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  "Title": "Scalable Bayesian Inference for Discrete Markov Random Fields",
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  "Description": "Estimation of discrete Markov random fields through the\npseudo-likelihood, for both Ising models (Ising (1925)\n<doi:10.1007/BF02980577>) and ordinal Markov random fields\n(Marsman et al. (2025) <doi:10.1017/psy.2024.4>). Point\nestimates, either maximum pseudo-likelihood or maximum a\nposteriori, are obtained through a trust region optimization\nalgorithm, with robust standard errors from the\nGodambe-Huber-White (GHW, or sandwich) estimator, for both full\nand constrained network structures. Bayesian inference corrects\nthe pseudo-posterior through coordinate rescaling (Arena and\nMarsman (2026) <doi:10.48550/arXiv.2601.17205>), which matches\nits covariance to the GHW covariance, and samples from it with\nthe Fisher adaptive Metropolis-adjusted Langevin algorithm\n(Titsias (2024) <doi:10.48550/arXiv.2305.14442>). For\ncomparison, the posterior based on the full likelihood can also\nbe sampled, exactly for small networks or with the double\nMetropolis-Hastings algorithm (Liang (2010)\n<doi:10.1080/00949650902882162>). Savage-Dickey Bayes factors\ntest each pairwise interaction, computed either by sampling\nimportance resampling (Skare et al. (2003)\n<doi:10.1111/1467-9469.00360>) or from the posterior draws.",
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