标题： 从各种不完整数据方案中估计离散马尔可夫模型 显示英文标题

标题： Estimating Discrete Markov Models From Various Incomplete Data Schemes

摘要： 离散平稳马尔可夫模型的参数是状态之间的转移概率。 传统上，数据是由在整个观察期间对于给定数量的个体的观测状态序列组成。 在这种情况下，转移概率的估计是通过从给定状态到另一个状态的一步移动进行计数来直接完成的。 然而，在许多实际问题中，推断要困难得多，因为状态序列并非完全可观测，即每个个体的状态仅在时间变量$t$的某些给定值下已知。 在本文中，我们对该领域进行了综述，重点介绍了用于执行贝叶斯推断并在缺失数据框架下评估转移概率后验分布的马尔可夫链蒙特卡洛（MCMC）算法。 我们还提出了一种加速经典梅特波里斯-哈斯廷斯技术的方法，用于典型的可靠性问题，利用矩阵行之间的依赖性来构建自适应MCMC。 显示英文摘要

摘要： The parameters of a discrete stationary Markov model are transition probabilities between states. Traditionally, data consists in sequences of observed states for a given number of individuals over the whole observation period. In such a case, the estimation of transition probabilities is straightforwardly made by counting one-step moves from a given state to another. In many real-life problems, however, the inference is much more difficult as state sequences are not fully observed, namely the state of each individual is known only for some given values of the time variable $t$. In this paper we give a review of this field, focusing on Monte Carlo Markov Chain (MCMC) algorithms to perform Bayesian inference and evaluate posterior distributions of the transition probabilities in this missing-data framework. We also propose a way to accelerate the classical Metropolis-Hastings technique for typical reliability problems, taking advantage of the dependence between the matrix rows to build an adaptive MCMC.