**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)*

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