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Gaussian processes (GPs) are Bayesian nonparametric generative models that provide interpretability of hyperparameters, admit closed-form expressions for training and inference, and are able to accurately represent uncertainty. To model…

Inference for GP models with non-Gaussian noises is computationally expensive when dealing with large datasets. Many recent inference methods approximate the posterior distribution with a simpler distribution defined on a small number of…

Gaussian processes (GPs) are a popular class of Bayesian nonparametric models, but its training can be computationally burdensome for massive training datasets. While there has been notable work on scaling up these models for big data,…

In this work we review the application of the theory of Gaussian processes to the modeling of noise in pulsar-timing data analysis, and we derive various useful and optimized representations for the likelihood expressions that are needed in…

We develop a fast variational approximation scheme for Gaussian process (GP) regression, where the spectrum of the covariance function is subjected to a sparse approximation. Our approach enables uncertainty in covariance function…

I describe ongoing work developing Bayesian methods for flexible modeling of arrival time series data without binning, aiming to improve detection and measurement of X-ray and gamma-ray pulsars, and of pulses in gamma-ray bursts. The…

This research proposes a flexible Bayesian extension of the composite Gaussian process (CGP) model of Ba and Joseph (2012) for predicting (stationary or) non-stationary $y(\mathbf{x})$. The CGP generalizes the regression plus stationary…

With the development of new remote sensing technology, large or even massive spatial datasets covering the globe become available. Statistical analysis of such data is challenging. This article proposes a semiparametric approach to model…

Gaussian processes (GPs) are important probabilistic tools for inference and learning in spatio-temporal modelling problems such as those in climate science and epidemiology. However, existing GP approximations do not simultaneously support…

Effective forces -- derived from experimental or {\it in silico} molecular dynamics time traces -- are critical in developing reduced and computationally efficient descriptions of otherwise complex dynamical problems. Thus, designing…

The Gaussian process (GP) is a widely used probabilistic machine learning method with implicit uncertainty characterization for stochastic function approximation, stochastic modeling, and analyzing real-world measurements of nonlinear…

In this work, a Gaussian process regression(GPR) model incorporated with given physical information in partial differential equations(PDEs) is developed: physics-assisted Gaussian processes(PAGP). The targets of this model can be divided…

Gaussian-process state-space models (GP-SSMs) provide a flexible nonparametric alternative for modeling time-series dynamics that are nonlinear or difficult to specify parametrically. While the Kalman filter is effective for linear-Gaussian…

We propose a novel approach for change-point detection and parameter learning in multivariate non-stationary time series exhibiting oscillatory behaviour. We approximate the process through a piecewise function defined by a sum of…

The non-stationary evolution of observable quantities in complex systems can frequently be described as a juxtaposition of quasi-stationary spells. Given that standard theoretical and data analysis approaches usually rely on the assumption…

Graphical models describe associations between variables through the notion of conditional independence. Gaussian graphical models are a widely used class of such models where the relationships are formalized by non-null entries of the…

Given discrete time observations over a fixed time interval, we study a nonparametric Bayesian approach to estimation of the volatility coefficient of a stochastic differential equation. We postulate a histogram-type prior on the volatility…

The Gaussian process (GP) regression model is a widely employed surrogate modeling technique for computer experiments, offering precise predictions and statistical inference for the computer simulators that generate experimental data.…

Gaussian process state-space models (GP-SSMs) are a very flexible family of models of nonlinear dynamical systems. They comprise a Bayesian nonparametric representation of the dynamics of the system and additional (hyper-)parameters…

This paper develops a unified and computationally efficient method for change-point estimation along the time dimension in a non-stationary spatio-temporal process. By modeling a non-stationary spatio-temporal process as a piecewise…