Soumyakanti Pan

Analysing non-Gaussian spatial-temporal data typically requires introducing spatial dependence in generalised linear models through the link function of an exponential family distribution. However, unlike in Gaussian likelihoods, inference is considerably encumbered by the inability to analytically integrate out the random effects and reduce the dimension of the parameter space. We devise an approach that obviates these issues by exploiting generalised conjugate multivariate distribution theory for exponential families, which enables exact sampling from analytically available posterior distributions conditional upon some fixed process parameters. We evaluate inferential performance on simulated data, compare with fully Bayesian inference using Markov chain Monte Carlo and apply our proposed method to analyse spatially-temporally referenced avian count data from the North American Breeding Bird Survey database.

Integrating over model uncertainty in factorial designs via Bayesian model averaging is hindered by the combinatorial explosion of interpretable interaction effects, often yielding a multimodal posterior, where standard Markov chain Monte Carlo algorithms encounter significant convergence issues. We propose a general computational framework that repurposes Rashomon sets, collections of high-performing models traditionally valued for prediction and interpretability, as a strategic "warm start" for estimating the full posterior. Our method, Rashomon-seeded annealing, initializes annealed importance sampling (AIS) by anchoring the starting density within these pre-identified, high-evidence regions while preserving global support over the entire model space. Rather than restricting inference to the Rashomon set and understating uncertainty, the AIS correction restores full posterior inference, turning the Rashomon certificate from an inferential truncation into a proposal mechanism. We demonstrate this approach using Rashomon Partition Sets (RPS) as a rigorous, certified seed constructor for factorial designs. The resulting algorithm yields consistent self-normalized posterior summaries, such as model-averaged cell means, credible intervals, and uncertainty summaries without exhaustive enumeration of the complete model space. This bridges the gap between high-evidence model discovery and rigorous Bayesian inference, and outlines a general strategy in which any high-posterior seed set can provide computational leverage for AIS-based model averaging.