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Estimating the size of hidden populations using Multiple Systems Estimation (MSE) is a critical task in quantitative sociology; however, practical application is often hindered by imperfect administrative data and computational constraints.…

There is increasing interest to develop Bayesian inferential algorithms for point process models with intractable likelihoods. A purpose of this paper is to illustrate the utility of using simulation based strategies, including Approximate…

Markov chain Monte Carlo (MCMC) is widely used for Bayesian inference in models of complex systems. Performance, however, is often unsatisfactory in models with many latent variables due to so-called poor mixing, necessitating development…

In this paper we consider the parameter estimation problem associated to partially-observed time changed SDEs, with observations that are given at discrete times. In particular we consider both likelihood and Bayesian estimation. We develop…

In this paper, we introduce a hierarchical extension of the stochastic blockmodel to identify multilevel community structures in networks. We also present a Markov chain Monte Carlo (MCMC) and a variational Bayes algorithm to fit the model…

Sequential Monte Carlo (SMC) methods are a widely used set of computational tools for inference in non-linear non-Gaussian state-space models. We propose a new SMC algorithm to compute the expectation of additive functionals recursively.…

This paper introduces a framework for speeding up Bayesian inference conducted in presence of large datasets. We design a Markov chain whose transition kernel uses an (unknown) fraction of (fixed size) of the available data that is randomly…

We introduce methodology for real-time inference in general-state-space hidden Markov models. Specifically, we extend recent advances in controlled sequential Monte Carlo (CSMC) methods-originally proposed for offline smoothing-to the…

We study the computational complexity of Markov chain Monte Carlo (MCMC) methods for high-dimensional Bayesian linear regression under sparsity constraints. We first show that a Bayesian approach can achieve variable-selection consistency…

This paper surveys various results about Markov chains on general (non-countable) state spaces. It begins with an introduction to Markov chain Monte Carlo (MCMC) algorithms, which provide the motivation and context for the theory which…

Markov chain Monte Carlo (MCMC) methods provide powerful framework for sampling unknown probability measures across a wide range of scientific applications. In some settings, the target distribution is supported on a lower-dimensional…

We consider a class of high-dimensional spatial filtering problems, where the spatial locations of observations are unknown and driven by the partially observed hidden signal. This problem is exceptionally challenging as not only is…

Bayesian analysis often concerns an evaluation of models with different dimensionality as is necessary in, for example, model selection or mixture models. To facilitate this evaluation, transdimensional Markov chain Monte Carlo (MCMC)…

In this paper, we propose a novel method of model-based time series clustering with mixtures of general state space models (MSSMs). Each component of MSSMs is associated with each cluster. An advantage of the proposed method is that it…

In engineering, accurately modeling nonlinear dynamic systems from data contaminated by noise is both essential and complex. Established Sequential Monte Carlo (SMC) methods, used for the Bayesian identification of these systems, facilitate…

Use each of n exact samples as the initial state for a MCMC sampler run for m steps. We give confidence intervals for accuracy of estimators which are always valid and which, in certain settings, are almost as good as the intervals one…

We introduce the Hamming Ball Sampler, a novel Markov Chain Monte Carlo algorithm, for efficient inference in statistical models involving high-dimensional discrete state spaces. The sampling scheme uses an auxiliary variable construction…

This paper presents an improved implicit sampling method for hierarchical Bayesian inverse problems. A widely used approach for sampling posterior distribution is based on Markov chain Monte Carlo (MCMC). However, the samples generated by…

We present a comprehensive comparison of different Markov Chain Monte Carlo (MCMC) sampling methods, evaluating their performance on both standard test problems and cosmological parameter estimation. Our analysis includes traditional…

Hierarchical data with multiple observations per group is ubiquitous in empirical sciences and is often analyzed using mixed-effects regression. In such models, Bayesian inference gives an estimate of uncertainty but is analytically…