Neural Networks as Tools for Posterior Estimation and Inference

Abstract

In this dissertation, we will discuss three applications for neural networks in the paradigm of Bayesian estimation and inference. In Chapter 2, we describe a likelihood-free method of estimating posterior quantiles using recurrent neural networks. This method is particularly useful for time series data with high-dimensional latent random variables. In Chapter 3, we propose a method for optimizing Bayesian adaptive enrichment design clinical trials using reinforcement learning. Through the simulation of many trials, we use policy gradient descent to train a neural network to optimally incorporate existing patient information into a simple adaptive enrollment criterion. Finally, in Chapter 4, we describe a mechanistically explicit forward model for Somatic Hypermutation (SHM). We estimate the parameters regulating this model with a neural network and manually selected summary statistics.