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In climate science and meteorology, high-resolution local precipitation (rain and snowfall) predictions are limited by the computational costs of simulation-based methods. Statistical downscaling, or super-resolution, is a common workaround…
Given a random text over a finite alphabet, we study the frequencies at which fixed-length words occur as subsequences. As the data size grows, the joint distribution of word counts exhibits a rich asymptotic structure. We investigate all…
As a result of extreme weather conditions, such as heavy precipitation, natural hillslopes can fail dramatically; these slope failures can occur on a dry day due to time lags between rainfall and pore-water pressure change at depth, or even…
Machine learning is playing an increasing role in hydrology, supplementing or replacing physics-based models. One notable example is the use of recurrent neural networks (RNNs) for forecasting streamflow given observed precipitation and…
Diffusion models have quickly become the go-to paradigm for generative modelling of perceptual signals (such as images and sound) through iterative refinement. Their success hinges on the fact that the underlying physical phenomena are…
We propose a new point of view on multidimensional continued fraction algorithms inspired by Rauzy induction. The generic behaviour of such an algorithm is described here as a random walk on a graph that we call simplicial system. These…
Highly resoluted and accurate daily precipitation data are required for impact models to perform adequately and to correctly measure high-risk events' impact. In order to produce such data, bias-correction is often needed. Most of those…
Here we define natural chaotic systems, like the earths weather and climate system, as chaotic systems which are open to the world so have constantly changing boundary conditions, and measurements of their states are subject to errors. In…
The Monte Carlo simulation (MCS) is a statistical methodology used in a large number of applications. It uses repeated random sampling to solve problems with a probability interpretation to obtain high-quality numerical results. The MCS is…
We introduce a topological object, called hairy Cantor set, which in many ways enjoys the universal features of objects like Jordan curve, Cantor set, Cantor bouquet, hairy Jordan curve, etc. We give an axiomatic characterisation of hairy…
The temporal and spatial resolution of rainfall data is crucial for environmental modeling studies in which its variability in space and time is considered as a primary factor. Rainfall products from different remote sensing instruments…
We propose a new conformal prediction method for time-series data with a guaranteed asymptotic conditional coverage rate, Sequential Conformalized Density Regions (SCDR), which is flexible enough to produce both prediction intervals and…
We investigate numerically the statistical properties of the large scale flow in Rayleigh--B\'enard convection. By using an external random perturbation on the temperature field, we were able to decrease the effective Prandtl number of the…
Recently Whitaker et al. (2017) considered Bayesian estimation of diffusion driven mixed effects models using data-augmentation. The missing data, diffusion bridges connecting discrete time observations, are drawn using a "residual bridge…
Statisticians often use Monte Carlo methods to approximate probability distributions, primarily with Markov chain Monte Carlo and importance sampling. Sequential Monte Carlo samplers are a class of algorithms that combine both techniques to…
Spatiotemporal data analysis is pivotal across various domains, such as transportation, meteorology, and healthcare. The data collected in real-world scenarios are often incomplete due to device malfunctions and network errors.…
We consider the Einstein-Maxwell-fluid constraint equations, and make use of the conformal method to construct and parametrize constant-mean-curvature hyperboloidal initial data sets that satisfy the shear-free condition. This condition is…
A new approach of obtaining stratified random samples from statistically dependent random variables is described. The proposed method can be used to obtain samples from the input space of a computer forward model in estimating expectations…
In many epidemiological contexts, disease occurrences and their rates are naturally modelled by counting processes and their intensities, allowing an analysis based on martingale methods. These methods lend themselves to extensions of…
A variety of real-world applications are modeled via hyperbolic conservation laws. To account for uncertainties or insufficient measurements, random coefficients may be incorporated. These random fields may depend discontinuously on the…