Sheehan N, Thomas A
School of Mathematical Sciences, University of Bath, Claverton Down, England.
Biometrics. 1993 Mar;49(1):163-75.
Techniques from image processing are now being considered for use in pedigree analysis. Although the method that we develop here was motivated by considering it as an analogue to the Gibbs sampler, we justify it independently using the ergodic theorem for aperiodic, irreducible, finite Markov chains. While it is trivial to show that aperiodicity holds, irreducibility is a more interesting condition. Proofs of irreducibility are provided for some special cases and counterexamples are provided for others. Where irreducibility does not hold, an alternative method using relaxed genetic parameters and rejection is recommended and justified.
图像处理技术目前正被考虑用于系谱分析。尽管我们在此开发的方法是通过将其视为吉布斯采样器的类似物而得到启发的，但我们使用非周期、不可约、有限马尔可夫链的遍历定理独立地证明了它的合理性。虽然证明非周期性成立很简单，但不可约性是一个更有趣的条件。我们为一些特殊情况提供了不可约性的证明，并为其他情况提供了反例。在不可约性不成立的情况下，建议并证明了一种使用松弛遗传参数和拒绝法的替代方法。
