Adaptive Statistical Inference Procedures for Multigroup Data and Phylogenetic Tree Inferences

Abstract

Multigroup data is a common data type in fields such as biology, the environmental sciences and the social sciences. This dissertation focuses on developing new statistical methodologies for multigroup data analysis. When data across groups are independent of each other, simultaneous statistical inferences for each group are often performed to analyze the data. We first present an adaptive multigroup confidence interval procedure. We construct confidence intervals that make use of information about across-group heterogeneity, resulting in constant coverage intervals that are narrower than standard t-intervals across groups. Then we present adaptive procedures for sign error control. We present a procedure that guarantees to control the sign error rate under a desired threshold, and another more powerful procedure that approximately controls the sign error rate under certain assumptions. When data across groups are dependent on each other, it is often of interest to capture the dependence relationships among groups. For the second part of the dissertation, we develop methodologies for such data type with a focus on phylogenetic tree inferences. We first present simple and consistent algorithms for the tree topology recovery and parameter estimation, and then present an iterative structural EM algorithm which improves the results from the simple algorithms.