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Restricted Boltzmann Machines (RBMs) offer a versatile architecture for unsupervised machine learning that can in principle approximate any target probability distribution with arbitrary accuracy. However, the RBM model is usually not…

Stochastic differential equations provide a powerful tool for modelling dynamic phenomena affected by random noise. In case of repeated observations of time series for several experimental units, it is often the case that some of the…

In Bayesian inference, predictive distributions are typically in the form of samples generated via Markov chain Monte Carlo (MCMC) or related algorithms. In this paper, we conduct a systematic analysis of how to make and evaluate…

Rare transitions in stochastic processes can often be rigorously described via an underlying large deviation principle. Recent breakthroughs in the classification of reversible stochastic processes as gradient flows have led to a connection…

We provide an algorithm based on weighted-ensemble (WE) methods, to accurately sample systems at steady state. Applying our method to different one- and two-dimensional models, we succeed to calculate steady state probabilities of order…

Stochastic kinetic models (SKMs) are increasingly used to account for the inherent stochasticity exhibited by interacting populations of species in areas such as epidemiology, population ecology and systems biology. Species numbers are…

Multiple importance sampling (MIS) is an indispensable tool in rendering that constructs robust sampling strategies by combining the respective strengths of individual distributions. Its efficiency can be greatly improved by carefully…

Resilience is becoming crucial for future wireless networks, which must withstand, adapt to, and recover from rare but potentially cascading disruptions. This paper develops a sequential Monte Carlo (SMC) simulation framework for such…

Electricity systems are experiencing increased effects of randomness and variability due to emerging stochastic assets. The increased effects introduce new uncertainties into power systems that can impact system operability and reliability.…

Epidemics are inherently stochastic, and stochastic models provide an appropriate way to describe and analyse such phenomena. Given temporal incidence data consisting of, for example, the number of new infections or removals in a given time…

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…

Applications of stochastic models often involve the evaluation of steady-state performance, which requires solving a set of balance equations. In most cases of interest, the number of equations is infinite or even uncountable. As a result,…

Markov decision processes (MDP) are a well-established model for sequential decision-making in the presence of probabilities. In robust MDP (RMDP), every action is associated with an uncertainty set of probability distributions, modelling…

A sampling procedure for the transition matrix Monte Carlo method is introduced that generates the density of states function over a wide parameter range with minimal coding effort.

In this paper, we provide a multiscale perspective on the problem of maximum marginal likelihood estimation. We consider and analyse a diffusion-based maximum marginal likelihood estimation scheme using ideas from multiscale dynamics. Our…

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…

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…

The interplay between stochastic chemical reactions and diffusion can generate rich spatiotemporal patterns. While the timescale for individual reaction or diffusion events may be very fast, the timescales for organization can be much…

In an experimental study of single enzyme reactions, it has been proposed that the rate constants of the enzymatic reactions fluctuate randomly, according to a given distribution. To quantify the uncertainty arising from random rate…

Since many environmental processes such as heat waves or precipitation are spatial in extent, it is likely that a single extreme event affects several locations and the areal modeling of extremes is therefore essential if the spatial…