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High-dimensional variable selection, with many more covariates than observations, is widely documented in standard regression models, but there are still few tools to address it in non-linear mixed-effects models where data are collected…

Parameters in climate models are usually calibrated manually, exploiting only small subsets of the available data. This precludes both optimal calibration and quantification of uncertainties. Traditional Bayesian calibration methods that…

Point forecasting of univariate time series is a challenging problem with extensive work having been conducted. However, nonparametric probabilistic forecasting of time series, such as in the form of quantiles or prediction intervals is an…

Dynamic linear regression models forecast the values of a time series based on a linear combination of a set of exogenous time series while incorporating a time series process for the error term. This error process is often assumed to…

The problem of Bayesian filtering and smoothing in nonlinear models with additive noise is an active area of research. Classical Taylor series as well as more recent sigma-point based methods are two well-known strategies to deal with these…

Spatio-Temporal Multivariate time series Forecast (STMF) uses the time series of $n$ spatially distributed variables in a period of recent past to forecast their values in a period of near future. It has important applications in…

In a Bayesian setting, inverse problems and uncertainty quantification (UQ) --- the propagation of uncertainty through a computational (forward) model --- are strongly connected. In the form of conditional expectation the Bayesian update…

Target tracking using observations from multiple sensors can achieve better estimation performance than a single sensor. The most famous estimation tool in target tracking is Kalman filter. There are several mathematical approaches to…

Nowadays the city-wide traffic contains hundreds of thousands of vehicles with different scenarios of their behavior. If a microscopic approach is used it leads to solving tremendous systems of ordinary differential equations whose…

Multivariate spatio-temporal data arise more and more frequently in a wide range of applications; however, there are relatively few general statistical methods that can readily use that incorporate spatial, temporal and variable…

In applications of Gaussian processes where quantification of uncertainty is of primary interest, it is necessary to accurately characterize the posterior distribution over covariance parameters. This paper proposes an adaptation of the…

Latent variable models have been playing a central role in psychometrics and related fields. In many modern applications, the inference based on latent variable models involves one or several of the following features: (1) the presence of…

In an age of exponentially increasing data generation, performing inference tasks by utilizing the available information in its entirety is not always an affordable option. The present paper puts forth approaches to render tracking of…

Societal and industrial infrastructures and systems increasingly leverage sensors that emit correlated time series. Forecasting of future values of such time series based on recorded historical values has important benefits. Automatically…

A new application of duality relations of stochastic processes is demonstrated. Although conventional usages of the duality relations need analytical solutions for the dual processes, we here employ numerical solutions of the dual processes…

Yield curve forecasting is an important problem in finance. In this work we explore the use of Gaussian Processes in conjunction with a dynamic modeling strategy, much like the Kalman Filter, to model the yield curve. Gaussian Processes…

Contemporary weather forecasts are typically based on ensemble prediction systems, which consist of multiple runs of numerical weather prediction models that vary with respect to in the initial conditions and/or the the parameterization of…

The estimation of spatiotemporal data from limited sensor measurements is a required task across many scientific disciplines. The sensor selection problem, which aims to optimize the placement of sensors, leverages innovations in greedy…

There is a lack of simple and scalable algorithms for uncertainty quantification. Bayesian methods quantify uncertainty through posterior and predictive distributions, but it is difficult to rapidly estimate summaries of these…

Optimization of expensive computer models with the help of Gaussian process emulators in now commonplace. However, when several (competing) objectives are considered, choosing an appropriate sampling strategy remains an open question. We…