
64 Current Trends in Bayesian Methodology with Applications
used as a proxy for the true value θ—and any prior p(θ, λ)—which descr ibes
the available knowledge about the parameter values—to provide s olutions for
both estimation and hypothesis testing. If both the loss function and the pr ior
distribution are continuous, precisely the same loss and the same prior may
be used to obtain a coherent, integrated set of solutions for b oth estimation
and testing, which may all be derived from the joint use of the corresponding
posterior density p(θ |z), and the pos terior expected loss function ℓ(θ
0
|z).
Moreover the prior used may well be improper, as will ...