Related papers: Spatial Process Gradients and Their Use in Sensiti…
We consider graphical models based on a recursive system of linear structural equations. This implies that there is an ordering, $\sigma$, of the variables such that each observed variable $Y_v$ is a linear function of a variable specific…
We consider the problem of learning a Gaussian variational approximation to the posterior distribution for a high-dimensional parameter, where we impose sparsity in the precision matrix to reflect appropriate conditional independence…
We show that the behavior of stochastic gradient descent is related to Bayesian statistics by showing that SGD is effectively diffusion on a fractal landscape, where the fractal dimension can be accounted for in a purely Bayesian way. By…
Risk assessment of hurricane-driven storm surge relies on deterministic computer models that produce outputs over a large spatial domain. The surge models can often be run at a range of fidelity levels, with greater precision yielding more…
While existing mathematical descriptions can accurately account for phenomena at microscopic scales (e.g. molecular dynamics), these are often high-dimensional, stochastic and their applicability over macroscopic time scales of physical…
The onset of life is often framed around membrane bound compartments and encoded metabolism, leaving unresolved how spatial organization arose before stable boundaries. In this context, environmental gradients are usually treated as…
Differentiable simulation is a promising toolkit for fast gradient-based policy optimization and system identification. However, existing approaches to differentiable simulation have largely tackled scenarios where obtaining smooth…
Accurately representing surface weather at the sub-kilometer scale is crucial for optimal decision-making in a wide range of applications. This motivates the use of statistical techniques to provide accurate and calibrated probabilistic…
Modeling data with non-stationary covariance structure is important to represent heterogeneity in geophysical and other environmental spatial processes. In this work, we investigate a multistage approach to modeling non-stationary…
Nonstationary non-Gaussian spatial data are common in many disciplines, including climate science, ecology, epidemiology, and social sciences. Examples include count data on disease incidence and binary satellite data on cloud mask…
Gaussian processes and random fields have a long history, covering multiple approaches to representing spatial and spatio-temporal dependence structures, such as covariance functions, spectral representations, reproducing kernel Hilbert…
Nonlinear dynamical stochastic models are ubiquitous in different areas. Excitable media models are typical examples with large state dimensions. Their statistical properties are often of great interest but are also very challenging to…
Functional data describe a wide range of processes, such as growth curves and spectral absorption. In this study, we analyze air pollution data from the In-service Aircraft for a Global Observing System, focusing on the spatial interactions…
Gaussian process regression is a widely-applied method for function approximation and uncertainty quantification. The technique has gained popularity recently in the machine learning community due to its robustness and interpretability. The…
Sensitivity analysis is a cornerstone of climate science, essential for understanding phenomena ranging from storm intensity to long-term climate feedbacks. However, computing these sensitivities using traditional physical models is often…
Wind direction plays an important role in the spread of pollutant levels over a geographical region. We discuss how to include wind directional information in the covariance function of spatial models. We follow the spatial convolution…
The $\delta N$ formalism provides a powerful non-perturbative framework for following the evolution of primordial curvature perturbations on super-horizon scales. However, its standard implementation relies on the separate universe…
The global sensitivity analysis method, used to quantify the influence of uncertain input variables on the response variability of a numerical model, is applicable to deterministic computer code (for which the same set of input variables…
We study Spatial Logistic Gaussian Process (SLGP) models for non-parametric estimation of probability density fields using scattered samples of heterogeneous sizes. SLGPs are examined from the perspective of random measures and their…
Due to their conjugate posteriors, Gaussian process priors are attractive for estimating the drift of stochastic differential equations with continuous time observations. However, their performance strongly depends on the choice of the…