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The literature in social network analysis has largely focused on methods and models which require complete network data; however there exist many networks which can only be studied via sampling methods due to the scale or complexity of the…
Many modern applications collect highly imbalanced categorical data, with some categories relatively rare. Bayesian hierarchical models combat data sparsity by borrowing information, while also quantifying uncertainty. However, posterior…
Hamiltonian Monte Carlo (HMC) is a state-of-the-art Markov chain Monte Carlo sampling algorithm for drawing samples from smooth probability densities over continuous spaces. We study the variant most widely used in practice, Metropolized…
This review treats the mathematical and algorithmic foundations of non-reversible Markov chains in the context of event-chain Monte Carlo (ECMC), a continuous-time lifted Markov chain that employs the factorized Metropolis algorithm. It…
The Metropolis-Hastings algorithm has been extensively studied in the estimation and simulation literature, with most prior work focusing on convergence behavior and asymptotic theory. However, its covariance structure-an important…
Metropolis-Hastings (MH) is a foundational Markov chain Monte Carlo (MCMC) algorithm. In this paper, we ask whether it is possible to formulate and analyse MH in terms of categorical probability, using a recent involutive framework for…
Markov chain Monte Carlo (MCMC) algorithms provide a very general recipe for estimating properties of complicated distributions. While their use has become commonplace and there is a large literature on MCMC theory and practice, MCMC users…
One of the most demanding calculations is to generate random samples from a specified probability distribution (usually with an unknown normalizing prefactor) in a high-dimensional configuration space. One often has to resort to using a…
Performing numerical integration when the integrand itself cannot be evaluated point-wise is a challenging task that arises in statistical analysis, notably in Bayesian inference for models with intractable likelihood functions. Markov…
Deterministic compartmental models are predominantly used in the modeling of infectious diseases, though stochastic models are considered more realistic, yet are complicated to estimate due to missing data. In this paper we present a novel…
Tasks such as record linkage and multi-target tracking, which involve reconstructing the set of objects that underlie some observed data, are particularly challenging for probabilistic inference. Recent work has achieved efficient and…
Sampling from the lattice Gaussian distribution plays an important role in various research fields. In this paper, the Markov chain Monte Carlo (MCMC)-based sampling technique is advanced in several fronts. Firstly, the spectral gap for the…
We examine the optimal scaling and the efficiency of the pseudo-marginal random walk Metropolis algorithm using a recently-derived result on the limiting efficiency as the dimension, $d\rightarrow \infty$. We prove that the optimal scaling…
In this paper we address the problem of Monte Carlo approximation of posterior probability distributions in stochastic kinetic models (SKMs). SKMs are multivariate Markov jump processes that model the interactions among species in…
Markov jump processes (MJPs) are continuous-time stochastic processes widely used in a variety of applied disciplines. Inference for MJPs typically proceeds via Markov chain Monte Carlo, the state-of-the-art being a uniformization-based…
Markov Chain Monte Carlo methods are widely used in signal processing and communications for statistical inference and stochastic optimization. In this work, we introduce an efficient adaptive Metropolis-Hastings algorithm to draw samples…
We develop a novel Markov chain Monte Carlo (MCMC) method that exploits a hierarchy of models of increasing complexity to efficiently generate samples from an unnormalized target distribution. Broadly, the method rewrites the Multilevel…
One of the major problems in adaptive filtering is the problem of system identification. It has been studied extensively due to its immense practical importance in a variety of fields. The underlying goal is to identify the impulse response…
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…
An irreversible Markov-chain Monte Carlo (MCMC) algorithm with skew detailed balance conditions originally proposed by Turitsyn et al. is extended to general discrete systems on the basis of the Metropolis-Hastings scheme. To evaluate the…