psrf function

Calculates Potential Scale Reduction Factor (psrf), also called the Rhat statistic, from models fit via mh or hmc

Gelman and Rubin's diagnostic assesses the mix of multiple MCMC chain with different initial parameter values Values close to 1 indicate that the posterior simulation has sufficiently converged, while values above 1 indicate that additional samples may be necessary to ensure convergence. A general guideline suggests that values less than 1.05 are good, between 1.05 and 1.10 are ok, and above 1.10 have not converged well.

psrf(object, burnin, ...)

Arguments

• object: an object of class hmclearn, usually a result of a call to mh or hmc
• burnin: optional numeric parameter for the number of initial MCMC samples to omit from the summary
• ...: currently unused

Returns

Numeric vector of Rhat statistics for each parameter

Examples

# poisson regression example
set.seed(7363)
X <- cbind(1, matrix(rnorm(40), ncol=2))
betavals <- c(0.8, -0.5, 1.1)
lmu <- X %*% betavals
y <- sapply(exp(lmu), FUN = rpois, n=1)

f <- hmc(N = 1000,
          theta.init = rep(0, 3),
          epsilon = 0.01,
          L = 10,
          logPOSTERIOR = poisson_posterior,
          glogPOSTERIOR = g_poisson_posterior,
          varnames = paste0("beta", 0:2),
          param = list(y=y, X=X),
          parallel=FALSE, chains=2)

psrf(f, burnin=100)

References

Gelman, A. and Rubin, D. (1992) Inference from Iterative Simulation Using Multiple Sequences. Statistical Science 7(4) 457-472.

Gelman, A., et. al. (2013) Bayesian Data Analysis. Chapman and Hall/CRC.

Gabry, Jonah and Mahr, Tristan (2019). bayesplot: Plotting for Bayesian Models. https://mc-stan.org/bayesplot/