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In this paper the choice of the Bernoulli distribution as biased distribution for importance sampling (IS) Monte-Carlo (MC) simulation of linear block codes over binary symmetric channels (BSCs) is studied. Based on the analytical…
Estimating a Gibbs density function given a sample is an important problem in computational statistics and statistical learning. Although the well established maximum likelihood method is commonly used, it requires the computation of the…
Inference for partially observed Markov process models has been a longstanding methodological challenge with many scientific and engineering applications. Iterated filtering algorithms maximize the likelihood function for partially observed…
Accurate estimates of long-term risk probabilities and their gradients are critical for many stochastic safe control methods. However, computing such risk probabilities in real-time and in unseen or changing environments is challenging.…
In parameter estimation problems one computes a posterior distribution over uncertain parameters defined jointly by a prior distribution, a model, and noisy data. Markov Chain Monte Carlo (MCMC) is often used for the numerical solution of…
The region of attraction characterizes well-behaved and safe operation of a nonlinear system and is hence sought after for verification. In this paper, a framework for probabilistic region of attraction estimation is developed that combines…
In rare-event simulation, an importance sampling (IS) estimator is regarded as efficient if its relative error, namely the ratio between its standard deviation and mean, is sufficiently controlled. It is widely known that when a rare-event…
We consider Monte Carlo approximations to the maximum likelihood estimator in models with intractable norming constants. This paper deals with adaptive Monte Carlo algorithms, which adjust control parameters in the course of simulation. We…
Ranking interfaces are everywhere in online platforms. There is thus an ever growing interest in their Off-Policy Evaluation (OPE), aiming towards an accurate performance evaluation of ranking policies using logged data. A de-facto approach…
We develop an interacting particle method (IPM) for computing the large deviation rate function of entropy production for diffusion processes, with emphasis on the vanishing-noise limit and high dimensions. The crucial ingredient to obtain…
We introduce a new method for online parameter estimation in stochastic interacting particle systems, based on continuous observation of a small number of particles from the system. Our method recursively updates the model parameters using…
Classical algorithms in numerical analysis for numerical integration (quadrature/cubature) follow the principle of approximate and integrate: the integrand is approximated by a simple function (e.g. a polynomial), which is then integrated…
This paper investigates the optimization problem of an infinite stage discrete time Markov decision process (MDP) with a long-run average metric considering both mean and variance of rewards together. Such performance metric is important…
We analyse the splitting algorithm performance in the estimation of rare event probabilities and this in a discrete multidimensional framework. For this we assume that each threshold is partitioned into disjoint subsets and the probability…
Importance sampling (IS) is a Monte Carlo technique for the approximation of intractable distributions and integrals with respect to them. The origin of IS dates from the early 1950s. In the last decades, the rise of the Bayesian paradigm…
Maximum entropy method is a constructive criterion for setting up a probability distribution maximally non-committal to missing information on the basis of partial knowledge, usually stated as constrains on expectation values of some…
We review probabilistic approaches to the Gross-Pitaevskii theory describing interacting dilute systems of particles. The main achievement are large deviations principles for the mean occupation measure of a large system of interacting…
A platform trial with a master protocol provides an infrastructure to ethically and efficiently evaluate multiple treatment options in multiple diseases. Given that certain study drugs can enter or exit a platform trial, the randomization…
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…
We propose a method of approximating multivariate Gaussian probabilities using dynamic programming. We show that solving the optimization problem associated with a class of discrete-time finite horizon Markov decision processes with…