Data:
list(M = 5000)

node mean sd MC error 2.5% median 97.5% start sample
N 1274.0 1295.0 10.86 109.0 722.0 4579.0 1001 10000

Jeffreys prior...
model {
Y N
for (j in 1:M) {
p[j] <- step(N - j + 0.01)/N
}
N ~ dcat(p.jeffreys[])
for (j in 1:5000) {
reciprocal[j] <- 1/j
p.jeffreys[j] <- reciprocal[j]/sum.recip
}
sum.recip <- sum(reciprocal[])
}

Data:</span
list(M = 5000)

node mean sd MC error 2.5% median 97.5% start sample
N 408.7 600.4 4.99 102.0 197.0 2372.0 1001 10000

Larger upper bound, M...</span
model {
Y N
for (j in 1:M) {
p[j] <- step(N - j + 0.01)/N
}
N ~ dcat(p.jeffreys[])
for (j in 1:15000) {
reciprocal[j] <- 1/j
p.jeffreys[j] <- reciprocal[j]/sum.recip
}
sum.recip <- sum(reciprocal[])
}

Data:</span
list(M = 15000 )