Analysis of MCMC Algorithms for Bayesian Linear Regression with Laplace Errors
Hee Min Choi, University of Florida
Let pi denote the intractable posterior density that results when the standard default prior is placed on the parameters in a linear regression model with iid Laplace errors. We analyze the Markov chains underlying two different Markov chain Monte Carlo algorithms for exploring pi. In particular, it is shown that the Markov operators associated with the data augmentation (DA) algorithm and a sandwich variant are both trace-class. Consequently, both Markov chains are geometrically ergodic. It is also established that for each i=1,2,3..., the ith largest eigenvalue of the sandwich operator is less than or equal to the corresponding eigenvalue of the DA operator. It follows that the sandwich algorithm converges at least as fast as the DA algorithm. (Joint work with Dr. James P. Hobert.)
Propensity Score Methods in Observational Studies Comparing Multiple Treatments
Bassam Dahman, Virginia Commonwealth University
The propensity score (PS) methods are commonly used now in observational studies. Health policy researchers utilize these methods to adjust for the confounding problems and reduce the bias in estimating the treatment effects that result from the non-random allocation of treatments in observational studies. A few PS methods are developed to estimate the treatment effects in the presence of more than two treatment groups. These include using PS as covariates or weights, or using them in matching. This paper reviews these methods, and describes the challenges in i) estimating the PS using different multinomial models ii) using these PS in matching iii) utilizing the different methods of using PS to adjusting for confounding. These methods were applied and compared in a comparative effectiveness study of the different treatments of newly diagnosed prostate cancer patients. Simulation studies built on the data extracted from SEER linked Medicare database were used to evaluate the properties of the different PS methods and to compare the estimates the treatment effects.
An Intuitive Correspondence Measure for Compositional Data with Applicationsin Understanding Metagenomic Systems
Z. John Daye, University of Arizona
Metagenomic data are often presented in terms of taxonomic compositions, i.e. the relative proportions of microbes in a biological sample. Compositional or proportional data have long being known as statistically challenging to model, due to constraints resulting from each composition being defined from counts of all microbes. In particular, no proper measures are available for determining dependency between co-existing members in metagenomic systems. In this talk, we will provide an intuitive measure of correspondences between compositions. It is robust against technical issues commonly associated with compositional data analysis, such as correlation negativity and subcomposition inconsistency. The procedure will be applied to identify complex interactions leading to biological diseases. This is a joint work with Lingling An.