Related papers: An overview of Marchenko methods
In this chapter, we review some of the most standard MCMC tools used in Bayesian computation, along with vignettes on standard misunderstandings of these approaches taken from Q \&~A's on the forum Cross-validated answered by the first…
The Markov Chain Monte Carlo (MCMC) algorithm is a widely recognised as an efficient method for sampling a specified posterior distribution. However, when the posterior is multi-modal, conventional MCMC algorithms either tend to become…
Monte Carlo methods play an important role in scientific computation, especially when problems have a vast phase space. In this lecture an introduction to the Monte Carlo method is given. Concepts such as Markov chains, detailed balance,…
Various methods have been developed independently to study the multifractality of measures in many different contexts. Although they all convey the same intuitive idea of giving a "dimension" to sets where a quantity scales similarly within…
This article studies the convergence properties of trans-dimensional MCMC algorithms when the total number of models is finite. It is shown that, for reversible and some non-reversible trans-dimensional Markov chains, under mild conditions,…
A fundamental challenge in Bayesian inference is efficient representation of a target distribution. Many non-parametric approaches do so by sampling a large number of points using variants of Markov Chain Monte Carlo (MCMC). We propose an…
After a brief digression on the current landscape of theoretical physics and on some open questions pertaining to coherence with experimental results, still to be settled, it is shown that the properties of the Deformed Minkowski space lead…
In this article we consider Bayesian estimation of static parameters for a class of partially observed McKean-Vlasov diffusion processes with discrete-time observations over a fixed time interval. This problem features several obstacles to…
The use of the Bayesian tools in system identification and model updating paradigms has been increased in the last ten years. Usually, the Bayesian techniques can be implemented to incorporate the uncertainties associated with measurements…
We have seen many developments in Marchenko equation-based methods for internal multiple attenuation in the past years. Starting from a wave-equation based method that required a smooth velocity model, there are now Marchenko equation-based…
The Marchenko method is developed in the inverse scattering problem for a linear system of first-order differential equations containing potentials proportional to the spectral parameter. The corresponding Marchenko system of integral…
We introduce and discuss Monte Carlo methods in quantum field theories. Methods of independent Monte Carlo, such as random sampling and importance sampling, and methods of dependent Monte Carlo, such as Metropolis sampling and Hamiltonian…
Markov Chain Monte Carlo methods have revolutionised mathematical computation and enabled statistical inference within many previously intractable models. In this context, Hamiltonian dynamics have been proposed as an efficient way of…
This article focuses on covariance estimation for multi-view data. Popular approaches rely on factor-analytic decompositions that have shared and view-specific latent factors. Posterior computation is conducted via expensive and brittle…
A unified set of hydrodynamic equations describing condensed phases of matter with broken continuous symmetries is derived using a generalization of the statistical-mechanical approach based on the local equilibrium distribution. The…
In this paper we consider the problem of computing the stationary distribution of nearly completely decomposable Markov processes, a well-established area in the classical theory of Markov processes with broad applications in the design,…
Discrete Markov random fields are undirected graphical models that capture complex conditional dependencies between discrete variables. Conducting exact posterior inference in these models is often computationally challenging because…
In this paper we build on previous work which uses inferences techniques, in particular Markov Chain Monte Carlo (MCMC) methods, to solve parameterized control problems. We propose a number of modifications in order to make this approach…
Many seismic imaging methods use wave field extrapolation operators to redatum sources and receivers from the surface into the subsurface. We discuss wave field extrapolation operators that account for internal multiple reflections, in…
In this work, an efficient numerical scheme is presented for seismic blind deconvolution in a multichannel scenario. The proposed method iterate with wo steps: first, wavelet estimation across all channels and second, refinement of the…