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Gaussian random fields on finite dimensional smooth manifolds whose variances reach their maximum value at smooth submanifolds are considered. Exact asymptotic behaviors of large excursion probabilities have been evaluated. Vector Gaussian…
In environmental science applications, extreme events frequently exhibit a complex spatio-temporal structure, which is difficult to describe flexibly and estimate in a computationally efficient way using state-of-art parametric…
We deal with the orbit determination problem for a class of maps of the cylinder generalizing the Chirikov standard map. The problem consists of determining the initial conditions and other parameters of an orbit from some observations. A…
We formulate a reduced-order strategy for efficiently forecasting complex high-dimensional dynamical systems entirely based on data streams. The first step of our method involves reconstructing the dynamics in a reduced-order subspace of…
Solving inverse problems using Bayesian methods can become prohibitively expensive when likelihood evaluations involve complex and large scale numerical models. A common approach to circumvent this issue is to approximate the forward model…
This paper presents a statistical analysis of air temperature data from 32 stations in Italy and the UK up to 2000 m above sea level, from 2002 to 2021. The data came from both highland and lowland areas, in order to evaluate both the…
Quantifying and reducing uncertainty in Earth system model parameterizations is essential to improving their reliability in decision-making. Forward uncertainty propagation is used to derive parameter sensitivity but requires physically…
Weather and climate forecasts are inherently uncertain due to chaotic dynamics, imperfect initial conditions, and incomplete representation of the underlying physical processes. Operational ensemble forecasts aim to represent these…
We propose a new approach to estimate the causal effects of maritime traffic when natural or policy experiments are not available. We apply this method to the case of Marseille, a large Mediterranean port city, where air pollution emitted…
This paper presents an approach to estimating the health effects of an environmental hazard. The approach is general in nature, but is applied here to the case of air pollution. It uses a computer model involving ambient pollution and…
We study the approximability of general convex sets in $\mathbb{R}^n$ by intersections of halfspaces, where the approximation quality is measured with respect to the standard Gaussian distribution $N(0,I_n)$ and the complexity of an…
The estimation of the amount of uncertainty featured by predictive machine learning models has acquired a great momentum in recent years. Uncertainty estimation provides the user with augmented information about the model's confidence in…
Due to lack of scientific understanding, some mechanisms may be missing in mathematical modeling of complex phenomena in science and engineering. These mathematical models thus contain some uncertainties such as uncertain parameters. One…
Uncertainty Quantification (UQ) is essential in probabilistic machine learning models, particularly for assessing the reliability of predictions. In this paper, we present a systematic framework for estimating both epistemic and aleatoric…
In disease mapping, the aim is to estimate the spatial pattern in disease risk over an extended geographical region, so that areas with elevated risks can be identified. A Bayesian hierarchical approach is typically used to produce such…
We address the common problem of calculating intervals in the presence of systematic uncertainties. We aim to investigate several approaches, but here describe just a Bayesian technique for setting upper limits. The particular example we…
A new method is proposed for estimating the rate of fugitive emissions of particulate matter from multiple time-dependent sources via measurements of deposition and concentration. We cast this source inversion problem within the Bayesian…
This paper shows how measures of uncertainty can be applied to existing population forecasts using Estonia as a case study. The measures of forecast uncertainty are relatively easy to calculate and meet several important criteria used by…
We develop a spatio-temporal model to forecast sensor output at five locations in North East England. The signal is described using coupled dynamic linear models, with spatial effects specified by a Gaussian process. Data streams are…
We consider a sequential decision making task where we are not allowed to evaluate parameters that violate an a priori unknown (safety) constraint. A common approach is to place a Gaussian process prior on the unknown constraint and allow…