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Aaron Pribadi

Picture of Aaron Pribadi.

Thesis

Algebraic Methods for Log-Linear Models

Advisor
Michael Orrison
Second Reader(s)
Weiqing Gu

Abstract

Techniques from representation theory (Diaconis, 1988) and algebraic geometry (Drton et al., 2008) have been applied to the statistical analysis of discrete data with log-linear models. With these ideas in mind, we discuss the selection of sparse log-linear models, especially for binary data and data on other structured sample spaces. When a sample space and its symmetry group satisfy certain conditions, we construct a natural spanning set for the space of functions on the sample space which respects the isotypic decomposition; these vectors may be used in algorithms for model selection. The construction is explicitly carried out for the case of binary data.

Proposal

Markov Bases for Sampling Conditional Distributions

Additional Materials

Poster