Bayesian Methods in Health Economics

Bayesian analysis in practice 135

want to include in the analysis the prediction for a yet unobserved replication

of y. For example, we might be interested in the value of the response variable

for the next individual, which we indicate with y

∗

and consider as exchangeable

with the observed vector y =(y

1

,...,y

N

).

In line with the discussion of §2.3.1, this means that the we assume a

common functional form for the distributions of y

∗

and y. Moreover, when

estimating the distribution of y

∗

, we consider the current uncertainty on the

parameters, i.e. that provided by the posterior distribution p(θ | y).

Suppose that in model M

1

above, the response y represents the birth

weight in grams of a newborn, while the covariate X is the gestational age, i.e.

the