Description Details Author(s) References Examples

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>.

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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`

.

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

Maintainer: Christina Knudson <knud8583@stthomas.edu>

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.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 | ```
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)
``` |

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