bivnormMH {Bolstad2}

Metropolis Hastings sampling from a Bivariate Normal distribution

Description

This function uses the MetropolisHastings algorithm to draw a sample from a correlated bivariate normal target density using a random walk candidate and an independent candidate density respectively where we are drawing both parameters in a single draw. It can also use the blockwise Metropolis Hastings algorithm and Gibbs sampling respectively to draw a sample from the correlated bivariate normal target.

Usage

bivnormMH(rho, rho1 = 0.9, sigma = c(1.2, 1.2), steps = 1000, type = "ind")

Arguments

rho

the correlation coefficient for the bivariate normal

rho1

the correlation of the candidate distribution. Only used when type = 'ind'

sigma

the standard deviations of the marginal distributions of the independent candidate density. Only used when type = 'ind'

steps

the number of Metropolis Hastings steps

type

the type of candidate generation to use. Can be one of 'rw' = random walk, 'ind' = independent normals, 'gibbs' = Gibbs sampling or 'block' = blockwise. It is sufficient to use 'r','i','g', or 'b'

Value

returns a list which contains a data frame called targetSample with members x and y. These are the samples from the target density.

Examples

## independent chain
chain1.df=bivnormMH(0.9)$targetSample

## random walk chain
chain2.df=bivnormMH(0.9, type = 'r')$targetSample


## blockwise MH chain
chain3.df=bivnormMH(0.9, type = 'b')$targetSample

## Gibbs sampling chain
chain4.df=bivnormMH(0.9, type = 'g')$targetSample

oldPar = par(mfrow=c(2,2))
plot(y ~ x, type = 'l', chain1.df, main = 'Independent')
plot(y ~ x, type = 'l', chain2.df, main = 'Random Walk')
plot(y ~ x, type = 'l', chain3.df, main = 'Blockwise')
plot(y ~ x, type = 'l', chain4.df, main = 'Gibbs')
par(oldPar)