stableGR-package: A Stable Gelman-Rubin Diagnostic for Markov Chain Monte Carlo

Description Details Author(s) References Examples

Description

Practitioners of Bayesian statistics often use Markov chain Monte Carlo (MCMC) samplers to sample from a posterior distribution. This package determines whether the MCMC sample is large enough to yield reliable estimates of the target distribution. In particular, this calculates a Gelman-Rubin convergence diagnostic using stable and consistent estimators of Monte Carlo variance. Additionally, this uses the connection between an MCMC sample's effective sample size and the Gelman-Rubin diagnostic to produce a threshold for terminating MCMC simulation. Finally, this informs the user whether enough samples have been collected and (if necessary) estimates the number of samples needed for a desired level of accuracy. The theory underlying these methods can be found in "Revisiting the Gelman-Rubin Diagnostic" by Vats and Knudson (2018) <arXiv:1812:09384>.

Details

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Practitioners of Bayesian statistics often use Markov chain Monte Carlo (MCMC) samplers to sample from a posterior distribution. This package determines whether the MCMC sample is large enough to yield reliable estimates of the target distribution. In particular, this calculates a Gelman-Rubin convergence diagnostic using stable and consistent estimators of Monte Carlo variance. Additionally, this uses the connection between an MCMC sample's effective sample size and the Gelman-Rubin diagnostic to produce a threshold for terminating MCMC simulation. Finally, this informs the user whether enough samples have been collected and (if necessary) estimates the number of samples needed for a desired level of accuracy. The theory underlying these methods can be found in "Revisiting the Gelman-Rubin Diagnostic" by Vats and Knudson (2018) <arXiv:1812:09384>.

This package is unique in a few ways. First, it uses stable variance estimators to calculate a stabilized Gelman-Rubin statistic. Second, it leverages the connection between effective sample size and the potential scale reduction factor (PSRF). Third, this diagnostic can be used whether MCMC samples were created from a single chain or multiple chains.

The main functions in the package are stable.GR, n.eff, and target.psrf. stable.GR returns the univariate PSRF, the multivariate PSRF, and the estimated effective sample size. n.eff returns informs the user whether sufficient MCMC samples have been collected; if not, n.eff also returns the estimated target sample size target.psrf creates a termination threshold for stable.GR; MCMC sampling can terminate when the MCMC samples' psrf is smaller than the value returned by target.psrf.

Author(s)

Christina Knudson [aut, cre], Dootika Vats [aut]

Maintainer: Christina Knudson <knud8583@stthomas.edu>

References

Vats, D. and Knudson, C. Revisiting the Gelman-Rubin Diagnostic. arXiv:1812.09384.

Vats, D. and Flegal, J. Lugsail lag windows and their application to MCMC. arXiv: 1809.04541.

Flegal, J. M. and Jones, G. L. (2010) Batch means and spectral variance estimators in Markov chain Monte Carlo. The Annals of Statistics, 38, 1034–1070.

Gelman, A and Rubin, DB (1992) Inference from iterative simulation using multiple sequences, Statistical Science, 7, 457-511.

Brooks, SP. and Gelman, A. (1998) General methods for monitoring convergence of iterative simulations. Journal of Computational and Graphical Statistics, 7, 434-455.

Examples

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library(stableGR)
set.seed(100)
p <- 2
n <- 100 # For real problems, use a MUCH larger n.

sig.mat = matrix(c(1, .8, .8, 1), ncol = 2, nrow = 2)

# Making 3 chains
chain1 <- mvn.gibbs(N = n, p = p, mu = rep(1,p), sigma = sig.mat)
chain2 <- mvn.gibbs(N = n, p = p, mu = rep(1,p), sigma = sig.mat)
chain3 <- mvn.gibbs(N = n, p = p, mu = rep(1,p), sigma = sig.mat)

# find GR diagnostic using all three chains
x <- list(chain1, chain2, chain3)
stable.GR(x) 

stableGR documentation built on Oct. 11, 2021, 9:08 a.m.