R: Gelfand's Convergence Diagnostic

Gelfand.Diagnostic {LaplacesDemon} | R Documentation

## Gelfand's Convergence Diagnostic

### Description

Gelfand et al. (1990) proposed a convergence diagnostic for Markov chains. The `Gelfand.Diagnostic` function is an interpretation of Gelfand's “thick felt-tip pen” MCMC convergence diagnostic. This diagnostic plots a series of kernel density plots at k intervals of cumulative samples. Given a vector of S samples from a marginal posterior distribution, theta, multiple kernel density lines are plotted together, where each includes samples from a different interval. It is assumed that `burnin` iterations have been discarded.

Gelfand et al. (1990) assert that convergence is violated when the plotted lines are farther apart than the width of a thick, felt-tip pen. This depends on the size of the plot, and, of course, the pen. The estimated width of a “thick felt-tip pen” is included as a black, vertical line. The pen in `Gelfand.Diagnostic` is included for historical reasons. This diagnostic requires numerous samples.

### Usage

    Gelfand.Diagnostic(x, k=3, pen=FALSE)

### Arguments

`x` | This required argument is a vector of marginal posterior samples, such as selected from the output of `LaplacesDemon`.
`k` | This argument specifies the number k of kernel density plots given cumulative intervals of samples. This argument defaults to k=3.
`pen` | Logical. This argument defaults to `pen=FALSE`. When `pen=TRUE`, the thick felt-tip pen is included as a black, vertical line.

### Value

The `Gelfand.Diagnostic` returns a plot.

### Author(s)

Statisticat, LLC. software@bayesian-inference.com

### References

Gelfand, A.E., Hills, S., Racine-Poon, A., and Smith, A.F.M. (1990). "Illustration of Bayesian Inference in Normal Data Models Using Gibbs Sampling". Journal of the American Statistical Association, 85, p. 972–985.

### See Also

`burnin` and `LaplacesDemon`.

### Examples

    library(LaplacesDemon)
    x <- rnorm(1000)
    Gelfand.Diagnostic(x)

[Package LaplacesDemon version 16.1.1 Index]