**I**n 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.

## Archive for Ron Gallant

## approximate Bayesian inference under informative sampling

Posted in Books, Statistics, Travel, University life with tags ABC, approximate Bayesian inference, Bayesian semi-parametrics, Bernstein-von Mises theorem, Biometrika, estimating equations, generalised method of moments, RER B, Ron Gallant, sampling on March 30, 2018 by xi'an## commentaries in financial econometrics

Posted in Books, Statistics, University life with tags 6th French Econometrics conference, Chris Sims, generalised method of moments, harmonic mean estimator, incoherent inference, inconsistent priors, σ-algebra, John Geweke, Journal of Financial Econometrics, MCMC algorithms, method of moments, path sampling, prior construction, Ron Gallant on April 27, 2016 by xi'an**M**y comment(arie)s on the moment approach to Bayesian inference by Ron Gallant have appeared, along with other comment(arie)s:

**Invited Article**

Reflections on the Probability Space Induced by Moment Conditions with

Implications for Bayesian Inference

A. Ronald Gallant . . . . . . . . . . . . . . . . . . . . . . . . . . . 229

**Commentaries**

Dante Amengual and Enrique Sentana .. . . . . . . . . . 248

John Geweke . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .253

Jae-Young Kim . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 258

Oliver Linton and Ruochen Wu . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .261

Christian P. Robert . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 265

Christopher A. Sims . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 272

Wei Wei and Asger Lunde . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .278

**Author Response**

A. Ronald Gallant . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .284

**W**hile commenting on commentaries is formally bound to induce an infinite loop [or l∞p], I remain puzzled by the main point of the paper, which is that setting a structural distribution on a moment function Z(x,θ) *plus* a prior p(θ) induces a distribution on the pair (x,θ) in a possibly weaker σ-algebra. (The two distributions may actually be incompatible.) Handling this framework requires checking that a posterior exists, which sounds rather unnatural (even though we also have to check properness of the posterior). And the meaning of such a posterior remains unclear, as for instance in this assertion that (4) above is a likelihood, when it does not define a density in x but on the object inside the exponential.

“…it is typically difficult to determine whether there exists a p(x|θ) such that the implied distribution of m(x,θ) is the one stated, and if not, what damage is done thereby” J. Geweke (p.254)

## comments on reflections

Posted in pictures, Statistics, University life with tags 6th French Econometrics conference, ABC, empirical likelihood, limited information inference, measure theory, moment prior, Ron Gallant on February 9, 2015 by xi'an**I** just arXived my comments about A. Ronald Gallant’s “Reflections on the Probability Space Induced by Moment Conditions with Implications for Bayesian Inference”, capitalising on the three posts I wrote around the discussion talk I gave at the 6th French Econometrics conference last year. Nothing new there, except that I may get a response from Ron Gallant as this is submitted as a discussion of his related paper in Journal of Financial Econometrics. While my conclusion is rather negative, I find the issue of setting prior and model based on a limited amount of information of much interest, with obvious links with ABC, empirical likelihood and other approximation methods.