Speaker：Yuchung Wang（Rutgers University,Camden Campus）

Time：2023-4-3, 15:00

Location：Conference Room 686 at the 6th floor of Shuli Building at Haiyun Campus

Abstract:

We propose the global likelihood sampler (GL) that can generate independent and identically distributed (IID) samples from the kernel of any multivariate and multimodal distribution. It requires neither a proposal distribution nor a starting value. GL is not MCMC so it does not need burn-in. Instead, GL uses randomized quasi-random number (QRN) as the pool of proposals. A batch of samples are selected from the pool, and the probabilities of selection are proportional to the likelihoods of the target distribution. The low discrepancy of QRN enables GL to globally investigate the target distribution, and ignore the low likelihood barriers among modes. Afterward, the pool of proposals is refreshed by a random rotation, another batch of samples are selected from the new pool. This rotation then taking samples are repeated a decent number of times, and produce many batches of samples. Taking one sample from each batch constitutes a thread of IID samples from which estimates of parameters are computed. After a decent number of threads, each parameter will have many estimates. GL bootstrap averages the estimates from different treads and calculates the Monte Carlo standard error (MCSE). MCSE is a good measure of the consistency of a sampler. Using three examples, we demonstrate GL’s ability to explore multimodal distributions more accurately than slice, Metropolis-Hastings, parallel tempering, evolution Monte Carlo, and equal-energy samplers. Implementation of GL bootstrap is straightforward and requires simple tuning.