Random Walk Metropolis-Hastings Algorithm

RWMH computes random draws of parameters using a specified proposal distribution. The default is the normal distribution

RWMH(data, propob = NULL, posterior = NULL, iter = 1500,
  burn = 500, vscale = 1.5, start = NULL, prior = "Normal",
  mu = 0, sig = 10)

Arguments

data	data required for the posterior distribution. First column is the outcome
propob	a list of mean and variance-covariance of the normal proposal distribution (default: NULL i.e. internally generated). Write list as propob=list(mode=mode,var=variance-covariance)
posterior	the posterior distribution. It is set to null in order to use the logit posterior. The user can specify log posterior as a function of parameters and data (pars,data). For a more flexible and generic implementation, use rwMHgen
iter	number of random draws desired
burn	burn-in period for the Random Walk MH algorithm
vscale	a positive value to scale up or down the variance-covariance matrix in the proposal distribution
start	starting values of parameters for the MH algorithm. It is automatically generated from the proposal distribution but the user can also specify.
prior	the prior distribution (default: "Normal", alternative: "Uniform")
mu	the mean of the normal prior distribution (default:0)
sig	the variance of the normal prior distribution (default:10)

Value

val a list of matrix of draws Matpram and the acceptance rate

Examples

y = indicat(faithful$waiting,70)
x = scale(cbind(faithful$eruptions,faithful$eruptions^2))
data = data.frame(y,x); propob<- lapl_aprx(y,x)
RWMHob_n<- RWMH(data=data,propob,iter = 102, burn = 2) # prior="Normal"
#> Random Walk MH algorithm successful. Acceptance ratio =  0.2843137  
RWMHob_u<- RWMH(data=data,propob,prior="Uniform",iter = 102, burn = 2)
#> Random Walk MH algorithm successful. Acceptance ratio =  0.372549  
par(mfrow=c(3,1));invisible(apply(RWMHob_n$Matpram,2,function(x)plot(density(x))))
invisible(apply(RWMHob_u$Matpram,2,function(x)plot(density(x))));par(mfrow=c(1,1))