2012/05/02 by Luca Martino, David Luengo, Martino, Luca +3
Computer Science · Mathematics · Physics and Astronomy · #Bayesian Methods and Mixture Models #Computation (stat.CO) #FOS: Computer and information sciences #Methodology (stat.ME) #Statistical Mechanics and Entropy #Statistical Methods and Bayesian Inference
paper · pdf · doi:10.48550/arxiv.1205.0482
openalex publication_date 2012/05/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this work we investigate the relationship among three classical sampling techniques: the inverse of density (Khintchine's theorem), the transformed rejection (TR) and the generalized ratio of uniforms (GRoU). Given a monotonic probability density function (PDF), we show that the transformed area obtained using the generalized ratio of uniforms method can be found equivalently by applying the transformed rejection sampling approach to the inverse function of the target density. Then we provide an extension of the classical inverse of density idea, showing that it is completely equivalent to the GRoU method for monotonic densities. Although we concentrate on monotonic probability density functions (PDFs), we also discuss how the results presented here can be extended to any non-monotonic PDF that can be decomposed into a collection of intervals where it is monotonically increasing or decreasing. In this general case, we show the connections with transformations of certain random variables and the generalized inverse PDF with the GRoU technique. Finally, we also introduce a GRoU technique to handle unbounded target densities.