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Markov Chain Monte Carlo (MCMC) algorithms are commonly used for their versatility in sampling from complicated probability distributions. However, as the dimension of the distribution gets larger, the computational costs for a satisfactory…
We analyse a multilevel Monte Carlo method for the approximation of distribution functions of univariate random variables. Since, by assumption, the target distribution is not known explicitly, approximations have to be used. We provide an…
We consider the problem of performing inference with imprecise continuous-time hidden Markov chains, that is, imprecise continuous-time Markov chains that are augmented with random output variables whose distribution depends on the hidden…
Markov Chain Monte Carlo (MCMC) algorithms are routinely used to draw samples from distributions with intractable normalization constants. However, standard MCMC algorithms do not apply to doubly-intractable distributions in which there are…
Piecewise-deterministic Markov processes form a general class of non-diffusion stochastic models that involve both deterministic trajectories and random jumps at random times. In this paper, we state a new characterization of the jump rate…
We propose a novel Markov chain Monte-Carlo (MCMC) method for reverse engineering the topological structure of stochastic reaction networks, a notoriously challenging problem that is relevant in many modern areas of research, like…
Adaptive multilevel splitting algorithms have been introduced rather recently for estimating tail distributions in a fast and efficient way. In particular, they can be used for computing the so-called reactive trajectories corresponding to…
Consider the batch-arrival $GI^X/M/c/N$ model with $c$ servers, general inter-arrival batch times, finite buffer, and exponential service times. Inter-arrival batch times, batch sizes, and service times are $i.i.d.$ and independent of each…
A new approach for optimal estimation of Markov chains with sparse transition matrices is presented.
We present a new Markov chain Monte Carlo method for estimating posterior probabilities of structural features in Bayesian networks. The method draws samples from the posterior distribution of partial orders on the nodes; for each sampled…
We introduce a general Monte Carlo method based on Nested Sampling (NS), for sampling complex probability distributions and estimating the normalising constant. The method uses one or more particles, which explore a mixture of nested…
Markov chain Monte Carlo methods are a powerful tool for sampling equilibrium configurations in complex systems. One problem these methods often face is slow convergence over large energy barriers. In this work, we propose a novel method…
We present an intuitive, conceptual, but semi-rigorous introduction to the celebrated Markov Chain Monte Carlo method using a simple model of population dynamics as our motivation and focusing on a few elementary distributions.…
Markov Chains with variable length are useful stochastic models for data compression that avoid the curse of dimensionality faced by that full Markov Chains. In this paper we introduce a Variable Length Markov Chain whose transition…
In sampling tasks, it is common for target distributions to be known up to a normalizing constant. However, in many situations, even evaluating the unnormalized distribution can be costly or infeasible. This issue arises in scenarios such…
We present an algorithm for learning mixtures of Markov chains and Markov decision processes (MDPs) from short unlabeled trajectories. Specifically, our method handles mixtures of Markov chains with optional control input by going through a…
At high levels, the asymptotic distribution of a stationary, regularly varying Markov chain is conveniently given by its tail process. The latter takes the form of a geometric random walk, the increment distribution depending on the sign of…
Markov chain Monte Carlo (MCMC) methods asymptotically sample from complex probability distributions. The pseudo-marginal MCMC framework only requires an unbiased estimator of the unnormalized probability distribution function to construct…
Time-homogeneous Markov chains are often used as disease progression models in studies of cost-effectiveness and optimal decision-making. Maximum likelihood estimation of these models can be challenging when data are collected at a time…
Many applications in the field of statistics require Markov chain Monte Carlo methods. Determining appropriate starting values and run lengths can be both analytically and empirically challenging. A desire to overcome these problems has led…