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Matias Quiroz

-- doctoral thesis --

Bayesian Inference in Large Data Problems

In the last decade or so, there has been a dramatic increase in storage facilities and the possibility of processing huge amounts of data. This has made large high-quality data sets widely accessible for practitioners. This technology innovation seriously challenges traditional modeling and inference methodology.

This thesis is devoted to developing inference and modeling tools to handle large data sets. Four included papers treat various important aspects of this topic, with a special emphasis on Bayesian inference by scalable Markov Chain Monte Carlo (MCMC) methods.

In the first paper, we propose a novel mixture-of-experts model for longitudinal data. The model and inference methodology allows for manageable computations with a large number of subjects. The model dramatically improves the out-of-sample predictive density forecasts compared to existing models.

The second paper aims at developing a scalable MCMC algorithm. Ideas from the survey sampling literature are used to estimate the likelihood on a random subset of data. The likelihood estimate is used within the pseudomarginal MCMC framework and we develop a theoretical framework for such algorithms based on subsets of the data.

The third paper further develops the ideas introduced in the second paper. We introduce the difference estimator in this framework and modify the methods for estimating the likelihood on a random subset of data. This results in scalable inference for a wider class of models.

Finally, the fourth paper brings the survey sampling tools for estimating the likelihood developed in the thesis into the delayed acceptance MCMC framework. We compare to an existing approach in the literature and document promising results for our algorithm.

Keywords:Bayesian inference, Large data sets, Markov chain Monte Carlo, Survey sampling, Pseudo-marginal MCMC, Delayed acceptance MCMC

ISBN 978-91-7649-199-7

Download Summarising chapter -->>
Download paper I -->> Dynamic mixture-of-experts models for longitudinal and disrete-time survival data
Download paper II -->> Speeding up MCMC by efficient data subsampling
Download paper III -->> Scalable MCMC for large data problems using data subsampling and the difference estimator
Download paper IV -->> Speeding up MCMC by delayed acceptance and data subsampling