MH {calibrator} R Documentation

## Very basic implementation of the Metropolis-Hastings algorithm

### Description

Very basic implementation of the Metropolis-Hastings algorithm using a multivariate Gaussian proposal distribution. Useful for sampling from p.eqn8.supp().

### Usage

MH(n, start, sigma, pi)


### Arguments

 n Number of samples to take start Start value sigma Variance matrix for kernel pi Functional proportional to the desired sampling pdf

### Details

This is a basic implementation. The proposal distribution~q(X|Y) is q(\cdot|X)=N(X,\sigma^2)

### Value

Returns a matrix whose rows are samples from \pi(). Note that the first few rows will be “burn-in”, so should be ignored

### Note

This function is a little slow because it is not vectorized.

### Author(s)

Robin K. S. Hankin

### References

• W. R. Gilks et al 1996. Markov Chain Monte Carlo in practice. Chapman and Hall, 1996. ISBN 0-412-05551-1

• N. Metropolis and others 1953. Equation of state calculations by fast computing machines. The Journal of Chemical Physics, volume 21, number 6, pages 1087-1092

p.eqn8.supp

### Examples

# First, a bivariate Gaussian:
A <- diag(3) + 0.7
x.gauss <- MH(n=1000, start=c(0,0,0),sigma=diag(3),pi=pi.gaussian)
cov(x.gauss)/solve(A) # Should be a matrix of 1s.

# Now something a bit weirder:
pi.triangle <- function(x){
1*as.numeric( (abs(x[1])<1.0) & (abs(x[2])<1.0) ) +
5*as.numeric( (abs(x[1])<0.5) & (abs(x[2])<0.5) ) *
as.numeric(x[1]>x[2])
}
x.tri <- MH(n=100,start=c(0,0),sigma=diag(2),pi=pi.triangle)
plot(x.tri,main="Try with a higher n")

# Now a Gaussian mixture model:
pi.2gauss <- function(x){