Estimation of the transition matrix of a discrete‐time Markov chain
总结了在观测间隔与模型周期一致、不一致或不等长时，如何用最大似然估计离散时间马尔可夫链的转移矩阵，并介绍了用自助法评估估计不确定性和构建置信区间。
Discrete-time Markov chains have been successfully used to investigate treatment programs and health care protocols for chronic diseases. In these situations, the transition matrix, which describes the natural progression of the disease, is often estimated from a cohort observed at common intervals. Estimation of the matrix, however, is often complicated by the complex relationship among transition probabilities. This paper summarizes methods to obtain the maximum likelihood estimate of the transition matrix when the cycle length of the model coincides with the observation interval, the cycle length does not coincide with the observation interval, and when the observation intervals are unequal in length. In addition, the bootstrap is discussed as a method to assess the uncertainty of the maximum likelihood estimate and to construct confidence intervals for functions of the transition matrix such as expected survival.