Efficient Gibbs Sampling for Transition Weights in Fleming–Viot Filtering and Smoothing

Bayesian inference for time-evolving distributions using Fleming–Viot driven dependent Dirichlet processes involves computing the transition probabilities of multidimensional pure-death processes, whose closed form is unavailable and whose approximation via standard Monte Carlo methods is computationally expensive and scales poorly. We propose an alternative Gibbs sampling approach that exploits a one– dimensional projection of the death process through its norm, updating exponential intertimes s equentially. Numerical experiments show that the proposed method significantly reduces computational cost while achieving comparable accuracy, providing an efficient tool for inference in high-dimensional applications in population genetics.