08/06/2026: The paper No-prior Bayes reIMagined, available here, has been accepted for publication in Statistical Science, with discussion. Here I explore the use of an inner probabilistic approximation of a provably valid possibilistic inferential model (IM) as an alternative to the standard default-prior Bayes solutions when no genuine prior information is available. This is a generalization of no-prior Bayes in the sense that, in cases where there is agreement on which default prior to use (right Haar measure in group transformation models), my new solution agrees with that Bayesian solution; but my solution is different in other cases and it has stronger reliability properties.
04/01/2026: The paper, An efficient Monte Carlo method for valid prior-free possibilistic statistical inference, available here, has been accepted for publication in the Journal of the American Statistical Association. Inferential models (IMs) are powerful in that they offer reliable probabilistic inference without priors. But the IM's reliability guarantees require relaxing probabilistic to possibilistic, which creates computational challenges. Ideally, one could sample from a "posterior distribution" that accurately represents the features of the possibilistic IM's output, but these details hadn't been worked out. This paper offers an efficient Monte Carlo sampling-based strategy for numerically approximating the IM, a striking improvement to the naive approach I'd previously been using.
03/01/2026: My recent review paper on possibilistic IMs, here, was published in the Journal of the American Statistical Association.
11/15/2025: The new paper, Valid and efficient possibilistic structure learning in Gaussian linear regression (with N. Singer and J. Williams), is now available here. This paper builds on the results in Part III by developing a framework in which necessarily incomplete knowledge about the model structure, e.g., sparsity, is encoded as a prior possibility distribution and then naturally incorporated into a possibilistic IM that offers valid structure learning—or, in other words, provably reliable marginal inference on the model structure.
10/01/2023: A new paper entitled Valid and efficient imprecise-probabilistic inference with partial priors, III. Marginalization is now available here and here. This is a follow-up to the investigations started in Parts I & II described below. What's new here is a focus on marginal inference. I propose a general marginalization strategy for possibilistic IMs, one that relies on profile likelihoods and can accommodate partial prior information if available. Validity properties are established and lots of illustrations are given.
11/29/2022: A new paper entitled Valid and efficient imprecise-probabilistic inference with partial priors, II. General framework is now available here and here. This is a follow-up to Part I mentioned below. What I didn't do in Part I was explain how valid and efficient imprecise-probabilistic inference with partial priors can be achieved. This new paper describes a valid and efficient inferential model (IM) construction, which turns out to be practical, conceptually simple, and not so much different from familiar things. Very strong properties are established for this IM and I show lots of examples.
![[Ryan Martin]](Images/mypic.jpg)