Bayesian Hierarchical Models to Address Problems in Neuroscience and Economics

Abstract

In the first chapter, motivated by a model used to analyze spike train data, we present a method for learning multiple probability vectors by using information from large samples to improve estimates for smaller samples. The method makes use of Polya-gamma data augmentation to construct a conjugate model whose posterior can estimate the weights of a mixture distribution. This novel method successfully uses borrows information from large samples to increase the precision and accuracy of estimates for smaller samples. In the second chapter, data from the Federal Communications Commission spectrum auction number 73 is analyzed. By analyzing the structure of the auctions bounds are placed on the valuations that govern the bidders' decisions in the auction. With these bounds, common models are estimated by imputing valuations and the results are compared with the estimates from standard methods used in the literature. The comparison shows some important differences between the approaches. A second model that accounts for the geographic relationship between the licenses sold finds strong evidence of a correlation between the value of adjacent licenses, as expected by economic theory.