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There is a class of statistical problems that arises in several contexts, the Lattice QCD problem of particle physics being one that has attracted the most attention. In essence, the problem boils down to the estimation of an infinite…

Markov Chain Monte Carlo (MCMC) methods have become a cornerstone of many modern scientific analyses by providing a straightforward approach to numerically estimate uncertainties in the parameters of a model using a sequence of random…

Parameterized complexity theory offers a framework for a refined analysis of hard algorithmic problems. Instead of expressing the running time of an algorithm as a function of the input size only, running times are expressed with respect to…

We develop an approach to time-consistent risk evaluation of continuous-time processes in Markov systems. Our analysis is based on dual representation of coherent risk measures, differentiability concepts for multivalued mappings, and a…

Cyber-physical systems often encompass complex concurrent behavior with timing constraints and probabilistic failures on demand. The analysis whether such systems with probabilistic timed behavior ad-here to a given specification is…

We solve the Chapman-Kolmogorov equation and study the exact splitting probabilities of the general stochastic process which describes polymer translocation through membrane pores within the broad class of Markov chains. Transition…

Stochastic gradient Markov chain Monte Carlo (MCMC) algorithms have received much attention in Bayesian computing for big data problems, but they are only applicable to a small class of problems for which the parameter space has a fixed…

Markov chain Monte Carlo (MCMC) is a powerful tool for sampling from complex probability distributions. Despite its versatility, MCMC often suffers from strong autocorrelation and the negative sign problem, leading to slowing down the…

Continuous-time Markov chains describing interacting processes exhibit a state space that grows exponentially in the number of processes. This state-space explosion renders the computation or storage of the time-marginal distribution, which…

Markov chains are convenient means of generating realizations of networks with a given (joint or otherwise) degree distribution, since they simply require a procedure for rewiring edges. The major challenge is to find the right number of…

The two-parameter Macdonald polynomials are a central object of algebraic combinatorics and representation theory. We give a Markov chain on partitions of k with eigenfunctions the coefficients of the Macdonald polynomials when expanded in…

We develop a general theory of Markov chains realizable as random walks on $\mathscr R$-trivial monoids. It provides explicit and simple formulas for the eigenvalues of the transition matrix, for multiplicities of the eigenvalues via…

A fundamental challenge in probabilistic modeling is to balance expressivity and inference efficiency. Tractable probabilistic models (TPMs) aim to directly address this tradeoff by imposing constraints that guarantee efficient inference of…

Ensuring that agents satisfy safety specifications can be crucial in safety-critical environments. While methods exist for controller synthesis with safe temporal specifications, most existing methods restrict safe temporal specifications…

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…

In recent years probabilistic model checking has become an important area of research because of the diffusion of computational systems of stochastic nature. Despite its great success, standard probabilistic model checking suffers the…

Approaches to Bayesian inference for problems with intractable likelihoods have become increasingly important in recent years. Approximate Bayesian computation (ABC) and "likelihood free" Markov chain Monte Carlo techniques are popular…

Verifying quantum systems has attracted a lot of interest in the last decades.In this paper, we study the quantitative model-checking of quantum continuous-time Markov chains (quantum CTMCs). The branching-time properties of quantum CTMCs…

The Markov chain Monte Carlo method is a versatile tool in statistical physics to evaluate multi-dimensional integrals numerically. For the method to work effectively, we must consider the following key issues: the choice of ensemble, the…

Markov chains and Markov decision processes (MDPs) are well-established probabilistic models. While finite Markov models are well-understood, analysing their infinite counterparts remains a significant challenge. Decisiveness has proven to…