/
3-state-space-models.R
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3-state-space-models.R
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# state-space models
n.years=25
N1 <-30
mean.lambda<-1.02
sigma2.lambda<-0.02 # process varitation
sigma2.y<-20 #observation error
y<-rep(NA, n.years)
N<-rep(NA, n.years)
N[1]<-N1
lambda<-rnorm(n.years-1, mean.lambda, sqrt(sigma2.lambda))
for (t in 1:(n.years-1)) {
N[t+1]<-N[t]*lambda[t]
}
for (t in 1:n.years) {
y[t]<-rnorm(1, N[t], sqrt(sigma2.y))
}
y
sink('ssm.jags')
cat("
model {
# Priors
N.est[1] ~ dunif(0, 500) # intital population size
mean.lambda ~ dunif(0, 5)
sigma.proc ~ dunif(0, 10)
sigma2.proc<-sigma.proc*sigma.proc
tau.proc<-pow(sigma.proc, -2)
sigma.obs ~ dunif(0,100)
sigma2.obs<-sigma.obs*sigma.obs
tau.obs<-pow(sigma.obs, -2)
# Likelihood
# State process
for (t in 1:(T-1)) {
lambda[t] ~ dnorm(mean.lambda, tau.proc)
N.est[t+1]<- N.est[t]*lambda[t]
} #t
# Observation process
for (t in 1:T) {
y[t] ~ dnorm(N.est[t], tau.obs)
} #t
}
", fill=TRUE)
sink()
jags.data<-list(y=y, T=n.years)
inits<-function() list(sigma.proc=runif(1, 0, 1), mean.lambda=runif(1, 0.1, 2),
sigma.obs=runif(1,0,10), N.est=c(runif(1, 20, 40), rep(NA, n.years-1)))
parameters<-c("lambda", "mean.lambda", "sigma2.obs", "sigma2.proc", "N.est")
# MCMC settings
ni <- 25000
nt <- 3
nb <- 10000
nc <- 3
# Call JAGS from R (BRT <1 min)
ssm <- jags(jags.data, inits, parameters, "ssm.jags", n.chains = nc, n.thin = nt, n.iter = ni, n.burnin = nb)
n.years=50
N1<-30
Snow_accumulation<-runif(n.years-1, 0.2, 5)
lambda<- 0.79 + 0.1*Snow_accumulation
sigma2.y<-20
y<-rep(NA, n.years)
N<-rep(NA, n.years)
N[1]<-N1
for (t in 1:(n.years-1)) {
N[t+1]<-N[t]*lambda[t]
}
for (t in 1:n.years) {
y[t]<-rnorm(1, N[t], sqrt(sigma2.y))
}
plot(N, type='l')
plot(y, type='l')
sink('ssm.jags')
cat("
model {
# Priors
N.est[1] ~ dunif(0, 500) # intital population size
a~dunif(-1,1)
b~dunif(-1,1)
sigma.obs ~ dunif(0,100)
sigma2.obs<-sigma.obs*sigma.obs
tau.obs<-pow(sigma.obs, -2)
# Likelihood
# State process
for (t in 1:(T-1)) {
lambda[t] <- a + b* Snow_accumulation[t]
N.est[t+1]<- N.est[t]*lambda[t]
} #t
# Observation process
for (t in 1:T) {
y[t] ~ dnorm(N.est[t], tau.obs)
} #t
}
", fill=TRUE)
sink()
y[10]<-NA
jags.data<-list(y=y, T=n.years, Snow_accumulation=Snow_accumulation)
inits<-function() list( a=runif(1, -1,1), b=runif(1, -1,1),
sigma.obs=runif(1,0,10), N.est=c(runif(1, 20, 40), rep(NA, n.years-1)))
parameters<-c("a", "b" ,"sigma2.obs", "N.est")
# MCMC settings
ni <- 50000
nt <- 3
nb <- 25000
nc <- 3
# Call JAGS from R (BRT <1 min)
ssm <- jags(jags.data, inits, parameters, "ssm.jags", n.chains = nc, n.thin = nt, n.iter = ni, n.burnin = nb)
ssm