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In this paper, we develop a new and effective approach to nonparametric quantile regression that accommodates ultrahigh-dimensional data arising from spatio-temporal processes. This approach proves advantageous in staving off computational…

Hourly predictions are critical for issuing flood warnings as the flood peaks on the hourly scale can be distinctly higher than the corresponding daily ones. Currently a popular hourly data-driven prediction scheme is multi-time-scale long…

Conformal prediction can yield statistically valid prediction intervals for any regression model, with no model modifications and small computational costs. To assess its practical value, we apply conformal methods to quantify uncertainty…

Quantile regression has been successfully used to study heterogeneous and heavy-tailed data. Varying-coefficient models are frequently used to capture changes in the effect of input variables on the response as a function of an index or…

Bayesian inference provides a flexible way of combining data with prior information. However, quantile regression is not equipped with a parametric likelihood, and therefore, Bayesian inference for quantile regression demands careful…

Parametric quantile regressions are a useful tool for creating probabilistic energy forecasts. Nonetheless, since classical quantile regressions are trained using a non-differentiable cost function, their creation using complex data mining…

Extreme floods pose escalating risks in a changing climate, yet forecasting remains challenging due to peak flow underestimation and high uncertainty. We introduce DRUM, a diffusion-based probabilistic deep learning approach that advances…

A collection of quantile curves provides a complete picture of conditional distributions. Properly centered and scaled versions of estimated curves at various quantile levels give rise to the so-called quantile regression process (QRP). In…

Predictions are a central part of water resources research. Historically, physically-based models have been preferred; however, they have largely failed at modeling hydrological processes at a catchment scale and there are some important…

Leveraging the recently emerging geometric approach to multivariate extremes and the flexibility of normalising flows on the hypersphere, we propose a principled deep-learning-based methodology that enables accurate joint tail extrapolation…

Verifying probabilistic forecasts for extreme events is a highly active research area because popular media and public opinions are naturally focused on extreme events, and biased conclusions are readily made. In this context, classical…

Multiple studies have now demonstrated that machine learning (ML) can give improved skill for predicting or simulating fairly typical weather events, for tasks such as short-term and seasonal weather forecasting, downscaling simulations to…

A geometric representation for multivariate extremes, based on the shapes of scaled sample clouds in light-tailed margins and their so-called limit sets, has recently been shown to connect several existing extremal dependence concepts.…

One of the commonly used approaches to modeling extremes is the peaks-over-threshold (POT) method. The POT method models exceedances over a threshold that is sufficiently high or low so that the exceedance has approximately a generalized…

While Gaussian processes are a mainstay for various engineering and scientific applications, the uncertainty estimates don't satisfy frequentist guarantees and can be miscalibrated in practice. State-of-the-art approaches for designing…

In recent years, climate extremes such as floods have created significant environmental and economic hazards for Australia. Deep learning methods have been promising for predicting extreme climate events; however, large flooding events…

Motivated by the analysis of extreme rainfall data, we introduce a general Bayesian hierarchical model for estimating the probability distribution of extreme values of intermittent random sequences, a common problem in geophysical and…

Extremile regression, as a least squares analog of quantile regression, is potentially useful tool for modeling and understanding the extreme tails of a distribution. However, existing extremile regression methods, as nonparametric…

Numerical simulation models associated with hydraulic engineering take a wide array of data into account to produce predictions: rainfall contribution to the drainage basin (characterized by soil nature, infiltration capacity and moisture),…

Uncertainty in return level estimates for rare events, like the intensity of large rainfall events, makes it difficult to develop strategies to mitigate related hazards, like flooding. Latent spatial extremes models reduce uncertainty by…