Bayesian Methods in Health Economics

Introduction to Bayesian inference 69

non-Normal, complex models. Such methods can be helpful in the analysis of

hierarchical models (cfr. §5.3).

Example: Checking and improving convergence of the Gibbs sam-

pling

One of the easiest ways to improve convergence is to break the correlation

between the variables to be estimated. The simplest example occurs in linear

regression analysis with observed data y

i

∼ Normal(μ

i

,σ

2

) for i =1,...,N.

First we consider one possible model, say M

1

, which assumes μ

i

= α +

βX

i

with simple minimally informative prior distributions on the regression

coefficients α, β ∼ Normal(0, 10000) independently, and on the logarithm of

the ...