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Title: On a quasi-stationary approach to Bayesian computation, with application to tall data
Author: Kumar, Divakar
Awarding Body: University of Warwick
Current Institution: University of Warwick
Date of Award: 2018
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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.
Supervisor: Roberts, Gareth O. ; Pollock, Murray Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available
Keywords: QA Mathematics ; QC Physics