Related papers: Probability density function for random photon ste…
We present a comprehensive methodology for the simulation of astronomical images from optical survey telescopes. We use a photon Monte Carlo approach to construct images by sampling photons from models of astronomical source populations,…
We study the persistent random walk of photons on a one-dimensional lattice of random transmittances. Transmittances at different sites are assumed independent, distributed according to a given probability density $f(t)$. Depending on the…
In this article, an overview of Bayesian methods for sequential simulation from posterior distributions of nonlinear and non-Gaussian dynamic systems is presented. The focus is mainly laid on sequential Monte Carlo methods, which are based…
We present a method which extends Monte Carlo studies to situations that require a large dynamic range in particle number. The underlying idea is that, in order to calculate the collisional evolution of a system, some particle interactions…
Simulating samples from arbitrary probability distributions is a major research program of statistical computing. Recent work has shown promise in an old idea, that sampling from a discrete distribution can be accomplished by perturbing and…
This paper introduces a Monte Carlo method for maximum likelihood inference in the context of discretely observed diffusion processes. The method gives unbiased and a.s.\@ continuous estimators of the likelihood function for a family of…
Statisticians often use Monte Carlo methods to approximate probability distributions, primarily with Markov chain Monte Carlo and importance sampling. Sequential Monte Carlo samplers are a class of algorithms that combine both techniques to…
A photon entering a scattering medium executes a three-dimensional random walk determined by the Henyey-Greenstein phase function. The photon either reaches the boundary for a first passage or is absorbed. Projecting the walk onto the axial…
We consider the scattering of neutrons and photons on solid volume rectangular targets. It is common to treat this problem using the Maxwell Boltzmann Transport Equation and to use underlying symmetries to simplify the calculation. For…
We briefly review the principles, mathematical bases, numerical shortcuts and applications of fast random walk (FRW) algorithms. This Monte Carlo technique allows one to simulate individual trajectories of diffusing particles in order to…
We examine using Monte Carlo simulations, photon transport in optically `thin' slabs whose thickness L is only a few times the transport mean free path $l^{*}$, with particles of different scattering anisotropies. The confined geometry…
Monte Carlo simulations of diffusion processes often introduce bias in the final result, due to time discretization. Using an auxiliary Poisson process, it is possible to run simulations which are unbiased. In this article, we propose such…
We propose a micro-macro parallel-in-time Parareal method for scalar McKean-Vlasov stochastic differential equations (SDEs). In the algorithm, the fine Parareal propagator is a Monte Carlo simulation of an ensemble of particles, while an…
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…
We independently develop a simulation code following the previous dynamical Monte Carlo simulation of the diffusive shock acceleration under the isotropic scattering law during the scattering process, and the same results are obtained.…
Motivated by applications to Bayesian inference for statistical models with orthogonal matrix parameters, we present $\textit{polar expansion},$ a general approach to Monte Carlo simulation from probability distributions on the Stiefel…
Modern signal processing (SP) methods rely very heavily on probability and statistics to solve challenging SP problems. SP methods are now expected to deal with ever more complex models, requiring ever more sophisticated computational…
Multispectral imaging plays an important role in many applications from astronomical imaging, earth observation to biomedical imaging. However, the current technologies are complex with multiple alignment-sensitive components, predetermined…
Models of stochastic processes are widely used in almost all fields of science. Theory validation, parameter estimation, and prediction all require model calibration and statistical inference using data. However, data are almost always…
A new method is presented for determining the Point Spread Function (PSF) of images that lack bright and isolated stars. It is based on the same principles as the MCS (Magain, Courbin, Sohy, 1998) image deconvolution algorithm. It uses the…