Before revision:  We also consider practical implementation and explicitly incorporate known covariates , such as seasonality patterns and trends, which may explain some of the relationship between two insurance processes( or at least help tease out those relationships ). We develop a filtering algorithm based on the reversible-jump Markov Chain Monte Carlo (RJMCMC) method to estimate the unobservable stochastic intensities .
After revision:  We also consider practical implementation and explicitly incorporate known covariates , such as seasonality patterns and trends, which may explain some of the relationship between two insurance processes( or at least help tease out those relationships . Finally, we develop a filtering algorithm based on the reversible-jump Markov Chain Monte Carlo (RJMCMC) method to estimate the unobservable stochastic intensities .