Rolling Pin Method: Efficient General Method of Joint Probability Modeling

This paper presents a novel efficient method of estimating the joint probability distribution of continuous random variables with arbitrary (nonmonotonic or monotonic) relationships. As the backbone of the method is a set of monotonization transformations that roll out the relationships, the method is named the rolling pin method. The method allows one to estimate joint probability distributions when the actual causal structure of the attributes is unknown or extremely intricate to be determined accurately. Once the relationships are monotonized by the transformations, an appropriate parametric copula function is used to describe the joint distribution of the transformed variables. The copula function allows modeling the joint distribution of the transformed variables with a few parameters. The monotonization transformations empower standard parametric copulas to (i) capture complicated unknown dependence structures, (ii) model multivariate joint probability distributions with different pairwise dependence structures using the same parametric copula, and (iii) model nonmonotonicity. The application and performance of the method are shown using two examples.