Chen Li (Feb. 14)

The Dirichlet process has been used extensively in Bayesian nonparametric modeling, and has proven to be very useful. Here we discuss the linear mixed model with Dirichlet process random e ects from a classical view, and derive the best linear unbiased estimator (BLUE) of the fixed e ffects. We also characterize the relationship between the BLUE and the OLS, and show how confidence intervals can be approximated. At Last, show some simulations studies and application results.

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Professor James Hobert (Feb. 7)

Two important questions that must be answered whenever a Markov chain Monte Carlo algorithm is used are (Q1) What is an appropriate burn-in? and (Q2) How long should the sampling continue after burn-in? One method of developing rigorous answers to these questions involves establishing drift and minorization conditions, which together imply that the underlying Markov chain is geometrically ergodic. In this talk, I will explain what drift and minorization are as well as how and why these conditions can be used to form rigorous answers to (Q1) and (Q2).

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Yuan Liao (Mar. 13)

Strong Law of Large Numbers for Weighted Sums of Random Elements in Banach Spaces are obtained for the following two broad cases; the results are new even when the underlying Banach space is the real line. (i) The random elements are independent. The underlying Banach space is assumed to satisfy the geometric condition that it is of Rademacher type p (p \in[1,2]). Special cases include results of Woyczy\'nski (1980), Teicher (1985), Adler, Rosalsky, and Taylor (1989), and Sung (1997). (2) Conditions are provided under which a general SLLN is obtained irrespective of the joint distributions of the random elements. No geometric conditions are imposed on the underlying Banach space. The results are general enough to include as special cases results of Petrov (1973), Teicher (1985), Sung (1997), and Rosalsky and Stoica (2010).

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Professor Alan Agresti, University of Florida (Emeritus) (Mar. 20)

This talk surveys confidence intervals that perform well for estimating parameters used in categorical data analysis. Considerable research has now shown that intervals resulting from inverting score tests perform much better than inverting Wald tests and usually better than inverting likelihood-ratio tests. For small samples, `exact' methods are conservative inferentially, but inverting a score test using the mid-P value provides a sensible compromise. Finally, we briefly review an approach for proportions and their differences that approximates the score intervals and is much better than the ordinary Wald intervals by adding pseudo data before forming the Wald intervals.

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Doug Sparks (Mar. 27)

Like most classical methods, linear regression lends itself easily to a Bayesian formulation. A variety of useful Bayesian techniques have evolved to meet specific needs, and many of these techniques provide advantages over their frequentist counterparts. However, analysis of the frequentist properties of Bayesian regression models sometimes reveals subtle but serious problems, especially in settings where the number of covariates p grows with the sample size n. In particular, Zellner's g-prior and its empirical and hierarchical extensions are a commonly used family of models for which the posterior can become inconsistent in surprising circumstances. These results will be provided and discussed, but broader issues with Bayesian regression models will also be addressed throughout the talk.

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