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Hydroclimatic processes are characterized by heterogeneous spatiotemporal correlation structures and marginal distributions that can be continuous, mixed-type, discrete or even binary. Simulating exactly such processes can greatly improve…

In this article, we consider the general task of performing Gaussian process regression (GPR) on pointwise observations of solutions of the 3 dimensional homogeneous free space wave equation.In a recent article, we obtained promising…

We reconsider a nonparametric density model based on Gaussian processes. By augmenting the model with latent P\'olya--Gamma random variables and a latent marked Poisson process we obtain a new likelihood which is conjugate to the model's…

In a traditional Gaussian graphical model, data homogeneity is routinely assumed with no extra variables affecting the conditional independence. In modern genomic datasets, there is an abundance of auxiliary information, which often gets…

Ensemble weather forecasts based on multiple runs of numerical weather prediction models typically show systematic errors and require post-processing to obtain reliable forecasts. Accurately modeling multivariate dependencies is crucial in…

The theoretical investigation of gas adsorption, storage, separation, diffusion and related transport processes in porous materials relies on a detailed knowledge of the potential energy surface of molecules in a stationary environment. In…

We propose an approach based on function evaluations and Bayesian inference to extract higher-order differential information of objective functions {from a given ensemble of particles}. Pointwise evaluation $\{V(x^i)\}_i$ of some potential…

There is significant interest in learning and optimizing a complex system composed of multiple sub-components, where these components may be agents or autonomous sensors. Among the rich literature on this topic, agent-based and…

Gaussian processes (GPs) are widely used in nonparametric regression, classification and spatio-temporal modeling, motivated in part by a rich literature on theoretical properties. However, a well known drawback of GPs that limits their use…

Many asymptotically minimax procedures for function estimation often rely on somewhat arbitrary and restrictive assumptions such as isotropy or spatial homogeneity. This work enhances the theoretical understanding of Bayesian additive…

We investigate two empirical Bayes methods and a hierarchical Bayes method for adapting the scale of a Gaussian process prior in a nonparametric regression model. We show that all methods lead to a posterior contraction rate that adapts to…

This work develops a Bayesian non-parametric approach to signal separation where the signals may vary according to latent variables. Our key contribution is to augment Gaussian Process Latent Variable Models (GPLVMs) for the case where each…

We consider a generalization of the discrete-time Self Healing Umbrella Sampling method, which is an adaptive importance technique useful to sample multimodal target distributions. The importance function is based on the weights (namely the…

Gaussian process regression is a machine learning approach which has been shown its power for estimation of unknown functions. However, Gaussian processes suffer from high computational complexity, as in a basic form they scale cubically…

Modeling spatial processes that exhibit both smooth and rough features poses a significant challenge. This is especially true in fields where complex physical variables are observed across spatial domains. Traditional spatial techniques,…

Fitting statistical models to spatiotemporal data requires finding the right balance between imposing smoothness and following the data. In the context of p-splines, we propose a Bayesian framework for choosing the smoothing parameter which…

There is increasing interest in the problem of nonparametric regression with high-dimensional predictors. When the number of predictors $D$ is large, one encounters a daunting problem in attempting to estimate a $D$-dimensional surface…

We investigate a novel non-parametric regression-based clustering algorithm for longitudinal data analysis. Combining natural cubic splines with Gaussian mixture models (GMM), the algorithm can produce smooth cluster means that describe the…

Surrogate models have become ubiquitous in science and engineering for their capability of emulating expensive computer codes, necessary to model and investigate complex phenomena. Bayesian emulators based on Gaussian processes adequately…

Bayesian nonparametric regression under a rescaled Gaussian process prior offers smoothness-adaptive function estimation with near minimax-optimal error rates. Hierarchical extensions of this approach, equipped with stochastic variable…