Towards efficient Bayesian inference: Cox processes and probabilistic integration

Thesis

In this thesis we present a variety of new, continuous, Bayesian Gaussian-process-driven Cox process models. These are used to model sparse event data distributed on a continuous domain, where the events may have a tendency to cluster. These find direct use in application areas ranging from disease incidence modelling through to statistical cosmology, where the distribution of galaxies in the universe is weakly clustered due to the effects of dark matter. They may also be deployed in a more abstract sense, for example as a structured prior for network communications.

In previous work, the difficulty of performing inference in Gaussian-process-driven Cox processes has hindered their application to large, high-dimensional datasets. We develop novel and computationally efficient inference schemes for these models as well as our own extensions to them, demonstrating an improvement on the existing state of the art using real data. In particular, we present the first known variational inference scheme for such models, which scales linearly with the size of the dataset.

Spurred on to consider the problem of computationally efficient Bayesian inference in general, we tackle model evidence estimation. Arriving at an accurate measure of model evidence quickly allows for the objective measure of model fit, and ensures we select a set of assumptions which most closely embody the data-generating process.

We deviate from the traditional core Monte Carlo estimator, and instead present a computationally efficient general Bayesian quadrature scheme for model evidence computation. This is the first such scheme which can be shown to be demonstrably wall-clock competitive with state of the art Monte Carlo approaches.

Authors: Gunter, T

• DOI: 10.5287/ora-6rqxrpk2x
• Type of award: DPhil
• Level of award: Doctoral
• Awarding institution: University of Oxford