There have been increasingly keen interests in recent years in detecting change points in climate data. Existing detection procedures are mostly constructed under the assumption of homoscedasticity in parametric models or via classic rank-test statistics in nonparametric models. The inference based on these procedures are sometimes invalidated by heteroscedasticity. We propose an empirical likelihood approach to tackle the problem. Empirical likelihood is a nonparametric technique for inference on functional population characteristics such as means and medians. One of the most appealing features of empirical likelihood methods is that it has large sampling properties similar to its counterpart likelihood-based parametric methods and enjoys both the robustness from its nonparametric nature and the efficiency from its likelihood construction. The bootstrap method is proposed to approximate the p-values of the empirical likelihood changepoint detection procedure. Simulation results show that the empirical likelihood method proposed with bootstrap p-value approximation performs very well. T he new approach is applied to the Argentia rainfall data that were analyzed by many other researchers. The proposed method is also extended to shochastic changepoint and regression changepoint models.

We present several strategies for the estimation of multidimensional probability distributions that arise in the context of climate models. The proposed strategies are evaluated with a surrogate climate model that is able to approximate the noise response behavior of a realistic atmospheric general circulation model. We show that versions of Adaptive Metropolis algorithms are superior to approximate posterior probability distributions of the surrogate model than optimization-type methods that are being used by climate scientists. We also discuss a non-parametric, surface approximation approach for calibration which is particularly suited for real climate models. The methods are general and would also be useful for other types of computer models that depend on expensive model runs. Additionally, we present some novel approaches to deal with extreme values that are attractive to study numerical output from regional climate models.

Objectives:
Familiarize with Border Health Issues.
Broad description and example from San Elizario, TX.
Gain knowledge of epidemiology applications.
Learn about the distribution of epidemiologists in the US.

Brain lesion count based on magnetic resonance imaging (MRI) is a key variable in the study of the disease progression of relapsing remitting multiple sclerosis (RRMS). We develop negative binomial (NB) models for such count data arising in RRMS Parallel Group (PG) and Baseline versus Treatment (BVT) trials, and describe the resulting likelihood ratio test (LRT), Rao's score test (RST) and Wald tests. We propose the univariate NB model for comparing the group means in PG trials and the bivariate NB model for comparing the means of the baseline and treatment periods in BVT trials. We perform the power analyses and sample size estimation using simulation and the exact distributions of the test statistics. We also carry out a robustness study for the PG trial. Aban, Cutter, and Mavinga (2009) have recently studied the properties of these tests for the PG trials using chi-square critical values. Their tests fail to maintain the desired significance level for small studies. Using the NB model, Sormani et al. (2001) had earlier proposed the use of nonparametric tests and did power analyses to compare the mean MRI counts in PG and in BVT trials. Generally, the LRT and one of the Wald tests with exact critical values perform well and provide substantial reduction over their proposed sample sizes in a variety of situations. (This is joint work with Mallik Rettiganti.)

We propose a class of time-domain models for analyzing possibly nonstationary time series. This class of models is formed as a mixture of time series models, whose mixing weights are a function of time. We consider specifically mixtures of autoregressive models with a common but unknown lag. The model parameters, including the number of mixture components, are estimated via Markov chain Monte Carlo methods. The methodology is illustrated with simulated and real data.

We consider inference for row effects in the presence of possible interactions in a two-way fixed effects model when the numbers of observations are themselves random variables following the multinomial distribution with unknown probabilities. This situation occurs commonly in survey-type studies where the observations are categorized into the cells of an ANOVA table after the sample is drawn. The paper focuses on testing the hypothesis of equality of row means. With the cell probabilities assumed unknown, there is no obvious sum of squares and F-ratio computed by the widely available statistical packages for testing this hypothesis. Under the multinomial assumption, we find the asymptotic joint distribution of the sample row means. The result is then used to construct a sensible asymptotic test of the equality of the corresponding row means and asymptotic simultaneous confidence intervals for contrasts. The talk is based on joint work with Steve Arnold (under review).