#Beverton-Holt stock-recruitment model of Alaskan pink salmon
#Data are from Quinn and Deriso, p. 105
#Uses reference prior of Millar (CJFAS, 2002)
#############################################################

model Ricker_Pink;
{
######Create y variable, log(R/S)#####
for (i in 1:N) { y[i] <- log(R[i]/S[i]) }

######Model the y variable######
for (i in 1:N) { 
  mean.y[i] <- alpha - b*S[i];
  y[i] ~ dnorm(mean.y[i],prec.y);
}

#####Deviance calculations####
for(i in 1:N) 
 { l[i] <- -0.5*log(2*3.141593)+0.5*log(prec.y)-0.5*pow((y[i]-mean.y[i]),2)*prec.y }
dev <- 2*sum(l[])

######Priors#####
alpha ~ dnorm(0,0.00001)
b ~ dnorm(0,0.00001)
prec.y ~ dgamma(0.001,0.001);
}

###Data###
list(N=30,
 S=c(1418,2835,1957,4033,2750,2891,3098,2001,3215,2443,2561,2834,2859,2295,
     1880,1579,1373,4183,2984,5059,2669,3949,4219,4290,3976,8799,2856,4289,
     2892,4577),
 R=c(2446,14934,10031,8050,7884,4430,13086,6051,7801,5846,6101,4175,2541,2194,
     1512,6704,5742,8809,4062,9277,15452,10343,8950,30011,3999,9917,4906,18215,
     9461,23359))
)
###Inits###
list(alpha=1,b=1,prec.y=1)