Methods for statistical analysis and prediction of discrete choices

The increasing availability of individual-level consumer data has facilitated the development of new methods for analyzing and predicting people's product choices. This thesis contributes to the existing body of literature with three chapters advancing the statistical analysis of discrete choice. In Chapter 1, I propose a new model seeking to elaborate on the role that choice set composition, known as context, plays in a discrete choice problem. Specifically, I generalize a state-of-the-art class of models stemming from recent research on neural normalization to the multi-attribute setting. I impose a structural model composition based on the brain synaptic plasticity literature, allowing for a particular form of correlation between product utilities. I highlight the properties of the model with a series of experiments and real-world empirical applications. In Chapter 2, I propose a new Monte Carlo method, called Hamiltonian Sequential Monte Carlo (HSMC), for the purpose of nonparametric estimation of unobserved consumer heterogeneity in discrete choice problems. HSMC combines the advantages of Sequential Monte Carlo (SMC) and Hamiltonian transition dynamics. SMC exploits gains from parallelization very efficiently as the core computational load involving the model likelihood is performed by many individual particles independently of one another. At the same time, by using first-derivative information, Hamiltonian transition dynamics has been shown to yield substantial gains in Markov chain mixing properties relative to the standard random walk proposal steps outside of the SMC context. I compare the performance of HSMC with SMC on a discrete choice model of consumer purchases with nonparametric consumer heterogeneity and show the favorable properties of HSMC. In Chapter 3, I propose a Bayesian method called Sequential Optimal Inference (SOI) providing an optimal sequence of questions in experiments. Experiments are frequently used to elicit preferences of potential consumers. Using SOI, the questions are adaptively designed to maximize the expected information and take into account the subjects' previous answers. The method also allows for real-time inference and provides updated posterior distributions while the experiment is performed. Existing methods were created for specific sub-cases. SOI is more general, nesting a large class of models and allowing for a number of inference objectives.Ph.D