There is a lot of statistic models based on marginal distribution and joint distribution relationships. Such statistical models are widely used in medicine, biology, finance, etc. Many modern medical datasets contain observations from multiple time points and treatment conditions. Adaptive shrinkage, a general method to estimate marginal prior distributions, has been developed to analyze such data for a single time point or condition, few method has been developed to analyze joint distribution for different time points or different conditions. The reason is mainly because the difficulty of constructing multi-dimensional prior distributions with dependent variables. A few Bayes' methods can be applied to these type data. Although, it is non-trivial and difficult to estimate joint distribution directly, we can easily estimate marginal prior distributions separately. In this thesis, I develop a simple, general and straightforward method to couple prior distributions for multi-dimensional genetic effects. The main goal is to research the relationship between the sign of effect of a phenotype at different time points. I couple prior distributions to model joint distribution and estimate parameters at multiple time points. Copula Estimation described from Copula Theory and Its Applications provides a parametric copula inference method for my estimation. I construct a model and develop a method to couple prior distributions to estimate my parameters at multiple time points by deriving useful expressions, applying R language for data simulations, and using maximum likelihood estimation. I simulate data from both the real copula model and multivariate normal distribution. The true model performs better in estimating the parameters. This copula model successfully bridge the gap between joint distribution and dependent marginal distributions. There is still more room to improve my copula model
