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

model BH_Pink;
{
#Convert data to millions
for(i in 1:N) { s[i] <- S[i]/1000 }
######Jeffreys prior#####
#Zero's trick for reference prior on b
#NOTE 1: Constraining to [0,1] to reproduce shape of Fig. 2 of Millar (2002)
#NOTE 2: Fig. 2 of Millar (2002) is not normalized - so y-axis differs from WinBUGS density plot y-axis

b~dunif(0,1)
for (i in 1:N) {why[i] <- s[i]/(1+b*s[i]) }
prior.b <- sd(why[]);
phi <- -log(prior.b)
zero <- 0;
zero ~ dpois(phi);
}

###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))
)
###Inits###
list(b=0.5)