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

α
j() i β
j() i α
j() i β
j()
i
# uj() i = P[ Si = j| Y= y]
= =
m m
α ( n) α ( i) β ( i)
∑
∑
l j j
l= 1 j=
1
(5.31)
#and then re-estimate the rates as follows:
n
j
∑uj()
i di
λˆ = ,
u () i
i=
1
#
j n
∑
i=
1
j
j = 1,..., m.
(5.32)
beta=alpha*beta
sumbeta=matrix(0,nrow=T,ncol=1,byrow=T)
for (r in 1:T){
sumbeta[r,]=sum(beta[r,])
}
sumbeta=sumbeta%*%oness
beta=beta/sumbeta
##Reestmate rates
#component 1
newdata1=cbind(x11,x21,x31,x141)
rate1=(t(beta[,1])%*%newdata1)/sum(beta[,1])
#component 2
newdata2=cbind(x12,x22,x32,x142)
rate2=(t(beta[,2])%*%newdata2)/sum(beta[,2])
#component 3
newdata3=cbind(x13,x23,x33,x143)
rate3=(t(beta[,3])%*%newdata3)/sum(beta[,3])
#Assign estimated parameters new variables
theta11