## Calculate the Gelman Rubin statistic

### Description

Calculate the Gelman Rubin statistic

### Usage

```GelmanRubin(theta)
GR(theta)
```

### Arguments

 `theta` A matrix containing samples from at least two chains on a parameter theta. Each chain should 2n iterations. The last n iterations will be used to calculate the statistic

### Value

A list containing n, the between chain variance B, the within chain variance W, the estimated variance of the parameter vHat, and the Gelman Rubin statistic R = √{vHat/W}

### References

Gelman, A. and Rubin, D.B. (1992) 'Inference from iterative simulations using multiple sequences with discussion.' Statistical Science 8, pp. 457-511

### Examples

```## take four chains sampling from a normal mixture density
theta0 <- c(0,1)
theta1 <- c(3,2)
p <- 0.6
candidate <- c(0, 3)

v1 <- normMixMH(theta0, theta1, p, candidate, steps = 200)
v2 <- normMixMH(theta0, theta1, p, candidate, steps = 200)
v3 <- normMixMH(theta0, theta1, p, candidate, steps = 200)
v4 <- normMixMH(theta0, theta1, p, candidate, steps = 200)

theta<-cbind(v1,v2,v3,v4)
GelmanRubin(theta)
```