approximate Bayesian inference under informative sampling

In the first issue of this year Biometrika, I spotted a paper with the above title, written by Wang, Kim, and Yang, and thought it was a particular case of ABC. However, when I read it on a rare metro ride to Dauphine, thanks to my hurting knee!, I got increasingly disappointed as the contents had nothing to do with ABC. The purpose of the paper was to derive a consistent and convergent posterior distribution based on a estimator of the parameter θ that is… consistent and convergent under informative sampling. Using for instance a Normal approximation to the sampling distribution of this estimator. Or to the sampling distribution of the pseudo-score function, S(θ) [which pseudo-normality reminded me of Ron Gallant’s approximations and of my comments on them]. The paper then considers a generalisation to the case of estimating equations, U(θ), which may again enjoy a Normal asymptotic distribution. Involving an object that does not make direct Bayesian sense, namely the posterior of the parameter θ given U(θ)…. (The algorithm proposed to generate from this posterior (8) is also a mystery.) Since the approach requires consistent estimators to start with and aims at reproducing frequentist coverage properties, I am thus at a loss as to why this pseudo-Bayesian framework is adopted.

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out /  Change )

Google photo

You are commenting using your Google account. Log Out /  Change )

Twitter picture

You are commenting using your Twitter account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )

Connecting to %s

This site uses Akismet to reduce spam. Learn how your comment data is processed.