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Bayesian synthesis

Yu, Qingzhao

Abstract Details

2006, Doctor of Philosophy, Ohio State University, Statistics.
In the practical implementation of a Bayesian analysis, we often face the problem of using the data multiple times by examining the training data in an exploratory fashion to select a model (likelihood and prior) and by obtaining the posterior distribution using the same set of data. This is contrary to the foundational underpinning of the Bayesian paradigm. Also, when several analysts use different methods to analyze the same data, we wish to efficiently combine the models that they produce. The ensuing aggregation of information should provide improved predictive performance. This thesis tackles these problems through the use of a novel modeling method based on data splitting. In a standard implementation of this method, several data analysts work independently on portions of a data set, eliciting separate models which are eventually updated and combined through Bayesian model averaging. This thesis provides theoretical results that characterize general conditions under which data-splitting results in improved estimation. These results suggest general principles of good modeling practice. Application of the method to popular real data sets and to simulated data sets has shown predictive performance superior to that of many automatic modeling techniques, including AIC, BIC, Smoothing Splines, CART, BART, Bayes Tree, Bagged CART, LARS and Bayesian Model Averaging. Compared to competing modeling methods, the Bayesian Synthesis approach 1) exhibits superior predictive performance for real data sets and simulations; 2) makes more efficient use of human knowledge; 3) selects sparser models with better explanatory ability and 4) avoids multiple uses of the data in the Bayesian framework.
Steven MacEachern (Advisor)

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Citations

  • Yu, Q. (2006). Bayesian synthesis [Doctoral dissertation, Ohio State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=osu1155324080

    APA Style (7th edition)

  • Yu, Qingzhao. Bayesian synthesis. 2006. Ohio State University, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=osu1155324080.

    MLA Style (8th edition)

  • Yu, Qingzhao. "Bayesian synthesis." Doctoral dissertation, Ohio State University, 2006. http://rave.ohiolink.edu/etdc/view?acc_num=osu1155324080

    Chicago Manual of Style (17th edition)