##############################################
R code to perform the analysis by the MCMC method using JAGS software
##############################################
#MCMC setting
n.chains<-3
n.iter<-50000
n.burnin<-10000
n.thin<-20
nmcmc<-n.chains*(n.iter-n.burnin)/n.thin

library("jagsUI")
############
##a=1: Adult / a=2: Juvenile
model_poigam <- list(list(), list())
for(a in 1:2){
  model.file <- "C:/Users/yuich/Dropbox/master thesis/script\\RESTmodel.txt" #set pass of the file
  sink(model.file)
  cat("model
      {
      for(t in 1:n.period){  
        #Estimating staying time in the REST model
        for(i in 1:Nstay[t]){  
          stay[i, t] ~ dlnorm(mm[t], tau[t])  #log-normal distribution is used to estimate staying time.
        }
        mstay[t] <- pow(2.718282,(mm[t]+1/tau[t]/2))
      
        #Estimating density at each camera in REST model
        for(i in 1:Ncam){
          pcy[i, t] ~ dpois(mu.y[i, t])
          y[i, t] ~ dpois(mu.y[i, t])
          mu.y[i, t] <- mu[i, t]*u[i, t]
          log(mu[i, t]) <- log(S)+log(eff[i, t])+log(rho[i, t])+log(actpro[t])-mm[t]-1/(2*tau[t])
          rho[i, t] <- exp(coeffs[5, t]+ 
          coeffs[1, t]*pc1[i]+ 
          coeffs[2, t]*pc2[i]+
          coeffs[3, t]*pc3[i]+
          coeffs[4, t]*pc4[i]) #Landscape variables are used to estimate local density(=rho).
          u[i, t] ~ dgamma(alpha,alpha)
        }

        #Prior distributions
        mm[t] ~ dgamma(0.1,0.1)
        tau[t]~ dgamma(0.1,0.1)
        r[t] ~ dgamma(0.1,0.01)
        for(i in 1:4){
          coeffs[i, t] ~ dunif(-3, 3) 
        }
      
        #Density estimate in 1km² grid cell
        for(m in 1:Nmesh){
          d_mesh[m, t] <- exp(coeffs[5, t]+
          coeffs[1, t]*pc1_m[m]+
          coeffs[2, t]*pc2_m[m]+
          coeffs[3, t]*pc3_m[m]+
          coeffs[4, t]*pc4_m[m])
        }
        #Estimating the density in management-units and the catchability 
        for(u in 1:Nunit){
          d_unit[u, t] <- inprod(d_mesh[1:Nmesh, t], envwgt[u, 1:Nmesh]) #Estimating the density in management-units
          cap_b[u, t] ~ dpois(lambda_b[u, t])
          lambda_b[u, t] <- catch_b[t]*d_unit[u, t] *eff_trap_b[u, t] #Estimating the catchability
          cap_s[u, t] ~ dpois(lambda_s[u, t])
          lambda_s[u, t] <- catch_s[t]*d_unit[u, t] *eff_trap_s[u, t]
        }
      #prior distribution
        catch_b[t] ~ dunif(0, 1) #Catchability of box traps
        catch_s[t] ~ dunif(0, 1) #Catchability of snare traps
      }

      #Prior distribution
      for(t in 2:n.period){
        coeffs[5, t] ~ dnorm(coeffs[5, t-1], tau_c)T(0, 5)
      }
      coeffs[5, 1] ~ dunif(0, 5)
      alpha <- 1/invalpha
      invalpha ~ dgamma(0.1, 0.1)
      }
      ")
sink()

datalist <- 
  list(y=RESTDATA$y[[a]], S=RESTDATA$S, eff=RESTDATA$eff[[a]], stay=RESTDATA$stay[[a]], Nstay=RESTDATA$nstay[[a]], 
       Ncam=RESTDATA$Ncam, n.period=RESTDATA$n.period[[a]], actpro=RESTDATA$actpro[[a]],
       u=matrix(1, RESTDATA$Ncam, RESTDATA$n.period[[a]]), invalpha=10,
       pc1=RESTDATA$pc_500mbuffer_agg[,1], pc2=RESTDATA$pc_500mbuffer_agg[,2], pc3=RESTDATA$pc_500mbuffer_agg[,3], pc4=RESTDATA$pc_500mbuffer_agg[,4],
       pc1_m=RESTDATA$pc_1kmmesh[,1], pc2_m=RESTDATA$pc_1kmmesh[,2], pc3_m=RESTDATA$pc_1kmmesh[,3], pc4_m=RESTDATA$pc_1kmmesh[,4],
       Nunit=RESTDATA$Nunit, Nmesh=RESTDATA$Nmesh, envwgt=RESTDATA$env_wgt,
       cap_b=RESTDATA$cap_b[[a]], eff_trap_b=RESTDATA$eff_trap_b[[a]],
       cap_s=RESTDATA$cap_s[[a]], eff_trap_s=RESTDATA$eff_trap_s[[a]],
       tau_c=1/4
  )
#####DATA DESCRIPTION
#y: the number of passage through the focal area
#S: size of the focal area
#eff: camera-trapping effort
#stay: staying time data
#Nstay: the number of staying time data
#Ncam: the total number of cameras
#n.period: the number of months
#actpro: activity proportion
#invalpha: dispersion parameter
#pc: landscape variables
#Nunit: the number of management units
#Nmesh: the number of 1km cells
#envwgt: proportion of habitat area at each mesh in each management unit
#cap: the number of captured individuals
#eff_trap: trapping efforts of harvest records
#####################

inits <- function(){
  list(mm=rep(1.5, RESTDATA$n.period[[a]]), tau=rep(1, RESTDATA$n.period[[a]]),
       coeffs=rbind(matrix(0, 4, RESTDATA$n.period[[a]]), rep(2, RESTDATA$n.period[[a]])),
       r=rep(0.1, RESTDATA$n.period[[a]]),
       catch_b=rep(0.1, RESTDATA$n.period[[a]]), catch_s=rep(0.1, RESTDATA$n.period[[a]])
  )
}
parameters <- c("rho","mstay","coeffs", "d_unit", "catch_b", "catch_s")

model_poigam[[a]] <- jags(datalist, inits,parameters, model.file,
                     n.chains=n.chains, n.iter=n.iter, n.burnin=n.burnin, n.thin=n.thin)
}