Related papers: Local Sequential MCMC for Data Assimilation with A…

Bayesian models have become very popular over the last years in several fields such as signal processing, statistics, and machine learning. Bayesian inference requires the approximation of complicated integrals involving posterior…

We propose an extension of the discretization approaches for multilayer shallow water models, aimed at making them more flexible and efficient for realistic applications to coastal flows. A novel discretization approach is proposed, in…

In this work we define a unified mathematical framework to deepen our understanding of the role of stochastic gradient (SG) noise on the behavior of Markov chain Monte Carlo sampling (SGMCMC) algorithms. Our formulation unlocks the design…

Approximate Bayesian computation (ABC) methods are standard tools for inferring parameters of complex models when the likelihood function is analytically intractable. A popular approach to improving the poor acceptance rate of the basic…

A novel adaptive Markov chain Monte Carlo algorithm is presented. The algorithm utilizes sparsity in the partial correlation structure of a density to efficiently estimate the covariance matrix through the Cholesky factor of the precision…

A standard way to move particles in a SMC sampler is to apply several steps of a MCMC (Markov chain Monte Carlo) kernel. Unfortunately, it is not clear how many steps need to be performed for optimal performance. In addition, the output of…

We consider importance sampling (IS) type weighted estimators based on Markov chain Monte Carlo (MCMC) targeting an approximate marginal of the target distribution. In the context of Bayesian latent variable models, the MCMC typically…

In this paper, we introduce a new, local formulation of the ensemble Kalman Filter approach for atmospheric data assimilation. Our scheme is based on the hypothesis that, when the Earth's surface is divided up into local regions of moderate…

Random Walk Metropolis Hastings (RWMH) algorithm, is quite inefficient in high dimensions because of its abysmally slow acceptance rate. The slow acceptance rate results from the fact that RWMH separately updates each coordinate of the…

Data Assimilation (DA) and Uncertainty quantification (UQ) are extensively used in analysing and reducing error propagation in high-dimensional spatial-temporal dynamics. Typical applications span from computational fluid dynamics (CFD) to…

Particle smoothers are SMC (Sequential Monte Carlo) algorithms designed to approximate the joint distribution of the states given observations from a state-space model. We propose dSMC (de-Sequentialized Monte Carlo), a new particle…

Many problems arising in applications result in the need to probe a probability distribution for functions. Examples include Bayesian nonparametric statistics and conditioned diffusion processes. Standard MCMC algorithms typically become…

Data assimilation is the process of estimating the state of a dynamical system over time by combining model predictions with measurements. This task becomes challenging when the system is nonlinear and high-dimensional. To address this,…

This paper introduces a decentralized state-dependent Markov chain synthesis (DSMC) algorithm for finite-state Markov chains. We present a state-dependent consensus protocol that achieves exponential convergence under mild technical…

The widespread use of Markov Chain Monte Carlo (MCMC) methods for high-dimensional applications has motivated research into the scalability of these algorithms with respect to the dimension of the problem. Despite this, numerous problems…

Sequential Monte Carlo (SMC) methods are a class of Monte Carlo methods that are used to obtain random samples of a high dimensional random variable in a sequential fashion. Many problems encountered in applications often involve different…

Proximal Markov Chain Monte Carlo is a novel construct that lies at the intersection of Bayesian computation and convex optimization, which helped popularize the use of nondifferentiable priors in Bayesian statistics. Existing formulations…

This paper introduces methodology for performing Bayesian inference sequentially on a sequence of posteriors on spaces of different dimensions. We show how this may be achieved through the use of sequential Monte Carlo (SMC) samplers (Del…

Deep learning has recently gained attention in the atmospheric and oceanic sciences for its potential to improve the accuracy of numerical simulations or to reduce computational costs. Super-resolution is one such technique for…

Using a very cheap Data Assimilation (DA) method, I show an alternative approach to classical DA for numerical climate models which produce a large amount of "big data". The problematic features of state-of-the-art high resolution Regional…