Nonparametric Bayesian Density Estimation with Gaussian Processes

Abstract

This thesis presents a comprehensive study on nonparametric Bayesian density estimation using Gaussian processes (GP). We explore the logistic Gaussian Process (LGP) and introduce an innovative approach termed the tree-logistic-link Gaussian process (TLLGP). This method aims to improve computational efficiency while maintaining modeling flexibility. We address the computational challenges traditionally associated with LGP by implementing a novel tree-based strategy, thereby reducing the complexity of posterior computations. Through a series of numerical experiments, we demonstrate the effectiveness of TLLGP in various scenarios, comparing its performance with other methods. The results highlight the advantages of our approach in terms of computational speed and accuracy in density estimation tasks. This work contributes to the fields of Bayesian statistics and machine learning by providing a more efficient tool for density estimation, especially beneficial for large high-dimensional data where traditional methods fall short due to their computational demands.