### Use of the Bolstad R library

# Bayesian inference for the Poisson mean lambda, one sample of size n,
# conjugate Gamma prior

library(Bolstad)

help(poisgamp)  # gamma prior

# poisgamp(y, r, v, ret = FALSE)

#######################################################################
# simplest call with an observation of 4 and a gamma(1,1), 
# i.e. an exponential prior on the lambda

poisgamp(4,1,1)

#######################################################################
##  Same as the previous example but a gamma(10,1) prior

poisgamp(4,10,1)

#######################################################################
##  Same as the previous example but an improper gamma(1,0) prior

poisgamp(4,1,0)

#######################################################################
## A random sample of 50 observations from a Poisson distribution with
## parameter lambda = 3 and  gamma(6,3) prior

y = rpois(50,3)
poisgamp(y,6,3)

#######################################################################
## In this example we have a random sample from a Poisson distribution
## with an unknown mean. We will use a gamma(6,3) prior to obtain the
## posterior gamma distribution, and use the R function qgamma to get a
## 95% credible interval for mu = lambda

y = c(3,4,4,3,3,4,2,3,1,7)
results = poisgamp(y,6,3)
ci = qgamma(c(0.025,0.975),results$r, results$v)
cat(paste("95% credible interval for mu: [",round(ci[1],3), ",", round(ci[2],3)),"]\n")