arXiv subjects

Sumeetpal Sidhu Singh

Publications and source records attributed to Sumeetpal Sidhu Singh.

3 recordsLinked to original sources

arXiv2021

Spatiotemporal blocking of the bouncy particle sampler for efficient inference in state space models

We propose a novel blocked version of the continuous-time bouncy particle sampler of [Bouchard-Côté et al., 2018] which is applicable to any differentiable probability density. This alternative implementation is motivated by blocked Gibbs sampling for state space models [Singh et al., 2017] and leads to significant improvement in terms of effective sample size per second, and furthermore, allows for significant parallelization of the resulting algorithm. The new algorithms are particularly efficient for latent state inference in high-dimensional state space models, where blocking in both space and time is necessary to avoid degeneracy of MCMC. The efficiency of our blocked bouncy particle sampler, in comparison with both the standard implementation of the bouncy particle sampler and the particle Gibbs algorithm of Andrieu et al. [2010], is illustrated numerically for both simulated data and a challenging real-world financial dataset.

stat.CO↗

arXiv2021

Backward It{ô}-Ventzell and stochastic interpolation formulae

We present a novel backward It{ô}-Ventzell formula and an extension of the Aleeksev-Gröbner interpolating formula to stochastic flows. We also present some natural spectral conditions that yield direct and simple proofs of time uniform estimates of the difference between the two stochastic flows when their drift and diffusion functions are not the same, yielding what seems to be the first results of this type for this class of anticipative models. We illustrate the impact of these results in the context of diffusion perturbation theory, interacting diffusions and discrete time approximations

math.PR↗

arXiv2021

Gradient-Based Markov Chain Monte Carlo for Bayesian Inference With Non-Differentiable Priors

The use of non-differentiable priors in Bayesian statistics has become increasingly popular, in particular in Bayesian imaging analysis. Current state of the art methods are approximate in the sense that they replace the posterior with a smooth approximation via Moreau-Yosida envelopes, and apply gradient-based discretized diffusions to sample from the resulting distribution. We characterize the error of the Moreau-Yosida approximation and propose a novel implementation using underdamped Langevin dynamics. In misson-critical cases, however, replacing the posterior with an approximation may not be a viable option. Instead, we show that Piecewise-Deterministic Markov Processes (PDMP) can be utilized for exact posterior inference from distributions satisfying almost everywhere differentiability. Furthermore, in contrast with diffusion-based methods, the suggested PDMP-based samplers place no assumptions on the prior shape, nor require access to a computationally cheap proximal operator, and consequently have a much broader scope of application. Through detailed numerical examples, including a non-differentiable circular distribution and a non-convex genomics model, we elucidate the relative strengths of these sampling methods on problems of moderate to high dimensions, underlining the benefits of PDMP-based methods when accurate sampling is decisive.

stat.ME↗