model {
for (i in 1:N) {
y[i] ~ dpois(m[i])
m[i] <- group[i]*mu # mean is 0 if group is 0
group[i] ~ dbern(p)
}
# proportion of claims that could be positive
p ~ dunif(0,1)
mu ~ dgamma(0.5, 0.0001) # approximate Jeffreys prior
}

Data:
list(N=35,
y=c(0,0,0,0,0,0,0,0,0,0,
1,1,1,1,1,2,2,2,2,2,
2,2,2,2,2,3,3,3,3,3,
3,3,4,4,5))
   
   node   mean   sd   MC error   2.5%   median   97.5%   start   sample
   mu   2.066   0.3145   0.004767   1.497   2.047   2.733   1001   10000
   p   0.8102   0.08947   0.001798   0.6252   0.8143   0.9701   1001   10000