Inverse Transformed Density Rejection for Unbounded Monotone Densities

A new algorithm for sampling from largely arbitrary monotone, unbounded densities is presented. The user has to provide a program to evaluate the density and its derivative and the location of the pole. Then the setup of the new algorithm constructs different hat functions for the pole region and tail region, respectively. For the pole region a new method is developed that uses a transformed density rejection hat function of the inverse density. As the order of the pole is calculated in the setup, conditions that guarantee correctness of the constructed hat functions are provided. Numerical experiments indicate that the new algorithm works correctly and moderately fast for many different unbounded densities.