Related papers: Modelling spatial heteroskedasticity by volatility…
Multi-model ensembles provide a pragmatic approach to the representation of model uncertainty in climate prediction. However, such representations are inherently ad hoc, and, as shown, probability distributions of climate variables based on…
In this paper, we are interested in testing if the volatility process is constant or not during a given time span by using high-frequency data with the presence of jumps and microstructure noise. Based on estimators of integrated volatility…
Mechanistic statistical models are commonly used to study the flow of biological processes. For example, in landscape genetics, the aim is to infer spatial mechanisms that govern gene flow in populations. Existing statistical approaches in…
The last decade has seen the success of stochastic parameterizations in short-term, medium-range and seasonal forecasts: operational weather centers now routinely use stochastic parameterization schemes to better represent model inadequacy…
Inspired by spatiotemporal observations from satellites of the trajectories of objects drifting near the surface of the ocean in the National Oceanic and Atmospheric Administration's `Global Drifter Program', this paper develops data-driven…
We combine geometric data analysis and stochastic modeling to describe the collective dynamics of complex systems. As an example we apply this approach to financial data and focus on the non-stationarity of the market correlation structure.…
Climate models have become an important tool in the study of climate and climate change, and ensemble experiments consisting of multiple climate-model runs are used in studying and quantifying the uncertainty in climate-model output.…
The theory of mesoscopic fluctuations is applied to inhomogeneous solids consisting of chaotically distributed regions with different crystalline structure. This approach makes it possible to describe statistical properties of such mixture…
Transport in Hamiltonian systems with weak chaotic perturbations has been much studied in the past. In this paper, we introduce a new class of problems: transport in Hamiltonian systems with slowly changing phase space structure that are…
In this paper, we propose a Bayesian matrix-variate spatiotemporal modeling framework for jointly analyzing multiple response variables observed at spatial locations over time. The approach relaxes the standard assumption of spatial…
Many imaging techniques for biological systems -- like fixation of cells coupled with fluorescence microscopy -- provide sharp spatial resolution in reporting locations of individuals at a single moment in time but also destroy the dynamics…
Multistability is a phenomenon prevalent in many natural systems. In climate, for example, it allows the possibility of irreversible consequences on planetary scale as a result of climate change. Indeed, a climate ``tipping element'' is a…
Statistical methods are required to evaluate and quantify the uncertainty in environmental processes, such as land and sea surface temperature, in a changing climate. Typically, annual harmonics are used to characterize the variation in the…
We develop new methodology to improve our understanding of the causal effects of multivariate air pollution exposures on public health. Typically, exposure to air pollution for an individual is measured at their home geographic region,…
Stochastic dynamical systems arise as models for fluid particle motion in geophysical flows with random velocity fields. Escape probability (from a fluid domain) and mean residence time (in a fluid domain) quantify fluid transport between…
Recent studies in ecology and epidemiology indicate that it is important to include spatial heterogeneity, synchronization and seasonality in the theoretical models. In this work, spatial heterogeneity is introduced via coupled map lattices…
This paper formulates a variational approach for treating observational uncertainty and/or computational model errors as stochastic transport in dynamical systems governed by action principles under nonholonomic constraints. For this…
Downscaling aims to link the behaviour of the atmosphere at fine scales to properties measurable at coarser scales, and has the potential to provide high resolution information at a lower computational and storage cost than numerical…
The spatio-temporal autoregressive moving average (STARMA) model is frequently used in several studies of multivariate time series data, where the assumption of stationarity is important, but it is not always guaranteed in practice. One way…
Stochastic dynamics is generated by a matrix of transition probabilities. Certain eigenvectors of this matrix provide observables, and when these are plotted in the appropriate multi-dimensional space the phases (in the sense of phase…