Dr. Kshitij Khare (Feb. 16)

In my talk I will present three families of Markov chains for which the eigenfunctions turn out to be well-known orthogonal polynomials. This knowledge can be used to come up with exact rates of convergence for these families of Markov chains. The first family of examples is two-component Gibbs samplers involving standard exponential families and their conjugate priors, the second family of examples is the multivariate normal autoregressive process and the third family of examples consists of simple models in population genetics. These are joint works with Persi Diaconis, Laurent Saloff-Coste and Hua Zhou.

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Rebecca Steorts (Mar. 2)

Often in small area estimation, model-based estimates differ widely from direct estimates, especially for areas with low sample sizes. While model-based estimates are useful, one difficulty with such estimates is that when aggregated, the overall model-based estimate for larger geographical areas may be quite different than from the corresponding direct estimate. In order to avoid this discrepancy, benchmarking can be can applied, which amounts to modifying the model-based estimates so that the aggregate estimate matches the overall direct estimate. We propose a general class of constrained Bayes estimators that achieves the desired benchmarking for weighted mean and weighted variability in a multiparameter setting that is motivated by work previously done by Louis (1984) and Ghosh (1992). Finally, we illustrate the methodology using U.S. Census data. This work was a collaboration with Gauri Datta, Malay Ghosh, and Jerry Maples.

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Anestis Touloumis (March 23)

he Generalized Estimating Equations (GEE) methodology, proposed by Liang and Zeger(1986), is one of the most popular methods to estimate the regression coefficients of a marginal model with correlated responses. Its popularity lies in two facts; it produces consistent estimates of the parameters of interest even when the correlation structure is misspecified and it avoids specification of the likelihood function which can be cumbersome especially for discrete variables. However, the efficiency of the GEE estimator depends on the form and on the parametrization of the correlation structure. In this talk, we consider the case of multinomial responses. In the literature, the correlation structure for multinomial responses has been modeled through the correlation coefficients or the global odds ratios. We argue that none of these parameterizations is appropriate for describing the association structure by extending the results of Chaganty and Joe (2004,2006). Instead, we suggest the use of the local odds ratios which is applicable and meaningful to both ordinal and nominal responses. Further, we present a modification in estimating the local odds ratios which avoids theoretical issues that existing methods have. An example to illustrate the suggested methods will be provided.

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Eugenia Buta (March 30)

We consider situations in Bayesian analysis where we have a family of priors nu_h on the parameter theta, where h varies continuously over a space H, and we deal with two related problems. The first involves sensitivity analysis and is stated as follows. Suppose we fix a function f of theta. How do we efficiently estimate the posterior expectation of f(theta) simultaneously for all h in H? The second problem is how do we identify subsets of H which give rise to reasonable choices of priors? We assume that we are able to generate Markov chain samples from the posterior for a finite number of the priors, and we develop a methodology, based on a combination of importance sampling and the use of control variates, for dealing with these two problems. The methodology applies very generally, and we show how it applies in particular to a commonly used model for variable selection in Bayesian linear regression, and give an illustration on a real data set.

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Tezcan Orzagat (April 6)

In this talk, we will present the stereotype model, which has been introduced by Anderson in 1984. The stereotype model, used for the ordinal response, is a special case of the multinomial logistic model, and hence it is more parsimonious. This model has not been widely used so far because of the lack of a standard program. We use GNM function of R, which is used to fit the generalized nonlinear models. We extend the stereotype model and introduce two kinds of partial stereotype models. The Wald confidence interval, the likelihood-ratio-based confidence interval, the score and the pseudo-score confidence intervals for the parameters are obtained and will be compared in terms of achieving error rates closer to the nominal level later on. However, we have observed that there are some cases that the parameters are infinite. This yielded a new study on the existence of the maximum likelihood estimates for the stereotype model and for some common models. The literature about the existence of MLE for these common models will be given shortly.

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Dr. Robert Lund (April 14)

This expository talk examines the statistical methods used to quantify records and extreme events. Our applications are on destructive hurricanes in the Atlantic Ocean and Gulf of Mexico. Extreme value methods are first introduced and contrasted to the classical central limit methods used to assess sample averages. A Poisson process with a periodic time-varying arrival cycle is used to describe the arrival times of hurricanes; extreme value distributions are employed to model the severity of the individual landfalling hurricanes. The results show that Hurricane Katrina has a return period of about twelve years, perhaps a much more common storm than the news media would have us believe.

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