Paradoxes and Priors in Bayesian Regression

Bibliographic Details
Main Author:	Som, Agniva
Language:	English
Published:	The Ohio State University / OhioLINK 2014
Subjects:	Statistics model selection shrinkage estimator consistency g prior hyper-g prior correlation coefficient model averaging mixture of normals hyperspherical coordinate system
Online Access:	http://rave.ohiolink.edu/etdc/view?acc_num=osu1406197897

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spelling	ndltd-OhioLink-oai-etd.ohiolink.edu-osu14061978972021-08-03T06:26:15Z Paradoxes and Priors in Bayesian Regression Som, Agniva Statistics model selection shrinkage estimator consistency g prior hyper-g prior correlation coefficient model averaging mixture of normals hyperspherical coordinate system The linear model has been by far the most popular and most attractive choice of a statistical model over the past century, ubiquitous in both frequentist and Bayesian literature. This dissertation studies the modeling implications of many common prior distributions in linear regression, including the popular g prior and its recent ameliorations. Formalization of desirable characteristics for model comparison and parameter estimation has led to the growth of appropriate mixtures of g priors that conform to the seven standard model selection criteria laid out by Bayarri et al. (2012). The existence of some of these properties (or lack thereof) is demonstrated by examining the behavior of the prior under suitable limits on the likelihood or on the prior itself. The first part of the dissertation introduces a new form of an asymptotic limit, the conditional information asymptotic, driven by a situation arising in many practical problems when one or more groups of regression coefficients are much larger than the rest. Under this asymptotic, many prominent “g-type” priors are shown to suffer from two new unsatisfactory behaviors, the Conditional Lindley's Paradox and Essentially Least Squares estimation. The cause behind these unwanted behaviors is the existence of a single, common mixing parameter in these priors that induces mono-shrinkage. The novel block g priors are proposed as a collection of independent g priors on distinct groups of predictor variables and improved further through mixing distributions on the multiple scale parameters. The block hyper-g and block hyper-g/n priors are shown to overcome the deficiencies of mono-shrinkage, and simultaneously display promising performance on other important prior selection criteria. The second part of the dissertation proposes a variation of the basic block g prior, defined through a reparameterized design, which has added computational benefits and also preserves the desirable properties of the original formulation.While construction of prior distributions for linear models usually focuses on the regression parameters themselves, it is often the case that functions of the parameters carry more meaning to a researcher than do the individual regression coefficients. If prior probability is not apportioned to the parameter space in a sensible manner, the implied priors on these summaries may clash greatly with reasonable prior knowledge. The third part of the dissertation examines the modeling implications of many traditional priors on an important model summary, the population correlation coefficient that measures the strength of a linear regression. After detailing deficiencies of standard priors, a new, science driven prior is introduced that directly models the strength of the linear regression. The resulting prior on the regression coefficients belongs to the class of normal scale mixture distributions in particular situations. Utilizing a fixed-dimensional reparameterization of the model, an efficient MCMC strategy that scales well with model size and requires little storage space is developed for posterior inference. 2014-12-30 English text The Ohio State University / OhioLINK http://rave.ohiolink.edu/etdc/view?acc_num=osu1406197897 http://rave.ohiolink.edu/etdc/view?acc_num=osu1406197897 unrestricted This thesis or dissertation is protected by copyright: all rights reserved. It may not be copied or redistributed beyond the terms of applicable copyright laws.
collection	NDLTD
language	English
sources	NDLTD
topic	Statistics model selection shrinkage estimator consistency g prior hyper-g prior correlation coefficient model averaging mixture of normals hyperspherical coordinate system
spellingShingle	Statistics model selection shrinkage estimator consistency g prior hyper-g prior correlation coefficient model averaging mixture of normals hyperspherical coordinate system Som, Agniva Paradoxes and Priors in Bayesian Regression
author	Som, Agniva
author_facet	Som, Agniva
author_sort	Som, Agniva
title	Paradoxes and Priors in Bayesian Regression
title_short	Paradoxes and Priors in Bayesian Regression
title_full	Paradoxes and Priors in Bayesian Regression
title_fullStr	Paradoxes and Priors in Bayesian Regression
title_full_unstemmed	Paradoxes and Priors in Bayesian Regression
title_sort	paradoxes and priors in bayesian regression
publisher	The Ohio State University / OhioLINK
publishDate	2014
url	http://rave.ohiolink.edu/etdc/view?acc_num=osu1406197897
work_keys_str_mv	AT somagniva paradoxesandpriorsinbayesianregression
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Paradoxes and Priors in Bayesian Regression

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