Phuong Thi, Thanh Truong, Mr Nguyen et al. · 2016
Model selection methods from the Bayesian perspective rely on full probability specification for each model under consideration. This includes the likelihood and the prior for each model. Beyond this, some methods employ the notions of prior and posterior probabilities on the models. Others omit this and rely on optimizing a criterion defined for each model. When the number of models under consideration is moderate, complete calculations of posterior probabilities or the selection criteria are feasible. For a large set of models, as is often the case in variable selection, various forms of stochastic searches can be quite effective. In this chapter we describe these three types of methods based on: (i) model probabilities, (ii) defined criterion, and (iii) stochastic search, and their use in survival analysis.
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G. Sophia Borgeest (8878787), Richard N. Henson (6628652), Meredith Shafto (8878790) et al. · Figshare · 2020
<p>Figure shows Bayesian model selection converging with frequentist inferences, with model evidence displayed in descending order.</p> <p>(TIF)</p>
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Junior Samuel López-Yépez (11565550), Juliane Martin (11520262), Oliver Hulme (11520265) et al. · Figshare · 2021
<p>Numbers on x axis indicate different models. 1—Indirect model, 2—F-Q, 3—F-Q up, 4—F-Q W/C, 5—Double trace, 6—LK model, 7—Generalized linear model (A). Humans, (B) mice.</p> <p>(EPS)</p>
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Lugrin, Thomas · Infoscience (Ecole Polytechnique Fédérale de Lausanne) · 2015
Frequentist and Bayesian approaches to statistics have long been seen as incompatible, but recent work has been done to try and unify them (Bayarri and Berger, 2004; Efron, 2005). Empirical Bayes, approximate Bayesian analysis, and the matching prior approach are examples of methods where prior elicitation is driven by a frequentist interpretation of the data. In this report, we review some standard frequentist and Bayesian model selection techniques and describe how objective Bayes theory can help in this decision-oriented framework, typically by enabling consideration of uncertainty in the model-building process. Objective Bayes mehtods are then used and compared with standard model selection methods on data from the financial sector in Switzerland, Greece, and the United States during 1999 to 2013; results show broad agreement between the methods, but conclusions are less clear-cut in the objective Bayes framework.
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Atsushi Inoue, Mototsugu Shintani · 2014
In this paper we establish the consistency of the model selection criterion based on the quasi-marginal likelihood obtained from Laplace-type estimators (LTE). We con-sider cases in which parameters are strongly identified, weakly identified and partially identified. Our Monte Carlo results confirm our consistency results. Our proposed procedure is applied to select among monetary macroeconomic models using US data. ∗We thank Matias Cattaneo, Larry Christiano, Kengo Kato, Lutz Kilian Jae-Young Kim and Vadim Marmer for helpful discussions and Mathias Trabandt for providing the data and code. We also thank the seminar and conference participants for helpful comments at the Bank of Canada, Gakushuin University, Hi-
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Mark I. Rowley (3161091), Anthonius C. C. Coolen (3161094), Borivoj Vojnovic (69214) et al. · Figshare · 2016
<p>In (a) an intensity image having pixels with intensity of about 750 photon counts, those on the left half of the image simulating a mono-exponential decay and those on the right half of the image simulating a bi-exponential decay; in (b) and (c) the Bayesian determined probability of the decay model being bi-exponential, , and the optimal decay model, , respectively, and in (d) the optimal model as determined by the <i>χ</i><sup>2</sup> model selection algorithm of [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0158404#pone.0158404.ref038" target="_blank">38</a>] using the ML parameter estimates. Similar images are shown for human cancer cells expressing GFP (e-h), showing largely mono-exponential characteristics, and for human breast cancer tissue (i-l) which has many ‘contaminants’ from heterogeneous tissue types giving rise to bi-exponential, or higher order, responses. See main text for details.</p>
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Aida Afshar, Yuke Zhang, Aldo Pacchiano · arXiv (Cornell University) · 2026
Online model selection in Bayesian bandits raises a fundamental exploration challenge: When an environment instance is sampled from a prior distribution, how can we design an adaptive strategy that explores multiple bandit learners and competes with the best one in hindsight? We address this problem by introducing a new Bayesian algorithm for online model selection in stochastic bandits. We prove an oracle-style guarantee of $O\left( d^* M \sqrt{T} + \sqrt{(MT)} \right)$ on the Bayesian regret, where $M$ is the number of base learners, $d^*$ is the regret coefficient of the optimal base learner, and $T$ is the time horizon. We also validate our method empirically across a range of stochastic bandit settings, demonstrating performance that is competitive with the best base learner. Additionally, we study the effect of sharing data among base learners and its role in mitigating prior mis-specification.
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Aida Afshar, Yuke Zhang, Aldo Pacchiano · ArXiv.org · 2026
Online model selection in Bayesian bandits raises a fundamental exploration challenge: When an environment instance is sampled from a prior distribution, how can we design an adaptive strategy that explores multiple bandit learners and competes with the best one in hindsight? We address this problem by introducing a new Bayesian algorithm for online model selection in stochastic bandits. We prove an oracle-style guarantee of $O\left( d^* M \sqrt{T} + \sqrt{(MT)} \right)$ on the Bayesian regret, where $M$ is the number of base learners, $d^*$ is the regret coefficient of the optimal base learner, and $T$ is the time horizon. We also validate our method empirically across a range of stochastic bandit settings, demonstrating performance that is competitive with the best base learner. Additionally, we study the effect of sharing data among base learners and its role in mitigating prior mis-specification.
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Veena Padmanaban (8339247), Yohannes Tsehay (8339250), Kevin J. Cheung (8339253) et al. · Figshare · 2020
<p>(A) Bootstrap replicates were used to increase robustness to limited number of tumors and organoids per tumor. Bootstraps were conducted for all 52 tumors and then, with increasing stringency, for tumors generating at least 2 through 10 organoids, with 30 tumors meeting the final requirement (solid line). The average number of organoids per tumor increased from 15.8 to 22.9 for these replicates (dashed line). (B) Three generative models were considered for between-tumor and within-tumor variation in logarithmic-scale organoid invasiveness: Model 0 assumes a single mean and variance shared by all tumors; Model 1 assumes a shared variance, but assigns each tumor its own mean; Model 2 assigns each tumor its own mean and variance. Converged estimates were obtained from 10,000 bootstrap replicates for thresholds of 1 organoid per tumor up to 10 organoids per tumor. For these thresholds, the posterior probability is 55-65% for Model 1 (green bars), with the remaining probability assigned to Model 2 (blue bars). Model 0 (red bars) had vanishing probability, not visible on this scale.</p>
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Susanne Dietrich (94165), Ingo Hertrich (331699), Hermann Ackermann (715943) · Figshare · 2015
<p>(a) Exceedance probabilities and posterior expectations (in parentheses) resulting from the BMS procedure. The analysis did not reveal a clear winning family. But, with high confidence (total exceedance probability, <i>p</i> = 0.83), pre-SMA received either input from V1 (Fam. 3) or from A1, while Pv/V1 are not connected with the remaining areas (Fam. 4). (b) Posterior model probabilities for all subjects, assigned to the families (see also <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0132196#pone.0132196.t002" target="_blank">Table 2</a>), indicating that blind subjects preferably chose Fam. 3, whereas Fam. 4 was much more likely for sighted individuals. More specifically, blind subjects showed high probability for the model m11, whereas sighted individuals primarily chose m13 or m27.</p>
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Larry Wasserman · Journal of Mathematical Psychology · 2000
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A Andrieu, Antoine Doucet, WJ Fitzgerald et al. · Cambridge University Engineering Department Publications Database · 2001
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Beniamino Hadj-Amar, Jack Jewson · ArXiv.org · 2026
Bayesian inference offers a powerful framework for variable selection by incorporating sparsity through prior beliefs and quantifying uncertainty about parameters, leading to consistent procedures with good finite-sample performance. However, accurately quantifying uncertainty requires a correctly specified model, and there is increasing awareness of the problems that model misspecification causes for variable selection. Current solutions to this problem either require a more complex model, detracting from the interpretability of the original variable selection task, or gain robustness by moving outside of rigorous Bayesian uncertainty quantification. This paper establishes the model quasi-posterior as a principled tool for variable selection. We prove that the model quasi-posterior shares many of the desirable properties of full Bayesian variable selection, but no longer necessitates a full likelihood specification. Instead, the quasi-posterior only requires the specification of mean and variance functions, and as a result, is robust to other aspects of the data. Laplace approximations are used to approximate the quasi-marginal likelihood when it is not available in closed form to provide computational tractability. We demonstrate through extensive simulation studies that the quasi-posterior improves variable selection accuracy across a range of data-generating scenarios, including linear models with heavy-tailed errors and overdispersed count data. We further illustrate the practical relevance of the proposed approach through applications to real datasets from social science and genomics
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Suraj Jagtap (15085726), Chitra Pattabiraman (9867594), Arun Sankaradoss (11188503) et al. · Figshare · 2023
<p>The clock models for running the BEAST analysis were selected based on (A) Akaike information criterion and (B) harmonic mean method. Lower AICM values and higher HM values denote a better model. Optimum values and models are shown in bold. (C) Chain lengths used BEAST MCMC analysis for each serotype for phylogeographic analysis.</p> <p>(XLSX)</p>
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Seth Sullivant · Graduate studies in mathematics · 2018
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Edward I. George, Daniel Yekutieli · 2012
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Karl Friston, W.D. Penny · NeuroImage · 2011
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Tomáš Macek · Digital Repository (National Repository of Grey Literature) · 2021
The Thesis deals with Bayesian model selection. In the theoretical part, readers will get to know with the priciple of Bayesian approach and the Thesis also states Bayes theorem, which has a key role in the given problematics. Next, it elucidates possibilities of choosing prior distribution and introduces Bayesian regression model, especially Zellner's method, which can be used to choose the most suitable model. In the practical part, this method is then implemented using R on real data from English Premier League football matches. From several statistics considered, the method will select the most suitable model, which means that it will select those statistics which are the most important for the match outcome. 1
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2010
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Yan Zhou, John A. D. Aston, Adam M. Johansen et al. · 2014
Positron emission tomography (PET) Linear Compartmental models Plasma input PET compartmental models Bayesian model selection for PET Robust modeling of the error structure Biologically informative priors Sequential Monte Carlo Algorithm setting for Bayesian modeling Computational challenge Accuracy of estimators Heterogeneous structure and algorithm tuning Computational cost and parallel computing
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