# code to play with a Poisson model with a gamma prior
# via simulations

# prior parameters
alpha<-1  
beta<-1

# the data
x<-20
t<-10

# bandwidth for the density estimate
bw<- 0.5

dPrior <- density(rgamma(100,alpha,beta),bw=bw, from=0)
dPosterior <- density(rgamma(100,alpha+x,beta+t),bw=bw, from=0)

plot(dPrior,xlim=c(-1,10),ylim=c(0,1.2),main="poisson model, gamma prior",col=1)
par(new=TRUE)
plot(dPosterior,xlim=c(-1,10),ylim=c(0,1.2),main="poisson model, gamma prior",col=2)
legend(6,1,c("prior","posterior"),lwd=c(1,1),col=c(1,2))