Dr. Jim Hobert (Sep. 15)

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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Demetris Athienitis (Sep. 22)

Robustness measures and procedures have traditionally been developed and implemented through the contamination model. A model that partially samples from a contaminant distribution. Hampel (1968), developed a heuristic tool, the influence function, that represents the rate of change in a statistic by adding an infinitesimal amount of contamination. Multiple robustness properties have been derived using this tool. We present a distortion model that takes a symmetric probability density function and skews it in a specific direction thereby distorting every realization of the distribution. The model used is based upon the Fechner class of distributions. A plethora of statistical procedures assume distributional symmetry and we set out to derive various robustness properties for the distortion model, of which symmetry is only a special case, by introducing the distortion sensitivity, an analog to Hampel's influence function.

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Dr. Luis Leon (Sep. 29)

We address inference for a human phage display experiment with three stages. The data are tripeptide counts by tissue and stage. The primary aim of the experiment is to identify ligands that bind with high affinity to a given tissue. We formalize the research question as inference about the monotonicity of mean counts over stages. The inference goal is then to identify a list of peptide-tissue pairs with significant increase over stages. We develop a semi-parametric model as a mixture of Poisson distributions with a Dirichlet process prior on the mixing measure. The posterior distribution under this model allows the desired inference about the monotonicity of mean counts. However, the desired inference summary as a list peptide-tissue pairs with significant increase involves a massive multiplicity problem. We consider two alternative approaches to address this multiplicity issue. First we propose an approach based on the control of the posterior expected false discovery rate. We notice that the implied solution ignores the relative size of the increase. This motivates a second approach based on a utility function that includes explicit weights for the size of the increase..

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Rebecca Steorts (Oct. 13)

Bayesian inference often requires evaluating integrals that are intractable. This requires numerical methodology such as Markov Chain Monte Carlo to be used to approximate posterior distributions of interest. Often models will be very complex and advanced software will be needed. BUGS (Bayesian Inference Using Gibbs Sampling) is an example of such software that can be extremely useful in these situations. I will briefly explain the three BUGS programs available (WinBUGS, OpenBUGS, JAGS). I will then give a tutorial on how to use JAGS (Just Another Gibbs Sampler) and explain how to analyze output from JAGS in R.

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Dhiman Bhadra (Oct. 20)

Case Control studies mark the single most important contribution that statisticians have made in the domain of Public Health and Epidemiology. The fundamental principle of these studies is to compare a group of subjects having a particular disease (cases) to a group of disease free subjects (controls) with respect to some potential risk factors. In a typical case control study design, the exposure information is collected only once for the cases and controls. However, some recent medical studies have indicated that a longitudinal approach of incorporating the entire exposure history, when available, may lead to better estimates of odds ratios. In this work, we have conducted an analysis of a case-control study when longitudinal exposure information are available for both the cases and controls. This has enableed us to analyze how the present disease status of a subject is being influenced by past exposure conditions conditional on the current ones. We have used semiparametric regression procedures in modeling the exposure profiles. Analysis has been carried out in a hierarchical Bayesian framework using MCMC procedures. Based on our analysis, we can conclude that past exposure observations do contribute significantly to our understanding of the present status of an individual.

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Vik Gopal (Nov. 3)
Search engines need to maintain an index of websites that is as up-to-date as possible. Otherwise, search queries would be answered inaccurately. Search engines use web crawlers to visit websites in order to check if they have changed. If they have, then the new version is indexed. This raises the question, "At what time point should I return to a particular website?". Keeping in mind that there is also a cost to visiting websites too frequently, we try to answer this question in both a frequentist and Bayesian setting.

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Kenny Lopiano (Nov. 17)

Additive models and generalized additive models(GAMs) are a very important tool for modeling a response variable Y as a function of several predictor variables X_1,X_2,...X_n that does not restrict the model to be linear in the parameters. With this in mind, we will provide brief overview of the existing methods associated with GAMs. We also provide an introduction to implementing such models using the R package mgcv.

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Nate Holt (Nov. 24)

In spatial modeling the predicted surface is often visualized using a 2D heat map. An example will show that 3D surface plots may reveal discrepancies between the predicted surfaces of competing spatial models that cannot be detected with 2D heat maps. I will also talk about fully funded summer school opportunities in North Carolina through SAMSI, the Statistics and Applied Mathematical Sciences Institute.

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