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Bayesian computation through geometric and variance reduction methods

Grant number: 16/21137-2
Support type:Regular Research Grants
Duration: February 01, 2017 - January 31, 2019
Field of knowledge:Physical Sciences and Mathematics - Probability and Statistics
Principal Investigator:Ricardo Sandes Ehlers
Grantee:Ricardo Sandes Ehlers
Home Institution: Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil

Abstract

This project aims at developing and apply computationally intensive methods which explore the geometry of the posterior distributions in the parameter spaces of statistical models under a Bayesian approach. We thus seek to improve the efficiency of MCMC methods in Bayesian computation since such strategies in general lead to convergence of the Markov chains with fewer iteration. These ideas will be combined with variance reduction techniques in Monte Carlo estimators. Since the computational costs per iteration involved are higher the cost-benefit will be investigated through simulation studies and real data analyses. We hope to provide empirical evidence that such methods are justified in practical applications so that the expected increased computational cost is compensated by a more efficient exploration of the posterior distribution. (AU)