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Markov chain Monte Carlo methods have become standard tools in statistics to sample from complex probability measures. Many available techniques rely on discrete-time reversible Markov chains whose transition kernels build up over the…
Recent work incorporating geometric ideas in Markov chain Monte Carlo is reviewed in order to highlight these advances and their possible application in a range of domains beyond Statistics. A full exposition of Markov chains and their use…
The theory of radiative transfer provides the link between the physical conditions in an astrophysical object and the observable radiation which it emits. Thus accurately modelling radiative transfer is often a necessary part of testing…
We study the Monte Carlo method for solving a linear system of the form $x = H x + b$. A sufficient condition for the method to work is $\| H \| < 1$, which greatly limits the usability of this method. We improve this condition by proposing…
Radiative transfer simulation is an important tool that allows us to generate synthetic images of various astrophysical objects. In the case of complex three-dimensional geometries, a Monte Carlo-based method that simulates photon packages…
Monte Carlo (MC) sampling methods are widely applied in Bayesian inference, system simulation and optimization problems. The Markov Chain Monte Carlo (MCMC) algorithms are a well-known class of MC methods which generate a Markov chain with…
An efficient Path Integral Monte Carlo procedure is proposed to simulate the behavior of quantum many-body dissipative systems described within the framework of the influence functional. Thermodynamic observables are obtained by Monte Carlo…
A Monte Carlo method for computing the action of a matrix exponential for a certain class of matrices on a vector is proposed. The method is based on generating random paths, which evolve through the indices of the matrix, governed by a…
Owing to their capability of summarising interactions between elements of a system, networks have become a common type of data in many fields. As networks can be inhomogeneous, in that different regions of the network may exhibit different…
We consider a quantum system coupled to a dissipative background with many degrees of freedom using the Monte Carlo Wave Function method. Instead of dealing with a density matrix which can be very high-dimensional, the method consists of…
The Monte Carlo technique is used to calculate electrical as well as thermoelectric transport properties across thin film heterostructures. We study a thin InGaAsP barrier layer sandwiched between two InGaAs contact layers, when the barrier…
We report on a new capability added to our general relativistic radiation-magnetohydrodynamics code, Cosmos++: an implicit Monte Carlo (IMC) treatment for radiation transport. The method is based on a Fleck-type implicit discretization of…
A Monte-Carlo algorithm for discrete statistical models that combines the full power of the Belief Propagation algorithm with the advantages of a detailed-balanced heat bath approach is presented. A sub-tree inside the factor graph is first…
A kinetic Monte Carlo method was used to simulate the diffusion of reptating polymer chains across the interface. A time-resolved fluorescence technique conjunction with direct energy transfer method was used to measure the extend of…
We present a population control method with sampling and regulation steps for Monte Carlo particles involved in the numerical simulation of a transport equation. We recall in the first section the difficulties related to the variance…
The basic problem in equilibrium statistical mechanics is to compute phase space average, in which Monte Carlo method plays a very important role. We begin with a review of nonlocal algorithms for Markov chain Monte Carlo simulation in…
We explore the application of Monte Carlo transport methods to solving coupled radiation-hydrodynamics problems. We use a time-dependent, frequency-dependent, 3-dimensional radiation transport code, that is special relativistic and includes…
A new code for evaluation of light absorption and scattering by interstellar dust grains is presented. The radiative transfer problem is solved using ray-tracing algorithm in a self-consistent and highly efficient way. The code demonstrates…
Many problems in materials science and biology involve particles interacting with strong, short-ranged bonds, that can break and form on experimental timescales. Treating such bonds as constraints can significantly speed up sampling their…
Monte Carlo approaches to radiation transport have several attractive properties such as simplicity of implementation, high accuracy, and good parallel scaling. Moreover, Monte Carlo methods can handle complicated geometries and are…