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Change point detection becomes more and more important as datasets increase in size, where unsupervised detection algorithms can help users process data. To detect change points, a number of unsupervised algorithms have been developed which…

In modern business modeling and analytics, data monitoring plays a critical role. Nowadays, sophisticated models often rely on hundreds or even thousands of input variables. Over time, structural changes such as abrupt level shifts or trend…

Gibbs sampling is a Markov Chain Monte Carlo (MCMC) method often used in Bayesian learning. MCMC methods can be difficult to deploy on parallel and distributed systems due to their inherently sequential nature. We study asynchronous Gibbs…

We propose a novel and unified framework for change-point estimation in multivariate time series. The proposed method is fully nonparametric, enjoys effortless tuning and is robust to temporal dependence. One salient and distinct feature of…

We develop a flexible spline-based Bayesian hidden Markov model stochastic weather generator to statistically model daily precipitation over time by season at individual locations. The model naturally accounts for missing data (considered…

Conformal prediction has been explored as a general and efficient way to provide uncertainty quantification for time series. However, current methods struggle to handle time series data with change points - sudden shifts in the underlying…

Hyperspectral unmixing is a blind source separation problem which consists in estimating the reference spectral signatures contained in a hyperspectral image, as well as their relative contribution to each pixel according to a given mixture…

Markov Chain Monte Carlo (MCMC) methods such as Gibbs sampling are finding widespread use in applied statistics and machine learning. These often lead to difficult computational problems, which are increasingly being solved on parallel and…

Hidden semi-Markov Models (HSMM's) - while broadly in use - are restricted to a discrete and uniform time grid. They are thus not well suited to explain often irregularly spaced discrete event data from continuous-time phenomena. We show…

Hidden Markov models can describe time series arising in various fields of science, by treating the data as noisy measurements of an arbitrarily complex Markov process. Sequential Monte Carlo (SMC) methods have become standard tools to…

Every day, weather forecasting centres around the world make use of noisy, incomplete observations of the atmosphere to update their weather forecasts. This process is known as data assimilation, data fusion or state estimation and is best…

Dynamic Bayesian predictive synthesis is a formal approach to coherently synthesizing multiple predictive distributions into a single distribution. In sequential analysis, the computation of the synthesized predictive distribution has…

We investigate real-time tracking of two correlated stochastic processes over a shared wireless channel. The joint evolution of the processes is modeled as a two-dimensional discrete-time Markov chain. Each process is observed by a…

Autonomous systems with machine learning-based perception can exhibit unpredictable behaviors that are difficult to quantify, let alone verify. Such behaviors are convenient to capture in probabilistic models, but probabilistic model…

We consider the problem of inference in discrete probabilistic models, that is, distributions over subsets of a finite ground set. These encompass a range of well-known models in machine learning, such as determinantal point processes and…

We develop a novel class of MCMC algorithms based on a stochastized Nesterov scheme. With an appropriate addition of noise, the result is a time-inhomogeneous underdamped Langevin equation, which we prove emits a specified target…

We propose a new Bayesian tracking and parameter learning algorithm for non-linear non-Gaussian multiple target tracking (MTT) models. We design a Markov chain Monte Carlo (MCMC) algorithm to sample from the posterior distribution of the…

Monte Carlo methods -- such as Markov chain Monte Carlo (MCMC) and piecewise deterministic Markov process (PDMP) samplers -- provide asymptotically exact estimators of expectations under a target distribution. There is growing interest in…

A nonhomogeneous hidden semi-Markov model is proposed to segment toroidal time series according to a finite number of latent regimes and, simultaneously, estimate the influence of time-varying covariates on the process' survival under each…

Markov chain Monte Carlo (MCMC) methods are foundational algorithms for Bayesian inference and probabilistic modeling. However, most MCMC algorithms are inherently sequential and their time complexity scales linearly with the sequence…