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Calibrated Bayes Factor and Bayesian Model Averaging

zheng, jiayin
http://orcid.org/0000-0001-6457-3068
http://rave.ohiolink.edu/etdc/view?acc_num=osu1518632917560265

Abstract Details

2018, Doctor of Philosophy, Ohio State University, Statistics.
There is a rich history of work on model selection and averaging in the statistics literature. The Bayesian paradigm provides an approach to model selection which successfully overcomes the drawbacks for which frequentist hypothesis testing has been criticized. Most commonly, Bayesian model selection methods are based on the Bayes factor. Additionally, the Bayes factor has applications outside the realm of model selection, such as model averaging. In a formal sense, as a supplement to the prior odds, the Bayes factor produces the posterior odds for a pair of models. These posterior odds can be translated to posterior probabilities and yields a full posterior distribution that assigns a probability to each model as well as a distribution over the parameters for each model. Then the Bayesian model averaging provides better prediction by making inferences based on a weighted average over all of the models considered. In this thesis, we first review the literatures on the model selection, with a focus on the Information criteria (Section 1.1.1). Then we focused on investigating the Bayesian model selection methods based on the Bayes factor, and their shortcomings (Section 1.2). Next we introduce several commonly used priors and the corresponding Bayes factors under the regression framework (Section 2.1.1). We mainly focus on model comparison and Bayesian model averaging under regression settings with those model specifi c prior distributions. We repeat part of simulation studies in Lu (2012) and add several additional commonly used prior distributions (Section 2.3), show that the calibrated Bayes factor alleviate the impact of the diffuse priors. We further develop another way of the calibrated Bayes factor by the log predictive likelihood which is a more automated and systematic model comparison method, especially with high dimensional data (Section 3.1). Moreover, we demonstrate use of the two ways of calibrated Bayes factors with two strategies Bayesian model averaging on Diabetes data and the Ozone data originally studied in Efron et al. (2004) and Breiman and Friedman (1985), respectively (Section 3.3). Both strategies provide smaller root squared error loss in several simulation studies and the real data analysis than the standard Bayesian model averaging.
Steven MacEachern (Advisor)
Xinyi Xu (Advisor)
166 p.
Statistics
model selection, Bayes factor, unit information prior, Bayesian model averaging

Recommended Citations

Citations

  • zheng, J. (2018). Calibrated Bayes Factor and Bayesian Model Averaging [Doctoral dissertation, Ohio State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=osu1518632917560265

    APA Style (7th edition)

  • zheng, jiayin. Calibrated Bayes Factor and Bayesian Model Averaging. 2018. Ohio State University, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=osu1518632917560265.

    MLA Style (8th edition)

  • zheng, jiayin. "Calibrated Bayes Factor and Bayesian Model Averaging." Doctoral dissertation, Ohio State University, 2018. http://rave.ohiolink.edu/etdc/view?acc_num=osu1518632917560265

    Chicago Manual of Style (17th edition)

osu1518632917560265
383
© 2018, some rights reserved.Creative Commons License Calibrated Bayes Factor and Bayesian Model Averaging by jiayin zheng is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License. Based on a work at etd.ohiolink.edu.
This open access ETD is published by The Ohio State University and OhioLINK.