Browsing by Author "Dr. Sujit K. Ghosh, Committee Co-Chair"

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    Bayesian Analysis and Matching Errors in Closed Population Capture Recapture Models
    (2005-03-01) Gosky, Ross Matthew; Dr. Leonard A. Stefanski, Committee Co-Chair; Dr. Sujit K. Ghosh, Committee Co-Chair; Dr. Kenneth Pollock, Committee Member; Dr. Cavell Brownie, Committee Member
    Capture-Recapture models are used to estimate the unknown sizes of animal populations. When the population is closed, with constant size, during the study, eight standard models exist for estimating population size. These models allow for variation in animal capture probabilities due to time effects, heterogeneity among animals, and behavioral effects after the first capture. Our research focuses on two areas: 1. Using Bayesian statistical modeling, we present versions of these eight models. We explore the use of Akaike's Information Criterion (AIC), and the Deviance Information Criterion (DIC) as tools for selecting the appropriate model for a given dataset. Through simulation, we show that AIC performs well in model selection. 2. A new, non-invasive method of capturing animals is to substitute captures of DNA profiles, through sources such as hair samples, for live animal captures. However, DNA profiles of close relatives may not be distinguishable from each other, and some animals in the population may not be uniquely identifiable. This problem leads to negative bias in estimating population size. We present a hierarchical statistical model which accounts for this type of matching error, leading to more accurate estimation of population size.
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    Shrinkage-Based Variable Selection Methods for Linear Regression and Mixed-Effects Models
    (2008-12-22) Krishna, Arun; Dr. Sujit K. Ghosh, Committee Co-Chair; Dr. Howard D. Bondell, Committee Chair
    KRISHNA, ARUN. Shrinkage-Based Variable Selection Methods for Linear Regression and Mixed-Effects Models. (Under the direction of Professors H. D. Bondell and S. K. Ghosh). In this dissertation we propose two new shrinkage-based variable selection approaches. We first propose a Bayesian selection technique for linear regression models, which allows for highly correlated predictors to enter or exit the model, simultaneously. The second variable selection method proposed is for linear mixed-effects models, where we develop a new technique to jointly select the important fixed and random effects parameters. We briefly summarize each of these methods below. The problem of selecting the correct subset of predictors within a linear model has received much attention in recent literature. Within the Bayesian framework, a popular choice of prior has been Zellner’s g-prior which is based on the inverse of empirical covariance matrix of the predictors. We propose an extension of Zellner’s gprior which allow for a power parameter on the empirical covariance of the predictors. The power parameter helps control the degree to which correlated predictors are smoothed towards or away from one another. In addition, the empirical covariance of the predictors is used to obtain suitable priors over model space. In this manner, the power parameter also helps to determine whether models containing highly collinear predictors are preferred or avoided. The proposed power parameter can be chosen via an empirical Bayes method which leads to a data adaptive choice of prior. Simulation studies and a real data example are presented to show how the power parameter is well determined from the degree of cross-correlation within predictors. The proposed modification compares favorably to the standard use of Zellner’s prior and an intrinsic prior in these examples. We propose a new method of simultaneously identifying the important predictors that correspond to both the fixed and random effects components in a linear mixedeffects model. A reparameterized version of the linear mixed-effects model using a modified Cholesky decomposition is proposed to aid in the selection by dropping out the random effect terms whose corresponding variance is set to zero. We propose a penalized joint log-likelihood procedure with an adaptive penalty for the selection and estimation of the fixed and random effects. A constrained EM algorithm is then used to obtain the final estimates. We further show that our penalized estimator enjoys the Oracle property, in that, asymptotically it performs as well as if the true model was known beforehand. We demonstrate the performance of our method based on a simulation study and a real data example.