# Capitulo #2.
# Ejemplo p'agina 53 sobre la tasa de mortalidad por asma
# Ejemplo Modelo Poisson
##############################
# Previa \theta ~ Gamma(3,5)

theta.prior=rgamma(1000,3,scale=1/5)
summary(theta.prior)

#   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
#0.06614 0.35020 0.54710 0.60530 0.78610 2.15800 

#########
# D. a posteriori \theta ~ Gamma(6,7)
theta.posterior=rgamma(1000,6,scale=1/7)

summary(theta.posterior)

#   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
# 0.1642  0.6149  0.8183  0.8635  1.0650  2.5310 

length(theta.posterior[(theta.posterior>1)])/1000
#[1] 0.294

###########
# D. a posterior con mas datos \theta ~Gamma(33,25)

theta.posterior.2=rgamma(1000,33,scale=1/25)

summary(theta.posterior.2)
#   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
# 0.7007  1.1530  1.3090  1.3190  1.4680  2.0770 

length(theta.posterior.2[(theta.posterior.2>1)])/1000
# [1] 0.924

par(mfrow=c(1,3),bty='n')
hist(theta.prior,xlab="theta",ylab="",main="Previa", xlim=c(0.0,3.0))
hist(theta.posterior,xlab="theta",ylab="",main="D a posteriori", xlim=c(0.0,3.0))
hist(theta.posterior.2,xlab="theta",ylab="",main="D a posteriori II", xlim=c(0.0,3.0))