**Abstract:**

I develop theoretical and methodological results for Markov chain Monte Carlo (MCMC) algorithms for two different Bayesian regression models. First, I consider a probit regression problem in which *Y*_{1},…,* Y _{n}* are independent Bernoulli random variables such that Pr(

Second, I consider multivariate regression models where the distribution of the errors is a scale mixture of normals. Let π denote the posterior density that results when the likelihood of *n* observations from the corresponding regression model is combined with the standard non-informative prior. I provide necessary and sufficient condition for the propriety of the posterior distribution, π. I develop two MCMC algorithms that can be used to explore the intractable density π. These algorithms are the data augmentation algorithm and the Haar PX-DA algorithm. I compare the two algorithms in terms of efficiency ordering. I establish drift and minorization conditions to study the convergence rates of these algorithms.

Adviser | James P. Hobert |

School | UNIVERSITY OF FLORIDA |

Source Type | Dissertation |

Subjects | Statistics |

Publication Number | 3425539 |

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