#######################################################
# Section 3.6 A Bayesian Test of the Fairness of a Coin
#######################################################
library(LearnBayes)
pbinom(5, 20, 0.5)
n = 20
y = 5
a = 10
p = 0.5
m1 = dbinom(y, n, p) * dbeta(p, a, a)/dbeta(p, a + y, a + n -
y)
lambda = dbinom(y, n, p)/(dbinom(y, n, p) + m1)
lambda
pbetat(p,.5,c(a,a),c(y,n-y))
prob.fair=function(log.a)
{
a = exp(log.a)
m2 = dbinom(y, n, p) * dbeta(p, a, a)/
dbeta(p, a + y, a + n - y)
dbinom(y, n, p)/(dbinom(y, n, p) + m2)
}
n = 20; y = 5; p = 0.5
curve(prob.fair(x), from=-4, to=5, xlab="log a",
ylab="Prob(coin is fair)", lwd=2)
S=readline(prompt="Type <Return> to continue : ")
n=20
y=5
a=10
p=.5
m2=0
for (k in 0:y)
m2=m2+dbinom(k,n,p)*dbeta(p,a,a)/dbeta(p,a+k,a+n-k)
lambda=pbinom(y,n,p)/(pbinom(y,n,p)+m2)
lambda
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