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Log-normal continuous random cascades form a class of multifractal processes that has already been successfully used in various fields. Several statistical issues related to this model are studied. We first make a quick but extensive review…
A machine-learning approach called "reservoir computing" has been used successfully for short-term prediction and attractor reconstruction of chaotic dynamical systems from time series data. We present a theoretical framework that describes…
Modeling the risk of extreme weather events in a changing climate is essential for developing effective adaptation and mitigation strategies. Although the available low-resolution climate models capture different scenarios, accurate risk…
This study proposes two straightforward yet effective approaches to reduce the required computational time of the training process for time-series modeling through a recurrent neural network (RNN) using multi-time-scale time-series data as…
Distributed models to forecast the spatial and temporal occurrence of rainfall-induced shallow landslides are based on deterministic laws. These models extend spatially the static stability models adopted in geotechnical engineering, and…
Accurate stochastic simulations of hourly precipitation are needed for impact studies at local spatial scales. Statistically, hourly precipitation data represent a difficult challenge. They are non-negative, skewed, heavy tailed, contain a…
We consider random labelings of finite graphs conditioned on a small fixed number of peaks. We introduce a continuum framework where a combinatorial graph is associated with a metric graph and edges are identified with intervals. Next we…
Rainfall estimation through the analysis of its impact on electromagnetic waves has sparked increasing interest in the research community. Recent studies have delved into its effects on cellular network performance, demonstrating the…
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),…
Descriptive statistics for parametric models are currently highly sensative to departures, gross errors, and/or random errors. Here, leveraging the structures of parametric distributions and their central moment kernel distributions, a…
Simulation of rainfall over a region for long time-sequences can be very useful for planning and policy-making, especially in India where the economy is heavily reliant on monsoon rainfall. However, such simulations should be able to…
We analyze distributions of rain-event sizes, rain-event durations, and dry-spell durations for data obtained from a network of 20 rain gauges scattered in a region of the NW Mediterranean coast. While power-law distributions model the…
This paper describes a statistical method for short-term forecasting of surface layer wind velocity amplitude relying on the notion of continuous cascades. Inspired by recent empirical findings that suggest the existence of some cascading…
Specific aspects of time series analysis are discussed. They are related to the analysis of atmospheric data that are pertinent to clouds. A brief introduction on some of the most interesting topics of current research on climate/weather…
We develop a flexible spline-based Bayesian hidden Markov model stochastic weather generator to statistically model daily precipitation over time by season at individual locations. The model naturally accounts for missing data (considered…
Analytical solutions are derived for the steady-state size distributions of precipitating rain and snow particles assuming growth via collection of suspended cloud particles. Application of the Liouville equation to the transfer of…
This study evaluates data-driven models from a dynamical system perspective, such as unstable fixed points, periodic orbits, chaotic saddle, Lyapunov exponents, manifold structures, and statistical values. We find that these dynamical…
We introduce a random dynamical system related to continued fraction expansions. It uses random combination of the Gauss map and the R\'enyi (or backwards) continued fraction map. We explore the continued fraction expansions that this…
We consider fixed-point equations for probability distributions on isometry classes of measured metric spaces. The construction is required to be recursive and tree-like, but we allow loops for the geodesics between points in the support of…
We consider the problem of modeling discrete-valued vector time series data using extensions of Chow-Liu tree models to capture both dependencies across time and dependencies across variables. Conditional Chow-Liu tree models are…