Related papers: On the concentration properties of Interacting par…
The past decade has seen a revived interest in the unavoidable or intrinsic noise in biochemical and genetic networks arising from the finite copy number of the participating species. That is, rather than modeling regulatory networks in…
In this paper we investigate the speed of convergence of the fluctuations of a general class of Feynman-Kac particle approximation models. We design an original approach based on new Berry-Esseen type estimates for abstract martingale…
This statistical physics thesis focuses on the study of three kinds of systems which display repulsive interactions: eigenvalues of random matrices, non-crossing random walks and trapped fermions. These systems share many links, which can…
The style of mathematical models known to probabilists as Interacting Particle Systems and exemplified by the Voter, Exclusion and Contact processes have found use in many academic disciplines. In many such disciplines the underlying…
Bayesian sampling is an important task in statistics and machine learning. Over the past decade, many ensemble-type sampling methods have been proposed. In contrast to the classical Markov chain Monte Carlo methods, these new methods deploy…
We present a simulation methodology for Bayesian estimation of rate parameters in Markov jump processes arising for example in stochastic kinetic models. To handle the problem of missing components and measurement errors in observed data,…
We present a sequential sampling methodology for weakly structural Markov laws, arising naturally in a Bayesian structure learning context for decomposable graphical models. As a key component of our suggested approach, we show that the…
We design a theoretic tree-based functional representation of a class of Feynman-Kac particle distributions, including an extension of the Wick product formula to interacting particle systems. These weak expansions rely on an original…
The paper presents a computational stochastic model of virtual cells irradiation, based on Quasi-Markov Chain Monte Carlo method and using biophysical input. The model is based on a stochastic tree of probabilities for each cell of the…
This paper presents a two-phase method for learning interaction kernels of stochastic many-particle systems. After transforming stochastic trajectories of every particle into the particle density function by the kernel density estimation…
Nonlinear non-Gaussian state-space models are ubiquitous in statistics, econometrics, information engineering and signal processing. Particle methods, also known as Sequential Monte Carlo (SMC) methods, provide reliable numerical…
This is lecture notes on the course "Stochastic Processes". In this format, the course was taught in the spring semesters 2017 and 2018 for third-year bachelor students of the Department of Control and Applied Mathematics, School of Applied…
Large deviations for additive path functionals of stochastic processes have attracted significant research interest, in particular in the context of stochastic particle systems and statistical physics. Efficient numerical `cloning'…
This paper explores the versatility and depth of Bayesian modeling by presenting a comprehensive range of applications and methods, combining Markov chain Monte Carlo (MCMC) techniques and variational approximations. Covering topics such as…
We analyse the stochastic comparison of interacting particle systems allowing for multiple arrivals, departures and non-conservative jumps of individuals between sites. That is, if $k$ individuals leave site $x$ for site $y$, a possibly…
Many complex systems are characterized by intriguing spatio-temporal structures. Their mathematical description relies on the analysis of appropriate correlation functions. Functional integral techniques provide a unifying formalism that…
We study the existence of densities for distributions of piecewise deterministic Markov processes. We also obtain relationships between invariant densities of the continuous time process and that of the process observed at jump times. In…
We study a class of multi-stage stochastic programs, which incorporate modeling features from Markov decision processes (MDPs). This class includes structured MDPs with continuous action and state spaces. We extend policy graphs to include…
We present a Markov-chain analysis of blockwise-stochastic algorithms for solving partially block-separable optimization problems. Our main contributions to the extensive literature on these methods are statements about the Markov operators…
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…