conv.diag {BANOVA}

Function to display the convergence diagnostics

Description

The Geweke diagnostic and the Heidelberg and Welch diagnostic are reported. These two convergence diagnostics are calculated based on only a single MCMC chain. Both diagnostics require a single chain and may be applied with any MCMC method. The functions geweke.diag, heidel.diag in coda package is used to compute this diagnostic.

Geweke's convergence diagnostic is calculated by taking the difference between the means from the first n_A iterations and the last n_B iterations. If the ratios n_A/n and n_B/n are fixed and nA +nB < n, then by the central limit theorem, the distribution of this diagnostic approaches a standard normal as n tends to infinity. In our package, n_A= .2*n and n_B= .5*n.

The Heidelberg and Welch diagnostic is based on a test statistic to accept or reject the null hypothesis that the Markov chain is from a stationary distribution. The present package reports the stationary test.The convergence test uses the Cramer-von Mises statistic to test for stationary. The test is successively applied on the chain. If the null hypothesis is rejected, the first 10% of the iterations are discarded and the stationarity test repeated. If the stationary test fails again, an additional 10% of the iterations are discarded and the test repeated again. The process continues until 50% of the iterations have been discarded and the test still rejects. In our package, eps = 0.1, pvalue = 0.05 are used as parameters of the function heidel.diag.

Usage

conv.diag(x)

Arguments

x

the object from BANOVA.*

Value

conv.diag returns a list of two diagnostics:

sol_geweke

The Geweke diagnostic

sol_heidel

The Heidelberg and Welch diagnostic

References

Plummer, M., Best, N., Cowles, K. and Vines K. (2006) CODA: Convergence Diagnosis and Output Analysis for MCMC, R News, Vol 6, pp. 7-11.

Geweke, J. Evaluating the accuracy of sampling-based approaches to calculating posterior moments, In Bayesian Statistics 4 (ed JM Bernado, JO Berger, AP Dawid and AFM Smith). Clarendon Press, Oxford, UK.

Heidelberger, P. and Welch, PD. (1981) A spectral method for confidence interval generation and run length control in simulations, Comm. ACM. Vol. 24, No.4, pp. 233-245.

Heidelberger, P. and Welch, PD. (1983) Simulation run length control in the presence of an initial transient, Opns Res., Vol.31, No.6, pp. 1109-44.

Schruben, LW. (1982) Detecting initialization bias in simulation experiments, Opns. Res., Vol. 30, No.3, pp. 569-590.

Examples

data(goalstudy)

library(rstan)
res1 <- BANOVA.run(bid~progress*prodvar, model_name = "Normal", data = goalstudy, 
id = 'id', iter = 100, thin = 1) 
conv.diag(res1)
# might need pairs() to confirm the convergence