Independence Metropolis-Hastings Algorithm

IndepMH computes random draws of parameters using a specified proposal distribution.

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

Arguments

data	data required for the posterior distribution
propob	a list of mean and variance-covariance of the normal proposal distribution; defaults to NULL. 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 indepMHgen
iter	number of random draws desired (default: 1500)
burn	burn-in period for the MH algorithm (default: 500)
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 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 pardraws and the acceptance rate

Examples

y = indicat(faithful$waiting,70)
x = scale(cbind(faithful$eruptions,faithful$eruptions^2))
data = data.frame(y,x); propob<- lapl_aprx(y,x)
IndepMH_n<- IndepMH(data=data,propob,iter = 102, burn = 2) # prior="Normal"
#> IndepMH algorithm successful. Acceptance ratio =  0.3921569  
IndepMH_u<- IndepMH(data=data,propob,prior="Uniform",iter = 102, burn = 2) # prior="Uniform"
#> IndepMH algorithm successful. Acceptance ratio =  0.4607843  
par(mfrow=c(3,1));invisible(apply(IndepMH_n$Matpram,2,function(x)plot(density(x))))
invisible(apply(IndepMH_u$Matpram,2,function(x)plot(density(x))));par(mfrow=c(1,1))