My research focuses on the development of a new methodology to solve statistical problems raised from neuroimaging data, including fMRI, MRIs, DTI and EEG. Generally, functional neuroimaging data are large in size both spatially and temporally. The analysis of these data includes various statistical topics: time series analysis, dimension reduction, classification, selection of variables, longitudinal data analysis, covariance estimation, etc. I am also interested in methods of selecting variables for repeatedly measured data. I have collaborated with many scientists in various fields including veterinary sciences, psychiatry, radiology, neurology, immunology and biomedical engineering.
My research interests include Monte Carlo methods, statistical computation, Bayesian analysis, latent class models, item response theory, and longitudinal analysis. Currently, I am working on the development of sampling algorithms to make statistical inferences in evaluations and educational networks.
In physical applications, dynamic models and observational data play a dual role in quantifying, predicting, and learning uncertainty, each representing incomplete and inaccurate sources of information. In data-rich problems, the laws of physics of the first principle limit the degrees of freedom of massive data sets, using our previous knowledge of complex processes. Respectively, in sparse data problems, dynamic models fill the spatial and temporal gaps in observational networks. However, many physical systems exhibit chaos and therefore observations are required to update predictions when there is sensitivity to initial conditions and uncertainty in model parameters. Data assimilation generally refers to the techniques used to combine information from models and observations to produce an optimal estimate of a probability density or test statistic. These techniques include Bayesian inference, dynamical systems, numerical analysis, and optimal control methods, among others. My research interests lie in this intersection, using dynamic and statistical tools to develop theory and study the applications of statistical learning algorithms in physical systems. My application interests include climate, geophysics, and the power grid.
I use techniques from the fields of dynamical systems, stochastic processes, probability and statistics to develop and analyze mathematical models of biological systems. I use these models to answer questions about ecology, evolution, epidemiology (infectious diseases) and immunology of populations. Recently, I have started working with methods of fitting nonlinear dynamic models to time series data. Using these models as statistical models presents a number of challenges, as the parameter estimators for these models are not guaranteed to be statistically as well behaved as, for example, the estimators for classical linear models. In addition to parameter estimation for dynamic models, I also use approximation methods that exploit the deeper links between deterministic models and their stochastic counterparts, as both of these modeling frameworks can be useful in applications.
My main research interests include the theory and applications of stable random variables, stable geometric, and other random variables and stochastic processes. A stable variable has the property of stability: the sum of n copies of X has the same type of distribution as X. More general notions of stability include cases where the number of variables n is itself a random variable and / or when variables are combined by operations other than addition. A heavy-tailed random variable is one that has a significant probability of ending up with a value relatively far from the center of the distribution. I have worked on applications of stable and related distributions in actuarial science, economics, financial mathematics, and other fields. My other research interests include computational statistics, characterizations of probability distributions, and stochastic simulation.
My research interests include probability, statistics, stochastic modeling, and interdisciplinary work. In particular, I study limit theory for random and deterministic sums of random quantities and estimation for heavy-tailed distributions. Stochastic modeling and interdisciplinary work spans finance and insurance, hydrology and water resources, atmospheric science and climate, environmental science, and biostatistics. Current research projects include statistical estimation of heavy-tailed hydrologic data, climatic and hydrologic extremes in the United States, and drinking water problems in Nevada and California.
My research focuses on stochastic analysis, in particular stochastic differential equations, as well as long-term stability; and in quantitative finance and actuarial science, where I use stochastic analysis and econometrics tools. I am also interested in other applications of Statistics and Probability, in particular Biology and Ecology.
My research interests are driven by interdisciplinary issues, often in the biomedical field. Recently, I participated in the construction of statistical computing tools allowing clinical researchers to interpret molecular data, at the scale of each patient (in order to carry out precision medicine). Common themes during these projects include large-scale hypothesis testing, high dimensionality, massively parallel computing, knowledge base integration, multivariate statistics, Bayesian analysis and clustering.
My research is motivated by the desire to understand the roles of stochasticity, structure and evolution in shaping the dynamics of biological systems. I develop and analyze mathematical models, combining methods of probability and statistics, dynamical systems and random graph theory to shed light on biological problems while generating new mathematical questions. In particular, I study stochastic processes on networks with applications in neuroscience and stochastic models in genetics.
Currently, I am working on optimal reduction techniques for complex ion channel gating models, which can be represented as a stochastic (Markov) process on a graph. I also study the relative contributions of network structure and node dynamics in determining the collective dynamics of a network, specifically thinking of neural networks involved in sleep-wake regulation. Finally, I am largely interested in mathematical and statistical applications in population genetics and evolution.
My research focuses on the theoretical and applied statistical analysis of complex dynamic systems (nonlinear), with an emphasis on the formation of spatio-temporal models and the development of extreme events. Specifically, I am working on multiscale methods of time series analysis, heavy tail random processes and spatial statistics. This choice is motivated by the essential common properties of the complex systems observed: they tend to evolve at multiple spatio-temporal scales; and have observables that exhibit a characteristic absence of size, long-range correlations in space-time and a not insignificant probability of assuming extremely large values. The underlying analysis methods include those of hierarchical aggregation and its reverse branching processes.
Examples of observed systems relevant to my research include the Earth’s lithosphere which generates destructive earthquakes, its atmosphere which produces El-Ninos, stock markets prone to financial crashes, etc. My current applications and current collaborations are in solid Earth geophysics (seismology, geodynamics), climate dynamics, computer finance, biology and hydrology.