Simplicity and Model Selection

Bayesian Philosophy of Science ◽

10.1093/oso/9780199672110.003.0010 ◽

2019 ◽

pp. 260-286

Author(s):

Jan Sprenger ◽

Stephan Hartmann

Keyword(s):

Bayesian Inference ◽

Model Selection ◽

Bayesian Model ◽

Scientific Theory ◽

Predictive Accuracy ◽

Practical Applications ◽

Philosophical Foundations ◽

Selection Strategies ◽

Statistical Model Selection ◽

Good Scientific Theory

Is simplicity a virtue of a good scientific theory, and are simpler theories more likely to be true or predictively successful? If so, how much should simplicity count vis-à-vis predictive accuracy? We address this question using Bayesian inference, focusing on the context of statistical model selection and an interpretation of simplicity via the degree of freedoms of a model. We rebut claims to prove the epistemic value of simplicity by means of showing its particular role in Bayesian model selection strategies (e.g., the BIC or the MML). Instead, we show that Bayesian inference in the context of model selection is usually done in a philosophically eclectic, instrumental fashion that is more tuned to practical applications than to philosophical foundations. Thus, these techniques cannot justify a particular “appropriate weight of simplicity in model selection”.

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A STATISTICAL FRAMEWORK FOR HAPLOTYPE BLOCK INFERENCE

Journal of Bioinformatics and Computational Biology ◽

10.1142/s021972000500151x ◽

2005 ◽

Vol 03 (05) ◽

pp. 1021-1038

Author(s):

AO YUAN ◽

GUANJIE CHEN ◽

CHARLES ROTIMI ◽

GEORGE E. BONNEY

Keyword(s):

Bayesian Inference ◽

Model Selection ◽

Haplotype Block ◽

Block Structure ◽

Real Data ◽

Data Sets ◽

Block Partitioning ◽

Haplotype Blocks ◽

Statistical Framework ◽

Statistical Model Selection

The existence of haplotype blocks transmitted from parents to offspring has been suggested recently. This has created an interest in the inference of the block structure and length. The motivation is that haplotype blocks that are characterized well will make it relatively easier to quickly map all the genes carrying human diseases. To study the inference of haplotype block systematically, we propose a statistical framework. In this framework, the optimal haplotype block partitioning is formulated as the problem of statistical model selection; missing data can be handled in a standard statistical way; population strata can be implemented; block structure inference/hypothesis testing can be performed; prior knowledge, if present, can be incorporated to perform a Bayesian inference. The algorithm is linear in the number of loci, instead of NP-hard for many such algorithms. We illustrate the applications of our method to both simulated and real data sets.

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Bayesian Model Selection in Fisheries Management and Ecology

Journal of Fish and Wildlife Management ◽

10.3996/042019-jfwm-024 ◽

2019 ◽

Vol 10 (2) ◽

pp. 691-707

Author(s):

Jason C. Doll ◽

Stephen J. Jacquemin

Keyword(s):

Bayesian Inference ◽

Model Selection ◽

Fisheries Management ◽

Bayesian Model ◽

Bayes Factor ◽

Evaluation Process ◽

Information Criterion ◽

Bayesian Model Selection ◽

Model Parameters ◽

Inference Methods

Abstract Researchers often test ecological hypotheses relating to a myriad of questions ranging from assemblage structure, population dynamics, demography, abundance, growth rate, and more using mathematical models that explain trends in data. To aid in the evaluation process when faced with competing hypotheses, we employ statistical methods to evaluate the validity of these multiple hypotheses with the goal of deriving the most robust conclusions possible. In fisheries management and ecology, frequentist methodologies have largely dominated this approach. However, in recent years, researchers have increasingly used Bayesian inference methods to estimate model parameters. Our aim with this perspective is to provide the practicing fisheries ecologist with an accessible introduction to Bayesian model selection. Here we discuss Bayesian inference methods for model selection in the context of fisheries management and ecology with empirical examples to guide researchers in the use of these methods. In this perspective we discuss three methods for selecting among competing models. For comparing two models we discuss Bayes factor and for more complex models we discuss Watanabe–Akaike information criterion and leave-one-out cross-validation. We also describe what kinds of information to report when conducting Bayesian inference. We conclude this review with a discussion of final thoughts about these model selection techniques.

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The Connection between Bayesian Inference and Information Theory for Model Selection, Information Gain and Experimental Design

Entropy ◽

10.3390/e21111081 ◽

2019 ◽

Vol 21 (11) ◽

pp. 1081 ◽

Cited By ~ 3

Author(s):

Sergey Oladyshkin ◽

Wolfgang Nowak

Keyword(s):

Information Theory ◽

Monte Carlo ◽

Bayesian Inference ◽

Experimental Design ◽

Model Selection ◽

Relative Entropy ◽

Information Entropy ◽

Bayesian Model ◽

Information Gain ◽

Information Criteria

We show a link between Bayesian inference and information theory that is useful for model selection, assessment of information entropy and experimental design. We align Bayesian model evidence (BME) with relative entropy and cross entropy in order to simplify computations using prior-based (Monte Carlo) or posterior-based (Markov chain Monte Carlo) BME estimates. On the one hand, we demonstrate how Bayesian model selection can profit from information theory to estimate BME values via posterior-based techniques. Hence, we use various assumptions including relations to several information criteria. On the other hand, we demonstrate how relative entropy can profit from BME to assess information entropy during Bayesian updating and to assess utility in Bayesian experimental design. Specifically, we emphasize that relative entropy can be computed avoiding unnecessary multidimensional integration from both prior and posterior-based sampling techniques. Prior-based computation does not require any assumptions, however posterior-based estimates require at least one assumption. We illustrate the performance of the discussed estimates of BME, information entropy and experiment utility using a transparent, non-linear example. The multivariate Gaussian posterior estimate includes least assumptions and shows the best performance for BME estimation, information entropy and experiment utility from posterior-based sampling.

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