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######################################################
# Section 4.2 Normal Data with Both Parameters Unknown
######################################################
library(LearnBayes)
data(marathontimes)
attach(marathontimes)
d = mycontour(normchi2post, c(220, 330, 500, 9000), time,
xlab="mean",ylab="variance")
S = sum((time - mean(time))^2)
n = length(time)
sigma2 = S/rchisq(1000, n - 1)
mu = rnorm(1000, mean = mean(time), sd = sqrt(sigma2)/sqrt(n))
points(mu, sigma2)
quantile(mu, c(0.025, 0.975))
quantile(sqrt(sigma2), c(0.025, 0.975))
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