We consider the problem of estimating the interacting neighborhood of a Markov Random Field model with finite support and homogeneous pairwise interactions based on relative positions of a two-dimensional lattice. Using a Bayesian framework, we propose a Reversible Jump Monte Carlo Markov Chain algorithm that jumps across subsets of a maximal range neighborhood, allowing us to perform model selection based on a marginal pseudoposterior distribution of models. To show the strength of our proposed methodology we perform a simulation study and apply it to a real dataset from a discrete texture image analysis.

翻译：本文研究了在二维格点相对位置条件下，具有有限支撑和齐次成对交互作用的马尔可夫随机场模型交互邻域估计问题。基于贝叶斯框架，我们提出了一种可逆跳跃蒙特卡洛马尔可夫链算法，该算法能在最大范围邻域的子集间进行跳跃，从而基于模型的边缘伪后验分布实现模型选择。为验证所提方法的有效性，我们进行了模拟研究，并将其应用于离散纹理图像分析的实际数据集。