Constrained Monte Carlo Maximum Likelihood for Dependent Data
研究了用马尔可夫链蒙特卡罗方法计算自逻辑模型等依赖数据指数族模型的最大似然估计，提出两阶段算法处理无解情况，并用DNA指纹数据验证，发现伪似然估计高估依赖性、条件似然估计因约束移除而失效。
SUMMARY Maximum likelihood estimates (MLEs) in autologistic models and other exponential family models for dependent data can be calculated with Markov chain Monte Carlo methods (the Metropolis algorithm or the Gibbs sampler), which simulate ergodic Markov chains having equilibrium distributions in the model. From one realization of such a Markov chain, a Monte Carlo approximant to the whole likelihood function can be constructed. The parameter value (if any) maximizing this function approximates the MLE. When no parameter point in the model maximizes the likelihood, the MLE in the closure of the exponential family may exist and can be calculated by a two-phase algorithm, first finding the support of the MLE by linear programming and then finding the distribution within the family conditioned on the support by maximizing the likelihood for that family. These methods are illustrated by a constrained autologistic model for DNA fingerprint data. MLEs are compared with maximum pseudolikelihood estimates (MPLEs) and with maximum conditional likelihood estimates (MCLEs), neither of which produce acceptable estimates, the MPLE because it overestimates dependence, and the MCLE because conditioning removes the constraints.