Lin S
Department of Statistics, University of California, Berkeley 94720, USA.
Biometrics. 1995 Mar;51(1):318-22.
Estimating probabilities on a pedigree by dependent samples, namely realizations of a Markov chain, has been explored as an alternative method when exact computation is not feasible. If the transition kernel of the Markov chain is aperiodic and irreducible, convergence of the estimates to the true probabilities is guaranteed by the ergodic theorem. However, reducibility is a potential problem for genetic pedigree analysis unless the Markov chain is constructed appropriately. In the present paper, we propose a scheme for constructing an irreducible Markov chain for pedigree data. Transitions between communicating classes, which can be found explicitly, are made by using a Metropolis jumping kernel. The method has been demonstrated to be much more efficient than other currently existing methods.
当精确计算不可行时，通过相关样本（即马尔可夫链的实现）来估计系谱上的概率已被探索为一种替代方法。如果马尔可夫链的转移核是非周期且不可约的，遍历定理保证估计值收敛到真实概率。然而，对于遗传系谱分析来说，可约性是一个潜在问题，除非马尔可夫链构建得当。在本文中，我们提出了一种为系谱数据构建不可约马尔可夫链的方案。通过使用Metropolis跳跃核来实现可明确找到的通信类之间的转移。该方法已被证明比目前现有的其他方法效率高得多。
