Gaussian Random Fields (GRFs) play a critical role in modeling and simulating environmental and climate-driven processes. The simulation of GRFs enables the representation of the variability of the process under study through the generation of multiple equally plausible realizations. Gaussian vectors corresponding to a sample of moderate size of a GRF can easily be simulated using the Cholesky...
We discuss some key considerations that are helpful in identifying orthogonal measures, including both established and novel approaches.
The nonparametric regression model with normal errors has been extensively studied, both from the frequentist and Bayesian viewpoint. A central result in Bayesian nonparametrics is that under assumptions on the prior, the data-generating distribution (assuming a true frequentist model) and a semi-metric d(.,.) on the space of regression functions that satisfy the so called testing condition,...
Gaussian processes have proven to be powerful and flexible tools for various statistical inference and machine learning tasks. However, they can be limited when the underlying datasets exhibit non-stationary or anisotropic properties. Deep Gaussian processes extend the capabilities of standard Gaussian processes by introducing a hierarchical structure, where the outputs of one Gaussian process...
Gaussian Processes (GPs) are widely used to model dependency in spatial statistics and machine learning, yet the exact computation suffers an intractable time complexity of O(n^3). Vecchia approximation allows scalable Bayesian inference of GPs in O(n) time by introducing sparsity in the spatial dependency structure that is characterized by a directed acyclic graph (DAG). Despite the...
Bayesian optimisation (BO) pairs Gaussian-process surrogates with exploration-aware acquisition rules to locate the optimum of costly, black-box functions in just a handful of trials. In this introductory talk we unpack how GPs supply calibrated uncertainty that powers the explore-exploit trade-off, walk through the classical BO loop and its staple acquisition functions, and outline practical...
The goal of this work is to use goal-directed sensitivity analysis in order to
reduce the cost of solving a robust optimization problem. Specifically, we focus on
quantifying the impact of uncertain inputs on feasible sets, which are subsets of the
design domain. While most sensitivity analysis methods deal with scalar outputs,
we introduce a novel approach for performing sensitivity...
By now Bayesian methods are routinely used in practice for solving inverse problems. In inverse problems the parameter or signal of interest is observed only indirectly, as an image of a given map, and the observations are typically further corrupted with noise. Bayes offers a natural way to regularize these problems via the prior distribution and provides a probabilistic solution, quantifying...
