Related papers: Estimating the spectral gap of a trace-class Marko…

Boson sampling is a promising candidate for quantum supremacy. It requires to sample from a complicated distribution, and is trusted to be intractable on classical computers. Among the various classical sampling methods, the Markov chain…

Single-chain Markov chain Monte Carlo simulates realizations from a Markov chain to estimate expectations with the empirical average. The single-chain simulation is generally of considerable length and restricts many advantages of modern…

Particle Markov Chain Monte Carlo methods are used to carry out inference in non-linear and non-Gaussian state space models, where the posterior density of the states is approximated using particles. Current approaches usually perform…

This paper proposes an eigenvalue-based small-sample approximation of the celebrated Markov Chain Monte Carlo that delivers an invariant steady-state distribution that is consistent with traditional Monte Carlo methods. The proposed…

MCMC methods (Monte Carlo Markov Chain) are a class of methods used to perform simulations per a probability distribution $P$. These methods are often used when we have difficulties to directly sample per a given probability distribution…

We demonstrate the use of a variational method to determine a quantitative lower bound on the rate of convergence of Markov Chain Monte Carlo (MCMC) algorithms as a function of the target density and proposal density. The bound relies on…

Many random processes can be simulated as the output of a deterministic model accepting random inputs. Such a model usually describes a complex mathematical or physical stochastic system and the randomness is introduced in the input…

We consider a vector of $N$ independent binary variables, each with a different probability of success. The distribution of the vector conditional on its sum is known as the conditional Bernoulli distribution. Assuming that $N$ goes to…

An efficient simulation-based methodology is proposed for the rolling window estimation of state space models, called particle rolling Markov chain Monte Carlo (MCMC) with double block sampling. In our method, which is based on Sequential…

Many applications in signal processing require the estimation of some parameters of interest given a set of observed data. More specifically, Bayesian inference needs the computation of {\it a-posteriori} estimators which are often…

The subject of the present study is the Monte Carlo path-integral evaluation of the moments of spectral functions. Such moments can be computed by formal differentiation of certain estimating functionals that are infinitely-differentiable…

The random numbers driving Markov chain Monte Carlo (MCMC) simulation are usually modeled as independent U(0,1) random variables. Tribble [Markov chain Monte Carlo algorithms using completely uniformly distributed driving sequences (2007)…

This paper introduces a class of Monte Carlo algorithms which are based upon the simulation of a Markov process whose quasi-stationary distribution coincides with a distribution of interest. This differs fundamentally from, say, current…

We elaborate the idea behind Markov chain Monte Carlo (MCMC) methods in a mathematically coherent, yet simple and understandable way. To this end, we proof a pivotal convergence theorem for finite Markov chains and a minimal version of the…

In the thesis we take the split chain approach to analyzing Markov chains and use it to establish fixed-width results for estimators obtained via Markov chain Monte Carlo procedures (MCMC). Theoretical results include necessary and…

We take on a Random Matrix theory viewpoint to study the spectrum of certain reversible Markov chains in random environment. As the number of states tends to infinity, we consider the global behavior of the spectrum, and the local behavior…

Orthogonal matrices play an important role in probability and statistics, particularly in high-dimensional statistical models. Parameterizing these models using orthogonal matrices facilitates dimension reduction and parameter…

Bayesian inference for Markov processes has become increasingly relevant in recent years. Problems of this type often have intractable likelihoods and prior knowledge about model rate parameters is often poor. Markov Chain Monte Carlo…

Switching dynamical systems are an expressive model class for the analysis of time-series data. As in many fields within the natural and engineering sciences, the systems under study typically evolve continuously in time, it is natural to…

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…