Rate of convergence for data augmentation and inverse Bayes formula method in the genetic linkage model

Many statistical problems can be formulated as the missing data problems. The data augmentation algorithm and the inverse Bayes formula are important tools for constructing iterative optimization or samplings via the introduction of unobserved data or latent variables. As a Markov Chain Monte Carlo method, the data augmentation algorithm has its autocorrelation. Nevertheless, the convergence rate of the data augmentation algorithm is not known in the Genetic Linkage Model, and the same is true for the inverse Bayes formula method. In this article, we analyze the convergence rates of the data augmentation algorithm and the inverse Bayes formula method in the genetic linkage model, and through simulation results we get their convergence rates.