Objective and data-driven Bayesian inference using TabPFN models

Neural posterior estimation with prior-data fitted networks (NPE-PFN) has emerged as a promising tool for Bayesian inference, enabling posterior approximation from simulated data generated under user-specified prior and likelihood models. Here, we adapt TabPFN-based NPE-PFN modeling for performing both objective Bayesian inference and data-driven Bayesian analysis. Importantly, while both contributions can be strait-forwardly implemented under the NPE-PFN framework, they cannot be implemented (or at least not as easily) under alternative computational approaches. In the objective Bayes front, we propose a new class of default prior distributions for which maximum a posteriori (MAP) and maximum likelihood (MLE) inferences coincide. These priors yield MAP/MLE equivalence independent of the chosen probability model, enabling more automatic Bayesian analysis without model-specific prior design. On the data-driven front, we show how the NPE-PFN machinery can be used to approximate MLE estimation through overconfident asymptotic Bayesian arguments allowing the implementation of empirical Bayes methodology. Simulation studies illustrate the flexibility and effectiveness of the proposed approaches.