Objective Bayesian Variable Selection

Casella, George; Moreno, Elı́as

doi:10.1198/016214505000000646

Cited by 121 publications

(143 citation statements)

References 1 publication

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“…Nonetheless, posterior probabilities (2) can still be formally defined using the Bayes factor with respect to the full model (8). A similar formulation, where the prior on the full model depends on which hypothesis is being tested, has also been adapted by Casella and Moreno (2006) in the context of intrinsic Bayes factors. Their rationale is that the full model is the scientific "null" and that all models should be judged against it.…”

Section: Full-based Bayes Factorsmentioning

confidence: 99%

“…Our last example uses the ground level ozone data analyzed in Breiman and Friedman (1985), and more recently by Miller (2001) and Casella and Moreno (2006). The dataset consists of daily measurements of the maximum ozone concentration near Los Angeles and 8 meteorological variables (the description for the variables is in Appendix C).…”

Section: Ozonementioning

confidence: 99%

“…The dataset consists of daily measurements of the maximum ozone concentration near Los Angeles and 8 meteorological variables (the description for the variables is in Appendix C). Following Miller (2001) and Casella and Moreno (2006), we examine regression models using the 8 meteorological variables, plus interactions and squares, leading to 44 possible predictors. Enumeration of all possible models is not feasible, so instead we use stochastic search to identify the highest probability models using the R package BAS.…”

Section: Ozonementioning

confidence: 99%

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Mixtures of g Priors for Bayesian Variable Selection

Liang

Paulo

Molina

et al. 2008

Journal of the American Statistical Association

984

1,333

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Zellner's g-prior remains a popular conventional prior for use in Bayesian variable selection, despite several undesirable consistency issues. In this paper, we study mixtures of g-priors as an alternative to default g-priors that resolve many of the problems with the original formulation, while maintaining the computational tractability that has made the g-prior so popular. We present theoretical properties of the mixture g-priors and provide real and simulated examples to compare the mixture formulation with fixed g-priors, Empirical Bayes approaches and other default procedures.

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Section: Full-based Bayes Factorsmentioning

confidence: 99%

Section: Ozonementioning

confidence: 99%

Section: Ozonementioning

confidence: 99%

See 1 more Smart Citation

Mixtures of g Priors for Bayesian Variable Selection

Liang

Paulo

Molina

et al. 2008

Journal of the American Statistical Association

984

1,333

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show abstract

“…We believe that our methodology can be successfully applied in this context, with the help of a suitable search algorithm over the space of all models. Since our approach is based on a pairwise comparison of nested models, some form of encompassing is required, if an MCMC strategy is adopted; see, in the context of variable selection, Liang et al (2008) using mixtures of g-priors, or Casella and Moreno (2006) using intrinsic priors. An alternative option is to use a Feature-Inclusion Stochastic Search, as implemented in Scott and Carvalho (2006) for undirected decomposable graphical models.…”

Section: Discussionmentioning

confidence: 99%

Moment Priors for Bayesian Model Choice with Applications to Directed Acyclic Graphs*

Consonni¹,

Rocca²

2011

Bayesian Statistics 9

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Standard-Nutzungsbedingungen:Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden.Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen.Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. We propose a new method for the objective comparison of two nested models based on non-local priors. More specifically, starting with a default prior under each of the two models, we construct a moment prior under the larger model, and then use the fractional Bayes factor for a comparison. Non-local priors have been recently introduced to obtain a better separation between nested models, thus accelerating the learning behaviour, relative to currently used local priors, when the smaller model holds. Although the argument showing the superior performance of non-local priors is asymptotic, the improvement they produce is already apparent for small to moderate samples sizes, which makes them a useful and practical tool. As a by-product, it turns out that routinely used objective methods, such as ordinary fractional Bayes factors, are alarmingly slow in learning that the smaller model holds. On the downside, when the larger model holds, non-local priors exhibit a weaker discriminatory power against sampling distributions close to the smaller model. However, this drawback becomes rapidly negligible as the sample size grows, because the learning rate of the Bayes factor under the larger model is exponentially fast, whether one uses local or non-local priors. We apply our methodology to directed acyclic graph models having a Gaussian distribution. Because of the recursive nature of the joint density, and the assumption of global parameter independence embodied in our prior, calculations need only be performed for individual vertices admitting a distinct parent structure under the two graphs; additionally we obtain closed-form expressions as in the ordinary conjugate case. We provide illustrations of our method for a simple three-variable case, as well as for a more elaborate seven-variable situation. Although we concentrate on pairwise comparisons of nested models, our procedure can be implemented to carry-out a search over the space of all models. Terms of use: Documents inJune 2010.

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“…[19], which is a reversible jump 20 style algorithm, with a model comparison approach using modified fractional Bayes factor. 21,22 The basic idea is to consider a finite number of possible C, denoted by {C min , . .…”

Section: Posterior Computationmentioning

confidence: 99%

A Bayesian Nonparametric Model for Reconstructing Tumor Subclones Based on Mutation Pairs

et al. 2015

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We present a feature allocation model to reconstruct tumor subclones based on mutation pairs. The key innovation lies in the use of a pair of proximal single nucleotide variants (SNVs) for the subclone reconstruction as opposed to a single SNV. Using the categorical extension of the Indian buffet process (cIBP) we define the subclones as a vector of categorical matrices corresponding to a set of mutation pairs. Through Bayesian inference we report posterior probabilities of the number, genotypes and population frequencies of subclones in one or more tumor sample. We demonstrate the proposed methods using simulated and real-world data. A free software package is available at http://www.compgenome.org/pairclone.

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Objective Bayesian Variable Selection

Cited by 121 publications

References 1 publication

Mixtures of g Priors for Bayesian Variable Selection

Mixtures of g Priors for Bayesian Variable Selection

Moment Priors for Bayesian Model Choice with Applications to Directed Acyclic Graphs*

A Bayesian Nonparametric Model for Reconstructing Tumor Subclones Based on Mutation Pairs

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