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，数据是在整个观察期间对于给定数量的个体所观测到的状态序列。 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的某些给定值下已知。 给出了该问题的综述，重点介绍了用于执行贝叶斯推断并在这种缺失数据框架下评估转移概率后验分布的蒙特卡洛马尔可夫链（MCMC）算法。 基于转移矩阵行之间的依赖性，然后提出了一种加速经典梅特罗波利斯-黑斯廷斯算法的自适应MCMC机制，并进行了实证研究。 显示英文摘要

摘要： The parameters of a discrete stationary Markov model are transition probabilities between states. Traditionally, data consist 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. A review of the problem is given, 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. Leaning on the dependence between the rows of the transition matrix, an adaptive MCMC mechanism accelerating the classical Metropolis-Hastings algorithm is then proposed and empirically studied.