Geweke.Diagnostic {LaplacesDemon} R Documentation

## Geweke's Convergence Diagnostic

### Description

Geweke (1992) proposed a convergence diagnostic for Markov chains. This diagnostic is based on a test for equality of the means of the first and last part of a Markov chain (by default the first 10% and the last 50%). If the samples are drawn from a stationary distribution of the chain, then the two means are equal and Geweke's statistic has an asymptotically standard normal distribution.

The test statistic is a standard Z-score: the difference between the two sample means divided by its estimated standard error. The standard error is estimated from the spectral density at zero, and so takes into account any autocorrelation.

The Z-score is calculated under the assumption that the two parts of the chain are asymptotically independent.

The Geweke.Diagnostic is a univariate diagnostic that is usually applied to each marginal posterior distribution. A multivariate form is not included. By chance alone due to multiple independent tests, 5% of the marginal posterior distributions should appear non-stationary when stationarity exists. Assessing multivariate convergence is difficult.

### Usage

Geweke.Diagnostic(x)

### Arguments

 x This required argument is a vector or matrix of posterior samples, such as from the output of the LaplacesDemon function. Each column vector in a matrix is a chain to be assessed. A minimum of 100 samples are required.

### Details

The Geweke.Diagnostic is essentially the same as the geweke.diag function in the coda package, but programmed to accept a simple vector or matrix, so it does not require an mcmc object.

### Value

A vector is returned, in which each element is a Z-score for a test of equality that compares the means of the first and last parts of each chain supplied as x to Geweke.Diagnostic.

### References

Geweke, J. (1992). "Evaluating the Accuracy of Sampling-Based Approaches to Calculating Posterior Moments". In Bayesian Statistics 4 (ed JM Bernardo, JO Berger, AP Dawid, and AFM Smith). Clarendon Press, Oxford, UK.

burnin, is.stationary, and LaplacesDemon
library(LaplacesDemon)