian mixture models, but when the time series are standardized such that the data reside on a hypersphere, this modeling assumption is questionable. The consequences of ignoring the underlying spherical manifold are rarely analyzed, in part due to the computational challenges imposed by directional statistics. In this letter, we discuss a Bayesian von Mises-Fisher (vMF) mixture model for data on the unit hypersphere and present an efficient inference procedure based on collapsed Markov chain Monte Carlo sampling. Comparing the vMF and gaussian mixture models on synthetic data, we demonstrate that the vMF model has a slight advantage inferring the true underlying clustering when compared to gaussian-based models on data generated from both a mixture of vMFs and a mixture of gaussians subsequently normalized. Thus, when performing model selection, the two models are not in agreement. Analyzing multisubject whole brain resting-state fMRI data from healthy adult subjects, we find that the vMF mixture model is considerably more reliable than the gaussian mixture model when comparing solutions across models trained on different groups of subjects, and again we find that the two models disagree on the optimal number of components. The analysis indicates that the fMRI data support more than a thousand clusters, and we confirm this is not a result of overfitting by demonstrating better prediction on data from held-out subjects. Our results highlight the utility of using directional statistics to model standardized fMRI data and demonstrate that whole brain segmentation of fMRI data requires a very large number of functional units in order to adequately account for the discernible statistical patterns in the data.

Teach a Confidence Interval for the Median in the First Statistics Course

ERIC Educational Resources Information Center

Howington, Eric B.

2017-01-01

Few introductory statistics courses consider statistical inference for the median. This article argues in favour of adding a confidence interval for the median to the first statistics course. Several methods suitable for introductory statistics students are identified and briefly reviewed.

Reconstruction of Atmospheric Tracer Releases with Optimal Resolution Features: Concentration Data Assimilation

NASA Astrophysics Data System (ADS)

Singh, Sarvesh Kumar; Turbelin, Gregory; Issartel, Jean-Pierre; Kumar, Pramod; Feiz, Amir Ali

2015-04-01

The fast growing urbanization, industrialization and military developments increase the risk towards the human environment and ecology. This is realized in several past mortality incidents, for instance, Chernobyl nuclear explosion (Ukraine), Bhopal gas leak (India), Fukushima-Daichi radionuclide release (Japan), etc. To reduce the threat and exposure to the hazardous contaminants, a fast and preliminary identification of unknown releases is required by the responsible authorities for the emergency preparedness and air quality analysis. Often, an early detection of such contaminants is pursued by a distributed sensor network. However, identifying the origin and strength of unknown releases following the sensor reported concentrations is a challenging task. This requires an optimal strategy to integrate the measured concentrations with the predictions given by the atmospheric dispersion models. This is an inverse problem. The measured concentrations are insufficient and atmospheric dispersion models suffer from inaccuracy due to the lack of process understanding, turbulence uncertainties, etc. These lead to a loss of information in the reconstruction process and thus, affect the resolution, stability and uniqueness of the retrieved source. An additional well known issue is the numerical artifact arisen at the measurement locations due to the strong concentration gradient and dissipative nature of the concentration. Thus, assimilation techniques are desired which can lead to an optimal retrieval of the unknown releases. In general, this is facilitated within the Bayesian inference and optimization framework with a suitable choice of a priori information, regularization constraints, measurement and background error statistics. An inversion technique is introduced here for an optimal reconstruction of unknown releases using limited concentration measurements. This is based on adjoint representation of the source-receptor relationship and utilization of a weight function which exhibits a priori information about the unknown releases apparent to the monitoring network. The properties of the weight function provide an optimal data resolution and model resolution to the retrieved source estimates. The retrieved source estimates are proved theoretically to be stable against the random measurement errors and their reliability can be interpreted in terms of the distribution of the weight functions. Further, the same framework can be extended for the identification of the point type releases by utilizing the maximum of the retrieved source estimates. The inversion technique has been evaluated with the several diffusion experiments, like, Idaho low wind diffusion experiment (1974), IIT Delhi tracer experiment (1991), European Tracer Experiment (1994), Fusion Field Trials (2007), etc. In case of point release experiments, the source parameters are mostly retrieved close to the true source parameters with least error. Primarily, the proposed technique overcomes two major difficulties incurred in the source reconstruction: (i) The initialization of the source parameters as required by the optimization based techniques. The converged solution depends on their initialization. (ii) The statistical knowledge about the measurement and background errors as required by the Bayesian inference based techniques. These are hypothetically assumed in case of no prior knowledge.

Pointwise probability reinforcements for robust statistical inference.

PubMed

Frénay, Benoît; Verleysen, Michel

2014-02-01

Statistical inference using machine learning techniques may be difficult with small datasets because of abnormally frequent data (AFDs). AFDs are observations that are much more frequent in the training sample that they should be, with respect to their theoretical probability, and include e.g. outliers. Estimates of parameters tend to be biased towards models which support such data. This paper proposes to introduce pointwise probability reinforcements (PPRs): the probability of each observation is reinforced by a PPR and a regularisation allows controlling the amount of reinforcement which compensates for AFDs. The proposed solution is very generic, since it can be used to robustify any statistical inference method which can be formulated as a likelihood maximisation. Experiments show that PPRs can be easily used to tackle regression, classification and projection: models are freed from the influence of outliers. Moreover, outliers can be filtered manually since an abnormality degree is obtained for each observation. Copyright © 2013 Elsevier Ltd. All rights reserved.

Probability, statistics, and computational science.

PubMed

Beerenwinkel, Niko; Siebourg, Juliane

2012-01-01

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

A Not-So-Fundamental Limitation on Studying Complex Systems with Statistics: Comment on Rabin (2011)

NASA Astrophysics Data System (ADS)

Thomas, Drew M.

2012-12-01

Although living organisms are affected by many interrelated and unidentified variables, this complexity does not automatically impose a fundamental limitation on statistical inference. Nor need one invoke such complexity as an explanation of the "Truth Wears Off" or "decline" effect; similar "decline" effects occur with far simpler systems studied in physics. Selective reporting and publication bias, and scientists' biases in favor of reporting eye-catching results (in general) or conforming to others' results (in physics) better explain this feature of the "Truth Wears Off" effect than Rabin's suggested limitation on statistical inference.

Are V1 Simple Cells Optimized for Visual Occlusions? A Comparative Study

PubMed Central

Bornschein, Jörg; Henniges, Marc; Lücke, Jörg

2013-01-01

Simple cells in primary visual cortex were famously found to respond to low-level image components such as edges. Sparse coding and independent component analysis (ICA) emerged as the standard computational models for simple cell coding because they linked their receptive fields to the statistics of visual stimuli. However, a salient feature of image statistics, occlusions of image components, is not considered by these models. Here we ask if occlusions have an effect on the predicted shapes of simple cell receptive fields. We use a comparative approach to answer this question and investigate two models for simple cells: a standard linear model and an occlusive model. For both models we simultaneously estimate optimal receptive fields, sparsity and stimulus noise. The two models are identical except for their component superposition assumption. We find the image encoding and receptive fields predicted by the models to differ significantly. While both models predict many Gabor-like fields, the occlusive model predicts a much sparser encoding and high percentages of ‘globular’ receptive fields. This relatively new center-surround type of simple cell response is observed since reverse correlation is used in experimental studies. While high percentages of ‘globular’ fields can be obtained using specific choices of sparsity and overcompleteness in linear sparse coding, no or only low proportions are reported in the vast majority of studies on linear models (including all ICA models). Likewise, for the here investigated linear model and optimal sparsity, only low proportions of ‘globular’ fields are observed. In comparison, the occlusive model robustly infers high proportions and can match the experimentally observed high proportions of ‘globular’ fields well. Our computational study, therefore, suggests that ‘globular’ fields may be evidence for an optimal encoding of visual occlusions in primary visual cortex. PMID:23754938

Structure Discovery in Large Semantic Graphs Using Extant Ontological Scaling and Descriptive Statistics

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

al-Saffar, Sinan; Joslyn, Cliff A.; Chappell, Alan R.

As semantic datasets grow to be very large and divergent, there is a need to identify and exploit their inherent semantic structure for discovery and optimization. Towards that end, we present here a novel methodology to identify the semantic structures inherent in an arbitrary semantic graph dataset. We first present the concept of an extant ontology as a statistical description of the semantic relations present amongst the typed entities modeled in the graph. This serves as a model of the underlying semantic structure to aid in discovery and visualization. We then describe a method of ontological scaling in which themore » ontology is employed as a hierarchical scaling filter to infer different resolution levels at which the graph structures are to be viewed or analyzed. We illustrate these methods on three large and publicly available semantic datasets containing more than one billion edges each. Keywords-Semantic Web; Visualization; Ontology; Multi-resolution Data Mining;« less

High-Reproducibility and High-Accuracy Method for Automated Topic Classification

NASA Astrophysics Data System (ADS)

Lancichinetti, Andrea; Sirer, M. Irmak; Wang, Jane X.; Acuna, Daniel; Körding, Konrad; Amaral, Luís A. Nunes

2015-01-01

Much of human knowledge sits in large databases of unstructured text. Leveraging this knowledge requires algorithms that extract and record metadata on unstructured text documents. Assigning topics to documents will enable intelligent searching, statistical characterization, and meaningful classification. Latent Dirichlet allocation (LDA) is the state of the art in topic modeling. Here, we perform a systematic theoretical and numerical analysis that demonstrates that current optimization techniques for LDA often yield results that are not accurate in inferring the most suitable model parameters. Adapting approaches from community detection in networks, we propose a new algorithm that displays high reproducibility and high accuracy and also has high computational efficiency. We apply it to a large set of documents in the English Wikipedia and reveal its hierarchical structure.

Bayesian Inference: with ecological applications

USGS Publications Warehouse

Link, William A.; Barker, Richard J.

2010-01-01

This text provides a mathematically rigorous yet accessible and engaging introduction to Bayesian inference with relevant examples that will be of interest to biologists working in the fields of ecology, wildlife management and environmental studies as well as students in advanced undergraduate statistics.. This text opens the door to Bayesian inference, taking advantage of modern computational efficiencies and easily accessible software to evaluate complex hierarchical models.

Theory-based Bayesian Models of Inductive Inference

DTIC Science & Technology

2010-07-19

Subjective randomness and natural scene statistics. Psychonomic Bulletin & Review . http://cocosci.berkeley.edu/tom/papers/randscenes.pdf Page 1...in press). Exemplar models as a mechanism for performing Bayesian inference. Psychonomic Bulletin & Review . http://cocosci.berkeley.edu/tom

Differences in Performance Among Test Statistics for Assessing Phylogenomic Model Adequacy.

PubMed

Duchêne, David A; Duchêne, Sebastian; Ho, Simon Y W

2018-05-18

Statistical phylogenetic analyses of genomic data depend on models of nucleotide or amino acid substitution. The adequacy of these substitution models can be assessed using a number of test statistics, allowing the model to be rejected when it is found to provide a poor description of the evolutionary process. A potentially valuable use of model-adequacy test statistics is to identify when data sets are likely to produce unreliable phylogenetic estimates, but their differences in performance are rarely explored. We performed a comprehensive simulation study to identify test statistics that are sensitive to some of the most commonly cited sources of phylogenetic estimation error. Our results show that, for many test statistics, traditional thresholds for assessing model adequacy can fail to reject the model when the phylogenetic inferences are inaccurate and imprecise. This is particularly problematic when analysing loci that have few variable informative sites. We propose new thresholds for assessing substitution model adequacy and demonstrate their effectiveness in analyses of three phylogenomic data sets. These thresholds lead to frequent rejection of the model for loci that yield topological inferences that are imprecise and are likely to be inaccurate. We also propose the use of a summary statistic that provides a practical assessment of overall model adequacy. Our approach offers a promising means of enhancing model choice in genome-scale data sets, potentially leading to improvements in the reliability of phylogenomic inference.

Applications of statistics to medical science (1) Fundamental concepts.

PubMed

Watanabe, Hiroshi

2011-01-01

The conceptual framework of statistical tests and statistical inferences are discussed, and the epidemiological background of statistics is briefly reviewed. This study is one of a series in which we survey the basics of statistics and practical methods used in medical statistics. Arguments related to actual statistical analysis procedures will be made in subsequent papers.

The role of causal criteria in causal inferences: Bradford Hill's "aspects of association".

PubMed

Ward, Andrew C

2009-06-17

As noted by Wesley Salmon and many others, causal concepts are ubiquitous in every branch of theoretical science, in the practical disciplines and in everyday life. In the theoretical and practical sciences especially, people often base claims about causal relations on applications of statistical methods to data. However, the source and type of data place important constraints on the choice of statistical methods as well as on the warrant attributed to the causal claims based on the use of such methods. For example, much of the data used by people interested in making causal claims come from non-experimental, observational studies in which random allocations to treatment and control groups are not present. Thus, one of the most important problems in the social and health sciences concerns making justified causal inferences using non-experimental, observational data. In this paper, I examine one method of justifying such inferences that is especially widespread in epidemiology and the health sciences generally - the use of causal criteria. I argue that while the use of causal criteria is not appropriate for either deductive or inductive inferences, they do have an important role to play in inferences to the best explanation. As such, causal criteria, exemplified by what Bradford Hill referred to as "aspects of [statistical] associations", have an indispensible part to play in the goal of making justified causal claims.

The role of causal criteria in causal inferences: Bradford Hill's "aspects of association"

PubMed Central

Ward, Andrew C

2009-01-01

As noted by Wesley Salmon and many others, causal concepts are ubiquitous in every branch of theoretical science, in the practical disciplines and in everyday life. In the theoretical and practical sciences especially, people often base claims about causal relations on applications of statistical methods to data. However, the source and type of data place important constraints on the choice of statistical methods as well as on the warrant attributed to the causal claims based on the use of such methods. For example, much of the data used by people interested in making causal claims come from non-experimental, observational studies in which random allocations to treatment and control groups are not present. Thus, one of the most important problems in the social and health sciences concerns making justified causal inferences using non-experimental, observational data. In this paper, I examine one method of justifying such inferences that is especially widespread in epidemiology and the health sciences generally – the use of causal criteria. I argue that while the use of causal criteria is not appropriate for either deductive or inductive inferences, they do have an important role to play in inferences to the best explanation. As such, causal criteria, exemplified by what Bradford Hill referred to as "aspects of [statistical] associations", have an indispensible part to play in the goal of making justified causal claims. PMID:19534788

Benchmarking Inverse Statistical Approaches for Protein Structure and Design with Exactly Solvable Models.

PubMed

Jacquin, Hugo; Gilson, Amy; Shakhnovich, Eugene; Cocco, Simona; Monasson, Rémi

2016-05-01

Inverse statistical approaches to determine protein structure and function from Multiple Sequence Alignments (MSA) are emerging as powerful tools in computational biology. However the underlying assumptions of the relationship between the inferred effective Potts Hamiltonian and real protein structure and energetics remain untested so far. Here we use lattice protein model (LP) to benchmark those inverse statistical approaches. We build MSA of highly stable sequences in target LP structures, and infer the effective pairwise Potts Hamiltonians from those MSA. We find that inferred Potts Hamiltonians reproduce many important aspects of 'true' LP structures and energetics. Careful analysis reveals that effective pairwise couplings in inferred Potts Hamiltonians depend not only on the energetics of the native structure but also on competing folds; in particular, the coupling values reflect both positive design (stabilization of native conformation) and negative design (destabilization of competing folds). In addition to providing detailed structural information, the inferred Potts models used as protein Hamiltonian for design of new sequences are able to generate with high probability completely new sequences with the desired folds, which is not possible using independent-site models. Those are remarkable results as the effective LP Hamiltonians used to generate MSA are not simple pairwise models due to the competition between the folds. Our findings elucidate the reasons for the success of inverse approaches to the modelling of proteins from sequence data, and their limitations.

Evaluation of an artificial intelligence guided inverse planning system: clinical case study.

PubMed

Yan, Hui; Yin, Fang-Fang; Willett, Christopher

2007-04-01

An artificial intelligence (AI) guided method for parameter adjustment of inverse planning was implemented on a commercial inverse treatment planning system. For evaluation purpose, four typical clinical cases were tested and the results from both plans achieved by automated and manual methods were compared. The procedure of parameter adjustment mainly consists of three major loops. Each loop is in charge of modifying parameters of one category, which is carried out by a specially customized fuzzy inference system. A physician prescribed multiple constraints for a selected volume were adopted to account for the tradeoff between prescription dose to the PTV and dose-volume constraints for critical organs. The searching process for an optimal parameter combination began with the first constraint, and proceeds to the next until a plan with acceptable dose was achieved. The initial setup of the plan parameters was the same for each case and was adjusted independently by both manual and automated methods. After the parameters of one category were updated, the intensity maps of all fields were re-optimized and the plan dose was subsequently re-calculated. When final plan arrived, the dose statistics were calculated from both plans and compared. For planned target volume (PTV), the dose for 95% volume is up to 10% higher in plans using the automated method than those using the manual method. For critical organs, an average decrease of the plan dose was achieved. However, the automated method cannot improve the plan dose for some critical organs due to limitations of the inference rules currently employed. For normal tissue, there was no significant difference between plan doses achieved by either automated or manual method. With the application of AI-guided method, the basic parameter adjustment task can be accomplished automatically and a comparable plan dose was achieved in comparison with that achieved by the manual method. Future improvements to incorporate case-specific inference rules are essential to fully automate the inverse planning process.

The hubris hypothesis: The downside of comparative optimism displays.

PubMed

Hoorens, Vera; Van Damme, Carolien; Helweg-Larsen, Marie; Sedikides, Constantine

2017-04-01

According to the hubris hypothesis, observers respond more unfavorably to individuals who express their positive self-views comparatively than to those who express their positive self-views non-comparatively, because observers infer that the former hold a more disparaging view of others and particularly of observers. Two experiments extended the hubris hypothesis in the domain of optimism. Observers attributed less warmth (but not less competence) to, and showed less interest in affiliating with, an individual displaying comparative optimism (the belief that one's future will be better than others' future) than with an individual displaying absolute optimism (the belief that one's future will be good). Observers responded differently to individuals displaying comparative versus absolute optimism, because they inferred that the former held a gloomier view of the observers' future. Consistent with previous research, observers still attributed more positive traits to a comparative or absolute optimist than to a comparative or absolute pessimist. Copyright © 2016. Published by Elsevier Inc.

Logical reasoning versus information processing in the dual-strategy model of reasoning.

PubMed

Markovits, Henry; Brisson, Janie; de Chantal, Pier-Luc

2017-01-01

One of the major debates concerning the nature of inferential reasoning is between counterexample-based strategies such as mental model theory and statistical strategies underlying probabilistic models. The dual-strategy model, proposed by Verschueren, Schaeken, & d'Ydewalle (2005a, 2005b), which suggests that people might have access to both kinds of strategy has been supported by several recent studies. These have shown that statistical reasoners make inferences based on using information about premises in order to generate a likelihood estimate of conclusion probability. However, while results concerning counterexample reasoners are consistent with a counterexample detection model, these results could equally be interpreted as indicating a greater sensitivity to logical form. In order to distinguish these 2 interpretations, in Studies 1 and 2, we presented reasoners with Modus ponens (MP) inferences with statistical information about premise strength and in Studies 3 and 4, naturalistic MP inferences with premises having many disabling conditions. Statistical reasoners accepted the MP inference more often than counterexample reasoners in Studies 1 and 2, while the opposite pattern was observed in Studies 3 and 4. Results show that these strategies must be defined in terms of information processing, with no clear relations to "logical" reasoning. These results have additional implications for the underlying debate about the nature of human reasoning. (PsycINFO Database Record (c) 2017 APA, all rights reserved).

Efficient sampling of parsimonious inversion histories with application to genome rearrangement in Yersinia.

PubMed

Miklós, István; Darling, Aaron E

2009-06-22

Inversions are among the most common mutations acting on the order and orientation of genes in a genome, and polynomial-time algorithms exist to obtain a minimal length series of inversions that transform one genome arrangement to another. However, the minimum length series of inversions (the optimal sorting path) is often not unique as many such optimal sorting paths exist. If we assume that all optimal sorting paths are equally likely, then statistical inference on genome arrangement history must account for all such sorting paths and not just a single estimate. No deterministic polynomial algorithm is known to count the number of optimal sorting paths nor sample from the uniform distribution of optimal sorting paths. Here, we propose a stochastic method that uniformly samples the set of all optimal sorting paths. Our method uses a novel formulation of parallel Markov chain Monte Carlo. In practice, our method can quickly estimate the total number of optimal sorting paths. We introduce a variant of our approach in which short inversions are modeled to be more likely, and we show how the method can be used to estimate the distribution of inversion lengths and breakpoint usage in pathogenic Yersinia pestis. The proposed method has been implemented in a program called "MC4Inversion." We draw comparison of MC4Inversion to the sampler implemented in BADGER and a previously described importance sampling (IS) technique. We find that on high-divergence data sets, MC4Inversion finds more optimal sorting paths per second than BADGER and the IS technique and simultaneously avoids bias inherent in the IS technique.

Inference of a Nonlinear Stochastic Model of the Cardiorespiratory Interaction

NASA Astrophysics Data System (ADS)

Smelyanskiy, V. N.; Luchinsky, D. G.; Stefanovska, A.; McClintock, P. V.

2005-03-01

We reconstruct a nonlinear stochastic model of the cardiorespiratory interaction in terms of a set of polynomial basis functions representing the nonlinear force governing system oscillations. The strength and direction of coupling and noise intensity are simultaneously inferred from a univariate blood pressure signal. Our new inference technique does not require extensive global optimization, and it is applicable to a wide range of complex dynamical systems subject to noise.

The Dopaminergic Midbrain Encodes the Expected Certainty about Desired Outcomes.

PubMed

Schwartenbeck, Philipp; FitzGerald, Thomas H B; Mathys, Christoph; Dolan, Ray; Friston, Karl

2015-10-01

Dopamine plays a key role in learning; however, its exact function in decision making and choice remains unclear. Recently, we proposed a generic model based on active (Bayesian) inference wherein dopamine encodes the precision of beliefs about optimal policies. Put simply, dopamine discharges reflect the confidence that a chosen policy will lead to desired outcomes. We designed a novel task to test this hypothesis, where subjects played a "limited offer" game in a functional magnetic resonance imaging experiment. Subjects had to decide how long to wait for a high offer before accepting a low offer, with the risk of losing everything if they waited too long. Bayesian model comparison showed that behavior strongly supported active inference, based on surprise minimization, over classical utility maximization schemes. Furthermore, midbrain activity, encompassing dopamine projection neurons, was accurately predicted by trial-by-trial variations in model-based estimates of precision. Our findings demonstrate that human subjects infer both optimal policies and the precision of those inferences, and thus support the notion that humans perform hierarchical probabilistic Bayesian inference. In other words, subjects have to infer both what they should do as well as how confident they are in their choices, where confidence may be encoded by dopaminergic firing. © The Author 2014. Published by Oxford University Press.

The Dopaminergic Midbrain Encodes the Expected Certainty about Desired Outcomes

PubMed Central

Schwartenbeck, Philipp; FitzGerald, Thomas H. B.; Mathys, Christoph; Dolan, Ray; Friston, Karl

2015-01-01

Dopamine plays a key role in learning; however, its exact function in decision making and choice remains unclear. Recently, we proposed a generic model based on active (Bayesian) inference wherein dopamine encodes the precision of beliefs about optimal policies. Put simply, dopamine discharges reflect the confidence that a chosen policy will lead to desired outcomes. We designed a novel task to test this hypothesis, where subjects played a “limited offer” game in a functional magnetic resonance imaging experiment. Subjects had to decide how long to wait for a high offer before accepting a low offer, with the risk of losing everything if they waited too long. Bayesian model comparison showed that behavior strongly supported active inference, based on surprise minimization, over classical utility maximization schemes. Furthermore, midbrain activity, encompassing dopamine projection neurons, was accurately predicted by trial-by-trial variations in model-based estimates of precision. Our findings demonstrate that human subjects infer both optimal policies and the precision of those inferences, and thus support the notion that humans perform hierarchical probabilistic Bayesian inference. In other words, subjects have to infer both what they should do as well as how confident they are in their choices, where confidence may be encoded by dopaminergic firing. PMID:25056572

Statistical inference for Hardy-Weinberg proportions in the presence of missing genotype information.

PubMed

Graffelman, Jan; Sánchez, Milagros; Cook, Samantha; Moreno, Victor

2013-01-01

In genetic association studies, tests for Hardy-Weinberg proportions are often employed as a quality control checking procedure. Missing genotypes are typically discarded prior to testing. In this paper we show that inference for Hardy-Weinberg proportions can be biased when missing values are discarded. We propose to use multiple imputation of missing values in order to improve inference for Hardy-Weinberg proportions. For imputation we employ a multinomial logit model that uses information from allele intensities and/or neighbouring markers. Analysis of an empirical data set of single nucleotide polymorphisms possibly related to colon cancer reveals that missing genotypes are not missing completely at random. Deviation from Hardy-Weinberg proportions is mostly due to a lack of heterozygotes. Inbreeding coefficients estimated by multiple imputation of the missings are typically lowered with respect to inbreeding coefficients estimated by discarding the missings. Accounting for missings by multiple imputation qualitatively changed the results of 10 to 17% of the statistical tests performed. Estimates of inbreeding coefficients obtained by multiple imputation showed high correlation with estimates obtained by single imputation using an external reference panel. Our conclusion is that imputation of missing data leads to improved statistical inference for Hardy-Weinberg proportions.

[Application of statistics on chronic-diseases-relating observational research papers].

PubMed

Hong, Zhi-heng; Wang, Ping; Cao, Wei-hua

2012-09-01

To study the application of statistics on Chronic-diseases-relating observational research papers which were recently published in the Chinese Medical Association Magazines, with influential index above 0.5. Using a self-developed criterion, two investigators individually participated in assessing the application of statistics on Chinese Medical Association Magazines, with influential index above 0.5. Different opinions reached an agreement through discussion. A total number of 352 papers from 6 magazines, including the Chinese Journal of Epidemiology, Chinese Journal of Oncology, Chinese Journal of Preventive Medicine, Chinese Journal of Cardiology, Chinese Journal of Internal Medicine and Chinese Journal of Endocrinology and Metabolism, were reviewed. The rate of clear statement on the following contents as: research objectives, t target audience, sample issues, objective inclusion criteria and variable definitions were 99.43%, 98.57%, 95.43%, 92.86% and 96.87%. The correct rates of description on quantitative and qualitative data were 90.94% and 91.46%, respectively. The rates on correctly expressing the results, on statistical inference methods related to quantitative, qualitative data and modeling were 100%, 95.32% and 87.19%, respectively. 89.49% of the conclusions could directly response to the research objectives. However, 69.60% of the papers did not mention the exact names of the study design, statistically, that the papers were using. 11.14% of the papers were in lack of further statement on the exclusion criteria. Percentage of the papers that could clearly explain the sample size estimation only taking up as 5.16%. Only 24.21% of the papers clearly described the variable value assignment. Regarding the introduction on statistical conduction and on database methods, the rate was only 24.15%. 18.75% of the papers did not express the statistical inference methods sufficiently. A quarter of the papers did not use 'standardization' appropriately. As for the aspect of statistical inference, the rate of description on statistical testing prerequisite was only 24.12% while 9.94% papers did not even employ the statistical inferential method that should be used. The main deficiencies on the application of Statistics used in papers related to Chronic-diseases-related observational research were as follows: lack of sample-size determination, variable value assignment description not sufficient, methods on statistics were not introduced clearly or properly, lack of consideration for pre-requisition regarding the use of statistical inferences.

Statistics and Informatics in Space Astrophysics

NASA Astrophysics Data System (ADS)

Feigelson, E.

2017-12-01

The interest in statistical and computational methodology has seen rapid growth in space-based astrophysics, parallel to the growth seen in Earth remote sensing. There is widespread agreement that scientific interpretation of the cosmic microwave background, discovery of exoplanets, and classifying multiwavelength surveys is too complex to be accomplished with traditional techniques. NASA operates several well-functioning Science Archive Research Centers providing 0.5 PBy datasets to the research community. These databases are integrated with full-text journal articles in the NASA Astrophysics Data System (200K pageviews/day). Data products use interoperable formats and protocols established by the International Virtual Observatory Alliance. NASA supercomputers also support complex astrophysical models of systems such as accretion disks and planet formation. Academic researcher interest in methodology has significantly grown in areas such as Bayesian inference and machine learning, and statistical research is underway to treat problems such as irregularly spaced time series and astrophysical model uncertainties. Several scholarly societies have created interest groups in astrostatistics and astroinformatics. Improvements are needed on several fronts. Community education in advanced methodology is not sufficiently rapid to meet the research needs. Statistical procedures within NASA science analysis software are sometimes not optimal, and pipeline development may not use modern software engineering techniques. NASA offers few grant opportunities supporting research in astroinformatics and astrostatistics.

Hierarchical modeling and inference in ecology: The analysis of data from populations, metapopulations and communities

USGS Publications Warehouse

Royle, J. Andrew; Dorazio, Robert M.

2008-01-01

A guide to data collection, modeling and inference strategies for biological survey data using Bayesian and classical statistical methods. This book describes a general and flexible framework for modeling and inference in ecological systems based on hierarchical models, with a strict focus on the use of probability models and parametric inference. Hierarchical models represent a paradigm shift in the application of statistics to ecological inference problems because they combine explicit models of ecological system structure or dynamics with models of how ecological systems are observed. The principles of hierarchical modeling are developed and applied to problems in population, metapopulation, community, and metacommunity systems. The book provides the first synthetic treatment of many recent methodological advances in ecological modeling and unifies disparate methods and procedures. The authors apply principles of hierarchical modeling to ecological problems, including * occurrence or occupancy models for estimating species distribution * abundance models based on many sampling protocols, including distance sampling * capture-recapture models with individual effects * spatial capture-recapture models based on camera trapping and related methods * population and metapopulation dynamic models * models of biodiversity, community structure and dynamics.

Truth, models, model sets, AIC, and multimodel inference: a Bayesian perspective

USGS Publications Warehouse

Barker, Richard J.; Link, William A.

2015-01-01

Statistical inference begins with viewing data as realizations of stochastic processes. Mathematical models provide partial descriptions of these processes; inference is the process of using the data to obtain a more complete description of the stochastic processes. Wildlife and ecological scientists have become increasingly concerned with the conditional nature of model-based inference: what if the model is wrong? Over the last 2 decades, Akaike's Information Criterion (AIC) has been widely and increasingly used in wildlife statistics for 2 related purposes, first for model choice and second to quantify model uncertainty. We argue that for the second of these purposes, the Bayesian paradigm provides the natural framework for describing uncertainty associated with model choice and provides the most easily communicated basis for model weighting. Moreover, Bayesian arguments provide the sole justification for interpreting model weights (including AIC weights) as coherent (mathematically self consistent) model probabilities. This interpretation requires treating the model as an exact description of the data-generating mechanism. We discuss the implications of this assumption, and conclude that more emphasis is needed on model checking to provide confidence in the quality of inference.

Comparison of a non-stationary voxelation-corrected cluster-size test with TFCE for group-Level MRI inference.

PubMed

Li, Huanjie; Nickerson, Lisa D; Nichols, Thomas E; Gao, Jia-Hong

2017-03-01

Two powerful methods for statistical inference on MRI brain images have been proposed recently, a non-stationary voxelation-corrected cluster-size test (CST) based on random field theory and threshold-free cluster enhancement (TFCE) based on calculating the level of local support for a cluster, then using permutation testing for inference. Unlike other statistical approaches, these two methods do not rest on the assumptions of a uniform and high degree of spatial smoothness of the statistic image. Thus, they are strongly recommended for group-level fMRI analysis compared to other statistical methods. In this work, the non-stationary voxelation-corrected CST and TFCE methods for group-level analysis were evaluated for both stationary and non-stationary images under varying smoothness levels, degrees of freedom and signal to noise ratios. Our results suggest that, both methods provide adequate control for the number of voxel-wise statistical tests being performed during inference on fMRI data and they are both superior to current CSTs implemented in popular MRI data analysis software packages. However, TFCE is more sensitive and stable for group-level analysis of VBM data. Thus, the voxelation-corrected CST approach may confer some advantages by being computationally less demanding for fMRI data analysis than TFCE with permutation testing and by also being applicable for single-subject fMRI analyses, while the TFCE approach is advantageous for VBM data. Hum Brain Mapp 38:1269-1280, 2017. © 2016 Wiley Periodicals, Inc. © 2016 Wiley Periodicals, Inc.

An application of an optimal statistic for characterizing relative orientations

NASA Astrophysics Data System (ADS)

Jow, Dylan L.; Hill, Ryley; Scott, Douglas; Soler, J. D.; Martin, P. G.; Devlin, M. J.; Fissel, L. M.; Poidevin, F.

2018-02-01

We present the projected Rayleigh statistic (PRS), a modification of the classic Rayleigh statistic, as a test for non-uniform relative orientation between two pseudo-vector fields. In the application here, this gives an effective way of investigating whether polarization pseudo-vectors (spin-2 quantities) are preferentially parallel or perpendicular to filaments in the interstellar medium. For example, there are other potential applications in astrophysics, e.g. when comparing small-scale orientations with larger scale shear patterns. We compare the efficiency of the PRS against histogram binning methods that have previously been used for characterizing the relative orientations of gas column density structures with the magnetic field projected on the plane of the sky. We examine data for the Vela C molecular cloud, where the column density is inferred from Herschel submillimetre observations, and the magnetic field from observations by the Balloon-borne Large-Aperture Submillimetre Telescope in the 250-, 350- and 500-μm wavelength bands. We find that the PRS has greater statistical power than approaches that bin the relative orientation angles, as it makes more efficient use of the information contained in the data. In particular, the use of the PRS to test for preferential alignment results in a higher statistical significance, in each of the four Vela C regions, with the greatest increase being by a factor 1.3 in the South-Nest region in the 250 - μ m band.

Incorporating Biological Knowledge into Evaluation of Casual Regulatory Hypothesis

NASA Technical Reports Server (NTRS)

Chrisman, Lonnie; Langley, Pat; Bay, Stephen; Pohorille, Andrew; DeVincenzi, D. (Technical Monitor)

2002-01-01

Biological data can be scarce and costly to obtain. The small number of samples available typically limits statistical power and makes reliable inference of causal relations extremely difficult. However, we argue that statistical power can be increased substantially by incorporating prior knowledge and data from diverse sources. We present a Bayesian framework that combines information from different sources and we show empirically that this lets one make correct causal inferences with small sample sizes that otherwise would be impossible.

A Review of Some Aspects of Robust Inference for Time Series.

DTIC Science & Technology

1984-09-01

REVIEW OF SOME ASPECTSOF ROBUST INFERNCE FOR TIME SERIES by Ad . Dougla Main TE "iAL REPOW No. 63 Septermber 1984 Department of Statistics University of ...clear. One cannot hope to have a good method for dealing with outliers in time series by using only an instantaneous nonlinear transformation of the data...AI.49 716 A REVIEWd OF SOME ASPECTS OF ROBUST INFERENCE FOR TIME 1/1 SERIES(U) WASHINGTON UNIV SEATTLE DEPT OF STATISTICS R D MARTIN SEP 84 TR-53

The researcher and the consultant: from testing to probability statements.

PubMed

Hamra, Ghassan B; Stang, Andreas; Poole, Charles

2015-09-01

In the first instalment of this series, Stang and Poole provided an overview of Fisher significance testing (ST), Neyman-Pearson null hypothesis testing (NHT), and their unfortunate and unintended offspring, null hypothesis significance testing. In addition to elucidating the distinction between the first two and the evolution of the third, the authors alluded to alternative models of statistical inference; namely, Bayesian statistics. Bayesian inference has experienced a revival in recent decades, with many researchers advocating for its use as both a complement and an alternative to NHT and ST. This article will continue in the direction of the first instalment, providing practicing researchers with an introduction to Bayesian inference. Our work will draw on the examples and discussion of the previous dialogue.

Spectral likelihood expansions for Bayesian inference

NASA Astrophysics Data System (ADS)

Nagel, Joseph B.; Sudret, Bruno

2016-03-01

A spectral approach to Bayesian inference is presented. It pursues the emulation of the posterior probability density. The starting point is a series expansion of the likelihood function in terms of orthogonal polynomials. From this spectral likelihood expansion all statistical quantities of interest can be calculated semi-analytically. The posterior is formally represented as the product of a reference density and a linear combination of polynomial basis functions. Both the model evidence and the posterior moments are related to the expansion coefficients. This formulation avoids Markov chain Monte Carlo simulation and allows one to make use of linear least squares instead. The pros and cons of spectral Bayesian inference are discussed and demonstrated on the basis of simple applications from classical statistics and inverse modeling.

Networking—a statistical physics perspective

NASA Astrophysics Data System (ADS)

Yeung, Chi Ho; Saad, David

2013-03-01

Networking encompasses a variety of tasks related to the communication of information on networks; it has a substantial economic and societal impact on a broad range of areas including transportation systems, wired and wireless communications and a range of Internet applications. As transportation and communication networks become increasingly more complex, the ever increasing demand for congestion control, higher traffic capacity, quality of service, robustness and reduced energy consumption requires new tools and methods to meet these conflicting requirements. The new methodology should serve for gaining better understanding of the properties of networking systems at the macroscopic level, as well as for the development of new principled optimization and management algorithms at the microscopic level. Methods of statistical physics seem best placed to provide new approaches as they have been developed specifically to deal with nonlinear large-scale systems. This review aims at presenting an overview of tools and methods that have been developed within the statistical physics community and that can be readily applied to address the emerging problems in networking. These include diffusion processes, methods from disordered systems and polymer physics, probabilistic inference, which have direct relevance to network routing, file and frequency distribution, the exploration of network structures and vulnerability, and various other practical networking applications.

Statistics, Computation, and Modeling in Cosmology

NASA Astrophysics Data System (ADS)

Jewell, Jeff; Guiness, Joe; SAMSI 2016 Working Group in Cosmology

2017-01-01

Current and future ground and space based missions are designed to not only detect, but map out with increasing precision, details of the universe in its infancy to the present-day. As a result we are faced with the challenge of analyzing and interpreting observations from a wide variety of instruments to form a coherent view of the universe. Finding solutions to a broad range of challenging inference problems in cosmology is one of the goals of the “Statistics, Computation, and Modeling in Cosmology” workings groups, formed as part of the year long program on ‘Statistical, Mathematical, and Computational Methods for Astronomy’, hosted by the Statistical and Applied Mathematical Sciences Institute (SAMSI), a National Science Foundation funded institute. Two application areas have emerged for focused development in the cosmology working group involving advanced algorithmic implementations of exact Bayesian inference for the Cosmic Microwave Background, and statistical modeling of galaxy formation. The former includes study and development of advanced Markov Chain Monte Carlo algorithms designed to confront challenging inference problems including inference for spatial Gaussian random fields in the presence of sources of galactic emission (an example of a source separation problem). Extending these methods to future redshift survey data probing the nonlinear regime of large scale structure formation is also included in the working group activities. In addition, the working group is also focused on the study of ‘Galacticus’, a galaxy formation model applied to dark matter-only cosmological N-body simulations operating on time-dependent halo merger trees. The working group is interested in calibrating the Galacticus model to match statistics of galaxy survey observations; specifically stellar mass functions, luminosity functions, and color-color diagrams. The group will use subsampling approaches and fractional factorial designs to statistically and computationally efficiently explore the Galacticus parameter space. The group will also use the Galacticus simulations to study the relationship between the topological and physical structure of the halo merger trees and the properties of the resulting galaxies.

Estimating inverse probability weights using super learner when weight-model specification is unknown in a marginal structural Cox model context.

PubMed

Karim, Mohammad Ehsanul; Platt, Robert W

2017-06-15

Correct specification of the inverse probability weighting (IPW) model is necessary for consistent inference from a marginal structural Cox model (MSCM). In practical applications, researchers are typically unaware of the true specification of the weight model. Nonetheless, IPWs are commonly estimated using parametric models, such as the main-effects logistic regression model. In practice, assumptions underlying such models may not hold and data-adaptive statistical learning methods may provide an alternative. Many candidate statistical learning approaches are available in the literature. However, the optimal approach for a given dataset is impossible to predict. Super learner (SL) has been proposed as a tool for selecting an optimal learner from a set of candidates using cross-validation. In this study, we evaluate the usefulness of a SL in estimating IPW in four different MSCM simulation scenarios, in which we varied the specification of the true weight model specification (linear and/or additive). Our simulations show that, in the presence of weight model misspecification, with a rich and diverse set of candidate algorithms, SL can generally offer a better alternative to the commonly used statistical learning approaches in terms of MSE as well as the coverage probabilities of the estimated effect in an MSCM. The findings from the simulation studies guided the application of the MSCM in a multiple sclerosis cohort from British Columbia, Canada (1995-2008), to estimate the impact of beta-interferon treatment in delaying disability progression. Copyright © 2017 John Wiley & Sons, Ltd. Copyright © 2017 John Wiley & Sons, Ltd.

D-Optimal Experimental Design for Contaminant Source Identification

NASA Astrophysics Data System (ADS)

Sai Baba, A. K.; Alexanderian, A.

2016-12-01

Contaminant source identification seeks to estimate the release history of a conservative solute given point concentration measurements at some time after the release. This can be mathematically expressed as an inverse problem, with a linear observation operator or a parameter-to-observation map, which we tackle using a Bayesian approach. Acquisition of experimental data can be laborious and expensive. The goal is to control the experimental parameters - in our case, the sparsity of the sensors, to maximize the information gain subject to some physical or budget constraints. This is known as optimal experimental design (OED). D-optimal experimental design seeks to maximize the expected information gain, and has long been considered the gold standard in the statistics community. Our goal is to develop scalable methods for D-optimal experimental designs involving large-scale PDE constrained problems with high-dimensional parameter fields. A major challenge for the OED, is that a nonlinear optimization algorithm for the D-optimality criterion requires repeated evaluation of objective function and gradient involving the determinant of large and dense matrices - this cost can be prohibitively expensive for applications of interest. We propose novel randomized matrix techniques that bring down the computational costs of the objective function and gradient evaluations by several orders of magnitude compared to the naive approach. The effect of randomized estimators on the accuracy and the convergence of the optimization solver will be discussed. The features and benefits of our new approach will be demonstrated on a challenging model problem from contaminant source identification involving the inference of the initial condition from spatio-temporal observations in a time-dependent advection-diffusion problem.

Hybrid regulatory models: a statistically tractable approach to model regulatory network dynamics.

PubMed

Ocone, Andrea; Millar, Andrew J; Sanguinetti, Guido

2013-04-01

Computational modelling of the dynamics of gene regulatory networks is a central task of systems biology. For networks of small/medium scale, the dominant paradigm is represented by systems of coupled non-linear ordinary differential equations (ODEs). ODEs afford great mechanistic detail and flexibility, but calibrating these models to data is often an extremely difficult statistical problem. Here, we develop a general statistical inference framework for stochastic transcription-translation networks. We use a coarse-grained approach, which represents the system as a network of stochastic (binary) promoter and (continuous) protein variables. We derive an exact inference algorithm and an efficient variational approximation that allows scalable inference and learning of the model parameters. We demonstrate the power of the approach on two biological case studies, showing that the method allows a high degree of flexibility and is capable of testable novel biological predictions. http://homepages.inf.ed.ac.uk/gsanguin/software.html. Supplementary data are available at Bioinformatics online.

Low-Pass Genome-Wide Sequencing and Variant Inference Using Identity-by-Descent in an Isolated Human Population

PubMed Central

Gusev, A.; Shah, M. J.; Kenny, E. E.; Ramachandran, A.; Lowe, J. K.; Salit, J.; Lee, C. C.; Levandowsky, E. C.; Weaver, T. N.; Doan, Q. C.; Peckham, H. E.; McLaughlin, S. F.; Lyons, M. R.; Sheth, V. N.; Stoffel, M.; De La Vega, F. M.; Friedman, J. M.; Breslow, J. L.

2012-01-01

Whole-genome sequencing in an isolated population with few founders directly ascertains variants from the population bottleneck that may be rare elsewhere. In such populations, shared haplotypes allow imputation of variants in unsequenced samples without resorting to complex statistical methods as in studies of outbred cohorts. We focus on an isolated population cohort from the Pacific Island of Kosrae, Micronesia, where we previously collected SNP array and rich phenotype data for the majority of the population. We report identification of long regions with haplotypes co-inherited between pairs of individuals and methodology to leverage such shared genetic content for imputation. Our estimates show that sequencing as few as 40 personal genomes allows for inference in up to 60% of the 3000-person cohort at the average locus. We ascertained a pilot data set of whole-genome sequences from seven Kosraean individuals, with average 5× coverage. This assay identified 5,735,306 unique sites of which 1,212,831 were previously unknown. Additionally, these variants are unusually enriched for alleles that are rare in other populations when compared to geographic neighbors (published Korean genome SJK). We used the presence of shared haplotypes between the seven Kosraen individuals to estimate expected imputation accuracy of known and novel homozygous variants at 99.6% and 97.3%, respectively. This study presents whole-genome analysis of a homogenous isolate population with emphasis on optimal rare variant inference. PMID:22135348

CADDIS Volume 4. Data Analysis: PECBO Appendix - R Scripts for Non-Parametric Regressions

EPA Pesticide Factsheets

Script for computing nonparametric regression analysis. Overview of using scripts to infer environmental conditions from biological observations, statistically estimating species-environment relationships, statistical scripts.

Test Theory Reconceived.

ERIC Educational Resources Information Center

Mislevy, Robert J.

Educational test theory consists of statistical and methodological tools to support inferences about examinees' knowledge, skills, and accomplishments. The evolution of test theory has been shaped by the nature of users' inferences which, until recently, have been framed almost exclusively in terms of trait and behavioral psychology. Progress in…

Data-driven sensitivity inference for Thomson scattering electron density measurement systems.

PubMed

Fujii, Keisuke; Yamada, Ichihiro; Hasuo, Masahiro

2017-01-01

We developed a method to infer the calibration parameters of multichannel measurement systems, such as channel variations of sensitivity and noise amplitude, from experimental data. We regard such uncertainties of the calibration parameters as dependent noise. The statistical properties of the dependent noise and that of the latent functions were modeled and implemented in the Gaussian process kernel. Based on their statistical difference, both parameters were inferred from the data. We applied this method to the electron density measurement system by Thomson scattering for the Large Helical Device plasma, which is equipped with 141 spatial channels. Based on the 210 sets of experimental data, we evaluated the correction factor of the sensitivity and noise amplitude for each channel. The correction factor varies by ≈10%, and the random noise amplitude is ≈2%, i.e., the measurement accuracy increases by a factor of 5 after this sensitivity correction. The certainty improvement in the spatial derivative inference was demonstrated.

Evaluating sufficient similarity for drinking-water disinfection by-product (DBP) mixtures with bootstrap hypothesis test procedures.

PubMed

Feder, Paul I; Ma, Zhenxu J; Bull, Richard J; Teuschler, Linda K; Rice, Glenn

2009-01-01

In chemical mixtures risk assessment, the use of dose-response data developed for one mixture to estimate risk posed by a second mixture depends on whether the two mixtures are sufficiently similar. While evaluations of similarity may be made using qualitative judgments, this article uses nonparametric statistical methods based on the "bootstrap" resampling technique to address the question of similarity among mixtures of chemical disinfectant by-products (DBP) in drinking water. The bootstrap resampling technique is a general-purpose, computer-intensive approach to statistical inference that substitutes empirical sampling for theoretically based parametric mathematical modeling. Nonparametric, bootstrap-based inference involves fewer assumptions than parametric normal theory based inference. The bootstrap procedure is appropriate, at least in an asymptotic sense, whether or not the parametric, distributional assumptions hold, even approximately. The statistical analysis procedures in this article are initially illustrated with data from 5 water treatment plants (Schenck et al., 2009), and then extended using data developed from a study of 35 drinking-water utilities (U.S. EPA/AMWA, 1989), which permits inclusion of a greater number of water constituents and increased structure in the statistical models.

Agile Text Mining for the 2014 i2b2/UTHealth Cardiac Risk Factors Challenge

PubMed Central

Cormack, James; Nath, Chinmoy; Milward, David; Raja, Kalpana; Jonnalagadda, Siddhartha R

2016-01-01

This paper describes the use of an agile text mining platform (Linguamatics’ Interactive Information Extraction Platform, I2E) to extract document-level cardiac risk factors in patient records as defined in the i2b2/UTHealth 2014 Challenge. The approach uses a data-driven rule-based methodology with the addition of a simple supervised classifier. We demonstrate that agile text mining allows for rapid optimization of extraction strategies, while post-processing can leverage annotation guidelines, corpus statistics and logic inferred from the gold standard data. We also show how data imbalance in a training set affects performance. Evaluation of this approach on the test data gave an F-Score of 91.7%, one percent behind the top performing system. PMID:26209007

Three-dimensional analysis of magnetometer array data

NASA Technical Reports Server (NTRS)

Richmond, A. D.; Baumjohann, W.

1984-01-01

A technique is developed for mapping magnetic variation fields in three dimensions using data from an array of magnetometers, based on the theory of optimal linear estimation. The technique is applied to data from the Scandinavian Magnetometer Array. Estimates of the spatial power spectra for the internal and external magnetic variations are derived, which in turn provide estimates of the spatial autocorrelation functions of the three magnetic variation components. Statistical errors involved in mapping the external and internal fields are quantified and displayed over the mapping region. Examples of field mapping and of separation into external and internal components are presented. A comparison between the three-dimensional field separation and a two-dimensional separation from a single chain of stations shows that significant differences can arise in the inferred internal component.

Local dependence in random graph models: characterization, properties and statistical inference

PubMed Central

Schweinberger, Michael; Handcock, Mark S.

2015-01-01

Summary Dependent phenomena, such as relational, spatial and temporal phenomena, tend to be characterized by local dependence in the sense that units which are close in a well-defined sense are dependent. In contrast with spatial and temporal phenomena, though, relational phenomena tend to lack a natural neighbourhood structure in the sense that it is unknown which units are close and thus dependent. Owing to the challenge of characterizing local dependence and constructing random graph models with local dependence, many conventional exponential family random graph models induce strong dependence and are not amenable to statistical inference. We take first steps to characterize local dependence in random graph models, inspired by the notion of finite neighbourhoods in spatial statistics and M-dependence in time series, and we show that local dependence endows random graph models with desirable properties which make them amenable to statistical inference. We show that random graph models with local dependence satisfy a natural domain consistency condition which every model should satisfy, but conventional exponential family random graph models do not satisfy. In addition, we establish a central limit theorem for random graph models with local dependence, which suggests that random graph models with local dependence are amenable to statistical inference. We discuss how random graph models with local dependence can be constructed by exploiting either observed or unobserved neighbourhood structure. In the absence of observed neighbourhood structure, we take a Bayesian view and express the uncertainty about the neighbourhood structure by specifying a prior on a set of suitable neighbourhood structures. We present simulation results and applications to two real world networks with ‘ground truth’. PMID:26560142

Statistical inference, the bootstrap, and neural-network modeling with application to foreign exchange rates.

PubMed

White, H; Racine, J

2001-01-01

We propose tests for individual and joint irrelevance of network inputs. Such tests can be used to determine whether an input or group of inputs "belong" in a particular model, thus permitting valid statistical inference based on estimated feedforward neural-network models. The approaches employ well-known statistical resampling techniques. We conduct a small Monte Carlo experiment showing that our tests have reasonable level and power behavior, and we apply our methods to examine whether there are predictable regularities in foreign exchange rates. We find that exchange rates do appear to contain information that is exploitable for enhanced point prediction, but the nature of the predictive relations evolves through time.

Active Inference, homeostatic regulation and adaptive behavioural control

PubMed Central

Pezzulo, Giovanni; Rigoli, Francesco; Friston, Karl

2015-01-01

We review a theory of homeostatic regulation and adaptive behavioural control within the Active Inference framework. Our aim is to connect two research streams that are usually considered independently; namely, Active Inference and associative learning theories of animal behaviour. The former uses a probabilistic (Bayesian) formulation of perception and action, while the latter calls on multiple (Pavlovian, habitual, goal-directed) processes for homeostatic and behavioural control. We offer a synthesis these classical processes and cast them as successive hierarchical contextualisations of sensorimotor constructs, using the generative models that underpin Active Inference. This dissolves any apparent mechanistic distinction between the optimization processes that mediate classical control or learning. Furthermore, we generalize the scope of Active Inference by emphasizing interoceptive inference and homeostatic regulation. The ensuing homeostatic (or allostatic) perspective provides an intuitive explanation for how priors act as drives or goals to enslave action, and emphasises the embodied nature of inference. PMID:26365173

FUNSTAT and statistical image representations

NASA Technical Reports Server (NTRS)

Parzen, E.

1983-01-01

General ideas of functional statistical inference analysis of one sample and two samples, univariate and bivariate are outlined. ONESAM program is applied to analyze the univariate probability distributions of multi-spectral image data.

The Sense of Confidence during Probabilistic Learning: A Normative Account.

PubMed

Meyniel, Florent; Schlunegger, Daniel; Dehaene, Stanislas

2015-06-01

Learning in a stochastic environment consists of estimating a model from a limited amount of noisy data, and is therefore inherently uncertain. However, many classical models reduce the learning process to the updating of parameter estimates and neglect the fact that learning is also frequently accompanied by a variable "feeling of knowing" or confidence. The characteristics and the origin of these subjective confidence estimates thus remain largely unknown. Here we investigate whether, during learning, humans not only infer a model of their environment, but also derive an accurate sense of confidence from their inferences. In our experiment, humans estimated the transition probabilities between two visual or auditory stimuli in a changing environment, and reported their mean estimate and their confidence in this report. To formalize the link between both kinds of estimate and assess their accuracy in comparison to a normative reference, we derive the optimal inference strategy for our task. Our results indicate that subjects accurately track the likelihood that their inferences are correct. Learning and estimating confidence in what has been learned appear to be two intimately related abilities, suggesting that they arise from a single inference process. We show that human performance matches several properties of the optimal probabilistic inference. In particular, subjective confidence is impacted by environmental uncertainty, both at the first level (uncertainty in stimulus occurrence given the inferred stochastic characteristics) and at the second level (uncertainty due to unexpected changes in these stochastic characteristics). Confidence also increases appropriately with the number of observations within stable periods. Our results support the idea that humans possess a quantitative sense of confidence in their inferences about abstract non-sensory parameters of the environment. This ability cannot be reduced to simple heuristics, it seems instead a core property of the learning process.

The Sense of Confidence during Probabilistic Learning: A Normative Account

PubMed Central

Meyniel, Florent; Schlunegger, Daniel; Dehaene, Stanislas

2015-01-01

Learning in a stochastic environment consists of estimating a model from a limited amount of noisy data, and is therefore inherently uncertain. However, many classical models reduce the learning process to the updating of parameter estimates and neglect the fact that learning is also frequently accompanied by a variable “feeling of knowing” or confidence. The characteristics and the origin of these subjective confidence estimates thus remain largely unknown. Here we investigate whether, during learning, humans not only infer a model of their environment, but also derive an accurate sense of confidence from their inferences. In our experiment, humans estimated the transition probabilities between two visual or auditory stimuli in a changing environment, and reported their mean estimate and their confidence in this report. To formalize the link between both kinds of estimate and assess their accuracy in comparison to a normative reference, we derive the optimal inference strategy for our task. Our results indicate that subjects accurately track the likelihood that their inferences are correct. Learning and estimating confidence in what has been learned appear to be two intimately related abilities, suggesting that they arise from a single inference process. We show that human performance matches several properties of the optimal probabilistic inference. In particular, subjective confidence is impacted by environmental uncertainty, both at the first level (uncertainty in stimulus occurrence given the inferred stochastic characteristics) and at the second level (uncertainty due to unexpected changes in these stochastic characteristics). Confidence also increases appropriately with the number of observations within stable periods. Our results support the idea that humans possess a quantitative sense of confidence in their inferences about abstract non-sensory parameters of the environment. This ability cannot be reduced to simple heuristics, it seems instead a core property of the learning process. PMID:26076466

Efficient Sampling of Parsimonious Inversion Histories with Application to Genome Rearrangement in Yersinia

PubMed Central

Darling, Aaron E.

2009-01-01

Inversions are among the most common mutations acting on the order and orientation of genes in a genome, and polynomial-time algorithms exist to obtain a minimal length series of inversions that transform one genome arrangement to another. However, the minimum length series of inversions (the optimal sorting path) is often not unique as many such optimal sorting paths exist. If we assume that all optimal sorting paths are equally likely, then statistical inference on genome arrangement history must account for all such sorting paths and not just a single estimate. No deterministic polynomial algorithm is known to count the number of optimal sorting paths nor sample from the uniform distribution of optimal sorting paths. Here, we propose a stochastic method that uniformly samples the set of all optimal sorting paths. Our method uses a novel formulation of parallel Markov chain Monte Carlo. In practice, our method can quickly estimate the total number of optimal sorting paths. We introduce a variant of our approach in which short inversions are modeled to be more likely, and we show how the method can be used to estimate the distribution of inversion lengths and breakpoint usage in pathogenic Yersinia pestis. The proposed method has been implemented in a program called “MC4Inversion.” We draw comparison of MC4Inversion to the sampler implemented in BADGER and a previously described importance sampling (IS) technique. We find that on high-divergence data sets, MC4Inversion finds more optimal sorting paths per second than BADGER and the IS technique and simultaneously avoids bias inherent in the IS technique. PMID:20333186

Building Intuitions about Statistical Inference Based on Resampling

ERIC Educational Resources Information Center

Watson, Jane; Chance, Beth

2012-01-01

Formal inference, which makes theoretical assumptions about distributions and applies hypothesis testing procedures with null and alternative hypotheses, is notoriously difficult for tertiary students to master. The debate about whether this content should appear in Years 11 and 12 of the "Australian Curriculum: Mathematics" has gone on…

Theory-based Bayesian models of inductive learning and reasoning.

PubMed

Tenenbaum, Joshua B; Griffiths, Thomas L; Kemp, Charles

2006-07-01

Inductive inference allows humans to make powerful generalizations from sparse data when learning about word meanings, unobserved properties, causal relationships, and many other aspects of the world. Traditional accounts of induction emphasize either the power of statistical learning, or the importance of strong constraints from structured domain knowledge, intuitive theories or schemas. We argue that both components are necessary to explain the nature, use and acquisition of human knowledge, and we introduce a theory-based Bayesian framework for modeling inductive learning and reasoning as statistical inferences over structured knowledge representations.

Data free inference with processed data products

DOE PAGES

Chowdhary, K.; Najm, H. N.

2014-07-12

Here, we consider the context of probabilistic inference of model parameters given error bars or confidence intervals on model output values, when the data is unavailable. We introduce a class of algorithms in a Bayesian framework, relying on maximum entropy arguments and approximate Bayesian computation methods, to generate consistent data with the given summary statistics. Once we obtain consistent data sets, we pool the respective posteriors, to arrive at a single, averaged density on the parameters. This approach allows us to perform accurate forward uncertainty propagation consistent with the reported statistics.

Statistics at the Chinese Universities.

DTIC Science & Technology

1981-09-01

education in China in the postwar years is pro- vided to give some perspective. My observa- tions on statistics at the Chinese universities are necessarily...has been accepted as a member society of ISI. 3. Education in China Understanding of statistics in universities in China will be enhanced through some...programaming), Statistical Mathematics (infer- ence, data analysis, industrial statistics , information theory), tiathematical Physics (dif- ferential

Shear wave prediction using committee fuzzy model constrained by lithofacies, Zagros basin, SW Iran

NASA Astrophysics Data System (ADS)

Shiroodi, Sadjad Kazem; Ghafoori, Mohammad; Ansari, Hamid Reza; Lashkaripour, Golamreza; Ghanadian, Mostafa

2017-02-01

The main purpose of this study is to introduce the geological controlling factors in improving an intelligence-based model to estimate shear wave velocity from seismic attributes. The proposed method includes three main steps in the framework of geological events in a complex sedimentary succession located in the Persian Gulf. First, the best attributes were selected from extracted seismic data. Second, these attributes were transformed into shear wave velocity using fuzzy inference systems (FIS) such as Sugeno's fuzzy inference (SFIS), adaptive neuro-fuzzy inference (ANFIS) and optimized fuzzy inference (OFIS). Finally, a committee fuzzy machine (CFM) based on bat-inspired algorithm (BA) optimization was applied to combine previous predictions into an enhanced solution. In order to show the geological effect on improving the prediction, the main classes of predominate lithofacies in the reservoir of interest including shale, sand, and carbonate were selected and then the proposed algorithm was performed with and without lithofacies constraint. The results showed a good agreement between real and predicted shear wave velocity in the lithofacies-based model compared to the model without lithofacies especially in sand and carbonate.

The role of familiarity in binary choice inferences.

PubMed

Honda, Hidehito; Abe, Keiga; Matsuka, Toshihiko; Yamagishi, Kimihiko

2011-07-01

In research on the recognition heuristic (Goldstein & Gigerenzer, Psychological Review, 109, 75-90, 2002), knowledge of recognized objects has been categorized as "recognized" or "unrecognized" without regard to the degree of familiarity of the recognized object. In the present article, we propose a new inference model--familiarity-based inference. We hypothesize that when subjective knowledge levels (familiarity) of recognized objects differ, the degree of familiarity of recognized objects will influence inferences. Specifically, people are predicted to infer that the more familiar object in a pair of two objects has a higher criterion value on the to-be-judged dimension. In two experiments, using a binary choice task, we examined inferences about populations in a pair of two cities. Results support predictions of familiarity-based inference. Participants inferred that the more familiar city in a pair was more populous. Statistical modeling showed that individual differences in familiarity-based inference lie in the sensitivity to differences in familiarity. In addition, we found that familiarity-based inference can be generally regarded as an ecologically rational inference. Furthermore, when cue knowledge about the inference criterion was available, participants made inferences based on the cue knowledge about population instead of familiarity. Implications of the role of familiarity in psychological processes are discussed.

Statistical modeling of software reliability

NASA Technical Reports Server (NTRS)

Miller, Douglas R.

1992-01-01

This working paper discusses the statistical simulation part of a controlled software development experiment being conducted under the direction of the System Validation Methods Branch, Information Systems Division, NASA Langley Research Center. The experiment uses guidance and control software (GCS) aboard a fictitious planetary landing spacecraft: real-time control software operating on a transient mission. Software execution is simulated to study the statistical aspects of reliability and other failure characteristics of the software during development, testing, and random usage. Quantification of software reliability is a major goal. Various reliability concepts are discussed. Experiments are described for performing simulations and collecting appropriate simulated software performance and failure data. This data is then used to make statistical inferences about the quality of the software development and verification processes as well as inferences about the reliability of software versions and reliability growth under random testing and debugging.

Quantum-Like Representation of Non-Bayesian Inference

NASA Astrophysics Data System (ADS)

Asano, M.; Basieva, I.; Khrennikov, A.; Ohya, M.; Tanaka, Y.

2013-01-01

This research is related to the problem of "irrational decision making or inference" that have been discussed in cognitive psychology. There are some experimental studies, and these statistical data cannot be described by classical probability theory. The process of decision making generating these data cannot be reduced to the classical Bayesian inference. For this problem, a number of quantum-like coginitive models of decision making was proposed. Our previous work represented in a natural way the classical Bayesian inference in the frame work of quantum mechanics. By using this representation, in this paper, we try to discuss the non-Bayesian (irrational) inference that is biased by effects like the quantum interference. Further, we describe "psychological factor" disturbing "rationality" as an "environment" correlating with the "main system" of usual Bayesian inference.

Inference of scale-free networks from gene expression time series.

PubMed

Daisuke, Tominaga; Horton, Paul

2006-04-01

Quantitative time-series observation of gene expression is becoming possible, for example by cell array technology. However, there are no practical methods with which to infer network structures using only observed time-series data. As most computational models of biological networks for continuous time-series data have a high degree of freedom, it is almost impossible to infer the correct structures. On the other hand, it has been reported that some kinds of biological networks, such as gene networks and metabolic pathways, may have scale-free properties. We hypothesize that the architecture of inferred biological network models can be restricted to scale-free networks. We developed an inference algorithm for biological networks using only time-series data by introducing such a restriction. We adopt the S-system as the network model, and a distributed genetic algorithm to optimize models to fit its simulated results to observed time series data. We have tested our algorithm on a case study (simulated data). We compared optimization under no restriction, which allows for a fully connected network, and under the restriction that the total number of links must equal that expected from a scale free network. The restriction reduced both false positive and false negative estimation of the links and also the differences between model simulation and the given time-series data.

Retrieving the ground state of spin glasses using thermal noise: Performance of quantum annealing at finite temperatures.

PubMed

Nishimura, Kohji; Nishimori, Hidetoshi; Ochoa, Andrew J; Katzgraber, Helmut G

2016-09-01

We study the problem to infer the ground state of a spin-glass Hamiltonian using data from another Hamiltonian with interactions disturbed by noise from the original Hamiltonian, motivated by the ground-state inference in quantum annealing on a noisy device. It is shown that the average Hamming distance between the inferred spin configuration and the true ground state is minimized when the temperature of the noisy system is kept at a finite value, and not at zero temperature. We present a spin-glass generalization of a well-established result that the ground state of a purely ferromagnetic Hamiltonian is best inferred at a finite temperature in the sense of smallest Hamming distance when the original ferromagnetic interactions are disturbed by noise. We use the numerical transfer-matrix method to establish the existence of an optimal finite temperature in one- and two-dimensional systems. Our numerical results are supported by mean-field calculations, which give an explicit expression of the optimal temperature to infer the spin-glass ground state as a function of variances of the distributions of the original interactions and the noise. The mean-field prediction is in qualitative agreement with numerical data. Implications on postprocessing of quantum annealing on a noisy device are discussed.

Finding undetected protein associations in cell signaling by belief propagation.

PubMed

Bailly-Bechet, M; Borgs, C; Braunstein, A; Chayes, J; Dagkessamanskaia, A; François, J-M; Zecchina, R

2011-01-11

External information propagates in the cell mainly through signaling cascades and transcriptional activation, allowing it to react to a wide spectrum of environmental changes. High-throughput experiments identify numerous molecular components of such cascades that may, however, interact through unknown partners. Some of them may be detected using data coming from the integration of a protein-protein interaction network and mRNA expression profiles. This inference problem can be mapped onto the problem of finding appropriate optimal connected subgraphs of a network defined by these datasets. The optimization procedure turns out to be computationally intractable in general. Here we present a new distributed algorithm for this task, inspired from statistical physics, and apply this scheme to alpha factor and drug perturbations data in yeast. We identify the role of the COS8 protein, a member of a gene family of previously unknown function, and validate the results by genetic experiments. The algorithm we present is specially suited for very large datasets, can run in parallel, and can be adapted to other problems in systems biology. On renowned benchmarks it outperforms other algorithms in the field.

Prediction of silicon oxynitride plasma etching using a generalized regression neural network

NASA Astrophysics Data System (ADS)

Kim, Byungwhan; Lee, Byung Teak

2005-08-01

A prediction model of silicon oxynitride (SiON) etching was constructed using a neural network. Model prediction performance was improved by means of genetic algorithm. The etching was conducted in a C2F6 inductively coupled plasma. A 24 full factorial experiment was employed to systematically characterize parameter effects on SiON etching. The process parameters include radio frequency source power, bias power, pressure, and C2F6 flow rate. To test the appropriateness of the trained model, additional 16 experiments were conducted. For comparison, four types of statistical regression models were built. Compared to the best regression model, the optimized neural network model demonstrated an improvement of about 52%. The optimized model was used to infer etch mechanisms as a function of parameters. The pressure effect was noticeably large only as relatively large ion bombardment was maintained in the process chamber. Ion-bombardment-activated polymer deposition played the most significant role in interpreting the complex effect of bias power or C2F6 flow rate. Moreover, [CF2] was expected to be the predominant precursor to polymer deposition.

Optimal predictions in everyday cognition: the wisdom of individuals or crowds?

PubMed

Mozer, Michael C; Pashler, Harold; Homaei, Hadjar

2008-10-01

Griffiths and Tenenbaum (2006) asked individuals to make predictions about the duration or extent of everyday events (e.g., cake baking times), and reported that predictions were optimal, employing Bayesian inference based on veridical prior distributions. Although the predictions conformed strikingly to statistics of the world, they reflect averages over many individuals. On the conjecture that the accuracy of the group response is chiefly a consequence of aggregating across individuals, we constructed simple, heuristic approximations to the Bayesian model premised on the hypothesis that individuals have access merely to a sample of k instances drawn from the relevant distribution. The accuracy of the group response reported by Griffiths and Tenenbaum could be accounted for by supposing that individuals each utilize only two instances. Moreover, the variability of the group data is more consistent with this small-sample hypothesis than with the hypothesis that people utilize veridical or nearly veridical representations of the underlying prior distributions. Our analyses lead to a qualitatively different view of how individuals reason from past experience than the view espoused by Griffiths and Tenenbaum. 2008 Cognitive Science Society, Inc.

Why environmental scientists are becoming Bayesians

Treesearch

James S. Clark

2005-01-01

Advances in computational statistics provide a general framework for the high dimensional models typically needed for ecological inference and prediction. Hierarchical Bayes (HB) represents a modelling structure with capacity to exploit diverse sources of information, to accommodate influences that are unknown (or unknowable), and to draw inference on large numbers of...

Pseudocontingencies and Choice Behavior in Probabilistic Environments with Context-Dependent Outcomes

ERIC Educational Resources Information Center

Meiser, Thorsten; Rummel, Jan; Fleig, Hanna

2018-01-01

Pseudocontingencies are inferences about correlations in the environment that are formed on the basis of statistical regularities like skewed base rates or varying base rates across environmental contexts. Previous research has demonstrated that pseudocontingencies provide a pervasive mechanism of inductive inference in numerous social judgment…

Cross-Situational Learning of Minimal Word Pairs

ERIC Educational Resources Information Center

Escudero, Paola; Mulak, Karen E.; Vlach, Haley A.

2016-01-01

"Cross-situational statistical learning" of words involves tracking co-occurrences of auditory words and objects across time to infer word-referent mappings. Previous research has demonstrated that learners can infer referents across sets of very phonologically distinct words (e.g., WUG, DAX), but it remains unknown whether learners can…

An expert system environment for the Generic VHSIC Spaceborne Computer (GVSC)

NASA Astrophysics Data System (ADS)

Cockerham, Ann; Labhart, Jay; Rowe, Michael; Skinner, James

The authors describe a Phase II Phillips Laboratory Small Business Innovative Research (SBIR) program being performed to implement a flexible and general-purpose inference environment for embedded space and avionics applications. This inference environment is being developed in Ada and takes special advantage of the target architecture, the GVSC. The GVSC implements the MIL-STD-1750A ISA and contains enhancements to allow access of up to 8 MBytes of memory. The inference environment makes use of the Merit Enhanced Traversal Engine (METE) algorithm, which employs the latest inference and knowledge representation strategies to optimize both run-time speed and memory utilization.

Statistical analysis of fNIRS data: a comprehensive review.

PubMed

Tak, Sungho; Ye, Jong Chul

2014-01-15

Functional near-infrared spectroscopy (fNIRS) is a non-invasive method to measure brain activities using the changes of optical absorption in the brain through the intact skull. fNIRS has many advantages over other neuroimaging modalities such as positron emission tomography (PET), functional magnetic resonance imaging (fMRI), or magnetoencephalography (MEG), since it can directly measure blood oxygenation level changes related to neural activation with high temporal resolution. However, fNIRS signals are highly corrupted by measurement noises and physiology-based systemic interference. Careful statistical analyses are therefore required to extract neuronal activity-related signals from fNIRS data. In this paper, we provide an extensive review of historical developments of statistical analyses of fNIRS signal, which include motion artifact correction, short source-detector separation correction, principal component analysis (PCA)/independent component analysis (ICA), false discovery rate (FDR), serially-correlated errors, as well as inference techniques such as the standard t-test, F-test, analysis of variance (ANOVA), and statistical parameter mapping (SPM) framework. In addition, to provide a unified view of various existing inference techniques, we explain a linear mixed effect model with restricted maximum likelihood (ReML) variance estimation, and show that most of the existing inference methods for fNIRS analysis can be derived as special cases. Some of the open issues in statistical analysis are also described. Copyright © 2013 Elsevier Inc. All rights reserved.

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.

Using MOEA with Redistribution and Consensus Branches to Infer Phylogenies.

PubMed

Min, Xiaoping; Zhang, Mouzhao; Yuan, Sisi; Ge, Shengxiang; Liu, Xiangrong; Zeng, Xiangxiang; Xia, Ningshao

2017-12-26

In recent years, to infer phylogenies, which are NP-hard problems, more and more research has focused on using metaheuristics. Maximum Parsimony and Maximum Likelihood are two effective ways to conduct inference. Based on these methods, which can also be considered as the optimal criteria for phylogenies, various kinds of multi-objective metaheuristics have been used to reconstruct phylogenies. However, combining these two time-consuming methods results in those multi-objective metaheuristics being slower than a single objective. Therefore, we propose a novel, multi-objective optimization algorithm, MOEA-RC, to accelerate the processes of rebuilding phylogenies using structural information of elites in current populations. We compare MOEA-RC with two representative multi-objective algorithms, MOEA/D and NAGA-II, and a non-consensus version of MOEA-RC on three real-world datasets. The result is, within a given number of iterations, MOEA-RC achieves better solutions than the other algorithms.

Accounting for measurement error: a critical but often overlooked process.

PubMed

Harris, Edward F; Smith, Richard N

2009-12-01

Due to instrument imprecision and human inconsistencies, measurements are not free of error. Technical error of measurement (TEM) is the variability encountered between dimensions when the same specimens are measured at multiple sessions. A goal of a data collection regimen is to minimise TEM. The few studies that actually quantify TEM, regardless of discipline, report that it is substantial and can affect results and inferences. This paper reviews some statistical approaches for identifying and controlling TEM. Statistically, TEM is part of the residual ('unexplained') variance in a statistical test, so accounting for TEM, which requires repeated measurements, enhances the chances of finding a statistically significant difference if one exists. The aim of this paper was to review and discuss common statistical designs relating to types of error and statistical approaches to error accountability. This paper addresses issues of landmark location, validity, technical and systematic error, analysis of variance, scaled measures and correlation coefficients in order to guide the reader towards correct identification of true experimental differences. Researchers commonly infer characteristics about populations from comparatively restricted study samples. Most inferences are statistical and, aside from concerns about adequate accounting for known sources of variation with the research design, an important source of variability is measurement error. Variability in locating landmarks that define variables is obvious in odontometrics, cephalometrics and anthropometry, but the same concerns about measurement accuracy and precision extend to all disciplines. With increasing accessibility to computer-assisted methods of data collection, the ease of incorporating repeated measures into statistical designs has improved. Accounting for this technical source of variation increases the chance of finding biologically true differences when they exist.

Developing a statistically powerful measure for quartet tree inference using phylogenetic identities and Markov invariants.

PubMed

Sumner, Jeremy G; Taylor, Amelia; Holland, Barbara R; Jarvis, Peter D

2017-12-01

Recently there has been renewed interest in phylogenetic inference methods based on phylogenetic invariants, alongside the related Markov invariants. Broadly speaking, both these approaches give rise to polynomial functions of sequence site patterns that, in expectation value, either vanish for particular evolutionary trees (in the case of phylogenetic invariants) or have well understood transformation properties (in the case of Markov invariants). While both approaches have been valued for their intrinsic mathematical interest, it is not clear how they relate to each other, and to what extent they can be used as practical tools for inference of phylogenetic trees. In this paper, by focusing on the special case of binary sequence data and quartets of taxa, we are able to view these two different polynomial-based approaches within a common framework. To motivate the discussion, we present three desirable statistical properties that we argue any invariant-based phylogenetic method should satisfy: (1) sensible behaviour under reordering of input sequences; (2) stability as the taxa evolve independently according to a Markov process; and (3) explicit dependence on the assumption of a continuous-time process. Motivated by these statistical properties, we develop and explore several new phylogenetic inference methods. In particular, we develop a statistically bias-corrected version of the Markov invariants approach which satisfies all three properties. We also extend previous work by showing that the phylogenetic invariants can be implemented in such a way as to satisfy property (3). A simulation study shows that, in comparison to other methods, our new proposed approach based on bias-corrected Markov invariants is extremely powerful for phylogenetic inference. The binary case is of particular theoretical interest as-in this case only-the Markov invariants can be expressed as linear combinations of the phylogenetic invariants. A wider implication of this is that, for models with more than two states-for example DNA sequence alignments with four-state models-we find that methods which rely on phylogenetic invariants are incapable of satisfying all three of the stated statistical properties. This is because in these cases the relevant Markov invariants belong to a class of polynomials independent from the phylogenetic invariants.

Imputation approaches for animal movement modeling

USGS Publications Warehouse

Scharf, Henry; Hooten, Mevin B.; Johnson, Devin S.

2017-01-01

The analysis of telemetry data is common in animal ecological studies. While the collection of telemetry data for individual animals has improved dramatically, the methods to properly account for inherent uncertainties (e.g., measurement error, dependence, barriers to movement) have lagged behind. Still, many new statistical approaches have been developed to infer unknown quantities affecting animal movement or predict movement based on telemetry data. Hierarchical statistical models are useful to account for some of the aforementioned uncertainties, as well as provide population-level inference, but they often come with an increased computational burden. For certain types of statistical models, it is straightforward to provide inference if the latent true animal trajectory is known, but challenging otherwise. In these cases, approaches related to multiple imputation have been employed to account for the uncertainty associated with our knowledge of the latent trajectory. Despite the increasing use of imputation approaches for modeling animal movement, the general sensitivity and accuracy of these methods have not been explored in detail. We provide an introduction to animal movement modeling and describe how imputation approaches may be helpful for certain types of models. We also assess the performance of imputation approaches in two simulation studies. Our simulation studies suggests that inference for model parameters directly related to the location of an individual may be more accurate than inference for parameters associated with higher-order processes such as velocity or acceleration. Finally, we apply these methods to analyze a telemetry data set involving northern fur seals (Callorhinus ursinus) in the Bering Sea. Supplementary materials accompanying this paper appear online.

Using a Five-Step Procedure for Inferential Statistical Analyses

ERIC Educational Resources Information Center

Kamin, Lawrence F.

2010-01-01

Many statistics texts pose inferential statistical problems in a disjointed way. By using a simple five-step procedure as a template for statistical inference problems, the student can solve problems in an organized fashion. The problem and its solution will thus be a stand-by-itself organic whole and a single unit of thought and effort. The…

Hybrid artificial intelligence approach based on neural fuzzy inference model and metaheuristic optimization for flood susceptibilitgy modeling in a high-frequency tropical cyclone area using GIS

NASA Astrophysics Data System (ADS)

Tien Bui, Dieu; Pradhan, Biswajeet; Nampak, Haleh; Bui, Quang-Thanh; Tran, Quynh-An; Nguyen, Quoc-Phi

2016-09-01

This paper proposes a new artificial intelligence approach based on neural fuzzy inference system and metaheuristic optimization for flood susceptibility modeling, namely MONF. In the new approach, the neural fuzzy inference system was used to create an initial flood susceptibility model and then the model was optimized using two metaheuristic algorithms, Evolutionary Genetic and Particle Swarm Optimization. A high-frequency tropical cyclone area of the Tuong Duong district in Central Vietnam was used as a case study. First, a GIS database for the study area was constructed. The database that includes 76 historical flood inundated areas and ten flood influencing factors was used to develop and validate the proposed model. Root Mean Square Error (RMSE), Mean Absolute Error (MAE), Receiver Operating Characteristic (ROC) curve, and area under the ROC curve (AUC) were used to assess the model performance and its prediction capability. Experimental results showed that the proposed model has high performance on both the training (RMSE = 0.306, MAE = 0.094, AUC = 0.962) and validation dataset (RMSE = 0.362, MAE = 0.130, AUC = 0.911). The usability of the proposed model was evaluated by comparing with those obtained from state-of-the art benchmark soft computing techniques such as J48 Decision Tree, Random Forest, Multi-layer Perceptron Neural Network, Support Vector Machine, and Adaptive Neuro Fuzzy Inference System. The results show that the proposed MONF model outperforms the above benchmark models; we conclude that the MONF model is a new alternative tool that should be used in flood susceptibility mapping. The result in this study is useful for planners and decision makers for sustainable management of flood-prone areas.

Design-based and model-based inference in surveys of freshwater mollusks

USGS Publications Warehouse

Dorazio, R.M.

1999-01-01

Well-known concepts in statistical inference and sampling theory are used to develop recommendations for planning and analyzing the results of quantitative surveys of freshwater mollusks. Two methods of inference commonly used in survey sampling (design-based and model-based) are described and illustrated using examples relevant in surveys of freshwater mollusks. The particular objectives of a survey and the type of information observed in each unit of sampling can be used to help select the sampling design and the method of inference. For example, the mean density of a sparsely distributed population of mollusks can be estimated with higher precision by using model-based inference or by using design-based inference with adaptive cluster sampling than by using design-based inference with conventional sampling. More experience with quantitative surveys of natural assemblages of freshwater mollusks is needed to determine the actual benefits of different sampling designs and inferential procedures.

Combined data preprocessing and multivariate statistical analysis characterizes fed-batch culture of mouse hybridoma cells for rational medium design.

PubMed

Selvarasu, Suresh; Kim, Do Yun; Karimi, Iftekhar A; Lee, Dong-Yup

2010-10-01

We present an integrated framework for characterizing fed-batch cultures of mouse hybridoma cells producing monoclonal antibody (mAb). This framework systematically combines data preprocessing, elemental balancing and statistical analysis technique. Initially, specific rates of cell growth, glucose/amino acid consumptions and mAb/metabolite productions were calculated via curve fitting using logistic equations, with subsequent elemental balancing of the preprocessed data indicating the presence of experimental measurement errors. Multivariate statistical analysis was then employed to understand physiological characteristics of the cellular system. The results from principal component analysis (PCA) revealed three major clusters of amino acids with similar trends in their consumption profiles: (i) arginine, threonine and serine, (ii) glycine, tyrosine, phenylalanine, methionine, histidine and asparagine, and (iii) lysine, valine and isoleucine. Further analysis using partial least square (PLS) regression identified key amino acids which were positively or negatively correlated with the cell growth, mAb production and the generation of lactate and ammonia. Based on these results, the optimal concentrations of key amino acids in the feed medium can be inferred, potentially leading to an increase in cell viability and productivity, as well as a decrease in toxic waste production. The study demonstrated how the current methodological framework using multivariate statistical analysis techniques can serve as a potential tool for deriving rational medium design strategies. Copyright © 2010 Elsevier B.V. All rights reserved.

Bayesian inference for joint modelling of longitudinal continuous, binary and ordinal events.

PubMed

Li, Qiuju; Pan, Jianxin; Belcher, John

2016-12-01

In medical studies, repeated measurements of continuous, binary and ordinal outcomes are routinely collected from the same patient. Instead of modelling each outcome separately, in this study we propose to jointly model the trivariate longitudinal responses, so as to take account of the inherent association between the different outcomes and thus improve statistical inferences. This work is motivated by a large cohort study in the North West of England, involving trivariate responses from each patient: Body Mass Index, Depression (Yes/No) ascertained with cut-off score not less than 8 at the Hospital Anxiety and Depression Scale, and Pain Interference generated from the Medical Outcomes Study 36-item short-form health survey with values returned on an ordinal scale 1-5. There are some well-established methods for combined continuous and binary, or even continuous and ordinal responses, but little work was done on the joint analysis of continuous, binary and ordinal responses. We propose conditional joint random-effects models, which take into account the inherent association between the continuous, binary and ordinal outcomes. Bayesian analysis methods are used to make statistical inferences. Simulation studies show that, by jointly modelling the trivariate outcomes, standard deviations of the estimates of parameters in the models are smaller and much more stable, leading to more efficient parameter estimates and reliable statistical inferences. In the real data analysis, the proposed joint analysis yields a much smaller deviance information criterion value than the separate analysis, and shows other good statistical properties too. © The Author(s) 2014.

Assessing the significance of pedobarographic signals using random field theory.

PubMed

Pataky, Todd C

2008-08-07

Traditional pedobarographic statistical analyses are conducted over discrete regions. Recent studies have demonstrated that regionalization can corrupt pedobarographic field data through conflation when arbitrary dividing lines inappropriately delineate smooth field processes. An alternative is to register images such that homologous structures optimally overlap and then conduct statistical tests at each pixel to generate statistical parametric maps (SPMs). The significance of SPM processes may be assessed within the framework of random field theory (RFT). RFT is ideally suited to pedobarographic image analysis because its fundamental data unit is a lattice sampling of a smooth and continuous spatial field. To correct for the vast number of multiple comparisons inherent in such data, recent pedobarographic studies have employed a Bonferroni correction to retain a constant family-wise error rate. This approach unfortunately neglects the spatial correlation of neighbouring pixels, so provides an overly conservative (albeit valid) statistical threshold. RFT generally relaxes the threshold depending on field smoothness and on the geometry of the search area, but it also provides a framework for assigning p values to suprathreshold clusters based on their spatial extent. The current paper provides an overview of basic RFT concepts and uses simulated and experimental data to validate both RFT-relevant field smoothness estimations and RFT predictions regarding the topological characteristics of random pedobarographic fields. Finally, previously published experimental data are re-analysed using RFT inference procedures to demonstrate how RFT yields easily understandable statistical results that may be incorporated into routine clinical and laboratory analyses.

Neuronal couplings between retinal ganglion cells inferred by efficient inverse statistical physics methods

PubMed Central

Cocco, Simona; Leibler, Stanislas; Monasson, Rémi

2009-01-01

Complexity of neural systems often makes impracticable explicit measurements of all interactions between their constituents. Inverse statistical physics approaches, which infer effective couplings between neurons from their spiking activity, have been so far hindered by their computational complexity. Here, we present 2 complementary, computationally efficient inverse algorithms based on the Ising and “leaky integrate-and-fire” models. We apply those algorithms to reanalyze multielectrode recordings in the salamander retina in darkness and under random visual stimulus. We find strong positive couplings between nearby ganglion cells common to both stimuli, whereas long-range couplings appear under random stimulus only. The uncertainty on the inferred couplings due to limitations in the recordings (duration, small area covered on the retina) is discussed. Our methods will allow real-time evaluation of couplings for large assemblies of neurons. PMID:19666487

Confidence crisis of results in biomechanics research.

PubMed

Knudson, Duane

2017-11-01

Many biomechanics studies have small sample sizes and incorrect statistical analyses, so reporting of inaccurate inferences and inflated magnitude of effects are common in the field. This review examines these issues in biomechanics research and summarises potential solutions from research in other fields to increase the confidence in the experimental effects reported in biomechanics. Authors, reviewers and editors of biomechanics research reports are encouraged to improve sample sizes and the resulting statistical power, improve reporting transparency, improve the rigour of statistical analyses used, and increase the acceptance of replication studies to improve the validity of inferences from data in biomechanics research. The application of sports biomechanics research results would also improve if a larger percentage of unbiased effects and their uncertainty were reported in the literature.

The Empirical Nature and Statistical Treatment of Missing Data

ERIC Educational Resources Information Center

Tannenbaum, Christyn E.

2009-01-01

Introduction. Missing data is a common problem in research and can produce severely misleading analyses, including biased estimates of statistical parameters, and erroneous conclusions. In its 1999 report, the APA Task Force on Statistical Inference encouraged authors to report complications such as missing data and discouraged the use of…

Cognitive Transfer Outcomes for a Simulation-Based Introductory Statistics Curriculum

ERIC Educational Resources Information Center

Backman, Matthew D.; Delmas, Robert C.; Garfield, Joan

2017-01-01

Cognitive transfer is the ability to apply learned skills and knowledge to new applications and contexts. This investigation evaluates cognitive transfer outcomes for a tertiary-level introductory statistics course using the CATALST curriculum, which exclusively used simulation-based methods to develop foundations of statistical inference. A…

The Role of the Sampling Distribution in Understanding Statistical Inference

ERIC Educational Resources Information Center

Lipson, Kay

2003-01-01

Many statistics educators believe that few students develop the level of conceptual understanding essential for them to apply correctly the statistical techniques at their disposal and to interpret their outcomes appropriately. It is also commonly believed that the sampling distribution plays an important role in developing this understanding.…

On the Origins of Suboptimality in Human Probabilistic Inference

PubMed Central

Acerbi, Luigi; Vijayakumar, Sethu; Wolpert, Daniel M.

2014-01-01

Humans have been shown to combine noisy sensory information with previous experience (priors), in qualitative and sometimes quantitative agreement with the statistically-optimal predictions of Bayesian integration. However, when the prior distribution becomes more complex than a simple Gaussian, such as skewed or bimodal, training takes much longer and performance appears suboptimal. It is unclear whether such suboptimality arises from an imprecise internal representation of the complex prior, or from additional constraints in performing probabilistic computations on complex distributions, even when accurately represented. Here we probe the sources of suboptimality in probabilistic inference using a novel estimation task in which subjects are exposed to an explicitly provided distribution, thereby removing the need to remember the prior. Subjects had to estimate the location of a target given a noisy cue and a visual representation of the prior probability density over locations, which changed on each trial. Different classes of priors were examined (Gaussian, unimodal, bimodal). Subjects' performance was in qualitative agreement with the predictions of Bayesian Decision Theory although generally suboptimal. The degree of suboptimality was modulated by statistical features of the priors but was largely independent of the class of the prior and level of noise in the cue, suggesting that suboptimality in dealing with complex statistical features, such as bimodality, may be due to a problem of acquiring the priors rather than computing with them. We performed a factorial model comparison across a large set of Bayesian observer models to identify additional sources of noise and suboptimality. Our analysis rejects several models of stochastic behavior, including probability matching and sample-averaging strategies. Instead we show that subjects' response variability was mainly driven by a combination of a noisy estimation of the parameters of the priors, and by variability in the decision process, which we represent as a noisy or stochastic posterior. PMID:24945142

SURE Estimates for a Heteroscedastic Hierarchical Model

PubMed Central

Xie, Xianchao; Kou, S. C.; Brown, Lawrence D.

2014-01-01

Hierarchical models are extensively studied and widely used in statistics and many other scientific areas. They provide an effective tool for combining information from similar resources and achieving partial pooling of inference. Since the seminal work by James and Stein (1961) and Stein (1962), shrinkage estimation has become one major focus for hierarchical models. For the homoscedastic normal model, it is well known that shrinkage estimators, especially the James-Stein estimator, have good risk properties. The heteroscedastic model, though more appropriate for practical applications, is less well studied, and it is unclear what types of shrinkage estimators are superior in terms of the risk. We propose in this paper a class of shrinkage estimators based on Stein’s unbiased estimate of risk (SURE). We study asymptotic properties of various common estimators as the number of means to be estimated grows (p → ∞). We establish the asymptotic optimality property for the SURE estimators. We then extend our construction to create a class of semi-parametric shrinkage estimators and establish corresponding asymptotic optimality results. We emphasize that though the form of our SURE estimators is partially obtained through a normal model at the sampling level, their optimality properties do not heavily depend on such distributional assumptions. We apply the methods to two real data sets and obtain encouraging results. PMID:25301976

A statistical method for lung tumor segmentation uncertainty in PET images based on user inference.

PubMed

Zheng, Chaojie; Wang, Xiuying; Feng, Dagan

2015-01-01

PET has been widely accepted as an effective imaging modality for lung tumor diagnosis and treatment. However, standard criteria for delineating tumor boundary from PET are yet to develop largely due to relatively low quality of PET images, uncertain tumor boundary definition, and variety of tumor characteristics. In this paper, we propose a statistical solution to segmentation uncertainty on the basis of user inference. We firstly define the uncertainty segmentation band on the basis of segmentation probability map constructed from Random Walks (RW) algorithm; and then based on the extracted features of the user inference, we use Principle Component Analysis (PCA) to formulate the statistical model for labeling the uncertainty band. We validated our method on 10 lung PET-CT phantom studies from the public RIDER collections [1] and 16 clinical PET studies where tumors were manually delineated by two experienced radiologists. The methods were validated using Dice similarity coefficient (DSC) to measure the spatial volume overlap. Our method achieved an average DSC of 0.878 ± 0.078 on phantom studies and 0.835 ± 0.039 on clinical studies.

Empirical evidence for acceleration-dependent amplification factors

USGS Publications Warehouse

Borcherdt, R.D.

2002-01-01

Site-specific amplification factors, Fa and Fv, used in current U.S. building codes decrease with increasing base acceleration level as implied by the Loma Prieta earthquake at 0.1g and extrapolated using numerical models and laboratory results. The Northridge earthquake recordings of 17 January 1994 and subsequent geotechnical data permit empirical estimates of amplification at base acceleration levels up to 0.5g. Distance measures and normalization procedures used to infer amplification ratios from soil-rock pairs in predetermined azimuth-distance bins significantly influence the dependence of amplification estimates on base acceleration. Factors inferred using a hypocentral distance norm do not show a statistically significant dependence on base acceleration. Factors inferred using norms implied by the attenuation functions of Abrahamson and Silva show a statistically significant decrease with increasing base acceleration. The decrease is statistically more significant for stiff clay and sandy soil (site class D) sites than for stiffer sites underlain by gravely soils and soft rock (site class C). The decrease in amplification with increasing base acceleration is more pronounced for the short-period amplification factor, Fa, than for the midperiod factor, Fv.

Karl Pearson and eugenics: personal opinions and scientific rigor.

PubMed

Delzell, Darcie A P; Poliak, Cathy D

2013-09-01

The influence of personal opinions and biases on scientific conclusions is a threat to the advancement of knowledge. Expertise and experience does not render one immune to this temptation. In this work, one of the founding fathers of statistics, Karl Pearson, is used as an illustration of how even the most talented among us can produce misleading results when inferences are made without caution or reference to potential bias and other analysis limitations. A study performed by Pearson on British Jewish schoolchildren is examined in light of ethical and professional statistical practice. The methodology used and inferences made by Pearson and his coauthor are sometimes questionable and offer insight into how Pearson's support of eugenics and his own British nationalism could have potentially influenced his often careless and far-fetched inferences. A short background into Pearson's work and beliefs is provided, along with an in-depth examination of the authors' overall experimental design and statistical practices. In addition, portions of the study regarding intelligence and tuberculosis are discussed in more detail, along with historical reactions to their work.

Marginal Structural Models with Counterfactual Effect Modifiers.

PubMed

Zheng, Wenjing; Luo, Zhehui; van der Laan, Mark J

2018-06-08

In health and social sciences, research questions often involve systematic assessment of the modification of treatment causal effect by patient characteristics. In longitudinal settings, time-varying or post-intervention effect modifiers are also of interest. In this work, we investigate the robust and efficient estimation of the Counterfactual-History-Adjusted Marginal Structural Model (van der Laan MJ, Petersen M. Statistical learning of origin-specific statically optimal individualized treatment rules. Int J Biostat. 2007;3), which models the conditional intervention-specific mean outcome given a counterfactual modifier history in an ideal experiment. We establish the semiparametric efficiency theory for these models, and present a substitution-based, semiparametric efficient and doubly robust estimator using the targeted maximum likelihood estimation methodology (TMLE, e.g. van der Laan MJ, Rubin DB. Targeted maximum likelihood learning. Int J Biostat. 2006;2, van der Laan MJ, Rose S. Targeted learning: causal inference for observational and experimental data, 1st ed. Springer Series in Statistics. Springer, 2011). To facilitate implementation in applications where the effect modifier is high dimensional, our third contribution is a projected influence function (and the corresponding projected TMLE estimator), which retains most of the robustness of its efficient peer and can be easily implemented in applications where the use of the efficient influence function becomes taxing. We compare the projected TMLE estimator with an Inverse Probability of Treatment Weighted estimator (e.g. Robins JM. Marginal structural models. In: Proceedings of the American Statistical Association. Section on Bayesian Statistical Science, 1-10. 1997a, Hernan MA, Brumback B, Robins JM. Marginal structural models to estimate the causal effect of zidovudine on the survival of HIV-positive men. 2000;11:561-570), and a non-targeted G-computation estimator (Robins JM. A new approach to causal inference in mortality studies with sustained exposure periods - application to control of the healthy worker survivor effect. Math Modell. 1986;7:1393-1512.). The comparative performance of these estimators is assessed in a simulation study. The use of the projected TMLE estimator is illustrated in a secondary data analysis for the Sequenced Treatment Alternatives to Relieve Depression (STAR*D) trial where effect modifiers are subject to missing at random.

In silico model-based inference: a contemporary approach for hypothesis testing in network biology

PubMed Central

Klinke, David J.

2014-01-01

Inductive inference plays a central role in the study of biological systems where one aims to increase their understanding of the system by reasoning backwards from uncertain observations to identify causal relationships among components of the system. These causal relationships are postulated from prior knowledge as a hypothesis or simply a model. Experiments are designed to test the model. Inferential statistics are used to establish a level of confidence in how well our postulated model explains the acquired data. This iterative process, commonly referred to as the scientific method, either improves our confidence in a model or suggests that we revisit our prior knowledge to develop a new model. Advances in technology impact how we use prior knowledge and data to formulate models of biological networks and how we observe cellular behavior. However, the approach for model-based inference has remained largely unchanged since Fisher, Neyman and Pearson developed the ideas in the early 1900’s that gave rise to what is now known as classical statistical hypothesis (model) testing. Here, I will summarize conventional methods for model-based inference and suggest a contemporary approach to aid in our quest to discover how cells dynamically interpret and transmit information for therapeutic aims that integrates ideas drawn from high performance computing, Bayesian statistics, and chemical kinetics. PMID:25139179

In silico model-based inference: a contemporary approach for hypothesis testing in network biology.

PubMed

Klinke, David J

2014-01-01

Inductive inference plays a central role in the study of biological systems where one aims to increase their understanding of the system by reasoning backwards from uncertain observations to identify causal relationships among components of the system. These causal relationships are postulated from prior knowledge as a hypothesis or simply a model. Experiments are designed to test the model. Inferential statistics are used to establish a level of confidence in how well our postulated model explains the acquired data. This iterative process, commonly referred to as the scientific method, either improves our confidence in a model or suggests that we revisit our prior knowledge to develop a new model. Advances in technology impact how we use prior knowledge and data to formulate models of biological networks and how we observe cellular behavior. However, the approach for model-based inference has remained largely unchanged since Fisher, Neyman and Pearson developed the ideas in the early 1900s that gave rise to what is now known as classical statistical hypothesis (model) testing. Here, I will summarize conventional methods for model-based inference and suggest a contemporary approach to aid in our quest to discover how cells dynamically interpret and transmit information for therapeutic aims that integrates ideas drawn from high performance computing, Bayesian statistics, and chemical kinetics. © 2014 American Institute of Chemical Engineers.

Spatio-temporal conditional inference and hypothesis tests for neural ensemble spiking precision

PubMed Central

Harrison, Matthew T.; Amarasingham, Asohan; Truccolo, Wilson

2014-01-01

The collective dynamics of neural ensembles create complex spike patterns with many spatial and temporal scales. Understanding the statistical structure of these patterns can help resolve fundamental questions about neural computation and neural dynamics. Spatio-temporal conditional inference (STCI) is introduced here as a semiparametric statistical framework for investigating the nature of precise spiking patterns from collections of neurons that is robust to arbitrarily complex and nonstationary coarse spiking dynamics. The main idea is to focus statistical modeling and inference, not on the full distribution of the data, but rather on families of conditional distributions of precise spiking given different types of coarse spiking. The framework is then used to develop families of hypothesis tests for probing the spatio-temporal precision of spiking patterns. Relationships among different conditional distributions are used to improve multiple hypothesis testing adjustments and to design novel Monte Carlo spike resampling algorithms. Of special note are algorithms that can locally jitter spike times while still preserving the instantaneous peri-stimulus time histogram (PSTH) or the instantaneous total spike count from a group of recorded neurons. The framework can also be used to test whether first-order maximum entropy models with possibly random and time-varying parameters can account for observed patterns of spiking. STCI provides a detailed example of the generic principle of conditional inference, which may be applicable in other areas of neurostatistical analysis. PMID:25380339

Wisdom of crowds for robust gene network inference

PubMed Central

Marbach, Daniel; Costello, James C.; Küffner, Robert; Vega, Nicci; Prill, Robert J.; Camacho, Diogo M.; Allison, Kyle R.; Kellis, Manolis; Collins, James J.; Stolovitzky, Gustavo

2012-01-01

Reconstructing gene regulatory networks from high-throughput data is a long-standing problem. Through the DREAM project (Dialogue on Reverse Engineering Assessment and Methods), we performed a comprehensive blind assessment of over thirty network inference methods on Escherichia coli, Staphylococcus aureus, Saccharomyces cerevisiae, and in silico microarray data. We characterize performance, data requirements, and inherent biases of different inference approaches offering guidelines for both algorithm application and development. We observe that no single inference method performs optimally across all datasets. In contrast, integration of predictions from multiple inference methods shows robust and high performance across diverse datasets. Thereby, we construct high-confidence networks for E. coli and S. aureus, each comprising ~1700 transcriptional interactions at an estimated precision of 50%. We experimentally test 53 novel interactions in E. coli, of which 23 were supported (43%). Our results establish community-based methods as a powerful and robust tool for the inference of transcriptional gene regulatory networks. PMID:22796662

Data mining and statistical inference in selective laser melting

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

Kamath, Chandrika

Selective laser melting (SLM) is an additive manufacturing process that builds a complex three-dimensional part, layer-by-layer, using a laser beam to fuse fine metal powder together. The design freedom afforded by SLM comes associated with complexity. As the physical phenomena occur over a broad range of length and time scales, the computational cost of modeling the process is high. At the same time, the large number of parameters that control the quality of a part make experiments expensive. In this paper, we describe ways in which we can use data mining and statistical inference techniques to intelligently combine simulations andmore » experiments to build parts with desired properties. We start with a brief summary of prior work in finding process parameters for high-density parts. We then expand on this work to show how we can improve the approach by using feature selection techniques to identify important variables, data-driven surrogate models to reduce computational costs, improved sampling techniques to cover the design space adequately, and uncertainty analysis for statistical inference. Here, our results indicate that techniques from data mining and statistics can complement those from physical modeling to provide greater insight into complex processes such as selective laser melting.« less

Data mining and statistical inference in selective laser melting

DOE PAGES

Kamath, Chandrika

2016-01-11

Selective laser melting (SLM) is an additive manufacturing process that builds a complex three-dimensional part, layer-by-layer, using a laser beam to fuse fine metal powder together. The design freedom afforded by SLM comes associated with complexity. As the physical phenomena occur over a broad range of length and time scales, the computational cost of modeling the process is high. At the same time, the large number of parameters that control the quality of a part make experiments expensive. In this paper, we describe ways in which we can use data mining and statistical inference techniques to intelligently combine simulations andmore » experiments to build parts with desired properties. We start with a brief summary of prior work in finding process parameters for high-density parts. We then expand on this work to show how we can improve the approach by using feature selection techniques to identify important variables, data-driven surrogate models to reduce computational costs, improved sampling techniques to cover the design space adequately, and uncertainty analysis for statistical inference. Here, our results indicate that techniques from data mining and statistics can complement those from physical modeling to provide greater insight into complex processes such as selective laser melting.« less

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.

Drug target inference through pathway analysis of genomics data

PubMed Central

Ma, Haisu; Zhao, Hongyu

2013-01-01

Statistical modeling coupled with bioinformatics is commonly used for drug discovery. Although there exist many approaches for single target based drug design and target inference, recent years have seen a paradigm shift to system-level pharmacological research. Pathway analysis of genomics data represents one promising direction for computational inference of drug targets. This article aims at providing a comprehensive review on the evolving issues is this field, covering methodological developments, their pros and cons, as well as future research directions. PMID:23369829

Applications of statistics to medical science, II overview of statistical procedures for general use.

PubMed

Watanabe, Hiroshi

2012-01-01

Procedures of statistical analysis are reviewed to provide an overview of applications of statistics for general use. Topics that are dealt with are inference on a population, comparison of two populations with respect to means and probabilities, and multiple comparisons. This study is the second part of series in which we survey medical statistics. Arguments related to statistical associations and regressions will be made in subsequent papers.

Action understanding and active inference

PubMed Central

Mattout, Jérémie; Kilner, James

2012-01-01

We have suggested that the mirror-neuron system might be usefully understood as implementing Bayes-optimal perception of actions emitted by oneself or others. To substantiate this claim, we present neuronal simulations that show the same representations can prescribe motor behavior and encode motor intentions during action–observation. These simulations are based on the free-energy formulation of active inference, which is formally related to predictive coding. In this scheme, (generalised) states of the world are represented as trajectories. When these states include motor trajectories they implicitly entail intentions (future motor states). Optimizing the representation of these intentions enables predictive coding in a prospective sense. Crucially, the same generative models used to make predictions can be deployed to predict the actions of self or others by simply changing the bias or precision (i.e. attention) afforded to proprioceptive signals. We illustrate these points using simulations of handwriting to illustrate neuronally plausible generation and recognition of itinerant (wandering) motor trajectories. We then use the same simulations to produce synthetic electrophysiological responses to violations of intentional expectations. Our results affirm that a Bayes-optimal approach provides a principled framework, which accommodates current thinking about the mirror-neuron system. Furthermore, it endorses the general formulation of action as active inference. PMID:21327826

PROBABILITY SAMPLING AND POPULATION INFERENCE IN MONITORING PROGRAMS

EPA Science Inventory

A fundamental difference between probability sampling and conventional statistics is that "sampling" deals with real, tangible populations, whereas "conventional statistics" usually deals with hypothetical populations that have no real-world realization. he focus here is on real ...

Statistical Inference in the Learning of Novel Phonetic Categories

ERIC Educational Resources Information Center

Zhao, Yuan

2010-01-01

Learning a phonetic category (or any linguistic category) requires integrating different sources of information. A crucial unsolved problem for phonetic learning is how this integration occurs: how can we update our previous knowledge about a phonetic category as we hear new exemplars of the category? One model of learning is Bayesian Inference,…

Conceptual Challenges in Coordinating Theoretical and Data-Centered Estimates of Probability

ERIC Educational Resources Information Center

Konold, Cliff; Madden, Sandra; Pollatsek, Alexander; Pfannkuch, Maxine; Wild, Chris; Ziedins, Ilze; Finzer, William; Horton, Nicholas J.; Kazak, Sibel

2011-01-01

A core component of informal statistical inference is the recognition that judgments based on sample data are inherently uncertain. This implies that instruction aimed at developing informal inference needs to foster basic probabilistic reasoning. In this article, we analyze and critique the now-common practice of introducing students to both…

Campbell's and Rubin's Perspectives on Causal Inference

ERIC Educational Resources Information Center

West, Stephen G.; Thoemmes, Felix

2010-01-01

Donald Campbell's approach to causal inference (D. T. Campbell, 1957; W. R. Shadish, T. D. Cook, & D. T. Campbell, 2002) is widely used in psychology and education, whereas Donald Rubin's causal model (P. W. Holland, 1986; D. B. Rubin, 1974, 2005) is widely used in economics, statistics, medicine, and public health. Campbell's approach focuses on…

Direct Evidence for a Dual Process Model of Deductive Inference

ERIC Educational Resources Information Center

Markovits, Henry; Brunet, Marie-Laurence; Thompson, Valerie; Brisson, Janie

2013-01-01

In 2 experiments, we tested a strong version of a dual process theory of conditional inference (cf. Verschueren et al., 2005a, 2005b) that assumes that most reasoners have 2 strategies available, the choice of which is determined by situational variables, cognitive capacity, and metacognitive control. The statistical strategy evaluates inferences…

The Role of Probability in Developing Learners' Models of Simulation Approaches to Inference

ERIC Educational Resources Information Center

Lee, Hollylynne S.; Doerr, Helen M.; Tran, Dung; Lovett, Jennifer N.

2016-01-01

Repeated sampling approaches to inference that rely on simulations have recently gained prominence in statistics education, and probabilistic concepts are at the core of this approach. In this approach, learners need to develop a mapping among the problem situation, a physical enactment, computer representations, and the underlying randomization…

From Blickets to Synapses: Inferring Temporal Causal Networks by Observation

ERIC Educational Resources Information Center

Fernando, Chrisantha

2013-01-01

How do human infants learn the causal dependencies between events? Evidence suggests that this remarkable feat can be achieved by observation of only a handful of examples. Many computational models have been produced to explain how infants perform causal inference without explicit teaching about statistics or the scientific method. Here, we…

It's a Girl! Random Numbers, Simulations, and the Law of Large Numbers

ERIC Educational Resources Information Center

Goodwin, Chris; Ortiz, Enrique

2015-01-01

Modeling using mathematics and making inferences about mathematical situations are becoming more prevalent in most fields of study. Descriptive statistics cannot be used to generalize about a population or make predictions of what can occur. Instead, inference must be used. Simulation and sampling are essential in building a foundation for…

Thou Shalt Not Bear False Witness against Null Hypothesis Significance Testing

ERIC Educational Resources Information Center

García-Pérez, Miguel A.

2017-01-01

Null hypothesis significance testing (NHST) has been the subject of debate for decades and alternative approaches to data analysis have been proposed. This article addresses this debate from the perspective of scientific inquiry and inference. Inference is an inverse problem and application of statistical methods cannot reveal whether effects…

Hypothesis-Testing Demands Trustworthy Data—A Simulation Approach to Inferential Statistics Advocating the Research Program Strategy

PubMed Central

Krefeld-Schwalb, Antonia; Witte, Erich H.; Zenker, Frank

2018-01-01

In psychology as elsewhere, the main statistical inference strategy to establish empirical effects is null-hypothesis significance testing (NHST). The recent failure to replicate allegedly well-established NHST-results, however, implies that such results lack sufficient statistical power, and thus feature unacceptably high error-rates. Using data-simulation to estimate the error-rates of NHST-results, we advocate the research program strategy (RPS) as a superior methodology. RPS integrates Frequentist with Bayesian inference elements, and leads from a preliminary discovery against a (random) H0-hypothesis to a statistical H1-verification. Not only do RPS-results feature significantly lower error-rates than NHST-results, RPS also addresses key-deficits of a “pure” Frequentist and a standard Bayesian approach. In particular, RPS aggregates underpowered results safely. RPS therefore provides a tool to regain the trust the discipline had lost during the ongoing replicability-crisis. PMID:29740363

NIRS-SPM: statistical parametric mapping for near infrared spectroscopy

NASA Astrophysics Data System (ADS)

Tak, Sungho; Jang, Kwang Eun; Jung, Jinwook; Jang, Jaeduck; Jeong, Yong; Ye, Jong Chul

2008-02-01

Even though there exists a powerful statistical parametric mapping (SPM) tool for fMRI, similar public domain tools are not available for near infrared spectroscopy (NIRS). In this paper, we describe a new public domain statistical toolbox called NIRS-SPM for quantitative analysis of NIRS signals. Specifically, NIRS-SPM statistically analyzes the NIRS data using GLM and makes inference as the excursion probability which comes from the random field that are interpolated from the sparse measurement. In order to obtain correct inference, NIRS-SPM offers the pre-coloring and pre-whitening method for temporal correlation estimation. For simultaneous recording NIRS signal with fMRI, the spatial mapping between fMRI image and real coordinate in 3-D digitizer is estimated using Horn's algorithm. These powerful tools allows us the super-resolution localization of the brain activation which is not possible using the conventional NIRS analysis tools.

Hypothesis-Testing Demands Trustworthy Data-A Simulation Approach to Inferential Statistics Advocating the Research Program Strategy.

PubMed

Krefeld-Schwalb, Antonia; Witte, Erich H; Zenker, Frank

2018-01-01

In psychology as elsewhere, the main statistical inference strategy to establish empirical effects is null-hypothesis significance testing (NHST). The recent failure to replicate allegedly well-established NHST-results, however, implies that such results lack sufficient statistical power, and thus feature unacceptably high error-rates. Using data-simulation to estimate the error-rates of NHST-results, we advocate the research program strategy (RPS) as a superior methodology. RPS integrates Frequentist with Bayesian inference elements, and leads from a preliminary discovery against a (random) H 0 -hypothesis to a statistical H 1 -verification. Not only do RPS-results feature significantly lower error-rates than NHST-results, RPS also addresses key-deficits of a "pure" Frequentist and a standard Bayesian approach. In particular, RPS aggregates underpowered results safely. RPS therefore provides a tool to regain the trust the discipline had lost during the ongoing replicability-crisis.

Application of Bayesian inference to the study of hierarchical organization in self-organized complex adaptive systems

NASA Astrophysics Data System (ADS)

Knuth, K. H.

2001-05-01

We consider the application of Bayesian inference to the study of self-organized structures in complex adaptive systems. In particular, we examine the distribution of elements, agents, or processes in systems dominated by hierarchical structure. We demonstrate that results obtained by Caianiello [1] on Hierarchical Modular Systems (HMS) can be found by applying Jaynes' Principle of Group Invariance [2] to a few key assumptions about our knowledge of hierarchical organization. Subsequent application of the Principle of Maximum Entropy allows inferences to be made about specific systems. The utility of the Bayesian method is considered by examining both successes and failures of the hierarchical model. We discuss how Caianiello's original statements suffer from the Mind Projection Fallacy [3] and we restate his assumptions thus widening the applicability of the HMS model. The relationship between inference and statistical physics, described by Jaynes [4], is reiterated with the expectation that this realization will aid the field of complex systems research by moving away from often inappropriate direct application of statistical mechanics to a more encompassing inferential methodology.

Computational Neuropsychology and Bayesian Inference.

PubMed

Parr, Thomas; Rees, Geraint; Friston, Karl J

2018-01-01

Computational theories of brain function have become very influential in neuroscience. They have facilitated the growth of formal approaches to disease, particularly in psychiatric research. In this paper, we provide a narrative review of the body of computational research addressing neuropsychological syndromes, and focus on those that employ Bayesian frameworks. Bayesian approaches to understanding brain function formulate perception and action as inferential processes. These inferences combine 'prior' beliefs with a generative (predictive) model to explain the causes of sensations. Under this view, neuropsychological deficits can be thought of as false inferences that arise due to aberrant prior beliefs (that are poor fits to the real world). This draws upon the notion of a Bayes optimal pathology - optimal inference with suboptimal priors - and provides a means for computational phenotyping. In principle, any given neuropsychological disorder could be characterized by the set of prior beliefs that would make a patient's behavior appear Bayes optimal. We start with an overview of some key theoretical constructs and use these to motivate a form of computational neuropsychology that relates anatomical structures in the brain to the computations they perform. Throughout, we draw upon computational accounts of neuropsychological syndromes. These are selected to emphasize the key features of a Bayesian approach, and the possible types of pathological prior that may be present. They range from visual neglect through hallucinations to autism. Through these illustrative examples, we review the use of Bayesian approaches to understand the link between biology and computation that is at the heart of neuropsychology.

Computational Neuropsychology and Bayesian Inference

PubMed Central

Parr, Thomas; Rees, Geraint; Friston, Karl J.

2018-01-01

Computational theories of brain function have become very influential in neuroscience. They have facilitated the growth of formal approaches to disease, particularly in psychiatric research. In this paper, we provide a narrative review of the body of computational research addressing neuropsychological syndromes, and focus on those that employ Bayesian frameworks. Bayesian approaches to understanding brain function formulate perception and action as inferential processes. These inferences combine ‘prior’ beliefs with a generative (predictive) model to explain the causes of sensations. Under this view, neuropsychological deficits can be thought of as false inferences that arise due to aberrant prior beliefs (that are poor fits to the real world). This draws upon the notion of a Bayes optimal pathology – optimal inference with suboptimal priors – and provides a means for computational phenotyping. In principle, any given neuropsychological disorder could be characterized by the set of prior beliefs that would make a patient’s behavior appear Bayes optimal. We start with an overview of some key theoretical constructs and use these to motivate a form of computational neuropsychology that relates anatomical structures in the brain to the computations they perform. Throughout, we draw upon computational accounts of neuropsychological syndromes. These are selected to emphasize the key features of a Bayesian approach, and the possible types of pathological prior that may be present. They range from visual neglect through hallucinations to autism. Through these illustrative examples, we review the use of Bayesian approaches to understand the link between biology and computation that is at the heart of neuropsychology. PMID:29527157

Conditional statistical inference with multistage testing designs.

PubMed

Zwitser, Robert J; Maris, Gunter

2015-03-01

In this paper it is demonstrated how statistical inference from multistage test designs can be made based on the conditional likelihood. Special attention is given to parameter estimation, as well as the evaluation of model fit. Two reasons are provided why the fit of simple measurement models is expected to be better in adaptive designs, compared to linear designs: more parameters are available for the same number of observations; and undesirable response behavior, like slipping and guessing, might be avoided owing to a better match between item difficulty and examinee proficiency. The results are illustrated with simulated data, as well as with real data.

Use of Tests of Statistical Significance and Other Analytic Choices in a School Psychology Journal: Review of Practices and Suggested Alternatives.

ERIC Educational Resources Information Center

Snyder, Patricia A.; Thompson, Bruce

The use of tests of statistical significance was explored, first by reviewing some criticisms of contemporary practice in the use of statistical tests as reflected in a series of articles in the "American Psychologist" and in the appointment of a "Task Force on Statistical Inference" by the American Psychological Association…

Applying dynamic Bayesian networks to perturbed gene expression data.

PubMed

Dojer, Norbert; Gambin, Anna; Mizera, Andrzej; Wilczyński, Bartek; Tiuryn, Jerzy

2006-05-08

A central goal of molecular biology is to understand the regulatory mechanisms of gene transcription and protein synthesis. Because of their solid basis in statistics, allowing to deal with the stochastic aspects of gene expressions and noisy measurements in a natural way, Bayesian networks appear attractive in the field of inferring gene interactions structure from microarray experiments data. However, the basic formalism has some disadvantages, e.g. it is sometimes hard to distinguish between the origin and the target of an interaction. Two kinds of microarray experiments yield data particularly rich in information regarding the direction of interactions: time series and perturbation experiments. In order to correctly handle them, the basic formalism must be modified. For example, dynamic Bayesian networks (DBN) apply to time series microarray data. To our knowledge the DBN technique has not been applied in the context of perturbation experiments. We extend the framework of dynamic Bayesian networks in order to incorporate perturbations. Moreover, an exact algorithm for inferring an optimal network is proposed and a discretization method specialized for time series data from perturbation experiments is introduced. We apply our procedure to realistic simulations data. The results are compared with those obtained by standard DBN learning techniques. Moreover, the advantages of using exact learning algorithm instead of heuristic methods are analyzed. We show that the quality of inferred networks dramatically improves when using data from perturbation experiments. We also conclude that the exact algorithm should be used when it is possible, i.e. when considered set of genes is small enough.

Standard deviation and standard error of the mean.

PubMed

Lee, Dong Kyu; In, Junyong; Lee, Sangseok

2015-06-01

In most clinical and experimental studies, the standard deviation (SD) and the estimated standard error of the mean (SEM) are used to present the characteristics of sample data and to explain statistical analysis results. However, some authors occasionally muddle the distinctive usage between the SD and SEM in medical literature. Because the process of calculating the SD and SEM includes different statistical inferences, each of them has its own meaning. SD is the dispersion of data in a normal distribution. In other words, SD indicates how accurately the mean represents sample data. However the meaning of SEM includes statistical inference based on the sampling distribution. SEM is the SD of the theoretical distribution of the sample means (the sampling distribution). While either SD or SEM can be applied to describe data and statistical results, one should be aware of reasonable methods with which to use SD and SEM. We aim to elucidate the distinctions between SD and SEM and to provide proper usage guidelines for both, which summarize data and describe statistical results.

Standard deviation and standard error of the mean

PubMed Central

In, Junyong; Lee, Sangseok

2015-01-01

In most clinical and experimental studies, the standard deviation (SD) and the estimated standard error of the mean (SEM) are used to present the characteristics of sample data and to explain statistical analysis results. However, some authors occasionally muddle the distinctive usage between the SD and SEM in medical literature. Because the process of calculating the SD and SEM includes different statistical inferences, each of them has its own meaning. SD is the dispersion of data in a normal distribution. In other words, SD indicates how accurately the mean represents sample data. However the meaning of SEM includes statistical inference based on the sampling distribution. SEM is the SD of the theoretical distribution of the sample means (the sampling distribution). While either SD or SEM can be applied to describe data and statistical results, one should be aware of reasonable methods with which to use SD and SEM. We aim to elucidate the distinctions between SD and SEM and to provide proper usage guidelines for both, which summarize data and describe statistical results. PMID:26045923

Active Inference, homeostatic regulation and adaptive behavioural control.

PubMed

Pezzulo, Giovanni; Rigoli, Francesco; Friston, Karl

2015-11-01

We review a theory of homeostatic regulation and adaptive behavioural control within the Active Inference framework. Our aim is to connect two research streams that are usually considered independently; namely, Active Inference and associative learning theories of animal behaviour. The former uses a probabilistic (Bayesian) formulation of perception and action, while the latter calls on multiple (Pavlovian, habitual, goal-directed) processes for homeostatic and behavioural control. We offer a synthesis these classical processes and cast them as successive hierarchical contextualisations of sensorimotor constructs, using the generative models that underpin Active Inference. This dissolves any apparent mechanistic distinction between the optimization processes that mediate classical control or learning. Furthermore, we generalize the scope of Active Inference by emphasizing interoceptive inference and homeostatic regulation. The ensuing homeostatic (or allostatic) perspective provides an intuitive explanation for how priors act as drives or goals to enslave action, and emphasises the embodied nature of inference. Copyright © 2015 The Authors. Published by Elsevier Ltd.. All rights reserved.

Visual shape perception as Bayesian inference of 3D object-centered shape representations.

PubMed

Erdogan, Goker; Jacobs, Robert A

2017-11-01

Despite decades of research, little is known about how people visually perceive object shape. We hypothesize that a promising approach to shape perception is provided by a "visual perception as Bayesian inference" framework which augments an emphasis on visual representation with an emphasis on the idea that shape perception is a form of statistical inference. Our hypothesis claims that shape perception of unfamiliar objects can be characterized as statistical inference of 3D shape in an object-centered coordinate system. We describe a computational model based on our theoretical framework, and provide evidence for the model along two lines. First, we show that, counterintuitively, the model accounts for viewpoint-dependency of object recognition, traditionally regarded as evidence against people's use of 3D object-centered shape representations. Second, we report the results of an experiment using a shape similarity task, and present an extensive evaluation of existing models' abilities to account for the experimental data. We find that our shape inference model captures subjects' behaviors better than competing models. Taken as a whole, our experimental and computational results illustrate the promise of our approach and suggest that people's shape representations of unfamiliar objects are probabilistic, 3D, and object-centered. (PsycINFO Database Record (c) 2017 APA, all rights reserved).

Ensemble forecast of human West Nile virus cases and mosquito infection rates

NASA Astrophysics Data System (ADS)

Defelice, Nicholas B.; Little, Eliza; Campbell, Scott R.; Shaman, Jeffrey

2017-02-01

West Nile virus (WNV) is now endemic in the continental United States; however, our ability to predict spillover transmission risk and human WNV cases remains limited. Here we develop a model depicting WNV transmission dynamics, which we optimize using a data assimilation method and two observed data streams, mosquito infection rates and reported human WNV cases. The coupled model-inference framework is then used to generate retrospective ensemble forecasts of historical WNV outbreaks in Long Island, New York for 2001-2014. Accurate forecasts of mosquito infection rates are generated before peak infection, and >65% of forecasts accurately predict seasonal total human WNV cases up to 9 weeks before the past reported case. This work provides the foundation for implementation of a statistically rigorous system for real-time forecast of seasonal outbreaks of WNV.

Ensemble forecast of human West Nile virus cases and mosquito infection rates.

PubMed

DeFelice, Nicholas B; Little, Eliza; Campbell, Scott R; Shaman, Jeffrey

2017-02-24

West Nile virus (WNV) is now endemic in the continental United States; however, our ability to predict spillover transmission risk and human WNV cases remains limited. Here we develop a model depicting WNV transmission dynamics, which we optimize using a data assimilation method and two observed data streams, mosquito infection rates and reported human WNV cases. The coupled model-inference framework is then used to generate retrospective ensemble forecasts of historical WNV outbreaks in Long Island, New York for 2001-2014. Accurate forecasts of mosquito infection rates are generated before peak infection, and >65% of forecasts accurately predict seasonal total human WNV cases up to 9 weeks before the past reported case. This work provides the foundation for implementation of a statistically rigorous system for real-time forecast of seasonal outbreaks of WNV.

Qualitative Discovery in Medical Databases

NASA Technical Reports Server (NTRS)

Maluf, David A.

2000-01-01

Implication rules have been used in uncertainty reasoning systems to confirm and draw hypotheses or conclusions. However a major bottleneck in developing such systems lies in the elicitation of these rules. This paper empirically examines the performance of evidential inferencing with implication networks generated using a rule induction tool called KAT. KAT utilizes an algorithm for the statistical analysis of empirical case data, and hence reduces the knowledge engineering efforts and biases in subjective implication certainty assignment. The paper describes several experiments in which real-world diagnostic problems were investigated; namely, medical diagnostics. In particular, it attempts to show that: (1) with a limited number of case samples, KAT is capable of inducing implication networks useful for making evidential inferences based on partial observations, and (2) observation driven by a network entropy optimization mechanism is effective in reducing the uncertainty of predicted events.

Agile text mining for the 2014 i2b2/UTHealth Cardiac risk factors challenge.

PubMed

Cormack, James; Nath, Chinmoy; Milward, David; Raja, Kalpana; Jonnalagadda, Siddhartha R

2015-12-01

This paper describes the use of an agile text mining platform (Linguamatics' Interactive Information Extraction Platform, I2E) to extract document-level cardiac risk factors in patient records as defined in the i2b2/UTHealth 2014 challenge. The approach uses a data-driven rule-based methodology with the addition of a simple supervised classifier. We demonstrate that agile text mining allows for rapid optimization of extraction strategies, while post-processing can leverage annotation guidelines, corpus statistics and logic inferred from the gold standard data. We also show how data imbalance in a training set affects performance. Evaluation of this approach on the test data gave an F-Score of 91.7%, one percent behind the top performing system. Copyright © 2015 Elsevier Inc. All rights reserved.

Quantum-state comparison and discrimination

NASA Astrophysics Data System (ADS)

Hayashi, A.; Hashimoto, T.; Horibe, M.

2018-05-01

We investigate the performance of discrimination strategy in the comparison task of known quantum states. In the discrimination strategy, one infers whether or not two quantum systems are in the same state on the basis of the outcomes of separate discrimination measurements on each system. In some cases with more than two possible states, the optimal strategy in minimum-error comparison is that one should infer the two systems are in different states without any measurement, implying that the discrimination strategy performs worse than the trivial "no-measurement" strategy. We present a sufficient condition for this phenomenon to happen. For two pure states with equal prior probabilities, we determine the optimal comparison success probability with an error margin, which interpolates the minimum-error and unambiguous comparison. We find that the discrimination strategy is not optimal except for the minimum-error case.

Long-term strategy for the statistical design of a forest health monitoring system

Treesearch

Hans T. Schreuder; Raymond L. Czaplewski

1993-01-01

A conceptual framework is given for a broad-scale survey of forest health that accomplishes three objectives: generate descriptive statistics; detect changes in such statistics; and simplify analytical inferences that identify, and possibly establish cause-effect relationships. Our paper discusses the development of sampling schemes to satisfy these three objectives,...

Assessing Understanding of Sampling Distributions and Differences in Learning amongst Different Learning Styles

ERIC Educational Resources Information Center

Beeman, Jennifer Leigh Sloan

2013-01-01

Research has found that students successfully complete an introductory course in statistics without fully comprehending the underlying theory or being able to exhibit statistical reasoning. This is particularly true for the understanding about the sampling distribution of the mean, a crucial concept for statistical inference. This study…

Using Action Research to Develop a Course in Statistical Inference for Workplace-Based Adults

ERIC Educational Resources Information Center

Forbes, Sharleen

2014-01-01

Many adults who need an understanding of statistical concepts have limited mathematical skills. They need a teaching approach that includes as little mathematical context as possible. Iterative participatory qualitative research (action research) was used to develop a statistical literacy course for adult learners informed by teaching in…

Applying Statistical Process Control to Clinical Data: An Illustration.

ERIC Educational Resources Information Center

Pfadt, Al; And Others

1992-01-01

Principles of statistical process control are applied to a clinical setting through the use of control charts to detect changes, as part of treatment planning and clinical decision-making processes. The logic of control chart analysis is derived from principles of statistical inference. Sample charts offer examples of evaluating baselines and…

Efficiency Analysis: Enhancing the Statistical and Evaluative Power of the Regression-Discontinuity Design.

ERIC Educational Resources Information Center

Madhere, Serge

An analytic procedure, efficiency analysis, is proposed for improving the utility of quantitative program evaluation for decision making. The three features of the procedure are explained: (1) for statistical control, it adopts and extends the regression-discontinuity design; (2) for statistical inferences, it de-emphasizes hypothesis testing in…

Ice particle mass-dimensional parameter retrieval and uncertainty analysis using an Optimal Estimation framework applied to in situ data

NASA Astrophysics Data System (ADS)

Xu, Zhuocan; Mace, Jay; Avalone, Linnea; Wang, Zhien

2015-04-01

The extreme variability of ice particle habits in precipitating clouds affects our understanding of these cloud systems in every aspect (i.e. radiation transfer, dynamics, precipitation rate, etc) and largely contributes to the uncertainties in the model representation of related processes. Ice particle mass-dimensional power law relationships, M=a*(D ^ b), are commonly assumed in models and retrieval algorithms, while very little knowledge exists regarding the uncertainties of these M-D parameters in real-world situations. In this study, we apply Optimal Estimation (OE) methodology to infer ice particle mass-dimensional relationship from ice particle size distributions and bulk water contents independently measured on board the University of Wyoming King Air during the Colorado Airborne Multi-Phase Cloud Study (CAMPS). We also utilize W-band radar reflectivity obtained on the same platform (King Air) offering a further constraint to this ill-posed problem (Heymsfield et al. 2010). In addition to the values of retrieved M-D parameters, the associated uncertainties are conveniently acquired in the OE framework, within the limitations of assumed Gaussian statistics. We find, given the constraints provided by the bulk water measurement and in situ radar reflectivity, that the relative uncertainty of mass-dimensional power law prefactor (a) is approximately 80% and the relative uncertainty of exponent (b) is 10-15%. With this level of uncertainty, the forward model uncertainty in radar reflectivity would be on the order of 4 dB or a factor of approximately 2.5 in ice water content. The implications of this finding are that inferences of bulk water from either remote or in situ measurements of particle spectra cannot be more certain than this when the mass-dimensional relationships are not known a priori which is almost never the case.

Model based inference from microvascular measurements: Combining experimental measurements and model predictions using a Bayesian probabilistic approach

PubMed Central

Rasmussen, Peter M.; Smith, Amy F.; Sakadžić, Sava; Boas, David A.; Pries, Axel R.; Secomb, Timothy W.; Østergaard, Leif

2017-01-01

Objective In vivo imaging of the microcirculation and network-oriented modeling have emerged as powerful means of studying microvascular function and understanding its physiological significance. Network-oriented modeling may provide the means of summarizing vast amounts of data produced by high-throughput imaging techniques in terms of key, physiological indices. To estimate such indices with sufficient certainty, however, network-oriented analysis must be robust to the inevitable presence of uncertainty due to measurement errors as well as model errors. Methods We propose the Bayesian probabilistic data analysis framework as a means of integrating experimental measurements and network model simulations into a combined and statistically coherent analysis. The framework naturally handles noisy measurements and provides posterior distributions of model parameters as well as physiological indices associated with uncertainty. Results We applied the analysis framework to experimental data from three rat mesentery networks and one mouse brain cortex network. We inferred distributions for more than five hundred unknown pressure and hematocrit boundary conditions. Model predictions were consistent with previous analyses, and remained robust when measurements were omitted from model calibration. Conclusion Our Bayesian probabilistic approach may be suitable for optimizing data acquisition and for analyzing and reporting large datasets acquired as part of microvascular imaging studies. PMID:27987383

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

NASA Astrophysics Data System (ADS)

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

2017-12-01

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

Inference for Stochastic Chemical Kinetics Using Moment Equations and System Size Expansion.

PubMed

Fröhlich, Fabian; Thomas, Philipp; Kazeroonian, Atefeh; Theis, Fabian J; Grima, Ramon; Hasenauer, Jan

2016-07-01

Quantitative mechanistic models are valuable tools for disentangling biochemical pathways and for achieving a comprehensive understanding of biological systems. However, to be quantitative the parameters of these models have to be estimated from experimental data. In the presence of significant stochastic fluctuations this is a challenging task as stochastic simulations are usually too time-consuming and a macroscopic description using reaction rate equations (RREs) is no longer accurate. In this manuscript, we therefore consider moment-closure approximation (MA) and the system size expansion (SSE), which approximate the statistical moments of stochastic processes and tend to be more precise than macroscopic descriptions. We introduce gradient-based parameter optimization methods and uncertainty analysis methods for MA and SSE. Efficiency and reliability of the methods are assessed using simulation examples as well as by an application to data for Epo-induced JAK/STAT signaling. The application revealed that even if merely population-average data are available, MA and SSE improve parameter identifiability in comparison to RRE. Furthermore, the simulation examples revealed that the resulting estimates are more reliable for an intermediate volume regime. In this regime the estimation error is reduced and we propose methods to determine the regime boundaries. These results illustrate that inference using MA and SSE is feasible and possesses a high sensitivity.

Inference for Stochastic Chemical Kinetics Using Moment Equations and System Size Expansion

PubMed Central

Thomas, Philipp; Kazeroonian, Atefeh; Theis, Fabian J.; Grima, Ramon; Hasenauer, Jan

2016-01-01

Quantitative mechanistic models are valuable tools for disentangling biochemical pathways and for achieving a comprehensive understanding of biological systems. However, to be quantitative the parameters of these models have to be estimated from experimental data. In the presence of significant stochastic fluctuations this is a challenging task as stochastic simulations are usually too time-consuming and a macroscopic description using reaction rate equations (RREs) is no longer accurate. In this manuscript, we therefore consider moment-closure approximation (MA) and the system size expansion (SSE), which approximate the statistical moments of stochastic processes and tend to be more precise than macroscopic descriptions. We introduce gradient-based parameter optimization methods and uncertainty analysis methods for MA and SSE. Efficiency and reliability of the methods are assessed using simulation examples as well as by an application to data for Epo-induced JAK/STAT signaling. The application revealed that even if merely population-average data are available, MA and SSE improve parameter identifiability in comparison to RRE. Furthermore, the simulation examples revealed that the resulting estimates are more reliable for an intermediate volume regime. In this regime the estimation error is reduced and we propose methods to determine the regime boundaries. These results illustrate that inference using MA and SSE is feasible and possesses a high sensitivity. PMID:27447730

The penumbra of learning: a statistical theory of synaptic tagging and capture.

PubMed

Gershman, Samuel J

2014-01-01

Learning in humans and animals is accompanied by a penumbra: Learning one task benefits from learning an unrelated task shortly before or after. At the cellular level, the penumbra of learning appears when weak potentiation of one synapse is amplified by strong potentiation of another synapse on the same neuron during a critical time window. Weak potentiation sets a molecular tag that enables the synapse to capture plasticity-related proteins synthesized in response to strong potentiation at another synapse. This paper describes a computational model which formalizes synaptic tagging and capture in terms of statistical learning mechanisms. According to this model, synaptic strength encodes a probabilistic inference about the dynamically changing association between pre- and post-synaptic firing rates. The rate of change is itself inferred, coupling together different synapses on the same neuron. When the inputs to one synapse change rapidly, the inferred rate of change increases, amplifying learning at other synapses.

Space-Time Data fusion for Remote Sensing Applications

NASA Technical Reports Server (NTRS)

Braverman, Amy; Nguyen, H.; Cressie, N.

2011-01-01

NASA has been collecting massive amounts of remote sensing data about Earth's systems for more than a decade. Missions are selected to be complementary in quantities measured, retrieval techniques, and sampling characteristics, so these datasets are highly synergistic. To fully exploit this, a rigorous methodology for combining data with heterogeneous sampling characteristics is required. For scientific purposes, the methodology must also provide quantitative measures of uncertainty that propagate input-data uncertainty appropriately. We view this as a statistical inference problem. The true but notdirectly- observed quantities form a vector-valued field continuous in space and time. Our goal is to infer those true values or some function of them, and provide to uncertainty quantification for those inferences. We use a spatiotemporal statistical model that relates the unobserved quantities of interest at point-level to the spatially aggregated, observed data. We describe and illustrate our method using CO2 data from two NASA data sets.

Inference of missing data and chemical model parameters using experimental statistics

NASA Astrophysics Data System (ADS)

Casey, Tiernan; Najm, Habib

2017-11-01

A method for determining the joint parameter density of Arrhenius rate expressions through the inference of missing experimental data is presented. This approach proposes noisy hypothetical data sets from target experiments and accepts those which agree with the reported statistics, in the form of nominal parameter values and their associated uncertainties. The data exploration procedure is formalized using Bayesian inference, employing maximum entropy and approximate Bayesian computation methods to arrive at a joint density on data and parameters. The method is demonstrated in the context of reactions in the H2-O2 system for predictive modeling of combustion systems of interest. Work supported by the US DOE BES CSGB. Sandia National Labs is a multimission lab managed and operated by Nat. Technology and Eng'g Solutions of Sandia, LLC., a wholly owned subsidiary of Honeywell Intl, for the US DOE NCSA under contract DE-NA-0003525.

Statistical numeracy as a moderator of (pseudo)contingency effects on decision behavior.

PubMed

Fleig, Hanna; Meiser, Thorsten; Ettlin, Florence; Rummel, Jan

2017-03-01

Pseudocontingencies denote contingency estimates inferred from base rates rather than from cell frequencies. We examined the role of statistical numeracy for effects of such fallible but adaptive inferences on choice behavior. In Experiment 1, we provided information on single observations as well as on base rates and tracked participants' eye movements. In Experiment 2, we manipulated the availability of information on cell frequencies and base rates between conditions. Our results demonstrate that a focus on base rates rather than cell frequencies benefits pseudocontingency effects. Learners who are more proficient in (conditional) probability calculation prefer to rely on cell frequencies in order to judge contingencies, though, as was evident from their gaze behavior. If cell frequencies are available in summarized format, they may infer the true contingency between options and outcomes. Otherwise, however, even highly numerate learners are susceptible to pseudocontingency effects. Copyright © 2017 Elsevier B.V. All rights reserved.

Fast and Accurate Multivariate Gaussian Modeling of Protein Families: Predicting Residue Contacts and Protein-Interaction Partners

PubMed Central

Feinauer, Christoph; Procaccini, Andrea; Zecchina, Riccardo; Weigt, Martin; Pagnani, Andrea

2014-01-01

In the course of evolution, proteins show a remarkable conservation of their three-dimensional structure and their biological function, leading to strong evolutionary constraints on the sequence variability between homologous proteins. Our method aims at extracting such constraints from rapidly accumulating sequence data, and thereby at inferring protein structure and function from sequence information alone. Recently, global statistical inference methods (e.g. direct-coupling analysis, sparse inverse covariance estimation) have achieved a breakthrough towards this aim, and their predictions have been successfully implemented into tertiary and quaternary protein structure prediction methods. However, due to the discrete nature of the underlying variable (amino-acids), exact inference requires exponential time in the protein length, and efficient approximations are needed for practical applicability. Here we propose a very efficient multivariate Gaussian modeling approach as a variant of direct-coupling analysis: the discrete amino-acid variables are replaced by continuous Gaussian random variables. The resulting statistical inference problem is efficiently and exactly solvable. We show that the quality of inference is comparable or superior to the one achieved by mean-field approximations to inference with discrete variables, as done by direct-coupling analysis. This is true for (i) the prediction of residue-residue contacts in proteins, and (ii) the identification of protein-protein interaction partner in bacterial signal transduction. An implementation of our multivariate Gaussian approach is available at the website http://areeweb.polito.it/ricerca/cmp/code. PMID:24663061

The space of ultrametric phylogenetic trees.

PubMed

Gavryushkin, Alex; Drummond, Alexei J

2016-08-21

The reliability of a phylogenetic inference method from genomic sequence data is ensured by its statistical consistency. Bayesian inference methods produce a sample of phylogenetic trees from the posterior distribution given sequence data. Hence the question of statistical consistency of such methods is equivalent to the consistency of the summary of the sample. More generally, statistical consistency is ensured by the tree space used to analyse the sample. In this paper, we consider two standard parameterisations of phylogenetic time-trees used in evolutionary models: inter-coalescent interval lengths and absolute times of divergence events. For each of these parameterisations we introduce a natural metric space on ultrametric phylogenetic trees. We compare the introduced spaces with existing models of tree space and formulate several formal requirements that a metric space on phylogenetic trees must possess in order to be a satisfactory space for statistical analysis, and justify them. We show that only a few known constructions of the space of phylogenetic trees satisfy these requirements. However, our results suggest that these basic requirements are not enough to distinguish between the two metric spaces we introduce and that the choice between metric spaces requires additional properties to be considered. Particularly, that the summary tree minimising the square distance to the trees from the sample might be different for different parameterisations. This suggests that further fundamental insight is needed into the problem of statistical consistency of phylogenetic inference methods. Copyright © 2016 The Authors. Published by Elsevier Ltd.. All rights reserved.

Inferring Characteristics of Sensorimotor Behavior by Quantifying Dynamics of Animal Locomotion

NASA Astrophysics Data System (ADS)

Leung, KaWai

Locomotion is one of the most well-studied topics in animal behavioral studies. Many fundamental and clinical research make use of the locomotion of an animal model to explore various aspects in sensorimotor behavior. In the past, most of these studies focused on population average of a specific trait due to limitation of data collection and processing power. With recent advance in computer vision and statistical modeling techniques, it is now possible to track and analyze large amounts of behavioral data. In this thesis, I present two projects that aim to infer the characteristics of sensorimotor behavior by quantifying the dynamics of locomotion of nematode Caenorhabditis elegans and fruit fly Drosophila melanogaster, shedding light on statistical dependence between sensing and behavior. In the first project, I investigate the possibility of inferring noxious sensory information from the behavior of Caenorhabditis elegans. I develop a statistical model to infer the heat stimulus level perceived by individual animals from their stereotyped escape responses after stimulation by an IR laser. The model allows quantification of analgesic-like effects of chemical agents or genetic mutations in the worm. At the same time, the method is able to differentiate perturbations of locomotion behavior that are beyond affecting the sensory system. With this model I propose experimental designs that allows statistically significant identification of analgesic-like effects. In the second project, I investigate the relationship of energy budget and stability of locomotion in determining the walking speed distribution of Drosophila melanogaster during aging. The locomotion stability at different age groups is estimated from video recordings using Floquet theory. I calculate the power consumption of different locomotion speed using a biomechanics model. In conclusion, the power consumption, not stability, predicts the locomotion speed distribution at different ages.

Towards a Phylogenetic Approach to the Composition of Species Complexes in the North and Central American Triatoma, Vectors of Chagas Disease

PubMed Central

de la Rúa, Nicholas M.; Bustamante, Dulce M.; Menes, Marianela; Stevens, Lori; Monroy, Carlota; Kilpatrick, William; Rizzo, Donna; Klotz, Stephen A.; Schmidt, Justin; Axen, Heather J.; Dorn, Patricia L.

2014-01-01

Phylogenetic relationships of insect vectors of parasitic diseases are important for understanding the evolution of epidemiologically relevant traits, and may be useful in vector control. The subfamily Triatominae (Hemiptera:Reduviidae) includes ~140 extant species arranged in five tribes comprised of 15 genera. The genus Triatoma is the most species-rich and contains important vectors of Trypanosoma cruzi, the causative agent of Chagas disease. Triatoma species were grouped into complexes originally by morphology and more recently with the addition of information from molecular phylogenetics (the four-complex hypothesis); however, without a strict adherence to monophyly. To date, the validity of proposed species complexes has not been tested by statistical tests of topology. The goal of this study was to clarify the systematics of 19 Triatoma species from North and Central America. We inferred their evolutionary relatedness using two independent data sets: the complete nuclear Internal Transcribed Spacer-2 ribosomal DNA (ITS-2 rDNA) and head morphometrics. In addition, we used the Shimodaira-Hasegawa statistical test of topology to assess the fit of the data to a set of competing systematic hypotheses (topologies). An unconstrained topology inferred from the ITS-2 data was compared to topologies constrained based on the four-complex hypothesis or one inferred from our morphometry results. The unconstrained topology represents a statistically significant better fit of the molecular data than either the four-complex or the morphometric topology. We propose an update to the composition of species complexes in the North and Central American Triatoma, based on a phylogeny inferred from ITS-2 as a first step towards updating the phylogeny of the complexes based on monophyly and statistical tests of topologies. PMID:24681261

Emerging Concepts of Data Integration in Pathogen Phylodynamics.

PubMed

Baele, Guy; Suchard, Marc A; Rambaut, Andrew; Lemey, Philippe

2017-01-01

Phylodynamics has become an increasingly popular statistical framework to extract evolutionary and epidemiological information from pathogen genomes. By harnessing such information, epidemiologists aim to shed light on the spatio-temporal patterns of spread and to test hypotheses about the underlying interaction of evolutionary and ecological dynamics in pathogen populations. Although the field has witnessed a rich development of statistical inference tools with increasing levels of sophistication, these tools initially focused on sequences as their sole primary data source. Integrating various sources of information, however, promises to deliver more precise insights in infectious diseases and to increase opportunities for statistical hypothesis testing. Here, we review how the emerging concept of data integration is stimulating new advances in Bayesian evolutionary inference methodology which formalize a marriage of statistical thinking and evolutionary biology. These approaches include connecting sequence to trait evolution, such as for host, phenotypic and geographic sampling information, but also the incorporation of covariates of evolutionary and epidemic processes in the reconstruction procedures. We highlight how a full Bayesian approach to covariate modeling and testing can generate further insights into sequence evolution, trait evolution, and population dynamics in pathogen populations. Specific examples demonstrate how such approaches can be used to test the impact of host on rabies and HIV evolutionary rates, to identify the drivers of influenza dispersal as well as the determinants of rabies cross-species transmissions, and to quantify the evolutionary dynamics of influenza antigenicity. Finally, we briefly discuss how data integration is now also permeating through the inference of transmission dynamics, leading to novel insights into tree-generative processes and detailed reconstructions of transmission trees. [Bayesian inference; birth–death models; coalescent models; continuous trait evolution; covariates; data integration; discrete trait evolution; pathogen phylodynamics.

Emerging Concepts of Data Integration in Pathogen Phylodynamics

PubMed Central

Baele, Guy; Suchard, Marc A.; Rambaut, Andrew; Lemey, Philippe

2017-01-01

Phylodynamics has become an increasingly popular statistical framework to extract evolutionary and epidemiological information from pathogen genomes. By harnessing such information, epidemiologists aim to shed light on the spatio-temporal patterns of spread and to test hypotheses about the underlying interaction of evolutionary and ecological dynamics in pathogen populations. Although the field has witnessed a rich development of statistical inference tools with increasing levels of sophistication, these tools initially focused on sequences as their sole primary data source. Integrating various sources of information, however, promises to deliver more precise insights in infectious diseases and to increase opportunities for statistical hypothesis testing. Here, we review how the emerging concept of data integration is stimulating new advances in Bayesian evolutionary inference methodology which formalize a marriage of statistical thinking and evolutionary biology. These approaches include connecting sequence to trait evolution, such as for host, phenotypic and geographic sampling information, but also the incorporation of covariates of evolutionary and epidemic processes in the reconstruction procedures. We highlight how a full Bayesian approach to covariate modeling and testing can generate further insights into sequence evolution, trait evolution, and population dynamics in pathogen populations. Specific examples demonstrate how such approaches can be used to test the impact of host on rabies and HIV evolutionary rates, to identify the drivers of influenza dispersal as well as the determinants of rabies cross-species transmissions, and to quantify the evolutionary dynamics of influenza antigenicity. Finally, we briefly discuss how data integration is now also permeating through the inference of transmission dynamics, leading to novel insights into tree-generative processes and detailed reconstructions of transmission trees. [Bayesian inference; birth–death models; coalescent models; continuous trait evolution; covariates; data integration; discrete trait evolution; pathogen phylodynamics. PMID:28173504

BEAGLE: an application programming interface and high-performance computing library for statistical phylogenetics.

PubMed

Ayres, Daniel L; Darling, Aaron; Zwickl, Derrick J; Beerli, Peter; Holder, Mark T; Lewis, Paul O; Huelsenbeck, John P; Ronquist, Fredrik; Swofford, David L; Cummings, Michael P; Rambaut, Andrew; Suchard, Marc A

2012-01-01

Phylogenetic inference is fundamental to our understanding of most aspects of the origin and evolution of life, and in recent years, there has been a concentration of interest in statistical approaches such as Bayesian inference and maximum likelihood estimation. Yet, for large data sets and realistic or interesting models of evolution, these approaches remain computationally demanding. High-throughput sequencing can yield data for thousands of taxa, but scaling to such problems using serial computing often necessitates the use of nonstatistical or approximate approaches. The recent emergence of graphics processing units (GPUs) provides an opportunity to leverage their excellent floating-point computational performance to accelerate statistical phylogenetic inference. A specialized library for phylogenetic calculation would allow existing software packages to make more effective use of available computer hardware, including GPUs. Adoption of a common library would also make it easier for other emerging computing architectures, such as field programmable gate arrays, to be used in the future. We present BEAGLE, an application programming interface (API) and library for high-performance statistical phylogenetic inference. The API provides a uniform interface for performing phylogenetic likelihood calculations on a variety of compute hardware platforms. The library includes a set of efficient implementations and can currently exploit hardware including GPUs using NVIDIA CUDA, central processing units (CPUs) with Streaming SIMD Extensions and related processor supplementary instruction sets, and multicore CPUs via OpenMP. To demonstrate the advantages of a common API, we have incorporated the library into several popular phylogenetic software packages. The BEAGLE library is free open source software licensed under the Lesser GPL and available from http://beagle-lib.googlecode.com. An example client program is available as public domain software.

BEAGLE: An Application Programming Interface and High-Performance Computing Library for Statistical Phylogenetics

PubMed Central

Ayres, Daniel L.; Darling, Aaron; Zwickl, Derrick J.; Beerli, Peter; Holder, Mark T.; Lewis, Paul O.; Huelsenbeck, John P.; Ronquist, Fredrik; Swofford, David L.; Cummings, Michael P.; Rambaut, Andrew; Suchard, Marc A.

2012-01-01

Abstract Phylogenetic inference is fundamental to our understanding of most aspects of the origin and evolution of life, and in recent years, there has been a concentration of interest in statistical approaches such as Bayesian inference and maximum likelihood estimation. Yet, for large data sets and realistic or interesting models of evolution, these approaches remain computationally demanding. High-throughput sequencing can yield data for thousands of taxa, but scaling to such problems using serial computing often necessitates the use of nonstatistical or approximate approaches. The recent emergence of graphics processing units (GPUs) provides an opportunity to leverage their excellent floating-point computational performance to accelerate statistical phylogenetic inference. A specialized library for phylogenetic calculation would allow existing software packages to make more effective use of available computer hardware, including GPUs. Adoption of a common library would also make it easier for other emerging computing architectures, such as field programmable gate arrays, to be used in the future. We present BEAGLE, an application programming interface (API) and library for high-performance statistical phylogenetic inference. The API provides a uniform interface for performing phylogenetic likelihood calculations on a variety of compute hardware platforms. The library includes a set of efficient implementations and can currently exploit hardware including GPUs using NVIDIA CUDA, central processing units (CPUs) with Streaming SIMD Extensions and related processor supplementary instruction sets, and multicore CPUs via OpenMP. To demonstrate the advantages of a common API, we have incorporated the library into several popular phylogenetic software packages. The BEAGLE library is free open source software licensed under the Lesser GPL and available from http://beagle-lib.googlecode.com. An example client program is available as public domain software. PMID:21963610

ADAPTIVE MATCHING IN RANDOMIZED TRIALS AND OBSERVATIONAL STUDIES

PubMed Central

van der Laan, Mark J.; Balzer, Laura B.; Petersen, Maya L.

2014-01-01

SUMMARY In many randomized and observational studies the allocation of treatment among a sample of n independent and identically distributed units is a function of the covariates of all sampled units. As a result, the treatment labels among the units are possibly dependent, complicating estimation and posing challenges for statistical inference. For example, cluster randomized trials frequently sample communities from some target population, construct matched pairs of communities from those included in the sample based on some metric of similarity in baseline community characteristics, and then randomly allocate a treatment and a control intervention within each matched pair. In this case, the observed data can neither be represented as the realization of n independent random variables, nor, contrary to current practice, as the realization of n/2 independent random variables (treating the matched pair as the independent sampling unit). In this paper we study estimation of the average causal effect of a treatment under experimental designs in which treatment allocation potentially depends on the pre-intervention covariates of all units included in the sample. We define efficient targeted minimum loss based estimators for this general design, present a theorem that establishes the desired asymptotic normality of these estimators and allows for asymptotically valid statistical inference, and discuss implementation of these estimators. We further investigate the relative asymptotic efficiency of this design compared with a design in which unit-specific treatment assignment depends only on the units’ covariates. Our findings have practical implications for the optimal design and analysis of pair matched cluster randomized trials, as well as for observational studies in which treatment decisions may depend on characteristics of the entire sample. PMID:25097298

Beyond P Values and Hypothesis Testing: Using the Minimum Bayes Factor to Teach Statistical Inference in Undergraduate Introductory Statistics Courses

ERIC Educational Resources Information Center

Page, Robert; Satake, Eiki

2017-01-01

While interest in Bayesian statistics has been growing in statistics education, the treatment of the topic is still inadequate in both textbooks and the classroom. Because so many fields of study lead to careers that involve a decision-making process requiring an understanding of Bayesian methods, it is becoming increasingly clear that Bayesian…

Exploring High School Students Beginning Reasoning about Significance Tests with Technology

ERIC Educational Resources Information Center

García, Víctor N.; Sánchez, Ernesto

2017-01-01

In the present study we analyze how students reason about or make inferences given a particular hypothesis testing problem (without having studied formal methods of statistical inference) when using Fathom. They use Fathom to create an empirical sampling distribution through computer simulation. It is found that most student´s reasoning rely on…

Anchoring quartet-based phylogenetic distances and applications to species tree reconstruction.

PubMed

Sayyari, Erfan; Mirarab, Siavash

2016-11-11

Inferring species trees from gene trees using the coalescent-based summary methods has been the subject of much attention, yet new scalable and accurate methods are needed. We introduce DISTIQUE, a new statistically consistent summary method for inferring species trees from gene trees under the coalescent model. We generalize our results to arbitrary phylogenetic inference problems; we show that two arbitrarily chosen leaves, called anchors, can be used to estimate relative distances between all other pairs of leaves by inferring relevant quartet trees. This results in a family of distance-based tree inference methods, with running times ranging between quadratic to quartic in the number of leaves. We show in simulated studies that DISTIQUE has comparable accuracy to leading coalescent-based summary methods and reduced running times.

SHIPS: Spectral Hierarchical Clustering for the Inference of Population Structure in Genetic Studies

PubMed Central

Bouaziz, Matthieu; Paccard, Caroline; Guedj, Mickael; Ambroise, Christophe

2012-01-01

Inferring the structure of populations has many applications for genetic research. In addition to providing information for evolutionary studies, it can be used to account for the bias induced by population stratification in association studies. To this end, many algorithms have been proposed to cluster individuals into genetically homogeneous sub-populations. The parametric algorithms, such as Structure, are very popular but their underlying complexity and their high computational cost led to the development of faster parametric alternatives such as Admixture. Alternatives to these methods are the non-parametric approaches. Among this category, AWclust has proven efficient but fails to properly identify population structure for complex datasets. We present in this article a new clustering algorithm called Spectral Hierarchical clustering for the Inference of Population Structure (SHIPS), based on a divisive hierarchical clustering strategy, allowing a progressive investigation of population structure. This method takes genetic data as input to cluster individuals into homogeneous sub-populations and with the use of the gap statistic estimates the optimal number of such sub-populations. SHIPS was applied to a set of simulated discrete and admixed datasets and to real SNP datasets, that are data from the HapMap and Pan-Asian SNP consortium. The programs Structure, Admixture, AWclust and PCAclust were also investigated in a comparison study. SHIPS and the parametric approach Structure were the most accurate when applied to simulated datasets both in terms of individual assignments and estimation of the correct number of clusters. The analysis of the results on the real datasets highlighted that the clusterings of SHIPS were the more consistent with the population labels or those produced by the Admixture program. The performances of SHIPS when applied to SNP data, along with its relatively low computational cost and its ease of use make this method a promising solution to infer fine-scale genetic patterns. PMID:23077494

An Artificial Intelligence Approach to Analyzing Student Errors in Statistics.

ERIC Educational Resources Information Center

Sebrechts, Marc M.; Schooler, Lael J.

1987-01-01

Describes the development of an artificial intelligence system called GIDE that analyzes student errors in statistics problems by inferring the students' intentions. Learning strategies involved in problem solving are discussed and the inclusion of goal structures is explained. (LRW)

Network inference using informative priors.

PubMed

Mukherjee, Sach; Speed, Terence P

2008-09-23

Recent years have seen much interest in the study of systems characterized by multiple interacting components. A class of statistical models called graphical models, in which graphs are used to represent probabilistic relationships between variables, provides a framework for formal inference regarding such systems. In many settings, the object of inference is the network structure itself. This problem of "network inference" is well known to be a challenging one. However, in scientific settings there is very often existing information regarding network connectivity. A natural idea then is to take account of such information during inference. This article addresses the question of incorporating prior information into network inference. We focus on directed models called Bayesian networks, and use Markov chain Monte Carlo to draw samples from posterior distributions over network structures. We introduce prior distributions on graphs capable of capturing information regarding network features including edges, classes of edges, degree distributions, and sparsity. We illustrate our approach in the context of systems biology, applying our methods to network inference in cancer signaling.

The effect of statistical noise on IMRT plan quality and convergence for MC-based and MC-correction-based optimized treatment plans.

PubMed

Siebers, Jeffrey V

2008-04-04

Monte Carlo (MC) is rarely used for IMRT plan optimization outside of research centres due to the extensive computational resources or long computation times required to complete the process. Time can be reduced by degrading the statistical precision of the MC dose calculation used within the optimization loop. However, this eventually introduces optimization convergence errors (OCEs). This study determines the statistical noise levels tolerated during MC-IMRT optimization under the condition that the optimized plan has OCEs <100 cGy (1.5% of the prescription dose) for MC-optimized IMRT treatment plans.Seven-field prostate IMRT treatment plans for 10 prostate patients are used in this study. Pre-optimization is performed for deliverable beams with a pencil-beam (PB) dose algorithm. Further deliverable-based optimization proceeds using: (1) MC-based optimization, where dose is recomputed with MC after each intensity update or (2) a once-corrected (OC) MC-hybrid optimization, where a MC dose computation defines beam-by-beam dose correction matrices that are used during a PB-based optimization. Optimizations are performed with nominal per beam MC statistical precisions of 2, 5, 8, 10, 15, and 20%. Following optimizer convergence, beams are re-computed with MC using 2% per beam nominal statistical precision and the 2 PTV and 10 OAR dose indices used in the optimization objective function are tallied. For both the MC-optimization and OC-optimization methods, statistical equivalence tests found that OCEs are less than 1.5% of the prescription dose for plans optimized with nominal statistical uncertainties of up to 10% per beam. The achieved statistical uncertainty in the patient for the 10% per beam simulations from the combination of the 7 beams is ~3% with respect to maximum dose for voxels with D>0.5D(max). The MC dose computation time for the OC-optimization is only 6.2 minutes on a single 3 Ghz processor with results clinically equivalent to high precision MC computations.

Reaction Time in Grade 5: Data Collection within the Practice of Statistics

ERIC Educational Resources Information Center

Watson, Jane; English, Lyn

2017-01-01

This study reports on a classroom activity for Grade 5 students investigating their reaction times. The investigation was part of a 3-year research project introducing students to informal inference and giving them experience carrying out the practice of statistics. For this activity the focus within the practice of statistics was on introducing…

An Inferentialist Perspective on the Coordination of Actions and Reasons Involved in Making a Statistical Inference

ERIC Educational Resources Information Center

Bakker, Arthur; Ben-Zvi, Dani; Makar, Katie

2017-01-01

To understand how statistical and other types of reasoning are coordinated with actions to reduce uncertainty, we conducted a case study in vocational education that involved statistical hypothesis testing. We analyzed an intern's research project in a hospital laboratory in which reducing uncertainties was crucial to make a valid statistical…

Humans treat unreliable filled-in percepts as more real than veridical ones

PubMed Central

Ehinger, Benedikt V; Häusser, Katja; Ossandón, José P; König, Peter

2017-01-01

Humans often evaluate sensory signals according to their reliability for optimal decision-making. However, how do we evaluate percepts generated in the absence of direct input that are, therefore, completely unreliable? Here, we utilize the phenomenon of filling-in occurring at the physiological blind-spots to compare partially inferred and veridical percepts. Subjects chose between stimuli that elicit filling-in, and perceptually equivalent ones presented outside the blind-spots, looking for a Gabor stimulus without a small orthogonal inset. In ambiguous conditions, when the stimuli were physically identical and the inset was absent in both, subjects behaved opposite to optimal, preferring the blind-spot stimulus as the better example of a collinear stimulus, even though no relevant veridical information was available. Thus, a percept that is partially inferred is paradoxically considered more reliable than a percept based on external input. In other words: Humans treat filled-in inferred percepts as more real than veridical ones. DOI: http://dx.doi.org/10.7554/eLife.21761.001 PMID:28506359

Causal inference in biology networks with integrated belief propagation.

PubMed

Chang, Rui; Karr, Jonathan R; Schadt, Eric E

2015-01-01

Inferring causal relationships among molecular and higher order phenotypes is a critical step in elucidating the complexity of living systems. Here we propose a novel method for inferring causality that is no longer constrained by the conditional dependency arguments that limit the ability of statistical causal inference methods to resolve causal relationships within sets of graphical models that are Markov equivalent. Our method utilizes Bayesian belief propagation to infer the responses of perturbation events on molecular traits given a hypothesized graph structure. A distance measure between the inferred response distribution and the observed data is defined to assess the 'fitness' of the hypothesized causal relationships. To test our algorithm, we infer causal relationships within equivalence classes of gene networks in which the form of the functional interactions that are possible are assumed to be nonlinear, given synthetic microarray and RNA sequencing data. We also apply our method to infer causality in real metabolic network with v-structure and feedback loop. We show that our method can recapitulate the causal structure and recover the feedback loop only from steady-state data which conventional method cannot.

Gene-network inference by message passing

NASA Astrophysics Data System (ADS)

Braunstein, A.; Pagnani, A.; Weigt, M.; Zecchina, R.

2008-01-01

The inference of gene-regulatory processes from gene-expression data belongs to the major challenges of computational systems biology. Here we address the problem from a statistical-physics perspective and develop a message-passing algorithm which is able to infer sparse, directed and combinatorial regulatory mechanisms. Using the replica technique, the algorithmic performance can be characterized analytically for artificially generated data. The algorithm is applied to genome-wide expression data of baker's yeast under various environmental conditions. We find clear cases of combinatorial control, and enrichment in common functional annotations of regulated genes and their regulators.

Distinguishing between statistical significance and practical/clinical meaningfulness using statistical inference.

PubMed

Wilkinson, Michael

2014-03-01

Decisions about support for predictions of theories in light of data are made using statistical inference. The dominant approach in sport and exercise science is the Neyman-Pearson (N-P) significance-testing approach. When applied correctly it provides a reliable procedure for making dichotomous decisions for accepting or rejecting zero-effect null hypotheses with known and controlled long-run error rates. Type I and type II error rates must be specified in advance and the latter controlled by conducting an a priori sample size calculation. The N-P approach does not provide the probability of hypotheses or indicate the strength of support for hypotheses in light of data, yet many scientists believe it does. Outcomes of analyses allow conclusions only about the existence of non-zero effects, and provide no information about the likely size of true effects or their practical/clinical value. Bayesian inference can show how much support data provide for different hypotheses, and how personal convictions should be altered in light of data, but the approach is complicated by formulating probability distributions about prior subjective estimates of population effects. A pragmatic solution is magnitude-based inference, which allows scientists to estimate the true magnitude of population effects and how likely they are to exceed an effect magnitude of practical/clinical importance, thereby integrating elements of subjective Bayesian-style thinking. While this approach is gaining acceptance, progress might be hastened if scientists appreciate the shortcomings of traditional N-P null hypothesis significance testing.

Bayesian multimodel inference for dose-response studies

USGS Publications Warehouse

Link, W.A.; Albers, P.H.

2007-01-01

Statistical inference in dose?response studies is model-based: The analyst posits a mathematical model of the relation between exposure and response, estimates parameters of the model, and reports conclusions conditional on the model. Such analyses rarely include any accounting for the uncertainties associated with model selection. The Bayesian inferential system provides a convenient framework for model selection and multimodel inference. In this paper we briefly describe the Bayesian paradigm and Bayesian multimodel inference. We then present a family of models for multinomial dose?response data and apply Bayesian multimodel inferential methods to the analysis of data on the reproductive success of American kestrels (Falco sparveriuss) exposed to various sublethal dietary concentrations of methylmercury.

Analysis of Bioactive Amino Acids from Fish Hydrolysates with a New Bioinformatic Intelligent System Approach.

PubMed

Elaziz, Mohamed Abd; Hemdan, Ahmed Monem; Hassanien, AboulElla; Oliva, Diego; Xiong, Shengwu

2017-09-07

The current economics of the fish protein industry demand rapid, accurate and expressive prediction algorithms at every step of protein production especially with the challenge of global climate change. This help to predict and analyze functional and nutritional quality then consequently control food allergies in hyper allergic patients. As, it is quite expensive and time-consuming to know these concentrations by the lab experimental tests, especially to conduct large-scale projects. Therefore, this paper introduced a new intelligent algorithm using adaptive neuro-fuzzy inference system based on whale optimization algorithm. This algorithm is used to predict the concentration levels of bioactive amino acids in fish protein hydrolysates at different times during the year. The whale optimization algorithm is used to determine the optimal parameters in adaptive neuro-fuzzy inference system. The results of proposed algorithm are compared with others and it is indicated the higher performance of the proposed algorithm.

Statistical Inference for Big Data Problems in Molecular Biophysics

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

Ramanathan, Arvind; Savol, Andrej; Burger, Virginia

2012-01-01

We highlight the role of statistical inference techniques in providing biological insights from analyzing long time-scale molecular simulation data. Technologi- cal and algorithmic improvements in computation have brought molecular simu- lations to the forefront of techniques applied to investigating the basis of living systems. While these longer simulations, increasingly complex reaching petabyte scales presently, promise a detailed view into microscopic behavior, teasing out the important information has now become a true challenge on its own. Mining this data for important patterns is critical to automating therapeutic intervention discovery, improving protein design, and fundamentally understanding the mech- anistic basis of cellularmore » homeostasis.« less

Tropical geometry of statistical models.

PubMed

Pachter, Lior; Sturmfels, Bernd

2004-11-16

This article presents a unified mathematical framework for inference in graphical models, building on the observation that graphical models are algebraic varieties. From this geometric viewpoint, observations generated from a model are coordinates of a point in the variety, and the sum-product algorithm is an efficient tool for evaluating specific coordinates. Here, we address the question of how the solutions to various inference problems depend on the model parameters. The proposed answer is expressed in terms of tropical algebraic geometry. The Newton polytope of a statistical model plays a key role. Our results are applied to the hidden Markov model and the general Markov model on a binary tree.

ddClone: joint statistical inference of clonal populations from single cell and bulk tumour sequencing data.

PubMed

Salehi, Sohrab; Steif, Adi; Roth, Andrew; Aparicio, Samuel; Bouchard-Côté, Alexandre; Shah, Sohrab P

2017-03-01

Next-generation sequencing (NGS) of bulk tumour tissue can identify constituent cell populations in cancers and measure their abundance. This requires computational deconvolution of allelic counts from somatic mutations, which may be incapable of fully resolving the underlying population structure. Single cell sequencing (SCS) is a more direct method, although its replacement of NGS is impeded by technical noise and sampling limitations. We propose ddClone, which analytically integrates NGS and SCS data, leveraging their complementary attributes through joint statistical inference. We show on real and simulated datasets that ddClone produces more accurate results than can be achieved by either method alone.

The Heuristic Value of p in Inductive Statistical Inference

PubMed Central

Krueger, Joachim I.; Heck, Patrick R.

2017-01-01

Many statistical methods yield the probability of the observed data – or data more extreme – under the assumption that a particular hypothesis is true. This probability is commonly known as ‘the’ p-value. (Null Hypothesis) Significance Testing ([NH]ST) is the most prominent of these methods. The p-value has been subjected to much speculation, analysis, and criticism. We explore how well the p-value predicts what researchers presumably seek: the probability of the hypothesis being true given the evidence, and the probability of reproducing significant results. We also explore the effect of sample size on inferential accuracy, bias, and error. In a series of simulation experiments, we find that the p-value performs quite well as a heuristic cue in inductive inference, although there are identifiable limits to its usefulness. We conclude that despite its general usefulness, the p-value cannot bear the full burden of inductive inference; it is but one of several heuristic cues available to the data analyst. Depending on the inferential challenge at hand, investigators may supplement their reports with effect size estimates, Bayes factors, or other suitable statistics, to communicate what they think the data say. PMID:28649206

Subjective randomness as statistical inference.

PubMed

Griffiths, Thomas L; Daniels, Dylan; Austerweil, Joseph L; Tenenbaum, Joshua B

2018-06-01

Some events seem more random than others. For example, when tossing a coin, a sequence of eight heads in a row does not seem very random. Where do these intuitions about randomness come from? We argue that subjective randomness can be understood as the result of a statistical inference assessing the evidence that an event provides for having been produced by a random generating process. We show how this account provides a link to previous work relating randomness to algorithmic complexity, in which random events are those that cannot be described by short computer programs. Algorithmic complexity is both incomputable and too general to capture the regularities that people can recognize, but viewing randomness as statistical inference provides two paths to addressing these problems: considering regularities generated by simpler computing machines, and restricting the set of probability distributions that characterize regularity. Building on previous work exploring these different routes to a more restricted notion of randomness, we define strong quantitative models of human randomness judgments that apply not just to binary sequences - which have been the focus of much of the previous work on subjective randomness - but also to binary matrices and spatial clustering. Copyright © 2018 Elsevier Inc. All rights reserved.

The Heuristic Value of p in Inductive Statistical Inference.

PubMed

Krueger, Joachim I; Heck, Patrick R

2017-01-01

Many statistical methods yield the probability of the observed data - or data more extreme - under the assumption that a particular hypothesis is true. This probability is commonly known as 'the' p -value. (Null Hypothesis) Significance Testing ([NH]ST) is the most prominent of these methods. The p -value has been subjected to much speculation, analysis, and criticism. We explore how well the p -value predicts what researchers presumably seek: the probability of the hypothesis being true given the evidence, and the probability of reproducing significant results. We also explore the effect of sample size on inferential accuracy, bias, and error. In a series of simulation experiments, we find that the p -value performs quite well as a heuristic cue in inductive inference, although there are identifiable limits to its usefulness. We conclude that despite its general usefulness, the p -value cannot bear the full burden of inductive inference; it is but one of several heuristic cues available to the data analyst. Depending on the inferential challenge at hand, investigators may supplement their reports with effect size estimates, Bayes factors, or other suitable statistics, to communicate what they think the data say.

Statistical inference of seabed sound-speed structure in the Gulf of Oman Basin.

PubMed

Sagers, Jason D; Knobles, David P

2014-06-01

Addressed is the statistical inference of the sound-speed depth profile of a thick soft seabed from broadband sound propagation data recorded in the Gulf of Oman Basin in 1977. The acoustic data are in the form of time series signals recorded on a sparse vertical line array and generated by explosive sources deployed along a 280 km track. The acoustic data offer a unique opportunity to study a deep-water bottom-limited thickly sedimented environment because of the large number of time series measurements, very low seabed attenuation, and auxiliary measurements. A maximum entropy method is employed to obtain a conditional posterior probability distribution (PPD) for the sound-speed ratio and the near-surface sound-speed gradient. The multiple data samples allow for a determination of the average error constraint value required to uniquely specify the PPD for each data sample. Two complicating features of the statistical inference study are addressed: (1) the need to develop an error function that can both utilize the measured multipath arrival structure and mitigate the effects of data errors and (2) the effect of small bathymetric slopes on the structure of the bottom interacting arrivals.

Experimental and environmental factors affect spurious detection of ecological thresholds

USGS Publications Warehouse

Daily, Jonathan P.; Hitt, Nathaniel P.; Smith, David; Snyder, Craig D.

2012-01-01

Threshold detection methods are increasingly popular for assessing nonlinear responses to environmental change, but their statistical performance remains poorly understood. We simulated linear change in stream benthic macroinvertebrate communities and evaluated the performance of commonly used threshold detection methods based on model fitting (piecewise quantile regression [PQR]), data partitioning (nonparametric change point analysis [NCPA]), and a hybrid approach (significant zero crossings [SiZer]). We demonstrated that false detection of ecological thresholds (type I errors) and inferences on threshold locations are influenced by sample size, rate of linear change, and frequency of observations across the environmental gradient (i.e., sample-environment distribution, SED). However, the relative importance of these factors varied among statistical methods and between inference types. False detection rates were influenced primarily by user-selected parameters for PQR (τ) and SiZer (bandwidth) and secondarily by sample size (for PQR) and SED (for SiZer). In contrast, the location of reported thresholds was influenced primarily by SED. Bootstrapped confidence intervals for NCPA threshold locations revealed strong correspondence to SED. We conclude that the choice of statistical methods for threshold detection should be matched to experimental and environmental constraints to minimize false detection rates and avoid spurious inferences regarding threshold location.

Spatial Statistical Data Fusion (SSDF)

NASA Technical Reports Server (NTRS)

Braverman, Amy J.; Nguyen, Hai M.; Cressie, Noel

2013-01-01

As remote sensing for scientific purposes has transitioned from an experimental technology to an operational one, the selection of instruments has become more coordinated, so that the scientific community can exploit complementary measurements. However, tech nological and scientific heterogeneity across devices means that the statistical characteristics of the data they collect are different. The challenge addressed here is how to combine heterogeneous remote sensing data sets in a way that yields optimal statistical estimates of the underlying geophysical field, and provides rigorous uncertainty measures for those estimates. Different remote sensing data sets may have different spatial resolutions, different measurement error biases and variances, and other disparate characteristics. A state-of-the-art spatial statistical model was used to relate the true, but not directly observed, geophysical field to noisy, spatial aggregates observed by remote sensing instruments. The spatial covariances of the true field and the covariances of the true field with the observations were modeled. The observations are spatial averages of the true field values, over pixels, with different measurement noise superimposed. A kriging framework is used to infer optimal (minimum mean squared error and unbiased) estimates of the true field at point locations from pixel-level, noisy observations. A key feature of the spatial statistical model is the spatial mixed effects model that underlies it. The approach models the spatial covariance function of the underlying field using linear combinations of basis functions of fixed size. Approaches based on kriging require the inversion of very large spatial covariance matrices, and this is usually done by making simplifying assumptions about spatial covariance structure that simply do not hold for geophysical variables. In contrast, this method does not require these assumptions, and is also computationally much faster. This method is fundamentally different than other approaches to data fusion for remote sensing data because it is inferential rather than merely descriptive. All approaches combine data in a way that minimizes some specified loss function. Most of these are more or less ad hoc criteria based on what looks good to the eye, or some criteria that relate only to the data at hand.

INFERENCE BUILDING BLOCKS

DTIC Science & Technology

2018-02-15

address the problem that probabilistic inference algorithms are diÿcult and tedious to implement, by expressing them in terms of a small number of...building blocks, which are automatic transformations on probabilistic programs. On one hand, our curation of these building blocks reflects the way human...reasoning with low-level computational optimization, so the speed and accuracy of the generated solvers are competitive with state-of-the-art systems. 15

Designing Personalization in Technology-Based Services

ERIC Educational Resources Information Center

Lee, Min Kyung

2013-01-01

Personalization technology has the potential to optimize service for each person's unique needs and characteristics. One way to optimize service is to allow people to customize the service themselves; another is to proactively tailor services based on information provided by people or inferred from their past behaviors. These approaches function…

Harnessing Diversity towards the Reconstructing of Large Scale Gene Regulatory Networks

PubMed Central

Yamanaka, Ryota; Kitano, Hiroaki

2013-01-01

Elucidating gene regulatory network (GRN) from large scale experimental data remains a central challenge in systems biology. Recently, numerous techniques, particularly consensus driven approaches combining different algorithms, have become a potentially promising strategy to infer accurate GRNs. Here, we develop a novel consensus inference algorithm, TopkNet that can integrate multiple algorithms to infer GRNs. Comprehensive performance benchmarking on a cloud computing framework demonstrated that (i) a simple strategy to combine many algorithms does not always lead to performance improvement compared to the cost of consensus and (ii) TopkNet integrating only high-performance algorithms provide significant performance improvement compared to the best individual algorithms and community prediction. These results suggest that a priori determination of high-performance algorithms is a key to reconstruct an unknown regulatory network. Similarity among gene-expression datasets can be useful to determine potential optimal algorithms for reconstruction of unknown regulatory networks, i.e., if expression-data associated with known regulatory network is similar to that with unknown regulatory network, optimal algorithms determined for the known regulatory network can be repurposed to infer the unknown regulatory network. Based on this observation, we developed a quantitative measure of similarity among gene-expression datasets and demonstrated that, if similarity between the two expression datasets is high, TopkNet integrating algorithms that are optimal for known dataset perform well on the unknown dataset. The consensus framework, TopkNet, together with the similarity measure proposed in this study provides a powerful strategy towards harnessing the wisdom of the crowds in reconstruction of unknown regulatory networks. PMID:24278007

Advances in Bayesian Modeling in Educational Research

ERIC Educational Resources Information Center

Levy, Roy

2016-01-01

In this article, I provide a conceptually oriented overview of Bayesian approaches to statistical inference and contrast them with frequentist approaches that currently dominate conventional practice in educational research. The features and advantages of Bayesian approaches are illustrated with examples spanning several statistical modeling…

Statistical mechanics of complex neural systems and high dimensional data

NASA Astrophysics Data System (ADS)

Advani, Madhu; Lahiri, Subhaneil; Ganguli, Surya

2013-03-01

Recent experimental advances in neuroscience have opened new vistas into the immense complexity of neuronal networks. This proliferation of data challenges us on two parallel fronts. First, how can we form adequate theoretical frameworks for understanding how dynamical network processes cooperate across widely disparate spatiotemporal scales to solve important computational problems? Second, how can we extract meaningful models of neuronal systems from high dimensional datasets? To aid in these challenges, we give a pedagogical review of a collection of ideas and theoretical methods arising at the intersection of statistical physics, computer science and neurobiology. We introduce the interrelated replica and cavity methods, which originated in statistical physics as powerful ways to quantitatively analyze large highly heterogeneous systems of many interacting degrees of freedom. We also introduce the closely related notion of message passing in graphical models, which originated in computer science as a distributed algorithm capable of solving large inference and optimization problems involving many coupled variables. We then show how both the statistical physics and computer science perspectives can be applied in a wide diversity of contexts to problems arising in theoretical neuroscience and data analysis. Along the way we discuss spin glasses, learning theory, illusions of structure in noise, random matrices, dimensionality reduction and compressed sensing, all within the unified formalism of the replica method. Moreover, we review recent conceptual connections between message passing in graphical models, and neural computation and learning. Overall, these ideas illustrate how statistical physics and computer science might provide a lens through which we can uncover emergent computational functions buried deep within the dynamical complexities of neuronal networks.

Multibaseline gravitational wave radiometry

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

Talukder, Dipongkar; Bose, Sukanta; Mitra, Sanjit

2011-03-15

We present a statistic for the detection of stochastic gravitational wave backgrounds (SGWBs) using radiometry with a network of multiple baselines. We also quantitatively compare the sensitivities of existing baselines and their network to SGWBs. We assess how the measurement accuracy of signal parameters, e.g., the sky position of a localized source, can improve when using a network of baselines, as compared to any of the single participating baselines. The search statistic itself is derived from the likelihood ratio of the cross correlation of the data across all possible baselines in a detector network and is optimal in Gaussian noise.more » Specifically, it is the likelihood ratio maximized over the strength of the SGWB and is called the maximized-likelihood ratio (MLR). One of the main advantages of using the MLR over past search strategies for inferring the presence or absence of a signal is that the former does not require the deconvolution of the cross correlation statistic. Therefore, it does not suffer from errors inherent to the deconvolution procedure and is especially useful for detecting weak sources. In the limit of a single baseline, it reduces to the detection statistic studied by Ballmer [Classical Quantum Gravity 23, S179 (2006).] and Mitra et al.[Phys. Rev. D 77, 042002 (2008).]. Unlike past studies, here the MLR statistic enables us to compare quantitatively the performances of a variety of baselines searching for a SGWB signal in (simulated) data. Although we use simulated noise and SGWB signals for making these comparisons, our method can be straightforwardly applied on real data.« less

Statistical Inference for Quality-Adjusted Survival Time

DTIC Science & Technology

2003-08-01

survival functions of QAL. If an influence function for a test statistic exists for complete data case, denoted as ’i, then a test statistic for...the survival function for the censoring variable. Zhao and Tsiatis (2001) proposed a test statistic where O is the influence function of the general...to 1 everywhere until a subject’s death. We have considered other forms of test statistics. One option is to use an influence function 0i that is

Intimate Partner Violence in the United States - 2010

MedlinePlus

... administration............................................................................. 9 Statistical testing and inference ................................................................... 9 Additional methodological information ..........................................................10 2. Prevalence and Frequency of Individual ...

Estimating the probability of rare events: addressing zero failure data.

PubMed

Quigley, John; Revie, Matthew

2011-07-01

Traditional statistical procedures for estimating the probability of an event result in an estimate of zero when no events are realized. Alternative inferential procedures have been proposed for the situation where zero events have been realized but often these are ad hoc, relying on selecting methods dependent on the data that have been realized. Such data-dependent inference decisions violate fundamental statistical principles, resulting in estimation procedures whose benefits are difficult to assess. In this article, we propose estimating the probability of an event occurring through minimax inference on the probability that future samples of equal size realize no more events than that in the data on which the inference is based. Although motivated by inference on rare events, the method is not restricted to zero event data and closely approximates the maximum likelihood estimate (MLE) for nonzero data. The use of the minimax procedure provides a risk adverse inferential procedure where there are no events realized. A comparison is made with the MLE and regions of the underlying probability are identified where this approach is superior. Moreover, a comparison is made with three standard approaches to supporting inference where no event data are realized, which we argue are unduly pessimistic. We show that for situations of zero events the estimator can be simply approximated with 1/2.5n, where n is the number of trials. © 2011 Society for Risk Analysis.

Learning Quantitative Sequence-Function Relationships from Massively Parallel Experiments

NASA Astrophysics Data System (ADS)

Atwal, Gurinder S.; Kinney, Justin B.

2016-03-01

A fundamental aspect of biological information processing is the ubiquity of sequence-function relationships—functions that map the sequence of DNA, RNA, or protein to a biochemically relevant activity. Most sequence-function relationships in biology are quantitative, but only recently have experimental techniques for effectively measuring these relationships been developed. The advent of such "massively parallel" experiments presents an exciting opportunity for the concepts and methods of statistical physics to inform the study of biological systems. After reviewing these recent experimental advances, we focus on the problem of how to infer parametric models of sequence-function relationships from the data produced by these experiments. Specifically, we retrace and extend recent theoretical work showing that inference based on mutual information, not the standard likelihood-based approach, is often necessary for accurately learning the parameters of these models. Closely connected with this result is the emergence of "diffeomorphic modes"—directions in parameter space that are far less constrained by data than likelihood-based inference would suggest. Analogous to Goldstone modes in physics, diffeomorphic modes arise from an arbitrarily broken symmetry of the inference problem. An analytically tractable model of a massively parallel experiment is then described, providing an explicit demonstration of these fundamental aspects of statistical inference. This paper concludes with an outlook on the theoretical and computational challenges currently facing studies of quantitative sequence-function relationships.

Dopamine, Affordance and Active Inference

PubMed Central

Friston, Karl J.; Shiner, Tamara; FitzGerald, Thomas; Galea, Joseph M.; Adams, Rick; Brown, Harriet; Dolan, Raymond J.; Moran, Rosalyn; Stephan, Klaas Enno; Bestmann, Sven

2012-01-01

The role of dopamine in behaviour and decision-making is often cast in terms of reinforcement learning and optimal decision theory. Here, we present an alternative view that frames the physiology of dopamine in terms of Bayes-optimal behaviour. In this account, dopamine controls the precision or salience of (external or internal) cues that engender action. In other words, dopamine balances bottom-up sensory information and top-down prior beliefs when making hierarchical inferences (predictions) about cues that have affordance. In this paper, we focus on the consequences of changing tonic levels of dopamine firing using simulations of cued sequential movements. Crucially, the predictions driving movements are based upon a hierarchical generative model that infers the context in which movements are made. This means that we can confuse agents by changing the context (order) in which cues are presented. These simulations provide a (Bayes-optimal) model of contextual uncertainty and set switching that can be quantified in terms of behavioural and electrophysiological responses. Furthermore, one can simulate dopaminergic lesions (by changing the precision of prediction errors) to produce pathological behaviours that are reminiscent of those seen in neurological disorders such as Parkinson's disease. We use these simulations to demonstrate how a single functional role for dopamine at the synaptic level can manifest in different ways at the behavioural level. PMID:22241972

Statistical primer: how to deal with missing data in scientific research?

PubMed

Papageorgiou, Grigorios; Grant, Stuart W; Takkenberg, Johanna J M; Mokhles, Mostafa M

2018-05-10

Missing data are a common challenge encountered in research which can compromise the results of statistical inference when not handled appropriately. This paper aims to introduce basic concepts of missing data to a non-statistical audience, list and compare some of the most popular approaches for handling missing data in practice and provide guidelines and recommendations for dealing with and reporting missing data in scientific research. Complete case analysis and single imputation are simple approaches for handling missing data and are popular in practice, however, in most cases they are not guaranteed to provide valid inferences. Multiple imputation is a robust and general alternative which is appropriate for data missing at random, surpassing the disadvantages of the simpler approaches, but should always be conducted with care. The aforementioned approaches are illustrated and compared in an example application using Cox regression.

Is the P-Value Really Dead? Assessing Inference Learning Outcomes for Social Science Students in an Introductory Statistics Course

ERIC Educational Resources Information Center

Lane-Getaz, Sharon

2017-01-01

In reaction to misuses and misinterpretations of p-values and confidence intervals, a social science journal editor banned p-values from its pages. This study aimed to show that education could address misuse and abuse. This study examines inference-related learning outcomes for social science students in an introductory course supplemented with…

Back to BaySICS: a user-friendly program for Bayesian Statistical Inference from Coalescent Simulations.

PubMed

Sandoval-Castellanos, Edson; Palkopoulou, Eleftheria; Dalén, Love

2014-01-01

Inference of population demographic history has vastly improved in recent years due to a number of technological and theoretical advances including the use of ancient DNA. Approximate Bayesian computation (ABC) stands among the most promising methods due to its simple theoretical fundament and exceptional flexibility. However, limited availability of user-friendly programs that perform ABC analysis renders it difficult to implement, and hence programming skills are frequently required. In addition, there is limited availability of programs able to deal with heterochronous data. Here we present the software BaySICS: Bayesian Statistical Inference of Coalescent Simulations. BaySICS provides an integrated and user-friendly platform that performs ABC analyses by means of coalescent simulations from DNA sequence data. It estimates historical demographic population parameters and performs hypothesis testing by means of Bayes factors obtained from model comparisons. Although providing specific features that improve inference from datasets with heterochronous data, BaySICS also has several capabilities making it a suitable tool for analysing contemporary genetic datasets. Those capabilities include joint analysis of independent tables, a graphical interface and the implementation of Markov-chain Monte Carlo without likelihoods.

Sparsity-Cognizant Algorithms with Applications to Communications, Signal Processing, and the Smart Grid

NASA Astrophysics Data System (ADS)

Zhu, Hao

Sparsity plays an instrumental role in a plethora of scientific fields, including statistical inference for variable selection, parsimonious signal representations, and solving under-determined systems of linear equations - what has led to the ground-breaking result of compressive sampling (CS). This Thesis leverages exciting ideas of sparse signal reconstruction to develop sparsity-cognizant algorithms, and analyze their performance. The vision is to devise tools exploiting the 'right' form of sparsity for the 'right' application domain of multiuser communication systems, array signal processing systems, and the emerging challenges in the smart power grid. Two important power system monitoring tasks are addressed first by capitalizing on the hidden sparsity. To robustify power system state estimation, a sparse outlier model is leveraged to capture the possible corruption in every datum, while the problem nonconvexity due to nonlinear measurements is handled using the semidefinite relaxation technique. Different from existing iterative methods, the proposed algorithm approximates well the global optimum regardless of the initialization. In addition, for enhanced situational awareness, a novel sparse overcomplete representation is introduced to capture (possibly multiple) line outages, and develop real-time algorithms for solving the combinatorially complex identification problem. The proposed algorithms exhibit near-optimal performance while incurring only linear complexity in the number of lines, which makes it possible to quickly bring contingencies to attention. This Thesis also accounts for two basic issues in CS, namely fully-perturbed models and the finite alphabet property. The sparse total least-squares (S-TLS) approach is proposed to furnish CS algorithms for fully-perturbed linear models, leading to statistically optimal and computationally efficient solvers. The S-TLS framework is well motivated for grid-based sensing applications and exhibits higher accuracy than existing sparse algorithms. On the other hand, exploiting the finite alphabet of unknown signals emerges naturally in communication systems, along with sparsity coming from the low activity of each user. Compared to approaches only accounting for either one of the two, joint exploitation of both leads to statistically optimal detectors with improved error performance.

STATISTICAL METHODOLOGY FOR THE SIMULTANEOUS ANALYSIS OF MULTIPLE TYPES OF OUTCOMES IN NONLINEAR THRESHOLD MODELS.

EPA Science Inventory

Multiple outcomes are often measured on each experimental unit in toxicology experiments. These multiple observations typically imply the existence of correlation between endpoints, and a statistical analysis that incorporates it may result in improved inference. When both disc...

The Love of Large Numbers: A Popularity Bias in Consumer Choice.

PubMed

Powell, Derek; Yu, Jingqi; DeWolf, Melissa; Holyoak, Keith J

2017-10-01

Social learning-the ability to learn from observing the decisions of other people and the outcomes of those decisions-is fundamental to human evolutionary and cultural success. The Internet now provides social evidence on an unprecedented scale. However, properly utilizing this evidence requires a capacity for statistical inference. We examined how people's interpretation of online review scores is influenced by the numbers of reviews-a potential indicator both of an item's popularity and of the precision of the average review score. Our task was designed to pit statistical information against social information. We modeled the behavior of an "intuitive statistician" using empirical prior information from millions of reviews posted on Amazon.com and then compared the model's predictions with the behavior of experimental participants. Under certain conditions, people preferred a product with more reviews to one with fewer reviews even though the statistical model indicated that the latter was likely to be of higher quality than the former. Overall, participants' judgments suggested that they failed to make meaningful statistical inferences.

Learning what to expect (in visual perception)

PubMed Central

Seriès, Peggy; Seitz, Aaron R.

2013-01-01

Expectations are known to greatly affect our experience of the world. A growing theory in computational neuroscience is that perception can be successfully described using Bayesian inference models and that the brain is “Bayes-optimal” under some constraints. In this context, expectations are particularly interesting, because they can be viewed as prior beliefs in the statistical inference process. A number of questions remain unsolved, however, for example: How fast do priors change over time? Are there limits in the complexity of the priors that can be learned? How do an individual’s priors compare to the true scene statistics? Can we unlearn priors that are thought to correspond to natural scene statistics? Where and what are the neural substrate of priors? Focusing on the perception of visual motion, we here review recent studies from our laboratories and others addressing these issues. We discuss how these data on motion perception fit within the broader literature on perceptual Bayesian priors, perceptual expectations, and statistical and perceptual learning and review the possible neural basis of priors. PMID:24187536

Statistical Inference for Porous Materials using Persistent Homology.

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

Moon, Chul; Heath, Jason E.; Mitchell, Scott A.

2017-12-01

We propose a porous materials analysis pipeline using persistent homology. We rst compute persistent homology of binarized 3D images of sampled material subvolumes. For each image we compute sets of homology intervals, which are represented as summary graphics called persistence diagrams. We convert persistence diagrams into image vectors in order to analyze the similarity of the homology of the material images using the mature tools for image analysis. Each image is treated as a vector and we compute its principal components to extract features. We t a statistical model using the loadings of principal components to estimate material porosity, permeability,more » anisotropy, and tortuosity. We also propose an adaptive version of the structural similarity index (SSIM), a similarity metric for images, as a measure to determine the statistical representative elementary volumes (sREV) for persistence homology. Thus we provide a capability for making a statistical inference of the uid ow and transport properties of porous materials based on their geometry and connectivity.« less

Philosophy and the practice of Bayesian statistics

PubMed Central

Gelman, Andrew; Shalizi, Cosma Rohilla

2015-01-01

A substantial school in the philosophy of science identifies Bayesian inference with inductive inference and even rationality as such, and seems to be strengthened by the rise and practical success of Bayesian statistics. We argue that the most successful forms of Bayesian statistics do not actually support that particular philosophy but rather accord much better with sophisticated forms of hypothetico-deductivism. We examine the actual role played by prior distributions in Bayesian models, and the crucial aspects of model checking and model revision, which fall outside the scope of Bayesian confirmation theory. We draw on the literature on the consistency of Bayesian updating and also on our experience of applied work in social science. Clarity about these matters should benefit not just philosophy of science, but also statistical practice. At best, the inductivist view has encouraged researchers to fit and compare models without checking them; at worst, theorists have actively discouraged practitioners from performing model checking because it does not fit into their framework. PMID:22364575

Philosophy and the practice of Bayesian statistics.

PubMed

Gelman, Andrew; Shalizi, Cosma Rohilla

2013-02-01

A substantial school in the philosophy of science identifies Bayesian inference with inductive inference and even rationality as such, and seems to be strengthened by the rise and practical success of Bayesian statistics. We argue that the most successful forms of Bayesian statistics do not actually support that particular philosophy but rather accord much better with sophisticated forms of hypothetico-deductivism. We examine the actual role played by prior distributions in Bayesian models, and the crucial aspects of model checking and model revision, which fall outside the scope of Bayesian confirmation theory. We draw on the literature on the consistency of Bayesian updating and also on our experience of applied work in social science. Clarity about these matters should benefit not just philosophy of science, but also statistical practice. At best, the inductivist view has encouraged researchers to fit and compare models without checking them; at worst, theorists have actively discouraged practitioners from performing model checking because it does not fit into their framework. © 2012 The British Psychological Society.

Prediction of BP reactivity to talking using hybrid soft computing approaches.

PubMed

Kaur, Gurmanik; Arora, Ajat Shatru; Jain, Vijender Kumar

2014-01-01

High blood pressure (BP) is associated with an increased risk of cardiovascular diseases. Therefore, optimal precision in measurement of BP is appropriate in clinical and research studies. In this work, anthropometric characteristics including age, height, weight, body mass index (BMI), and arm circumference (AC) were used as independent predictor variables for the prediction of BP reactivity to talking. Principal component analysis (PCA) was fused with artificial neural network (ANN), adaptive neurofuzzy inference system (ANFIS), and least square-support vector machine (LS-SVM) model to remove the multicollinearity effect among anthropometric predictor variables. The statistical tests in terms of coefficient of determination (R (2)), root mean square error (RMSE), and mean absolute percentage error (MAPE) revealed that PCA based LS-SVM (PCA-LS-SVM) model produced a more efficient prediction of BP reactivity as compared to other models. This assessment presents the importance and advantages posed by PCA fused prediction models for prediction of biological variables.

Optimal Design of Experiments by Combining Coarse and Fine Measurements

NASA Astrophysics Data System (ADS)

Lee, Alpha A.; Brenner, Michael P.; Colwell, Lucy J.

2017-11-01

In many contexts, it is extremely costly to perform enough high-quality experimental measurements to accurately parametrize a predictive quantitative model. However, it is often much easier to carry out large numbers of experiments that indicate whether each sample is above or below a given threshold. Can many such categorical or "coarse" measurements be combined with a much smaller number of high-resolution or "fine" measurements to yield accurate models? Here, we demonstrate an intuitive strategy, inspired by statistical physics, wherein the coarse measurements are used to identify the salient features of the data, while the fine measurements determine the relative importance of these features. A linear model is inferred from the fine measurements, augmented by a quadratic term that captures the correlation structure of the coarse data. We illustrate our strategy by considering the problems of predicting the antimalarial potency and aqueous solubility of small organic molecules from their 2D molecular structure.

Ab Initio and Monte Carlo Approaches For the MagnetocaloricEffect in Co- and In-Doped Ni-Mn-Ga Heusler Alloys

NASA Astrophysics Data System (ADS)

Sokolovskiy, Vladimir; Grünebohm, Anna; Buchelnikov, Vasiliy; Entel, Peter

2014-09-01

This special issue collects contributions from the participants of the "Information in Dynamical Systems and Complex Systems" workshop, which cover a wide range of important problems and new approaches that lie in the intersection of information theory and dynamical systems. The contributions include theoretical characterization and understanding of the different types of information flow and causality in general stochastic processes, inference and identification of coupling structure and parameters of system dynamics, rigorous coarse-grain modeling of network dynamical systems, and exact statistical testing of fundamental information-theoretic quantities such as the mutual information. The collective efforts reported herein reflect a modern perspective of the intimate connection between dynamical systems and information flow, leading to the promise of better understanding and modeling of natural complex systems and better/optimal design of engineering systems.

78 FR 24138 - Implementing Public Safety Broadband Provisions of the Middle Class Tax Relief and Job Creation...

Federal Register 2010, 2011, 2012, 2013, 2014

2013-04-24

... Bureau, Statistical Abstract of the United States: 2011, Table 427 (2007). \\28\\ The 2007 U.S Census data.... (U.S. CENSUS BUREAU, STATISTICAL ABSTRACT OF THE UNITED STATES 2011, Table 428.) The criterion by... Statistical Abstract of the U.S., that inference is further supported by the fact that in both Tables, many...

Graphical models for optimal power flow

DOE PAGES

Dvijotham, Krishnamurthy; Chertkov, Michael; Van Hentenryck, Pascal; ...

2016-09-13

Optimal power flow (OPF) is the central optimization problem in electric power grids. Although solved routinely in the course of power grid operations, it is known to be strongly NP-hard in general, and weakly NP-hard over tree networks. In this paper, we formulate the optimal power flow problem over tree networks as an inference problem over a tree-structured graphical model where the nodal variables are low-dimensional vectors. We adapt the standard dynamic programming algorithm for inference over a tree-structured graphical model to the OPF problem. Combining this with an interval discretization of the nodal variables, we develop an approximation algorithmmore » for the OPF problem. Further, we use techniques from constraint programming (CP) to perform interval computations and adaptive bound propagation to obtain practically efficient algorithms. Compared to previous algorithms that solve OPF with optimality guarantees using convex relaxations, our approach is able to work for arbitrary tree-structured distribution networks and handle mixed-integer optimization problems. Further, it can be implemented in a distributed message-passing fashion that is scalable and is suitable for “smart grid” applications like control of distributed energy resources. In conclusion, numerical evaluations on several benchmark networks show that practical OPF problems can be solved effectively using this approach.« less

Identifiability of sorption parameters in stirred flow-through reactor experiments and their identification with a Bayesian approach.

PubMed

Nicoulaud-Gouin, V; Garcia-Sanchez, L; Giacalone, M; Attard, J C; Martin-Garin, A; Bois, F Y

2016-10-01

This paper addresses the methodological conditions -particularly experimental design and statistical inference- ensuring the identifiability of sorption parameters from breakthrough curves measured during stirred flow-through reactor experiments also known as continuous flow stirred-tank reactor (CSTR) experiments. The equilibrium-kinetic (EK) sorption model was selected as nonequilibrium parameterization embedding the K d approach. Parameter identifiability was studied formally on the equations governing outlet concentrations. It was also studied numerically on 6 simulated CSTR experiments on a soil with known equilibrium-kinetic sorption parameters. EK sorption parameters can not be identified from a single breakthrough curve of a CSTR experiment, because K d,1 and k - were diagnosed collinear. For pairs of CSTR experiments, Bayesian inference allowed to select the correct models of sorption and error among sorption alternatives. Bayesian inference was conducted with SAMCAT software (Sensitivity Analysis and Markov Chain simulations Applied to Transfer models) which launched the simulations through the embedded simulation engine GNU-MCSim, and automated their configuration and post-processing. Experimental designs consisting in varying flow rates between experiments reaching equilibrium at contamination stage were found optimal, because they simultaneously gave accurate sorption parameters and predictions. Bayesian results were comparable to maximum likehood method but they avoided convergence problems, the marginal likelihood allowed to compare all models, and credible interval gave directly the uncertainty of sorption parameters θ. Although these findings are limited to the specific conditions studied here, in particular the considered sorption model, the chosen parameter values and error structure, they help in the conception and analysis of future CSTR experiments with radionuclides whose kinetic behaviour is suspected. Copyright © 2016 Elsevier Ltd. All rights reserved.

Data mining in forecasting PVT correlations of crude oil systems based on Type1 fuzzy logic inference systems

NASA Astrophysics Data System (ADS)

El-Sebakhy, Emad A.

2009-09-01

Pressure-volume-temperature properties are very important in the reservoir engineering computations. There are many empirical approaches for predicting various PVT properties based on empirical correlations and statistical regression models. Last decade, researchers utilized neural networks to develop more accurate PVT correlations. These achievements of neural networks open the door to data mining techniques to play a major role in oil and gas industry. Unfortunately, the developed neural networks correlations are often limited, and global correlations are usually less accurate compared to local correlations. Recently, adaptive neuro-fuzzy inference systems have been proposed as a new intelligence framework for both prediction and classification based on fuzzy clustering optimization criterion and ranking. This paper proposes neuro-fuzzy inference systems for estimating PVT properties of crude oil systems. This new framework is an efficient hybrid intelligence machine learning scheme for modeling the kind of uncertainty associated with vagueness and imprecision. We briefly describe the learning steps and the use of the Takagi Sugeno and Kang model and Gustafson-Kessel clustering algorithm with K-detected clusters from the given database. It has featured in a wide range of medical, power control system, and business journals, often with promising results. A comparative study will be carried out to compare their performance of this new framework with the most popular modeling techniques, such as neural networks, nonlinear regression, and the empirical correlations algorithms. The results show that the performance of neuro-fuzzy systems is accurate, reliable, and outperform most of the existing forecasting techniques. Future work can be achieved by using neuro-fuzzy systems for clustering the 3D seismic data, identification of lithofacies types, and other reservoir characterization.

Augmenting Latent Dirichlet Allocation and Rank Threshold Detection with Ontologies

DTIC Science & Technology

2010-03-01

Probabilistic Latent Semantic Indexing (PLSI) is an automated indexing information retrieval model [20]. It is based on a statistical latent class model which is...uses a statistical foundation that is more accurate in finding hidden semantic relationships [20]. The model uses factor analysis of count data, number...principle of statistical infer- ence which asserts that all of the information in a sample is contained in the likelihood function [20]. The statistical

Attentional and Contextual Priors in Sound Perception.

PubMed

Wolmetz, Michael; Elhilali, Mounya

2016-01-01

Behavioral and neural studies of selective attention have consistently demonstrated that explicit attentional cues to particular perceptual features profoundly alter perception and performance. The statistics of the sensory environment can also provide cues about what perceptual features to expect, but the extent to which these more implicit contextual cues impact perception and performance, as well as their relationship to explicit attentional cues, is not well understood. In this study, the explicit cues, or attentional prior probabilities, and the implicit cues, or contextual prior probabilities, associated with different acoustic frequencies in a detection task were simultaneously manipulated. Both attentional and contextual priors had similarly large but independent impacts on sound detectability, with evidence that listeners tracked and used contextual priors for a variety of sound classes (pure tones, harmonic complexes, and vowels). Further analyses showed that listeners updated their contextual priors rapidly and optimally, given the changing acoustic frequency statistics inherent in the paradigm. A Bayesian Observer model accounted for both attentional and contextual adaptations found with listeners. These results bolster the interpretation of perception as Bayesian inference, and suggest that some effects attributed to selective attention may be a special case of contextual prior integration along a feature axis.

Spatial analysis of relative humidity during ungauged periods in a mountainous region

NASA Astrophysics Data System (ADS)

Um, Myoung-Jin; Kim, Yeonjoo

2017-08-01

Although atmospheric humidity influences environmental and agricultural conditions, thereby influencing plant growth, human health, and air pollution, efforts to develop spatial maps of atmospheric humidity using statistical approaches have thus far been limited. This study therefore aims to develop statistical approaches for inferring the spatial distribution of relative humidity (RH) for a mountainous island, for which data are not uniformly available across the region. A multiple regression analysis based on various mathematical models was used to identify the optimal model for estimating monthly RH by incorporating not only temperature but also location and elevation. Based on the regression analysis, we extended the monthly RH data from weather stations to cover the ungauged periods when no RH observations were available. Then, two different types of station-based data, the observational data and the data extended via the regression model, were used to form grid-based data with a resolution of 100 m. The grid-based data that used the extended station-based data captured the increasing RH trend along an elevation gradient. Furthermore, annual RH values averaged over the regions were examined. Decreasing temporal trends were found in most cases, with magnitudes varying based on the season and region.

Attentional and Contextual Priors in Sound Perception

PubMed Central

Wolmetz, Michael; Elhilali, Mounya

2016-01-01

Behavioral and neural studies of selective attention have consistently demonstrated that explicit attentional cues to particular perceptual features profoundly alter perception and performance. The statistics of the sensory environment can also provide cues about what perceptual features to expect, but the extent to which these more implicit contextual cues impact perception and performance, as well as their relationship to explicit attentional cues, is not well understood. In this study, the explicit cues, or attentional prior probabilities, and the implicit cues, or contextual prior probabilities, associated with different acoustic frequencies in a detection task were simultaneously manipulated. Both attentional and contextual priors had similarly large but independent impacts on sound detectability, with evidence that listeners tracked and used contextual priors for a variety of sound classes (pure tones, harmonic complexes, and vowels). Further analyses showed that listeners updated their contextual priors rapidly and optimally, given the changing acoustic frequency statistics inherent in the paradigm. A Bayesian Observer model accounted for both attentional and contextual adaptations found with listeners. These results bolster the interpretation of perception as Bayesian inference, and suggest that some effects attributed to selective attention may be a special case of contextual prior integration along a feature axis. PMID:26882228

An Optimal Algorithm towards Successive Location Privacy in Sensor Networks with Dynamic Programming

NASA Astrophysics Data System (ADS)

Zhao, Baokang; Wang, Dan; Shao, Zili; Cao, Jiannong; Chan, Keith C. C.; Su, Jinshu

In wireless sensor networks, preserving location privacy under successive inference attacks is extremely critical. Although this problem is NP-complete in general cases, we propose a dynamic programming based algorithm and prove it is optimal in special cases where the correlation only exists between p immediate adjacent observations.

Inference Control Mechanism for Statistical Database: Frequency-Imposed Data Distortions.

ERIC Educational Resources Information Center

Liew, Chong K.; And Others

1985-01-01

Introduces two data distortion methods (Frequency-Imposed Distortion, Frequency-Imposed Probability Distortion) and uses a Monte Carlo study to compare their performance with that of other distortion methods (Point Distortion, Probability Distortion). Indications that data generated by these two methods produce accurate statistics and protect…

Implementing and analyzing the multi-threaded LP-inference

NASA Astrophysics Data System (ADS)

Bolotova, S. Yu; Trofimenko, E. V.; Leschinskaya, M. V.

2018-03-01

The logical production equations provide new possibilities for the backward inference optimization in intelligent production-type systems. The strategy of a relevant backward inference is aimed at minimization of a number of queries to external information source (either to a database or an interactive user). The idea of the method is based on the computing of initial preimages set and searching for the true preimage. The execution of each stage can be organized independently and in parallel and the actual work at a given stage can also be distributed between parallel computers. This paper is devoted to the parallel algorithms of the relevant inference based on the advanced scheme of the parallel computations “pipeline” which allows to increase the degree of parallelism. The author also provides some details of the LP-structures implementation.

Notes on power of normality tests of error terms in regression models

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

Střelec, Luboš

2015-03-10

Normality is one of the basic assumptions in applying statistical procedures. For example in linear regression most of the inferential procedures are based on the assumption of normality, i.e. the disturbance vector is assumed to be normally distributed. Failure to assess non-normality of the error terms may lead to incorrect results of usual statistical inference techniques such as t-test or F-test. Thus, error terms should be normally distributed in order to allow us to make exact inferences. As a consequence, normally distributed stochastic errors are necessary in order to make a not misleading inferences which explains a necessity and importancemore » of robust tests of normality. Therefore, the aim of this contribution is to discuss normality testing of error terms in regression models. In this contribution, we introduce the general RT class of robust tests for normality, and present and discuss the trade-off between power and robustness of selected classical and robust normality tests of error terms in regression models.« less

An argument for mechanism-based statistical inference in cancer

PubMed Central

Ochs, Michael; Price, Nathan D.; Tomasetti, Cristian; Younes, Laurent

2015-01-01

Cancer is perhaps the prototypical systems disease, and as such has been the focus of extensive study in quantitative systems biology. However, translating these programs into personalized clinical care remains elusive and incomplete. In this perspective, we argue that realizing this agenda—in particular, predicting disease phenotypes, progression and treatment response for individuals—requires going well beyond standard computational and bioinformatics tools and algorithms. It entails designing global mathematical models over network-scale configurations of genomic states and molecular concentrations, and learning the model parameters from limited available samples of high-dimensional and integrative omics data. As such, any plausible design should accommodate: biological mechanism, necessary for both feasible learning and interpretable decision making; stochasticity, to deal with uncertainty and observed variation at many scales; and a capacity for statistical inference at the patient level. This program, which requires a close, sustained collaboration between mathematicians and biologists, is illustrated in several contexts, including learning bio-markers, metabolism, cell signaling, network inference and tumorigenesis. PMID:25381197

Network inference using informative priors

PubMed Central

Mukherjee, Sach; Speed, Terence P.

2008-01-01

Recent years have seen much interest in the study of systems characterized by multiple interacting components. A class of statistical models called graphical models, in which graphs are used to represent probabilistic relationships between variables, provides a framework for formal inference regarding such systems. In many settings, the object of inference is the network structure itself. This problem of “network inference” is well known to be a challenging one. However, in scientific settings there is very often existing information regarding network connectivity. A natural idea then is to take account of such information during inference. This article addresses the question of incorporating prior information into network inference. We focus on directed models called Bayesian networks, and use Markov chain Monte Carlo to draw samples from posterior distributions over network structures. We introduce prior distributions on graphs capable of capturing information regarding network features including edges, classes of edges, degree distributions, and sparsity. We illustrate our approach in the context of systems biology, applying our methods to network inference in cancer signaling. PMID:18799736

Bayesian Inference for Functional Dynamics Exploring in fMRI Data.

PubMed

Guo, Xuan; Liu, Bing; Chen, Le; Chen, Guantao; Pan, Yi; Zhang, Jing

2016-01-01

This paper aims to review state-of-the-art Bayesian-inference-based methods applied to functional magnetic resonance imaging (fMRI) data. Particularly, we focus on one specific long-standing challenge in the computational modeling of fMRI datasets: how to effectively explore typical functional interactions from fMRI time series and the corresponding boundaries of temporal segments. Bayesian inference is a method of statistical inference which has been shown to be a powerful tool to encode dependence relationships among the variables with uncertainty. Here we provide an introduction to a group of Bayesian-inference-based methods for fMRI data analysis, which were designed to detect magnitude or functional connectivity change points and to infer their functional interaction patterns based on corresponding temporal boundaries. We also provide a comparison of three popular Bayesian models, that is, Bayesian Magnitude Change Point Model (BMCPM), Bayesian Connectivity Change Point Model (BCCPM), and Dynamic Bayesian Variable Partition Model (DBVPM), and give a summary of their applications. We envision that more delicate Bayesian inference models will be emerging and play increasingly important roles in modeling brain functions in the years to come.

Designing a parallel evolutionary algorithm for inferring gene networks on the cloud computing environment.

PubMed

Lee, Wei-Po; Hsiao, Yu-Ting; Hwang, Wei-Che

2014-01-16

To improve the tedious task of reconstructing gene networks through testing experimentally the possible interactions between genes, it becomes a trend to adopt the automated reverse engineering procedure instead. Some evolutionary algorithms have been suggested for deriving network parameters. However, to infer large networks by the evolutionary algorithm, it is necessary to address two important issues: premature convergence and high computational cost. To tackle the former problem and to enhance the performance of traditional evolutionary algorithms, it is advisable to use parallel model evolutionary algorithms. To overcome the latter and to speed up the computation, it is advocated to adopt the mechanism of cloud computing as a promising solution: most popular is the method of MapReduce programming model, a fault-tolerant framework to implement parallel algorithms for inferring large gene networks. This work presents a practical framework to infer large gene networks, by developing and parallelizing a hybrid GA-PSO optimization method. Our parallel method is extended to work with the Hadoop MapReduce programming model and is executed in different cloud computing environments. To evaluate the proposed approach, we use a well-known open-source software GeneNetWeaver to create several yeast S. cerevisiae sub-networks and use them to produce gene profiles. Experiments have been conducted and the results have been analyzed. They show that our parallel approach can be successfully used to infer networks with desired behaviors and the computation time can be largely reduced. Parallel population-based algorithms can effectively determine network parameters and they perform better than the widely-used sequential algorithms in gene network inference. These parallel algorithms can be distributed to the cloud computing environment to speed up the computation. By coupling the parallel model population-based optimization method and the parallel computational framework, high quality solutions can be obtained within relatively short time. This integrated approach is a promising way for inferring large networks.

Designing a parallel evolutionary algorithm for inferring gene networks on the cloud computing environment

PubMed Central

2014-01-01

Background To improve the tedious task of reconstructing gene networks through testing experimentally the possible interactions between genes, it becomes a trend to adopt the automated reverse engineering procedure instead. Some evolutionary algorithms have been suggested for deriving network parameters. However, to infer large networks by the evolutionary algorithm, it is necessary to address two important issues: premature convergence and high computational cost. To tackle the former problem and to enhance the performance of traditional evolutionary algorithms, it is advisable to use parallel model evolutionary algorithms. To overcome the latter and to speed up the computation, it is advocated to adopt the mechanism of cloud computing as a promising solution: most popular is the method of MapReduce programming model, a fault-tolerant framework to implement parallel algorithms for inferring large gene networks. Results This work presents a practical framework to infer large gene networks, by developing and parallelizing a hybrid GA-PSO optimization method. Our parallel method is extended to work with the Hadoop MapReduce programming model and is executed in different cloud computing environments. To evaluate the proposed approach, we use a well-known open-source software GeneNetWeaver to create several yeast S. cerevisiae sub-networks and use them to produce gene profiles. Experiments have been conducted and the results have been analyzed. They show that our parallel approach can be successfully used to infer networks with desired behaviors and the computation time can be largely reduced. Conclusions Parallel population-based algorithms can effectively determine network parameters and they perform better than the widely-used sequential algorithms in gene network inference. These parallel algorithms can be distributed to the cloud computing environment to speed up the computation. By coupling the parallel model population-based optimization method and the parallel computational framework, high quality solutions can be obtained within relatively short time. This integrated approach is a promising way for inferring large networks. PMID:24428926

Mathematical inference and control of molecular networks from perturbation experiments

NASA Astrophysics Data System (ADS)

Mohammed-Rasheed, Mohammed

One of the main challenges facing biologists and mathematicians in the post genomic era is to understand the behavior of molecular networks and harness this understanding into an educated intervention of the cell. The cell maintains its function via an elaborate network of interconnecting positive and negative feedback loops of genes, RNA and proteins that send different signals to a large number of pathways and molecules. These structures are referred to as genetic regulatory networks (GRNs) or molecular networks. GRNs can be viewed as dynamical systems with inherent properties and mechanisms, such as steady-state equilibriums and stability, that determine the behavior of the cell. The biological relevance of the mathematical concepts are important as they may predict the differentiation of a stem cell, the maintenance of a normal cell, the development of cancer and its aberrant behavior, and the design of drugs and response to therapy. Uncovering the underlying GRN structure from gene/protein expression data, e.g., microarrays or perturbation experiments, is called inference or reverse engineering of the molecular network. Because of the high cost and time consuming nature of biological experiments, the number of available measurements or experiments is very small compared to the number of molecules (genes, RNA and proteins). In addition, the observations are noisy, where the noise is due to the measurements imperfections as well as the inherent stochasticity of genetic expression levels. Intra-cellular activities and extra-cellular environmental attributes are also another source of variability. Thus, the inference of GRNs is, in general, an under-determined problem with a highly noisy set of observations. The ultimate goal of GRN inference and analysis is to be able to intervene within the network, in order to force it away from undesirable cellular states and into desirable ones. However, it remains a major challenge to design optimal intervention strategies in order to affect the time evolution of molecular activity in a desirable manner. In this proposal, we address both the inference and control problems of GRNs. In the first part of the thesis, we consider the control problem. We assume that we are given a general topology network structure, whose dynamics follow a discrete-time Markov chain model. We subsequently develop a comprehensive framework for optimal perturbation control of the network. The aim of the perturbation is to drive the network away from undesirable steady-states and to force it to converge to a unique desirable steady-state. The proposed framework does not make any assumptions about the topology of the initial network (e.g., ergodicity, weak and strong connectivity), and is thus applicable to general topology networks. We define the optimal perturbation as the minimum-energy perturbation measured in terms of the Frobenius norm between the initial and perturbed networks. We subsequently demonstrate that there exists at most one optimal perturbation that forces the network into the desirable steady-state. In the event where the optimal perturbation does not exist, we construct a family of sub-optimal perturbations that approximate the optimal solution arbitrarily closely. In the second part of the thesis, we address the inference problem of GRNs from time series data. We model the dynamics of the molecules using a system of ordinary differential equations corrupted by additive white noise. For large-scale networks, we formulate the inference problem as a constrained maximum likelihood estimation problem. We derive the molecular interactions that maximize the likelihood function while constraining the network to be sparse. We further propose a procedure to recover weak interactions based on the Bayesian information criterion. For small-size networks, we investigated the inference of a globally stable 7-gene melanoma genetic regulatory network from genetic perturbation experiments. We considered five melanoma cell lines, who exhibit different motility/invasion behavior under the same perturbation experiment of gene Wnt5a. The results of the simulations validate both the steady state levels and the experimental data of the perturbation experiments of all five cell lines. The goal of this study is to answer important questions that link the response of the network to perturbations, as measured by the experiments, to its structure, i.e., connectivity. Answers to these questions shed novel insights on the structure of networks and how they react to perturbations.

Joint Clustering and Component Analysis of Correspondenceless Point Sets: Application to Cardiac Statistical Modeling.

PubMed

Gooya, Ali; Lekadir, Karim; Alba, Xenia; Swift, Andrew J; Wild, Jim M; Frangi, Alejandro F

2015-01-01

Construction of Statistical Shape Models (SSMs) from arbitrary point sets is a challenging problem due to significant shape variation and lack of explicit point correspondence across the training data set. In medical imaging, point sets can generally represent different shape classes that span healthy and pathological exemplars. In such cases, the constructed SSM may not generalize well, largely because the probability density function (pdf) of the point sets deviates from the underlying assumption of Gaussian statistics. To this end, we propose a generative model for unsupervised learning of the pdf of point sets as a mixture of distinctive classes. A Variational Bayesian (VB) method is proposed for making joint inferences on the labels of point sets, and the principal modes of variations in each cluster. The method provides a flexible framework to handle point sets with no explicit point-to-point correspondences. We also show that by maximizing the marginalized likelihood of the model, the optimal number of clusters of point sets can be determined. We illustrate this work in the context of understanding the anatomical phenotype of the left and right ventricles in heart. To this end, we use a database containing hearts of healthy subjects, patients with Pulmonary Hypertension (PH), and patients with Hypertrophic Cardiomyopathy (HCM). We demonstrate that our method can outperform traditional PCA in both generalization and specificity measures.

Modeling jointly low, moderate, and heavy rainfall intensities without a threshold selection

NASA Astrophysics Data System (ADS)

Naveau, Philippe; Huser, Raphael; Ribereau, Pierre; Hannart, Alexis

2016-04-01

In statistics, extreme events are often defined as excesses above a given large threshold. This definition allows hydrologists and flood planners to apply Extreme-Value Theory (EVT) to their time series of interest. Even in the stationary univariate context, this approach has at least two main drawbacks. First, working with excesses implies that a lot of observations (those below the chosen threshold) are completely disregarded. The range of precipitation is artificially shopped down into two pieces, namely large intensities and the rest, which necessarily imposes different statistical models for each piece. Second, this strategy raises a nontrivial and very practical difficultly: how to choose the optimal threshold which correctly discriminates between low and heavy rainfall intensities. To address these issues, we propose a statistical model in which EVT results apply not only to heavy, but also to low precipitation amounts (zeros excluded). Our model is in compliance with EVT on both ends of the spectrum and allows a smooth transition between the two tails, while keeping a low number of parameters. In terms of inference, we have implemented and tested two classical methods of estimation: likelihood maximization and probability weighed moments. Last but not least, there is no need to choose a threshold to define low and high excesses. The performance and flexibility of this approach are illustrated on simulated and hourly precipitation recorded in Lyon, France.

Uncertainty quantification for nuclear density functional theory and information content of new measurements.

PubMed

McDonnell, J D; Schunck, N; Higdon, D; Sarich, J; Wild, S M; Nazarewicz, W

2015-03-27

Statistical tools of uncertainty quantification can be used to assess the information content of measured observables with respect to present-day theoretical models, to estimate model errors and thereby improve predictive capability, to extrapolate beyond the regions reached by experiment, and to provide meaningful input to applications and planned measurements. To showcase new opportunities offered by such tools, we make a rigorous analysis of theoretical statistical uncertainties in nuclear density functional theory using Bayesian inference methods. By considering the recent mass measurements from the Canadian Penning Trap at Argonne National Laboratory, we demonstrate how the Bayesian analysis and a direct least-squares optimization, combined with high-performance computing, can be used to assess the information content of the new data with respect to a model based on the Skyrme energy density functional approach. Employing the posterior probability distribution computed with a Gaussian process emulator, we apply the Bayesian framework to propagate theoretical statistical uncertainties in predictions of nuclear masses, two-neutron dripline, and fission barriers. Overall, we find that the new mass measurements do not impose a constraint that is strong enough to lead to significant changes in the model parameters. The example discussed in this study sets the stage for quantifying and maximizing the impact of new measurements with respect to current modeling and guiding future experimental efforts, thus enhancing the experiment-theory cycle in the scientific method.

Modular Spectral Inference Framework Applied to Young Stars and Brown Dwarfs

NASA Technical Reports Server (NTRS)

Gully-Santiago, Michael A.; Marley, Mark S.

2017-01-01

In practice, synthetic spectral models are imperfect, causing inaccurate estimates of stellar parameters. Using forward modeling and statistical inference, we derive accurate stellar parameters for a given observed spectrum by emulating a grid of precomputed spectra to track uncertainties. Spectral inference as applied to brown dwarfs re: Synthetic spectral models (Marley et al 1996 and 2014) via the newest grid spans a massive multi-dimensional grid applied to IGRINS spectra, improving atmospheric models for JWST. When applied to young stars(10Myr) with large starpots, they can be measured spectroscopically, especially in the near-IR with IGRINS.

Inference of neuronal network spike dynamics and topology from calcium imaging data

PubMed Central

Lütcke, Henry; Gerhard, Felipe; Zenke, Friedemann; Gerstner, Wulfram; Helmchen, Fritjof

2013-01-01

Two-photon calcium imaging enables functional analysis of neuronal circuits by inferring action potential (AP) occurrence (“spike trains”) from cellular fluorescence signals. It remains unclear how experimental parameters such as signal-to-noise ratio (SNR) and acquisition rate affect spike inference and whether additional information about network structure can be extracted. Here we present a simulation framework for quantitatively assessing how well spike dynamics and network topology can be inferred from noisy calcium imaging data. For simulated AP-evoked calcium transients in neocortical pyramidal cells, we analyzed the quality of spike inference as a function of SNR and data acquisition rate using a recently introduced peeling algorithm. Given experimentally attainable values of SNR and acquisition rate, neural spike trains could be reconstructed accurately and with up to millisecond precision. We then applied statistical neuronal network models to explore how remaining uncertainties in spike inference affect estimates of network connectivity and topological features of network organization. We define the experimental conditions suitable for inferring whether the network has a scale-free structure and determine how well hub neurons can be identified. Our findings provide a benchmark for future calcium imaging studies that aim to reliably infer neuronal network properties. PMID:24399936

Type Ia Supernova Light Curve Inference: Hierarchical Models for Nearby SN Ia in the Optical and Near Infrared

NASA Astrophysics Data System (ADS)

Mandel, Kaisey; Kirshner, R. P.; Narayan, G.; Wood-Vasey, W. M.; Friedman, A. S.; Hicken, M.

2010-01-01

I have constructed a comprehensive statistical model for Type Ia supernova light curves spanning optical through near infrared data simultaneously. The near infrared light curves are found to be excellent standard candles (sigma(MH) = 0.11 +/- 0.03 mag) that are less vulnerable to systematic error from dust extinction, a major confounding factor for cosmological studies. A hierarchical statistical framework incorporates coherently multiple sources of randomness and uncertainty, including photometric error, intrinsic supernova light curve variations and correlations, dust extinction and reddening, peculiar velocity dispersion and distances, for probabilistic inference with Type Ia SN light curves. Inferences are drawn from the full probability density over individual supernovae and the SN Ia and dust populations, conditioned on a dataset of SN Ia light curves and redshifts. To compute probabilistic inferences with hierarchical models, I have developed BayeSN, a Markov Chain Monte Carlo algorithm based on Gibbs sampling. This code explores and samples the global probability density of parameters describing individual supernovae and the population. I have applied this hierarchical model to optical and near infrared data of over 100 nearby Type Ia SN from PAIRITEL, the CfA3 sample, and the literature. Using this statistical model, I find that SN with optical and NIR data have a smaller residual scatter in the Hubble diagram than SN with only optical data. The continued study of Type Ia SN in the near infrared will be important for improving their utility as precise and accurate cosmological distance indicators.

Statistical inference involving binomial and negative binomial parameters.

PubMed

García-Pérez, Miguel A; Núñez-Antón, Vicente

2009-05-01

Statistical inference about two binomial parameters implies that they are both estimated by binomial sampling. There are occasions in which one aims at testing the equality of two binomial parameters before and after the occurrence of the first success along a sequence of Bernoulli trials. In these cases, the binomial parameter before the first success is estimated by negative binomial sampling whereas that after the first success is estimated by binomial sampling, and both estimates are related. This paper derives statistical tools to test two hypotheses, namely, that both binomial parameters equal some specified value and that both parameters are equal though unknown. Simulation studies are used to show that in small samples both tests are accurate in keeping the nominal Type-I error rates, and also to determine sample size requirements to detect large, medium, and small effects with adequate power. Additional simulations also show that the tests are sufficiently robust to certain violations of their assumptions.

Econophysical visualization of Adam Smith’s invisible hand

NASA Astrophysics Data System (ADS)

Cohen, Morrel H.; Eliazar, Iddo I.

2013-02-01

Consider a complex system whose macrostate is statistically observable, but yet whose operating mechanism is an unknown black-box. In this paper we address the problem of inferring, from the system’s macrostate statistics, the system’s intrinsic force yielding the observed statistics. The inference is established via two diametrically opposite approaches which result in the very same intrinsic force: a top-down approach based on the notion of entropy, and a bottom-up approach based on the notion of Langevin dynamics. The general results established are applied to the problem of visualizing the intrinsic socioeconomic force-Adam Smith’s invisible hand-shaping the distribution of wealth in human societies. Our analysis yields quantitative econophysical representations of figurative socioeconomic forces, quantitative definitions of “poor” and “rich”, and a quantitative characterization of the “poor-get-poorer” and the “rich-get-richer” phenomena.

Online Updating of Statistical Inference in the Big Data Setting.

PubMed

Schifano, Elizabeth D; Wu, Jing; Wang, Chun; Yan, Jun; Chen, Ming-Hui

2016-01-01

We present statistical methods for big data arising from online analytical processing, where large amounts of data arrive in streams and require fast analysis without storage/access to the historical data. In particular, we develop iterative estimating algorithms and statistical inferences for linear models and estimating equations that update as new data arrive. These algorithms are computationally efficient, minimally storage-intensive, and allow for possible rank deficiencies in the subset design matrices due to rare-event covariates. Within the linear model setting, the proposed online-updating framework leads to predictive residual tests that can be used to assess the goodness-of-fit of the hypothesized model. We also propose a new online-updating estimator under the estimating equation setting. Theoretical properties of the goodness-of-fit tests and proposed estimators are examined in detail. In simulation studies and real data applications, our estimator compares favorably with competing approaches under the estimating equation setting.

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.

Probabilistic Signal Recovery and Random Matrices

DTIC Science & Technology

2016-12-08

applications in statistics , biomedical data analysis, quantization, dimen- sion reduction, and networks science. 1. High-dimensional inference and geometry Our...low-rank approxima- tion, with applications to community detection in networks, Annals of Statistics 44 (2016), 373–400. [7] C. Le, E. Levina, R...approximation, with applications to community detection in networks, Annals of Statistics 44 (2016), 373–400. C. Le, E. Levina, R. Vershynin, Concentration

The Use of a Context-Based Information Retrieval Technique

DTIC Science & Technology

2009-07-01

provided in context. Latent Semantic Analysis (LSA) is a statistical technique for inferring contextual and structural information, and previous studies...WAIS). 10 DSTO-TR-2322 1.4.4 Latent Semantic Analysis LSA, which is also known as latent semantic indexing (LSI), uses a statistical and...1.4.6 Language Models In contrast, natural language models apply algorithms that combine statistical information with semantic information. Semantic

Neuro-fuzzy and neural network techniques for forecasting sea level in Darwin Harbor, Australia

NASA Astrophysics Data System (ADS)

Karimi, Sepideh; Kisi, Ozgur; Shiri, Jalal; Makarynskyy, Oleg

2013-03-01

Accurate predictions of sea level with different forecast horizons are important for coastal and ocean engineering applications, as well as in land drainage and reclamation studies. The methodology of tidal harmonic analysis, which is generally used for obtaining a mathematical description of the tides, is data demanding requiring processing of tidal observation collected over several years. In the present study, hourly sea levels for Darwin Harbor, Australia were predicted using two different, data driven techniques, adaptive neuro-fuzzy inference system (ANFIS) and artificial neural network (ANN). Multi linear regression (MLR) technique was used for selecting the optimal input combinations (lag times) of hourly sea level. The input combination comprises current sea level as well as five previous level values found to be optimal. For the ANFIS models, five different membership functions namely triangular, trapezoidal, generalized bell, Gaussian and two Gaussian membership function were tested and employed for predicting sea level for the next 1 h, 24 h, 48 h and 72 h. The used ANN models were trained using three different algorithms, namely, Levenberg-Marquardt, conjugate gradient and gradient descent. Predictions of optimal ANFIS and ANN models were compared with those of the optimal auto-regressive moving average (ARMA) models. The coefficient of determination, root mean square error and variance account statistics were used as comparison criteria. The obtained results indicated that triangular membership function was optimal for predictions with the ANFIS models while adaptive learning rate and Levenberg-Marquardt were most suitable for training the ANN models. Consequently, ANFIS and ANN models gave similar forecasts and performed better than the developed for the same purpose ARMA models for all the prediction intervals.

An Introduction to Confidence Intervals for Both Statistical Estimates and Effect Sizes.

ERIC Educational Resources Information Center

Capraro, Mary Margaret

This paper summarizes methods of estimating confidence intervals, including classical intervals and intervals for effect sizes. The recent American Psychological Association (APA) Task Force on Statistical Inference report suggested that confidence intervals should always be reported, and the fifth edition of the APA "Publication Manual"…

Balancing Treatment and Control Groups in Quasi-Experiments: An Introduction to Propensity Scoring

ERIC Educational Resources Information Center

Connelly, Brian S.; Sackett, Paul R.; Waters, Shonna D.

2013-01-01

Organizational and applied sciences have long struggled with improving causal inference in quasi-experiments. We introduce organizational researchers to propensity scoring, a statistical technique that has become popular in other applied sciences as a means for improving internal validity. Propensity scoring statistically models how individuals in…

Modeling Cross-Situational Word-Referent Learning: Prior Questions

ERIC Educational Resources Information Center

Yu, Chen; Smith, Linda B.

2012-01-01

Both adults and young children possess powerful statistical computation capabilities--they can infer the referent of a word from highly ambiguous contexts involving many words and many referents by aggregating cross-situational statistical information across contexts. This ability has been explained by models of hypothesis testing and by models of…

Temporal and Statistical Information in Causal Structure Learning

ERIC Educational Resources Information Center

McCormack, Teresa; Frosch, Caren; Patrick, Fiona; Lagnado, David

2015-01-01

Three experiments examined children's and adults' abilities to use statistical and temporal information to distinguish between common cause and causal chain structures. In Experiment 1, participants were provided with conditional probability information and/or temporal information and asked to infer the causal structure of a 3-variable mechanical…

Secondary Analysis of National Longitudinal Transition Study 2 Data

ERIC Educational Resources Information Center

Hicks, Tyler A.; Knollman, Greg A.

2015-01-01

This review examines published secondary analyses of National Longitudinal Transition Study 2 (NLTS2) data, with a primary focus upon statistical objectives, paradigms, inferences, and methods. Its primary purpose was to determine which statistical techniques have been common in secondary analyses of NLTS2 data. The review begins with an…

Some General Goals in Teaching Statistics.

ERIC Educational Resources Information Center

Blalock, H. M.

1987-01-01

States that regardless of the content or level of a statistics course, five goals to reach are: (1) overcoming fears, resistances, and tendencies to memorize; (2) the importance of intellectual honesty and integrity; (3) understanding relationship between deductive and inductive inferences; (4) learning to play role of reasonable critic; and (5)…

Propensity Score Analysis: An Alternative Statistical Approach for HRD Researchers

ERIC Educational Resources Information Center

Keiffer, Greggory L.; Lane, Forrest C.

2016-01-01

Purpose: This paper aims to introduce matching in propensity score analysis (PSA) as an alternative statistical approach for researchers looking to make causal inferences using intact groups. Design/methodology/approach: An illustrative example demonstrated the varying results of analysis of variance, analysis of covariance and PSA on a heuristic…

Technology Focus: Using Technology to Explore Statistical Inference

ERIC Educational Resources Information Center

Garofalo, Joe; Juersivich, Nicole

2007-01-01

There is much research that documents what many teachers know, that students struggle with many concepts in probability and statistics. This article presents two sample activities the authors use to help preservice teachers develop ideas about how they can use technology to promote their students' ability to understand mathematics and connect…

The Impact of an Instructional Intervention Designed to Support Development of Stochastic Understanding of Probability Distribution

ERIC Educational Resources Information Center

Conant, Darcy Lynn

2013-01-01

Stochastic understanding of probability distribution undergirds development of conceptual connections between probability and statistics and supports development of a principled understanding of statistical inference. This study investigated the impact of an instructional course intervention designed to support development of stochastic…

Basic Statistical Concepts and Methods for Earth Scientists

USGS Publications Warehouse

Olea, Ricardo A.

2008-01-01

INTRODUCTION Statistics is the science of collecting, analyzing, interpreting, modeling, and displaying masses of numerical data primarily for the characterization and understanding of incompletely known systems. Over the years, these objectives have lead to a fair amount of analytical work to achieve, substantiate, and guide descriptions and inferences.

Metacontrast Inferred from Reaction Time and Verbal Report: Replication and Comments on the Feher-Biederman Experiment

ERIC Educational Resources Information Center

Amundson, Vickie E.; Bernstein, Ira H.

1973-01-01

Authors note that Fehrer and Biederman's two statistical tests were not of equal power and that their conclusion could be a statistical artifact of both the lesser power of the verbal report comparison and the insensitivity of their particular verbal report indicator. (Editor)

Derivative Free Optimization of Complex Systems with the Use of Statistical Machine Learning Models

DTIC Science & Technology

2015-09-12

AFRL-AFOSR-VA-TR-2015-0278 DERIVATIVE FREE OPTIMIZATION OF COMPLEX SYSTEMS WITH THE USE OF STATISTICAL MACHINE LEARNING MODELS Katya Scheinberg...COMPLEX SYSTEMS WITH THE USE OF STATISTICAL MACHINE LEARNING MODELS 5a.  CONTRACT NUMBER 5b.  GRANT NUMBER FA9550-11-1-0239 5c.  PROGRAM ELEMENT...developed, which has been the focus of our research. 15. SUBJECT TERMS optimization, Derivative-Free Optimization, Statistical Machine Learning 16. SECURITY

Optimal experimental design for parameter estimation of a cell signaling model.

PubMed

Bandara, Samuel; Schlöder, Johannes P; Eils, Roland; Bock, Hans Georg; Meyer, Tobias

2009-11-01

Differential equation models that describe the dynamic changes of biochemical signaling states are important tools to understand cellular behavior. An essential task in building such representations is to infer the affinities, rate constants, and other parameters of a model from actual measurement data. However, intuitive measurement protocols often fail to generate data that restrict the range of possible parameter values. Here we utilized a numerical method to iteratively design optimal live-cell fluorescence microscopy experiments in order to reveal pharmacological and kinetic parameters of a phosphatidylinositol 3,4,5-trisphosphate (PIP(3)) second messenger signaling process that is deregulated in many tumors. The experimental approach included the activation of endogenous phosphoinositide 3-kinase (PI3K) by chemically induced recruitment of a regulatory peptide, reversible inhibition of PI3K using a kinase inhibitor, and monitoring of the PI3K-mediated production of PIP(3) lipids using the pleckstrin homology (PH) domain of Akt. We found that an intuitively planned and established experimental protocol did not yield data from which relevant parameters could be inferred. Starting from a set of poorly defined model parameters derived from the intuitively planned experiment, we calculated concentration-time profiles for both the inducing and the inhibitory compound that would minimize the predicted uncertainty of parameter estimates. Two cycles of optimization and experimentation were sufficient to narrowly confine the model parameters, with the mean variance of estimates dropping more than sixty-fold. Thus, optimal experimental design proved to be a powerful strategy to minimize the number of experiments needed to infer biological parameters from a cell signaling assay.

Statistical inference approach to structural reconstruction of complex networks from binary time series

NASA Astrophysics Data System (ADS)

Ma, Chuang; Chen, Han-Shuang; Lai, Ying-Cheng; Zhang, Hai-Feng

2018-02-01

Complex networks hosting binary-state dynamics arise in a variety of contexts. In spite of previous works, to fully reconstruct the network structure from observed binary data remains challenging. We articulate a statistical inference based approach to this problem. In particular, exploiting the expectation-maximization (EM) algorithm, we develop a method to ascertain the neighbors of any node in the network based solely on binary data, thereby recovering the full topology of the network. A key ingredient of our method is the maximum-likelihood estimation of the probabilities associated with actual or nonexistent links, and we show that the EM algorithm can distinguish the two kinds of probability values without any ambiguity, insofar as the length of the available binary time series is reasonably long. Our method does not require any a priori knowledge of the detailed dynamical processes, is parameter-free, and is capable of accurate reconstruction even in the presence of noise. We demonstrate the method using combinations of distinct types of binary dynamical processes and network topologies, and provide a physical understanding of the underlying reconstruction mechanism. Our statistical inference based reconstruction method contributes an additional piece to the rapidly expanding "toolbox" of data based reverse engineering of complex networked systems.

A statistical model for interpreting computerized dynamic posturography data

NASA Technical Reports Server (NTRS)

Feiveson, Alan H.; Metter, E. Jeffrey; Paloski, William H.

2002-01-01

Computerized dynamic posturography (CDP) is widely used for assessment of altered balance control. CDP trials are quantified using the equilibrium score (ES), which ranges from zero to 100, as a decreasing function of peak sway angle. The problem of how best to model and analyze ESs from a controlled study is considered. The ES often exhibits a skewed distribution in repeated trials, which can lead to incorrect inference when applying standard regression or analysis of variance models. Furthermore, CDP trials are terminated when a patient loses balance. In these situations, the ES is not observable, but is assigned the lowest possible score--zero. As a result, the response variable has a mixed discrete-continuous distribution, further compromising inference obtained by standard statistical methods. Here, we develop alternative methodology for analyzing ESs under a stochastic model extending the ES to a continuous latent random variable that always exists, but is unobserved in the event of a fall. Loss of balance occurs conditionally, with probability depending on the realized latent ES. After fitting the model by a form of quasi-maximum-likelihood, one may perform statistical inference to assess the effects of explanatory variables. An example is provided, using data from the NIH/NIA Baltimore Longitudinal Study on Aging.

Statistical inference of protein structural alignments using information and compression.

PubMed

Collier, James H; Allison, Lloyd; Lesk, Arthur M; Stuckey, Peter J; Garcia de la Banda, Maria; Konagurthu, Arun S

2017-04-01

Structural molecular biology depends crucially on computational techniques that compare protein three-dimensional structures and generate structural alignments (the assignment of one-to-one correspondences between subsets of amino acids based on atomic coordinates). Despite its importance, the structural alignment problem has not been formulated, much less solved, in a consistent and reliable way. To overcome these difficulties, we present here a statistical framework for the precise inference of structural alignments, built on the Bayesian and information-theoretic principle of Minimum Message Length (MML). The quality of any alignment is measured by its explanatory power-the amount of lossless compression achieved to explain the protein coordinates using that alignment. We have implemented this approach in MMLigner , the first program able to infer statistically significant structural alignments. We also demonstrate the reliability of MMLigner 's alignment results when compared with the state of the art. Importantly, MMLigner can also discover different structural alignments of comparable quality, a challenging problem for oligomers and protein complexes. Source code, binaries and an interactive web version are available at http://lcb.infotech.monash.edu.au/mmligner . arun.konagurthu@monash.edu. Supplementary data are available at Bioinformatics online. © The Author 2017. Published by Oxford University Press. All rights reserved. For Permissions, please e-mail: journals.permissions@oup.com

Statistical inference with quantum measurements: methodologies for nitrogen vacancy centers in diamond

NASA Astrophysics Data System (ADS)

Hincks, Ian; Granade, Christopher; Cory, David G.

2018-01-01

The analysis of photon count data from the standard nitrogen vacancy (NV) measurement process is treated as a statistical inference problem. This has applications toward gaining better and more rigorous error bars for tasks such as parameter estimation (e.g. magnetometry), tomography, and randomized benchmarking. We start by providing a summary of the standard phenomenological model of the NV optical process in terms of Lindblad jump operators. This model is used to derive random variables describing emitted photons during measurement, to which finite visibility, dark counts, and imperfect state preparation are added. NV spin-state measurement is then stated as an abstract statistical inference problem consisting of an underlying biased coin obstructed by three Poisson rates. Relevant frequentist and Bayesian estimators are provided, discussed, and quantitatively compared. We show numerically that the risk of the maximum likelihood estimator is well approximated by the Cramér-Rao bound, for which we provide a simple formula. Of the estimators, we in particular promote the Bayes estimator, owing to its slightly better risk performance, and straightforward error propagation into more complex experiments. This is illustrated on experimental data, where quantum Hamiltonian learning is performed and cross-validated in a fully Bayesian setting, and compared to a more traditional weighted least squares fit.

Statistical inference approach to structural reconstruction of complex networks from binary time series.

PubMed

Ma, Chuang; Chen, Han-Shuang; Lai, Ying-Cheng; Zhang, Hai-Feng

2018-02-01

Complex networks hosting binary-state dynamics arise in a variety of contexts. In spite of previous works, to fully reconstruct the network structure from observed binary data remains challenging. We articulate a statistical inference based approach to this problem. In particular, exploiting the expectation-maximization (EM) algorithm, we develop a method to ascertain the neighbors of any node in the network based solely on binary data, thereby recovering the full topology of the network. A key ingredient of our method is the maximum-likelihood estimation of the probabilities associated with actual or nonexistent links, and we show that the EM algorithm can distinguish the two kinds of probability values without any ambiguity, insofar as the length of the available binary time series is reasonably long. Our method does not require any a priori knowledge of the detailed dynamical processes, is parameter-free, and is capable of accurate reconstruction even in the presence of noise. We demonstrate the method using combinations of distinct types of binary dynamical processes and network topologies, and provide a physical understanding of the underlying reconstruction mechanism. Our statistical inference based reconstruction method contributes an additional piece to the rapidly expanding "toolbox" of data based reverse engineering of complex networked systems.

PREFACE: ELC International Meeting on Inference, Computation, and Spin Glasses (ICSG2013)

NASA Astrophysics Data System (ADS)

Kabashima, Yoshiyuki; Hukushima, Koji; Inoue, Jun-ichi; Tanaka, Toshiyuki; Watanabe, Osamu

2013-12-01

The close relationship between probability-based inference and statistical mechanics of disordered systems has been noted for some time. This relationship has provided researchers with a theoretical foundation in various fields of information processing for analytical performance evaluation and construction of efficient algorithms based on message-passing or Monte Carlo sampling schemes. The ELC International Meeting on 'Inference, Computation, and Spin Glasses (ICSG2013)', was held in Sapporo 28-30 July 2013. The meeting was organized as a satellite meeting of STATPHYS25 in order to offer a forum where concerned researchers can assemble and exchange information on the latest results and newly established methodologies, and discuss future directions of the interdisciplinary studies between statistical mechanics and information sciences. Financial support from Grant-in-Aid for Scientific Research on Innovative Areas, MEXT, Japan 'Exploring the Limits of Computation (ELC)' is gratefully acknowledged. We are pleased to publish 23 papers contributed by invited speakers of ICSG2013 in this volume of Journal of Physics: Conference Series. We hope that this volume will promote further development of this highly vigorous interdisciplinary field between statistical mechanics and information/computer science. Editors and ICSG2013 Organizing Committee: Koji Hukushima Jun-ichi Inoue (Local Chair of ICSG2013) Yoshiyuki Kabashima (Editor-in-Chief) Toshiyuki Tanaka Osamu Watanabe (General Chair of ICSG2013)

Measuring the Number of M Dwarfs per M Dwarf Using Kepler Eclipsing Binaries

NASA Astrophysics Data System (ADS)

Shan, Yutong; Johnson, John A.; Morton, Timothy D.

2015-11-01

We measure the binarity of detached M dwarfs in the Kepler field with orbital periods in the range of 1-90 days. Kepler’s photometric precision and nearly continuous monitoring of stellar targets over time baselines ranging from 3 months to 4 years make its detection efficiency for eclipsing binaries nearly complete over this period range and for all radius ratios. Our investigation employs a statistical framework akin to that used for inferring planetary occurrence rates from planetary transits. The obvious simplification is that eclipsing binaries have a vastly improved detection efficiency that is limited chiefly by their geometric probabilities to eclipse. For the M-dwarf sample observed by the Kepler Mission, the fractional incidence of eclipsing binaries implies that there are {0.11}-0.04+0.02 close stellar companions per apparently single M dwarf. Our measured binarity is higher than previous inferences of the occurrence rate of close binaries via radial velocity techniques, at roughly the 2σ level. This study represents the first use of eclipsing binary detections from a high quality transiting planet mission to infer binary statistics. Application of this statistical framework to the eclipsing binaries discovered by future transit surveys will establish better constraints on short-period M+M binary rate, as well as binarity measurements for stars of other spectral types.

Lifetime Prediction for Degradation of Solar Mirrors using Step-Stress Accelerated Testing (Presentation)

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

Lee, J.; Elmore, R.; Kennedy, C.

This research is to illustrate the use of statistical inference techniques in order to quantify the uncertainty surrounding reliability estimates in a step-stress accelerated degradation testing (SSADT) scenario. SSADT can be used when a researcher is faced with a resource-constrained environment, e.g., limits on chamber time or on the number of units to test. We apply the SSADT methodology to a degradation experiment involving concentrated solar power (CSP) mirrors and compare the results to a more traditional multiple accelerated testing paradigm. Specifically, our work includes: (1) designing a durability testing plan for solar mirrors (3M's new improved silvered acrylic "Solarmore » Reflector Film (SFM) 1100") through the ultra-accelerated weathering system (UAWS), (2) defining degradation paths of optical performance based on the SSADT model which is accelerated by high UV-radiant exposure, and (3) developing service lifetime prediction models for solar mirrors using advanced statistical inference. We use the method of least squares to estimate the model parameters and this serves as the basis for the statistical inference in SSADT. Several quantities of interest can be estimated from this procedure, e.g., mean-time-to-failure (MTTF) and warranty time. The methods allow for the estimation of quantities that may be of interest to the domain scientists.« less

Ancestral sequence reconstruction in primate mitochondrial DNA: compositional bias and effect on functional inference.

PubMed

Krishnan, Neeraja M; Seligmann, Hervé; Stewart, Caro-Beth; De Koning, A P Jason; Pollock, David D

2004-10-01

Reconstruction of ancestral DNA and amino acid sequences is an important means of inferring information about past evolutionary events. Such reconstructions suggest changes in molecular function and evolutionary processes over the course of evolution and are used to infer adaptation and convergence. Maximum likelihood (ML) is generally thought to provide relatively accurate reconstructed sequences compared to parsimony, but both methods lead to the inference of multiple directional changes in nucleotide frequencies in primate mitochondrial DNA (mtDNA). To better understand this surprising result, as well as to better understand how parsimony and ML differ, we constructed a series of computationally simple "conditional pathway" methods that differed in the number of substitutions allowed per site along each branch, and we also evaluated the entire Bayesian posterior frequency distribution of reconstructed ancestral states. We analyzed primate mitochondrial cytochrome b (Cyt-b) and cytochrome oxidase subunit I (COI) genes and found that ML reconstructs ancestral frequencies that are often more different from tip sequences than are parsimony reconstructions. In contrast, frequency reconstructions based on the posterior ensemble more closely resemble extant nucleotide frequencies. Simulations indicate that these differences in ancestral sequence inference are probably due to deterministic bias caused by high uncertainty in the optimization-based ancestral reconstruction methods (parsimony, ML, Bayesian maximum a posteriori). In contrast, ancestral nucleotide frequencies based on an average of the Bayesian set of credible ancestral sequences are much less biased. The methods involving simpler conditional pathway calculations have slightly reduced likelihood values compared to full likelihood calculations, but they can provide fairly unbiased nucleotide reconstructions and may be useful in more complex phylogenetic analyses than considered here due to their speed and flexibility. To determine whether biased reconstructions using optimization methods might affect inferences of functional properties, ancestral primate mitochondrial tRNA sequences were inferred and helix-forming propensities for conserved pairs were evaluated in silico. For ambiguously reconstructed nucleotides at sites with high base composition variability, ancestral tRNA sequences from Bayesian analyses were more compatible with canonical base pairing than were those inferred by other methods. Thus, nucleotide bias in reconstructed sequences apparently can lead to serious bias and inaccuracies in functional predictions.

Inferring genetic interactions via a nonlinear model and an optimization algorithm.

PubMed

Chen, Chung-Ming; Lee, Chih; Chuang, Cheng-Long; Wang, Chia-Chang; Shieh, Grace S

2010-02-26

Biochemical pathways are gradually becoming recognized as central to complex human diseases and recently genetic/transcriptional interactions have been shown to be able to predict partial pathways. With the abundant information made available by microarray gene expression data (MGED), nonlinear modeling of these interactions is now feasible. Two of the latest advances in nonlinear modeling used sigmoid models to depict transcriptional interaction of a transcription factor (TF) for a target gene, but do not model cooperative or competitive interactions of several TFs for a target. An S-shape model and an optimization algorithm (GASA) were developed to infer genetic interactions/transcriptional regulation of several genes simultaneously using MGED. GASA consists of a genetic algorithm (GA) and a simulated annealing (SA) algorithm, which is enhanced by a steepest gradient descent algorithm to avoid being trapped in local minimum. Using simulated data with various degrees of noise, we studied how GASA with two model selection criteria and two search spaces performed. Furthermore, GASA was shown to outperform network component analysis, the time series network inference algorithm (TSNI), GA with regular GA (GAGA) and GA with regular SA. Two applications are demonstrated. First, GASA is applied to infer a subnetwork of human T-cell apoptosis. Several of the predicted interactions are supported by the literature. Second, GASA was applied to infer the transcriptional factors of 34 cell cycle regulated targets in S. cerevisiae, and GASA performed better than one of the latest advances in nonlinear modeling, GAGA and TSNI. Moreover, GASA is able to predict multiple transcription factors for certain targets, and these results coincide with experiments confirmed data in YEASTRACT. GASA is shown to infer both genetic interactions and transcriptional regulatory interactions well. In particular, GASA seems able to characterize the nonlinear mechanism of transcriptional regulatory interactions (TIs) in yeast, and may be applied to infer TIs in other organisms. The predicted genetic interactions of a subnetwork of human T-cell apoptosis coincide with existing partial pathways, suggesting the potential of GASA on inferring biochemical pathways.

Relating phylogenetic trees to transmission trees of infectious disease outbreaks.

PubMed

Ypma, Rolf J F; van Ballegooijen, W Marijn; Wallinga, Jacco

2013-11-01

Transmission events are the fundamental building blocks of the dynamics of any infectious disease. Much about the epidemiology of a disease can be learned when these individual transmission events are known or can be estimated. Such estimations are difficult and generally feasible only when detailed epidemiological data are available. The genealogy estimated from genetic sequences of sampled pathogens is another rich source of information on transmission history. Optimal inference of transmission events calls for the combination of genetic data and epidemiological data into one joint analysis. A key difficulty is that the transmission tree, which describes the transmission events between infected hosts, differs from the phylogenetic tree, which describes the ancestral relationships between pathogens sampled from these hosts. The trees differ both in timing of the internal nodes and in topology. These differences become more pronounced when a higher fraction of infected hosts is sampled. We show how the phylogenetic tree of sampled pathogens is related to the transmission tree of an outbreak of an infectious disease, by the within-host dynamics of pathogens. We provide a statistical framework to infer key epidemiological and mutational parameters by simultaneously estimating the phylogenetic tree and the transmission tree. We test the approach using simulations and illustrate its use on an outbreak of foot-and-mouth disease. The approach unifies existing methods in the emerging field of phylodynamics with transmission tree reconstruction methods that are used in infectious disease epidemiology.

Quakefinder: A scalable data mining system for detecting earthquakes from space

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

Stolorz, P.; Dean, C.

1996-12-31

We present an application of novel massively parallel datamining techniques to highly precise inference of important physical processes from remote sensing imagery. Specifically, we have developed and applied a system, Quakefinder, that automatically detects and measures tectonic activity in the earth`s crust by examination of satellite data. We have used Quakefinder to automatically map the direction and magnitude of ground displacements due to the 1992 Landers earthquake in Southern California, over a spatial region of several hundred square kilometers, at a resolution of 10 meters, to a (sub-pixel) precision of 1 meter. This is the first calculation that has evermore » been able to extract area-mapped information about 2D tectonic processes at this level of detail. We outline the architecture of the Quakefinder system, based upon a combination of techniques drawn from the fields of statistical inference, massively parallel computing and global optimization. We confirm the overall correctness of the procedure by comparison of our results with known locations of targeted faults obtained by careful and time-consuming field measurements. The system also performs knowledge discovery by indicating novel unexplained tectonic activity away from the primary faults that has never before been observed. We conclude by discussing the future potential of this data mining system in the broad context of studying subtle spatio-temporal processes within massive image streams.« less

Cancer Survival Estimates Due to Non-Uniform Loss to Follow-Up and Non-Proportional Hazards

PubMed

K M, Jagathnath Krishna; Mathew, Aleyamma; Sara George, Preethi

2017-06-25

Background: Cancer survival depends on loss to follow-up (LFU) and non-proportional hazards (non-PH). If LFU is high, survival will be over-estimated. If hazard is non-PH, rank tests will provide biased inference and Cox-model will provide biased hazard-ratio. We assessed the bias due to LFU and non-PH factor in cancer survival and provided alternate methods for unbiased inference and hazard-ratio. Materials and Methods: Kaplan-Meier survival were plotted using a realistic breast cancer (BC) data-set, with >40%, 5-year LFU and compared it using another BC data-set with <15%, 5-year LFU to assess the bias in survival due to high LFU. Age at diagnosis of the latter data set was used to illustrate the bias due to a non-PH factor. Log-rank test was employed to assess the bias in p-value and Cox-model was used to assess the bias in hazard-ratio for the non-PH factor. Schoenfeld statistic was used to test the non-PH of age. For the non-PH factor, we employed Renyi statistic for inference and time dependent Cox-model for hazard-ratio. Results: Five-year BC survival was 69% (SE: 1.1%) vs. 90% (SE: 0.7%) for data with low vs. high LFU respectively. Age (<45, 46-54 & >54 years) was a non-PH factor (p-value: 0.036). However, survival by age was significant (log-rank p-value: 0.026), but not significant using Renyi statistic (p=0.067). Hazard ratio (HR) for age using Cox-model was 1.012 (95%CI: 1.004 -1.019) and the same using time-dependent Cox-model was in the other direction (HR: 0.997; 95% CI: 0.997- 0.998). Conclusion: Over-estimated survival was observed for cancer with high LFU. Log-rank statistic and Cox-model provided biased results for non-PH factor. For data with non-PH factors, Renyi statistic and time dependent Cox-model can be used as alternate methods to obtain unbiased inference and estimates. Creative Commons Attribution License

Unraveling multiple changes in complex climate time series using Bayesian inference

NASA Astrophysics Data System (ADS)

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

2016-04-01

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

Bayesian Parameter Inference and Model Selection by Population Annealing in Systems Biology

PubMed Central

Murakami, Yohei

2014-01-01

Parameter inference and model selection are very important for mathematical modeling in systems biology. Bayesian statistics can be used to conduct both parameter inference and model selection. Especially, the framework named approximate Bayesian computation is often used for parameter inference and model selection in systems biology. However, Monte Carlo methods needs to be used to compute Bayesian posterior distributions. In addition, the posterior distributions of parameters are sometimes almost uniform or very similar to their prior distributions. In such cases, it is difficult to choose one specific value of parameter with high credibility as the representative value of the distribution. To overcome the problems, we introduced one of the population Monte Carlo algorithms, population annealing. Although population annealing is usually used in statistical mechanics, we showed that population annealing can be used to compute Bayesian posterior distributions in the approximate Bayesian computation framework. To deal with un-identifiability of the representative values of parameters, we proposed to run the simulations with the parameter ensemble sampled from the posterior distribution, named “posterior parameter ensemble”. We showed that population annealing is an efficient and convenient algorithm to generate posterior parameter ensemble. We also showed that the simulations with the posterior parameter ensemble can, not only reproduce the data used for parameter inference, but also capture and predict the data which was not used for parameter inference. Lastly, we introduced the marginal likelihood in the approximate Bayesian computation framework for Bayesian model selection. We showed that population annealing enables us to compute the marginal likelihood in the approximate Bayesian computation framework and conduct model selection depending on the Bayes factor. PMID:25089832

Active inference and robot control: a case study

PubMed Central

Nizard, Ange; Friston, Karl; Pezzulo, Giovanni

2016-01-01

Active inference is a general framework for perception and action that is gaining prominence in computational and systems neuroscience but is less known outside these fields. Here, we discuss a proof-of-principle implementation of the active inference scheme for the control or the 7-DoF arm of a (simulated) PR2 robot. By manipulating visual and proprioceptive noise levels, we show under which conditions robot control under the active inference scheme is accurate. Besides accurate control, our analysis of the internal system dynamics (e.g. the dynamics of the hidden states that are inferred during the inference) sheds light on key aspects of the framework such as the quintessentially multimodal nature of control and the differential roles of proprioception and vision. In the discussion, we consider the potential importance of being able to implement active inference in robots. In particular, we briefly review the opportunities for modelling psychophysiological phenomena such as sensory attenuation and related failures of gain control, of the sort seen in Parkinson's disease. We also consider the fundamental difference between active inference and optimal control formulations, showing that in the former the heavy lifting shifts from solving a dynamical inverse problem to creating deep forward or generative models with dynamics, whose attracting sets prescribe desired behaviours. PMID:27683002

Value Driven Information Processing and Fusion

DTIC Science & Technology

2016-03-01

consensus approach allows a decentralized approach to achieve the optimal error exponent of the centralized counterpart, a conclusion that is signifi...SECURITY CLASSIFICATION OF: The objective of the project is to develop a general framework for value driven decentralized information processing...including: optimal data reduction in a network setting for decentralized inference with quantization constraint; interactive fusion that allows queries and

Assay optimization: a statistical design of experiments approach.

PubMed

Altekar, Maneesha; Homon, Carol A; Kashem, Mohammed A; Mason, Steven W; Nelson, Richard M; Patnaude, Lori A; Yingling, Jeffrey; Taylor, Paul B

2007-03-01

With the transition from manual to robotic HTS in the last several years, assay optimization has become a significant bottleneck. Recent advances in robotic liquid handling have made it feasible to reduce assay optimization timelines with the application of statistically designed experiments. When implemented, they can efficiently optimize assays by rapidly identifying significant factors, complex interactions, and nonlinear responses. This article focuses on the use of statistically designed experiments in assay optimization.

Strategies for improving approximate Bayesian computation tests for synchronous diversification.

PubMed

Overcast, Isaac; Bagley, Justin C; Hickerson, Michael J

2017-08-24

Estimating the variability in isolation times across co-distributed taxon pairs that may have experienced the same allopatric isolating mechanism is a core goal of comparative phylogeography. The use of hierarchical Approximate Bayesian Computation (ABC) and coalescent models to infer temporal dynamics of lineage co-diversification has been a contentious topic in recent years. Key issues that remain unresolved include the choice of an appropriate prior on the number of co-divergence events (Ψ), as well as the optimal strategies for data summarization. Through simulation-based cross validation we explore the impact of the strategy for sorting summary statistics and the choice of prior on Ψ on the estimation of co-divergence variability. We also introduce a new setting (β) that can potentially improve estimation of Ψ by enforcing a minimal temporal difference between pulses of co-divergence. We apply this new method to three empirical datasets: one dataset each of co-distributed taxon pairs of Panamanian frogs and freshwater fishes, and a large set of Neotropical butterfly sister-taxon pairs. We demonstrate that the choice of prior on Ψ has little impact on inference, but that sorting summary statistics yields substantially more reliable estimates of co-divergence variability despite violations of assumptions about exchangeability. We find the implementation of β improves estimation of Ψ, with improvement being most dramatic given larger numbers of taxon pairs. We find equivocal support for synchronous co-divergence for both of the Panamanian groups, but we find considerable support for asynchronous divergence among the Neotropical butterflies. Our simulation experiments demonstrate that using sorted summary statistics results in improved estimates of the variability in divergence times, whereas the choice of hyperprior on Ψ has negligible effect. Additionally, we demonstrate that estimating the number of pulses of co-divergence across co-distributed taxon-pairs is improved by applying a flexible buffering regime over divergence times. This improves the correlation between Ψ and the true variability in isolation times and allows for more meaningful interpretation of this hyperparameter. This will allow for more accurate identification of the number of temporally distinct pulses of co-divergence that generated the diversification pattern of a given regional assemblage of sister-taxon-pairs.

An Architecture for Performance Optimization in a Collaborative Knowledge-Based Approach for Wireless Sensor Networks

PubMed Central

Gadeo-Martos, Manuel Angel; Fernandez-Prieto, Jose Angel; Canada-Bago, Joaquin; Velasco, Juan Ramon

2011-01-01

Over the past few years, Intelligent Spaces (ISs) have received the attention of many Wireless Sensor Network researchers. Recently, several studies have been devoted to identify their common capacities and to set up ISs over these networks. However, little attention has been paid to integrating Fuzzy Rule-Based Systems into collaborative Wireless Sensor Networks for the purpose of implementing ISs. This work presents a distributed architecture proposal for collaborative Fuzzy Rule-Based Systems embedded in Wireless Sensor Networks, which has been designed to optimize the implementation of ISs. This architecture includes the following: (a) an optimized design for the inference engine; (b) a visual interface; (c) a module to reduce the redundancy and complexity of the knowledge bases; (d) a module to evaluate the accuracy of the new knowledge base; (e) a module to adapt the format of the rules to the structure used by the inference engine; and (f) a communications protocol. As a real-world application of this architecture and the proposed methodologies, we show an application to the problem of modeling two plagues of the olive tree: prays (olive moth, Prays oleae Bern.) and repilo (caused by the fungus Spilocaea oleagina). The results show that the architecture presented in this paper significantly decreases the consumption of resources (memory, CPU and battery) without a substantial decrease in the accuracy of the inferred values. PMID:22163687