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Probabilistic models are conceptually powerful tools for finding structure in data, but their practical effectiveness is often limited by our ability to perform inference in them. Exact inference is frequently intractable, so approximate…
There has been substantial interest in developing Markov chain Monte Carlo algorithms based on piecewise-deterministic Markov processes. However existing algorithms can only be used if the target distribution of interest is differentiable…
We introduce a model of long-range interacting particles evolving under a stochastic Monte Carlo dynamics, in which possible increase or decrease in the values of the dynamical variables is accepted with preassigned probabilities. For…
In this article, we propose a Milstein finite difference scheme for a stochastic partial differential equation (SPDE) describing a large particle system. We show, by means of Fourier analysis, that the discretisation on an unbounded domain…
We investigate the systematic mechanism for designing fast mixing Markov chain Monte Carlo algorithms to sample from discrete point processes under the Dobrushin uniqueness condition for Gibbs measures. Discrete point processes are defined…
We combine parallelization and cluster Monte Carlo for hard sphere systems and present a parallelized event chain algorithm for the hard disk system in two dimensions. For parallelization we use a spatial partitioning approach into…
The need to calibrate increasingly complex statistical models requires a persistent effort for further advances on available, computationally intensive Monte Carlo methods. We study here an advanced version of familiar Markov Chain Monte…
We present a Markov chain Monte Carlo scheme based on merges and splits of groups that is capable of efficiently sampling from the posterior distribution of network partitions, defined according to the stochastic block model (SBM). We…
Performing reliable Bayesian inference on a big data scale is becoming a keystone in the modern era of machine learning. A workhorse class of methods to achieve this task are Markov chain Monte Carlo (MCMC) algorithms and their design to…
Switching dynamical systems are an expressive model class for the analysis of time-series data. As in many fields within the natural and engineering sciences, the systems under study typically evolve continuously in time, it is natural to…
The seminal 2009 paper by Bernard, Krauth, and Wilson marked a paradigm shift in Monte Carlo sampling. By abandoning the restrictive condition of detailed balance in favor of the more fundamental principle of global balance, they introduced…
In recent years, a better understanding of the Monte Carlo method has provided us with many new techniques in different areas of statistical physics. Of particular interest are so called cluster methods, which exploit the considerable…
A new computational algorithm, the discrete singular convolution (DSC), is introduced for computational electromagnetics. The basic philosophy behind the DSC algorithm for the approximation of functions and their derivatives is studied.…
The dynamics of sheared inelastic-hard-sphere systems are studied using non-equilibrium molecular dynamics simulations and direct simulation Monte Carlo. In the molecular dynamics simulations Lees-Edwards boundary conditions are used to…
We propose a stochastic gradient Markov chain Monte Carlo (SG-MCMC) algorithm for scalable inference in mixed-membership stochastic blockmodels (MMSB). Our algorithm is based on the stochastic gradient Riemannian Langevin sampler and…
In past decades, enormous effort has been expended to develop algorithms and even to construct special-purpose computers in order to efficiently evaluate total energies and forces for long-range-interacting particle systems, with the…
Explicit simulations of fluid mixtures of highly size-dispersed particles are constrained by numerical challenges associated with identifying pair-interaction neighbors. Recent algorithmic developments have ameliorated these difficulties to…
Group-level behaviour of particles undergoing a velocity jump process with hard-sphere interactions is investigated. We derive $N$-particle transport equations that include the possibility of collisions between particles and apply different…
Recently several authors studied the segregation of particles for a system composed of mono-dispersed inelastic spheres contained in a box divided by a wall in the middle. The system exhibited a symmetry breaking leading to an…
The method of block coordinate gradient descent (BCD) has been a powerful method for large-scale optimization. This paper considers the BCD method that successively updates a series of blocks selected according to a Markov chain. This kind…