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########################
# Section 2.6 Prediction
########################
library(LearnBayes)
p=seq(0.05, 0.95, by=.1)
prior = c(1, 5.2, 8, 7.2, 4.6, 2.1, 0.7, 0.1, 0, 0)
prior=prior/sum(prior)
m=20; ys=0:20
pred=pdiscp(p, prior, m, ys)
cbind(0:20,pred)
ab=c(3.26, 7.19)
m=20; ys=0:20
pred=pbetap(ab, m, ys)
p=rbeta(1000,3.26, 7.19)
y = rbinom(1000, 20, p)
table(y)
freq=table(y)
ys=as.integer(names(freq))
predprob=freq/sum(freq)
plot(ys,predprob,type="h",xlab="y",
ylab="Predictive Probability")
dist=cbind(ys,predprob)
covprob=.9
discint(dist,covprob)
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