Towards efficient Bayesian inference : Cox processes and probabilistic integration

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...

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Main Author: Gunter, Tom
Other Authors: Roberts, Stephen ; Osborne, Michael
Published: University of Oxford 2017
Online Access:https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.748732
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spelling ndltd-bl.uk-oai-ethos.bl.uk-7487322019-01-08T03:16:25ZTowards efficient Bayesian inference : Cox processes and probabilistic integrationGunter, TomRoberts, Stephen ; Osborne, Michael2017In 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.University of Oxfordhttps://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.748732http://ora.ox.ac.uk/objects/uuid:32ccb7f8-6eaf-420f-bf97-113d3504dfa5Electronic Thesis or Dissertation
collection NDLTD
sources NDLTD
description 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.
author2 Roberts, Stephen ; Osborne, Michael
author_facet Roberts, Stephen ; Osborne, Michael
Gunter, Tom
author Gunter, Tom
spellingShingle Gunter, Tom
Towards efficient Bayesian inference : Cox processes and probabilistic integration
author_sort Gunter, Tom
title Towards efficient Bayesian inference : Cox processes and probabilistic integration
title_short Towards efficient Bayesian inference : Cox processes and probabilistic integration
title_full Towards efficient Bayesian inference : Cox processes and probabilistic integration
title_fullStr Towards efficient Bayesian inference : Cox processes and probabilistic integration
title_full_unstemmed Towards efficient Bayesian inference : Cox processes and probabilistic integration
title_sort towards efficient bayesian inference : cox processes and probabilistic integration
publisher University of Oxford
publishDate 2017
url https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.748732
work_keys_str_mv AT guntertom towardsefficientbayesianinferencecoxprocessesandprobabilisticintegration
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