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Bayesian inference for models with infinite-dimensionally generated intractable components

Antoniano Villalobos, Isadora (2012) Bayesian inference for models with infinite-dimensionally generated intractable components. Doctor of Philosophy (PhD) thesis, University of Kent. (doi:10.22024/UniKent/01.02.94176) (KAR id:94176)

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In recent years, great effort has been placed on the development of flexible statistical models, which can capture the rich and diverse structures found in real data. Complex models are often intractable, and they require non trivial techniques for inference. In the Bayesian setting, the most common intractability problem is related with nor­malizing constants which cannot be calculated directly. In this case, MCMC methods are a usefrd tool for posterior simulation of the model parameters, and many ideas have been developed to enable the con­struction of the chains with the desired stationary densities. Fre­quently, ideas applied for posterior simulation from doubly-intractable distributions involve an approximation error; general exact methods are only available for models in which both the data and the param­eters take values in fnite-dimensional spaces.

In the present work we propose a novel idea, based on a series ex­pansion representation of the intractable functions, to enable MCMC simulation for models in which either the data or the parameters are infinite-dimensional. We achieve this by introducing a suitable set of latent variables with unknown and possibly infinite dimension. The MCMC construction is then made for a tractable latent model, from which the density of interest can be recovered through marginaliza­tion.

We illustrate the applicability of the method in various situations. We show that the latent variable construction of the retrospective re­jection sampler commonly known as exact simulation algorithm for diffusions, is a particular case of the latent variable construction we propose. We provide an idea for an alternative exact simulation and inference scheme, through a Markov chain construction. We also present two related nonparamctric mixture models, for time series and regression analysis. Their novelty is in the construction of the mixture weights, which gives them great flexibility but introduces an intractable component generated by the infinite-dimensional parame­ters; we show how our methodology can be applied to enable MCMC inference for these models. We also show how our ideas can be used for inference when the power likelihood for nonparametric mixture models is used; a problem which is of interest in many settings and, to our knowledge, has not been solved without the introduction of some approximation error.

Finally, we discuss the matter of Bayesian consistency for Markov models. Unrelated to the driving theme of the thesis, the problem naturally arises from some of the models studied. We make a first step towards a general result for strong consistency which can be used both for discretely observed diffusions and for the time series model we propose.

Item Type: Thesis (Doctor of Philosophy (PhD))
Thesis advisor: Walker, Stephen G.
DOI/Identification number: 10.22024/UniKent/01.02.94176
Additional information: This thesis has been digitised by EThOS, the British Library digitisation service, for purposes of preservation and dissemination. It was uploaded to KAR on 25 April 2022 in order to hold its content and record within University of Kent systems. It is available Open Access using a Creative Commons Attribution, Non-commercial, No Derivatives ( licence so that the thesis and its author, can benefit from opportunities for increased readership and citation. This was done in line with University of Kent policies ( If you feel that your rights are compromised by open access to this thesis, or if you would like more information about its availability, please contact us at and we will seriously consider your claim under the terms of our Take-Down Policy (
Uncontrolled keywords: Flexible, Markov, Bayesian, statistics, statistical models
Subjects: Q Science > QA Mathematics (inc Computing science)
Divisions: Divisions > Division of Computing, Engineering and Mathematical Sciences > School of Mathematics, Statistics and Actuarial Science
SWORD Depositor: SWORD Copy
Depositing User: SWORD Copy
Date Deposited: 22 Sep 2022 09:03 UTC
Last Modified: 20 Nov 2023 14:45 UTC
Resource URI: (The current URI for this page, for reference purposes)

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