Approximate computations for binary Markov random fields and their use in Bayesian models

作     者：Austad, Haakon Michael Tjelmeland, Hakon 

作者机构：Norwegian Univ Sci & Technol Dept Math Sci N-7491 Trondheim Norway If P&C Oslo Norway 

出 版 物：《STATISTICS AND COMPUTING》 (统计学与计算)

年 卷 期：2017年第27卷第5期

页      面：1271-1292页

核心收录：

学科分类：0202[经济学-应用经济学] 02[经济学] 020208[经济学-统计学] 07[理学] 0714[理学-统计学（可授理学、经济学学位）] 0812[工学-计算机科学与技术（可授工学、理学学位）] 

主　　题：Approximate inference Bayesian analysis Discrete Markov random fields Image analysis Pseudo-Boolean functions Spatial data Variable elimination algorithm 

摘      要：Discrete Markov random fields form a natural class of models to represent images and spatial datasets. The use of such models is, however, hampered by a computationally intractable normalising constant. This makes parameter estimation and a fully Bayesian treatment of discrete Markov random fields difficult. We apply approximation theory for pseudo-Boolean functions to binary Markov random fields and construct approximations and upper and lower bounds for the associated computationally intractable normalising constant. As a by-product of this process we also get a partially ordered Markov model approximation of the binary Markov random field. We present numerical examples with both the pairwise interaction Ising model and with higher-order interaction models, showing the quality of our approximations and bounds. We also present simulation examples and one real data example demonstrating how the approximations and bounds can be applied for parameter estimation and to handle a fully Bayesian model computationally.