Bayesian Nonparametric Conditional Density Modeling in Causal Inference and Clustering with a Heavy-Tail Extension

The presence of a heavy tail is a feature of many scenarios when risk management involves extremely rare events. While parametric distributions may give adequate representation of the mode of data, they are likely to misrepresent heavy tails, and completely nonparametric approaches lack a rigorous mechanism for tail extrapolation; see Pickands (1975) . The package 'CausalMixGPD' implements tools for Bayesian analysis of heavy-tailed outcomes by combining Dirichlet process mixture models for the body of the distribution with optional generalized Pareto tails. The method allows for unconditional and covariate-modulated mixtures, implements MCMC estimation using 'nimble', and extends to mixtures of different arms' outcomes with application to causal inference in the Rubin (1974) framework. Posterior summaries include density functions, quantiles, expected values, survival functions, and causal effects, with an emphasis on tail quantiles and functional measures sensitive to the tail.