Simple disease incidence 
Buck CE, Cavanagh WG, & Litton CD (1996) Bayesian approach to interpreting archaeological data.  Wiley: Chichester
p146-159 and 169

© Andrew Millard 2001 

model{
p ~ dbeta(alpha,beta)  #  prior on underlying prevelance
d ~ dbin(p, n)  # likelihood of d observed cases in n excavated skeletons
}

Data

Case I limited excavation (p146-148)
list(alpha=1, beta=1,d=3, n=5)
alpha=1, beta=1 gives a uniform (0,1) prior on p



Case II larger excavation (p149)
list(alpha=1, beta=1,d=15, n=25)

Case III limited excavation with informative prior (p 149-152)
list(alpha=3, beta=3,d=3, n=5)

Case IV revision of belief after second excavation (p169)
list(alpha=4, beta=3, d=12, n=20)
alpha=4, beta=3 represents the posterior from Case I

alternatively we can code both data sets into one model, with exactly the same result:

model{
p ~ dbeta(alpha,beta)  #  prior on underlying prevelance
d[1] ~ dbin(p, n[1])  # likelihood of d observed cases in n excavated skeletons
d[2] ~ dbin(p, n[2])

}
list(alpha=1, beta=1, d=c(3,12), n=c(5,20))