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Our purpose is to explore, in the context of loop ensembles on finite graphs, the relations between combinatorial group theory, loops topology, loop measures, and signatures of discrete paths. We determine the distributions of the loop…

We propose approaches for testing implementations of Markov Chain Monte Carlo methods as well as of general Monte Carlo methods. Based on statistical hypothesis tests, these approaches can be used in a unit testing framework to, for…

We study the topology of a random cubical complex associated to Bernoulli site percolation on a cubical grid. We begin by establishing a limit law for homotopy types. More precisely, looking within an expanding window, we define a sequence…

Perfect sampling is a technique that uses coupling arguments to provide a sample from the stationary distribution of a Markov chain in a finite time without ever computing the distribution. This technique is very efficient if all the events…

A stochastic algorithm is proposed, finding the set of generalized means associated to a probability measure on a compact Riemannian manifold M and a continuous cost function on the product of M by itself. Generalized means include p-means…

We discuss a Monte Carlo Markov Chain (MCMC) procedure for the random sampling of some one-dimensional lattice paths with constraints, for various constraints. We show that an approach inspired by optimal transport allows us to bound…

In this paper we develop a general framework for constructing and analysing coupled Markov chain Monte Carlo samplers, allowing for both (possibly degenerate) diffusion and piecewise deterministic Markov processes. For many performance…

The purpose of this paper is twofold. First, we provide a novel characterization of independence of random vectors based on the checkerboard approximation to a multivariate copula. Using this result, we then propose a new family of tests of…

A general theory is provided delivering convergence of maximal cyclically monotone mappings containing the supports of coupling measures of sequences of pairs of possibly random probability measures on Euclidean space. The theory is based…

Trace monoids and heaps of pieces appear in various contexts in combinatorics. They also constitute a model used in computer science to describe the executions of asynchronous systems. The design of a natural probabilistic layer on top of…

Monte Carlo methods are widely used to estimate observables in many-body quantum systems. However, conventional sampling schemes often require a large number of samples to achieve sufficient accuracy. In this work we propose the…

Monte Carlo experiments produce samples in order to estimate features of a given distribution. However, simultaneous estimation of means and quantiles has received little attention, despite being common practice. In this setting we…

Sequential Monte Carlo Samplers are a class of stochastic algorithms for Monte Carlo integral estimation w.r.t. probability distributions, which combine elements of Markov chain Monte Carlo methods and importance sampling/resampling…

Oriented loops on an orientable surface are, up to equivalence by free homotopy, in one-to-one correspondence with the conjugacy classes of the surface's fundamental group. These conjugacy classes can be expressed (not uniquely in the case…

We present a probabilistic theory of random walks in turbid media with non-scattering regions. It is shown that important characteristics such as diffusion constants, average step lengths, crossing statistics and void spacings can be…

Markov Chain Monte Carlo (MCMC) requires to evaluate the full data likelihood at different parameter values iteratively and is often computationally infeasible for large data sets. In this paper, we propose to approximate the log-likelihood…

Markov chain Monte Carlo (MCMC) sampling of densities restricted to linearly constrained domains is an important task arising in Bayesian treatment of inverse problems in the natural sciences. While efficient algorithms for uniform polytope…

In this text we expose basic cases of some fundamental ideas and methods of topology. Namely, of homotopy, degree, fundamental group, covering, Whitehead invariant, etc. This is done by considering the elementary example: closed polygonal…

The problem of sampling constrained continuous distributions has frequently appeared in many machine/statistical learning models. Many Monte Carlo Markov Chain (MCMC) sampling methods have been adapted to handle different types of…

We present a novel technique for the determination of the topological susceptibility (related to the variance of the distribution of global topological charge) from lattice gauge theory simulations, based on maximum-likelihood analysis of…