Bayesian Methods in Health Economics

Introduction to Bayesian inference 49

obtained as

p(θ | y)=

p(y | θ)p(θ)

p(y)

=

k × p(y | θ)



k × p(y | θ)dθ

=

p(y | θ)



p(y | θ)dθ

=

L(θ)



L(θ)dθ

.

Thus, under a Uniform prior, the posterior distribution is computed by nor-

malising the likelihood function, which makes clear why Bayesian analyses

based on flat priors are essentially identical with maximum likelihood estima-

tions (in particular, the posterior mode is identical with the MLE).

Example: Estimating the proportion of female births in Paris

We consider here the famous data analysed by Laplace on the number of female

births in Paris. In 1710, John Arbuthnot, a Scottish medical doctor with a

passion for ...