Hi all,
I'm trying to write a function to implement a Metropolis-within-Gibbs
algorithm for two parameters.I'm including a naive version here so as to be
able to spot the error I got. So I first generate the vectors, X and R,
that will help to start the algorithm using (for example):
n=8; m=5; p=0.1; t=0.9 ; JH=10;
R <- numeric(m)
W <- numeric(m)
V <- numeric(m)
U <- numeric(m)
X <- numeric(m)
Bay.alpha<- numeric (JH)
Bay.beta<- numeric (JH)
Bay.Surv <- numeric (JH)
hyp=c(3,15,6,22.5)
theta<-c(0.2,2)
alpha.curr<-theta[1]
beta.curr<- theta[2]
R[1]<-rbinom(1, n-m, p)
for (i in 2:m-1) {
R[i]<-rbinom(1,n-m-sum(R[1:i-1]),p)
}
R[m]<-n-m-sum(R[1:m-1])
W<-runif(m, min = 0, max = 1)
for (i in 1:m){
V[i]<-W[i]^(1/(i+sum(R[(m-i+1):m])))
}
for (i in 1:m){
U[i]<- 1- prod(V[(m-i+1):m])
}
for (i in 1:m){
X[i]<- ((-1/theta[1])*log(1-U[i]))^(1/theta[2])
}
Then, I defined three functions 1- alpha.update() for updating alpha (Gibbs
step) 2- bettarg(), for the target distribution of beta 3- beta.update()
for updating beta using a Metropolis Hastings technique.
alpha.update=function(X, R, alpha.curr, beta.curr ,m, hyp)
{
o<-numeric(m)
for (i in 1:m) {
o[i]<- (1+R[i])*((X[i])^(beta.curr))
}
sh<-sum(o) + hyp[2] + (hyp[4]* beta.curr)
rg<-rgamma(1, shape= m+hyp[1]+hyp[3] , rate = sh )
return(rg)
}
bettarg<- function(X, R, alpha.curr, beta.curr ,m, hyp)
{
o<-numeric(m)
for (i in 1:m) {
o[i]<- (1+R[i])*((X[i])^( beta.curr))
}
bt<- beta.curr ^(m+hyp[3]-1) * prod((X)^( beta.curr -1)) *
exp(-1*alpha.curr *(sum(o) + (hyp[4]* beta.curr)))
return(bt)
}
beta.update<- function (X, R, alpha.curr, beta.curr ,m, hyp, cand.sd)
{
beta.cand<- rnorm(1, mean = beta.curr, sd = cand.sd)
AB<- bettarg (X, R, alpha.curr, beta.curr = beta.cand ,m, hyp)
CD<- bettarg (X, R, alpha.curr, beta.curr ,m, hyp)
accept.prob <- AB/CD
if (runif(1) <= accept.prob)
beta.cand
else beta.curr
}
Then I started a tiny chain using ten iterations but got this ERROR:
for (k in 1:JH)
{
alpha.curr<- alpha.update(X, R, alpha.curr, beta.curr ,m, hyp)
Bay.alpha[k]<-alpha.curr
beta.curr<- beta.update (X, R, alpha.curr, beta.curr ,m, hyp, cand.sd=2)
Bay.beta[k]<- beta.curr
Bay.Surv [k]<- exp (-1*Bay.alpha[k] * (t)^Bay.beta[k])
}
Error in if (runif(1) <= accept.prob) beta.cand else beta.curr :
missing value where TRUE/FALSE needed
In addition: Warning message:
In rgamma(1, shape = m + hyp[1] + hyp[3], rate = sh) : NAs produced
I ran the code several times for only one iteration but everything was fine
with no errors or warnings, so I don't know from where does the missing
value/ NA come from?
In addition, I want to calculate the acceptance rate for the
Metropolis-Hastings step, is this possible?
Any help would be appreciated.
Thanks,
Maram Salem
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