multivariate poisson hidden markov models for analysis of spatial ...

dens=matrix(0,nrow=T,ncol=N)
alpha=matrix(0,nrow=T,ncol=N)
beta=matrix(0,nrow=T,ncol=N)
scale=matrix(c(1,rep(0,T-1)),nrow=1,ncol=T)
ones=matrix(1,nrow=T,ncol=1)
####E-step, compute density values
dens=cbind(threep11,threep22,threep33)
####E-step, forward recursion and likelihood computation
##Use a uniform a priori probability for the initial state
#[Refer to equation (5.25) and (5.26)]
#The forward and backward variables
α ( i) = P[ y , y ,..., y , S = j]
and
#
j 1 2 n i
( i) = P[ y ,..., y | S = j]
(5.25)
# β
j i+
1 n i
#which yield the quantities of interest by
α
j() i β
j() i α
j() i β
j()
i
# uˆ j
() i = =
m
∑αl
( n)
α () i β () i
l
∑
j=
1
j
j
and
# vˆ
jk
( i)
=
P
jk
f ( y ; λ
i
∑
l
k
) α
j
( i −1)
β
k
( i)
. (5.26)
α ( n)
l
alpha[1,]=dens[1,]/N
for (t in 2:T){
alpha[t,]=(alpha[t-1,]%*%TRANS)*dens[t,]
#####Systematic scaling
scale[,t]=sum(alpha[t,])
alpha[t,]=alpha[t,]/scale[,t]
}
###compute likelihood
loglike[nit]