arXiv subjects

Daniel Würzler Barreto

Publications and source records attributed to Daniel Würzler Barreto.

2 recordsLinked to original sources

arXiv2026

Recursive Adaptive Importance Sampling with Optimal Replenishment

Increased access to computing resources has led to the development of algorithms that can run efficiently on multi-core processing units or in distributed computing environments. In the context of Bayesian inference, many parallel computing approaches to fit statistical models have been proposed using Markov chain Monte Carlo methods, but they either have limited gains due to high latency cost or rely on model-specific decompositions. Alternatively, adaptive importance sampling, sequential Monte Carlo, and recursive Bayesian methods provide a parallel-friendly and asymptotically exact framework with well-developed theory for error estimation. We consider a recursive adaptive importance sampling approach that alternates between fast recursive weight updates and sample replenishment steps to balance computational effort while ensuring sample quality. A naive implementation can be unstable and inefficient, so we derive theoretical results to determine the optimal replenishment frequency based on the posterior concentration rate, thus attaining an asymptotically optimal trade-off. We demonstrate the efficacy of our method in simulated experiments and an application of sea surface temperature prediction in the Gulf of Mexico using Gaussian processes.

stat.ME↗

arXiv2026

Making Recursive Bayesian Inference Robust

While Bayesian inference has become increasingly popular with advances in computational resources, its algorithms can be computationally prohibitive and may not scale with large datasets. This has led to growing interest in alternative algorithms, such as approximation methods and variants of Markov chain Monte Carlo. Among these approaches, prior proposal-recursive Bayesian (PP-RB) inference facilitates scalable Bayesian computation by recursively updating the posterior distribution across stages and utilizing parallel computing resources. While the well-known ``degeneracy'' issue in PP-RB has been studied, another limitation that PP-RB can yield incorrect inferences when posterior distributions shift substantially between stages has remained unsolved. To address this, we propose parallel-tempered prior proposal-recursive Bayesian (PPP-RB) inference, which extends PP-RB by leveraging the key idea underlying Metropolis-coupled Markov chain Monte Carlo. We show both theoretically and empirically that PPP-RB targets the true posterior distribution. We illustrate PPP-RB through numerical studies and real data analysis in application to earthquake count data and sea surface salinity in the North Atlantic region. In these applications, we compare PPP-RB with PP-RB and a standard MCMC, demonstrating that PPP-RB is more efficient in terms of effective sample size per elapsed time.

stat.ME↗