Kumar, Divakar (2018) On a quasi-stationary approach to bayesian computation, with application to tall data. PhD thesis, University of Warwick.

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Abstract

Markov Chain Monte Carlo (MCMC) techniques have traditionally been used in a Bayesian inference to simulate from an intractable distribution of parameters. However, the current age of Big data demands more scalable and robust algorithms for the inferences to be computationally feasible. Existing MCMC-based scalable methodologies often uses discretization within their construction and hence they are inexact. A newly proposed field of the Quasi-Stationary Monte Carlo (QSMC) methodology has paved the way for a scalable Bayesian inference in a Big data setting, at the same time, its exactness remains intact. Contrary to MCMC, a QSMC method constructs a Markov process whose quasi-stationary distribution is given by the target. A recently proposed QSMC method called the Scalable Langevin Exact (ScaLE) algorithm has been constructed by suitably combining the exact method of diffusion, the Sequential Monte Carlo methodology for quasi-stationarity and sub-sampling ideas to produce a sub-linear cost in a Big data setting. This thesis uses the mathematical foundations of the ScaLE methodology as a building block and carefully combines a recently proposed regenerative mechanism for quasistationarity to produce a new class of QSMC algorithm called the Regenerating ScaLE (ReScaLE). Further, it provides various empirical results towards the sublinear scalability of ReScaLE and illustrates its application to a real world big data problem where a traditional MCMC method is likely to suffer from a huge computational cost. This work takes further inroads into some current limitations faced by ReScaLE and proposes various algorithmic modifications for targeting quasistationarity. The empirical evidences suggests that these modifications reduce the computational cost and improve the speed of convergence.

Item Type:	Thesis or Dissertation (PhD)
Subjects:	Q Science > QA Mathematics Q Science > QC Physics
Library of Congress Subject Headings (LCSH):	Quasi-uniform spaces, Bayesian statistical decision theory, Big data, Markov processes, SVG (Document markup language)
Official Date:	September 2018
Dates:	Date Event September 2018 Published
Institution:	University of Warwick
Theses Department:	Department of Statistics
Thesis Type:	PhD
Publication Status:	Unpublished
Sponsors:	Roberts, Gareth O.; Pollock, Murray
Format of File:	pdf
Extent:	xvii, 173 leaves: illustration, charts
Language:	eng

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