Monte Carlo

Monte Carlo based Inference for State-space Models

Sumeetpal Singh, Reader, Engineering Statistics, Department of Engineering, University of Cambridge

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KAUST

State-space models are widely used for the analysis of time-series data but full Bayesian inference is still elusive. I will review some applications of state-space models and recent endeavours towards efficient Monte Carlo sampling, in particular using Particle filtering and more recent Particle Markov Chain Monte Carlo methods. I will discuss the theoretical scalability of these methods with respect to the length of the observed time-series. Our theoretical results on their efficiency align well with many documented instances of their effectiveness based on extensive numerical studies. The talk will conclude with some open challenges to be pursued.

Efficient MCMC Sampling with Dimension-Free Convergence Rate using ADMM-type Splitting

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B1 L3 R3119

In this paper, we propose a detailed theoretical study of one of these algorithms known as the split Gibbs sampler. Under regularity conditions, we establish explicit convergence rates for this scheme using Ricci curvature and coupling ideas. We support our theory with numerical illustrations.

Derivative-Free Global Minimization: Relaxation, Monte Carlo and Sampling

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B9 L2 H2 H2

We develop a derivative-free global minimization algorithm that is based on a gradient flow of a relaxed functional. We combine relaxation ideas, Monte Carlo methods, and resampling techniques with advanced error estimates. Compared with well-established algorithms, the proposed algorithm has a high success rate in a broad class of functions, including convex, non-convex, and non-smooth functions, while keeping the number of evaluations of the objective function small.

Multigrid Monte Carlo Revisited: Theory and Bayesian Inference

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B1 L3 R3119

Abstract The fast simulation of Gaussian random fields plays a pivotal role in many research areas such as Uncertainty Quantification, data science and spatial statistics. In theory, it is a well understood and solved problem, but in practice the efficiency and performance of traditional sampling procedures degenerates quickly when the random field is discretised on a grid with spatial resolution going to zero. Most existing algorithms, such as Cholesky factorisation samplers, do not scale well on large-scale parallel computers. On the other hand, stationary, iterative approaches such as the

Nadhir Ben Rached

Introduction Nadhir went to RWTH Aachen University, Aachen, Germany as a ​​Postdoctoral Research Fellow​. Education and early career Nadhir obtained his M.S and Ph.D. degree in Applied Mathematics and Computational Science, King Abdullah University of Science and Technology (KAUST), Thuwal, Saudi Arabia between 2012 - 2018. Research Interest Efficient Monte Carlo approach for rare event simulation Accurate Performance Analysis of Wireless Communication Systems Computational Finance Stochastic Differential Equations Numerical Analysis Selected Publications Graduation Project, Adaptive Monte