Untying the Gordian knot of Bayesian inference in Markov networks - Desuó Neto, Luiz (2025)
This work addresses the double intractability of Bayesian inference in Markov random fields by developing three novel strategies that bypass the partition function while preserving probabilistic coherence. The first strategy extends Besags pseudolikelihood approximation with copulabased local likelihoods to model continuous dependencies without requiring global normalization. The second strategy introduces copula hyperstructures that render complex undirected models decomposable via chordal graph factorization, enabling exact inference through junctiontree methods. The third strategy constructs semiparametric MRFs by combining Bernsteinpolynomial marginals with a WhittleMatérn stochastic partial differential equationbased covariance representation, yielding efficient inference and nonparanormal flexibility. Empirical evaluation on simulated and real-world datasets for extreme precipitation spatial distribution demonstrates that the proposed method outperforms two established Bayesian spatial baselines in predictive accuracy and uncertainty quantification. By unifying copula theory with structured Bayesian probabilistic modeling, this work advances the theoretical perspective of Markov random fields while delivering practical, interpretable tools for high-dimensional networked systems, bridging the gap between probabilistic coherence and computational tractability in complex environmental processes.