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Activity Number: 463
Type: Invited
Date/Time: Wednesday, August 12, 2015 : 8:30 AM to 10:20 AM
Sponsor: Section on Bayesian Statistical Science
Abstract #314522 View Presentation
Title: High-Dimensional MCMC Output Analysis
Author(s): Galin Jones* and Dootika Vats and James M. Flegal
Companies: University of Minnesota and University of Minnesota and UC Riverside
Keywords: Monte Carlo ; Markov chain ; standard error ; batch means ; Bayesian computation
Abstract:

We consider calculating a Monte Carlo standard error (MCSE) when the the number of quantities being estimated via MCMC is large. In particular, we base the MCSE on an estimate of the covariance matrix of an asymptotic multivariate normal distribution We consider spectral and batch means methods for estimating this matrix and establish strong consistency of the resulting estimators. Conditions for convergence of the eigenvalues of the batch means and spectral estimators is also addressed. Using these theoretical results we develop rigorous stopping rules for terminating the simulation effort based on both fixed-width and relative fixed-width methods. Finally, we consider the finite sample properties of the methods in several examples and discuss possible extensions. This is joint work with James Flegal and Dootika Vats.


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