The Implementation And Application Of MCMC In Statistical Analysis Of Medical Studies

So far, computational problems is the key point of Bayesian methods. MCMC is being increasingly used as an effective approach for such problems. Having a study on MCMC can boost the widerapplications of Bayesian statistics.Although there are many algorithms for MCMC provided by foreign statisticians, few of those are really easy to implement on computer. So, our aim is to construct a software frame under which users can not only evaluate their Bayesian models, but also expand the environment itself to suit their specified models. Based on the MCMC theory we introduced Monte Carlo methods and object oriented programming technique to implement our application. During this process we also made an attempt to find a general programming method for MCMC and how to apply it to Bayesian models.We summarized our implementing approach as such: first, determine the form of the model and its parameters' prior distributions, then construct the DAG graph according to the model you set and build the full conditional distribution for each parameter, then sample from full conditional distribution using ARS and loop this process until enough samples are obtained. According to this idea, we wrote some codes and built a computational software, though in its initial form. In our application, we set up a development environment where other developers can build their computations merely by using some defining and assigning syntaxes without knowing any details of implementation. We have definedmany commonly used distributions including uniform, binomial,Poisson, normal, gamma, beta and Pareto distributions. The results are represented by mean, median, standard deviation, quartiles, skewness and kurtosis. The statistical charts include histogram and trace plot. In addition, our software supports richer types of data than WinBUGS. It supports paradox, dbase, MS Access, MS Excel, ASCII TXT.We applied our software to a single and a multiple linear regression, a logistic regression with random effects, a variance components model, a normal hierarchical model, a crossover design for bio-equivalence test, a Poisson model and a Meta analysis. Most of our evaluations were similar to those of WinBUGS. The restriction of our software is that model we assumed must be of generalized linear model. The efficiency of our software is a little lower than that of WinBUGS. Its user interface needs further development.In this article, We also discussed some issues about strategies for improving MCMC.Our idea for implementing MCMC proved right and the software we developed runs stably. Our software is an open system and can be easily expanded.