标题： 自适应ABC模型选择与隐藏Gibbs随机场的几何概括统计量 显示英文标题

标题： Adaptive ABC model choice and geometric summary statistics for hidden Gibbs random fields

摘要： 由于似然函数中含有无法求解的规范化常数，选择隐马尔可夫随机场的不同依赖结构可能非常具有挑战性。 我们通过近似贝叶斯计算（ABC）回答了这个问题，该方法在贝叶斯框架下提供了一种模型选择方法。 这继 Grelaud 等人（2009）的工作之后，他们展示了直接观察到的吉布斯随机场的充分统计量。 但当随机场是潜在的时，充分性失效，我们补充了与几何汇总统计相关的集合。 构建这些直观统计量的一般方法依赖于基于观察颜色和可能的潜在图的站点聚类分析。 基于这些统计量的ABC模型选择效率通过局部错误率来评估，这可能有独立的兴趣。 作为副产品，我们推导出一种ABC算法，该算法能够根据数据集调整汇总统计量的维度，而不影响模型选择。 显示英文摘要

摘要： Selecting between different dependency structures of hidden Markov random field can be very challenging, due to the intractable normalizing constant in the likelihood. We answer this question with approximate Bayesian computation (ABC) which provides a model choice method in the Bayesian paradigm. This comes after the work of Grelaud et al. (2009) who exhibited sufficient statistics on directly observed Gibbs random fields. But when the random field is latent, the sufficiency falls and we complement the set with geometric summary statistics. The general approach to construct these intuitive statistics relies on a clustering analysis of the sites based on the observed colors and plausible latent graphs. The efficiency of ABC model choice based on these statistics is evaluated via a local error rate which may be of independent interest. As a byproduct we derived an ABC algorithm that adapts the dimension of the summary statistics to the dataset without distorting the model selection.