My research focuses on developing novel methods for solving statistical problems arising from neuroimaging data, including fMRI, sMRI, DTI, and EEG. In general, the functional neuroimaging data is highly dimensioned in terms of space and time. The analysis of this data covers various statistical topics: time series analysis, dimension reduction, classification, variable selection, longitudinal data analysis, covariance estimation, etc. I am also interested in variable selection methods for repeatedly measured data. I’ve worked with many scientists in a variety of fields including veterinary science, psychiatry, radiology, neurology, immunology, and biomedical engineering.
My research interests include Monte Carlo methods, statistical computing, Bayesian analysis, latent class models, item response theory, and longitudinal analysis. I am currently working on developing sampling algorithms to perform statistical inferences in educational assessments and networks.
In physical applications, dynamic models and observational data play a dual role in quantifying uncertainty, predicting, and learning, each of which is a source of incomplete and inaccurate information. In the case of data-rich problems, basic physical laws limit the degrees of freedom of massive data sets and use our previous findings on complex processes. Accordingly, dynamic models fill spatial and temporal gaps in observation networks in the case of data-saving problems. However, many physical systems are in chaos, and so observations are required to update predictions when there is sensitivity to initial conditions and uncertainty in the model parameters. Data assimilation generally refers to the techniques used to combine the information from models and observations to produce an optimal estimate of a probability density or test statistic. These techniques include Bayesian inference methods, dynamic systems, numerical analysis, and optimal control, among others. My research interests lie in this intersection, using dynamic and statistical tools to develop theories for statistical learning algorithms in physical systems and to investigate applications. My application interests include climate, geophysics, and the power grid.
I use techniques from the fields of dynamic systems, stochastic processes, probability and statistics to develop and analyze mathematical models of biological systems. I use these models to answer questions that arise in population ecology, evolution, epidemiology (infectious diseases), and immunology. Recently I started working with methods for fitting nonlinear dynamic models to time series data. The use of these models as statistical models poses a number of challenges, since parameter estimates for these models are not guaranteed to behave statistically well, such as estimates for classical linear models. In addition to parameter estimation for dynamic models, I also use approximation methods that exploit the deeper relationships between deterministic models and their stochastic counterparts, as these two modeling frameworks can both be useful in applications.
My main research interests include theory and applications of stable, geometrically stable, and other heavy-tailed 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 concepts of stability include cases in which the number of variables n is itself a random variable and / or when the variable is due to other operations can be combined as adding. A heavy-tailed random variable is a variable that, with a non-negligible probability, leads to a value that is relatively far from the center of the distribution. I’ve worked on applications of stable and related distributions in actuarial, economics, financial, and other areas. My other research interests include computer statistics, characterization of probability distributions, and stochastic simulation.
My research interests include probability, statistics, stochastic modeling, and interdisciplinary work. In particular, I investigate the limit theory for random and deterministic sums of random quantities and the estimation for heavy-tailed distributions. Stochastic modeling and interdisciplinary work include finance and insurance, hydrology and water resources, atmospheric science and climate, environmental science and biostatistics. Current research includes statistical estimates for data from heavy-tailed hydrology, climate, and hydrological extremes in the United States, and clean water issues in Nevada and California.
My research is in stochastic analysis, especially in stochastic differential equations, as well as in long-term stability; and in Quantitative Finance and Actuarial Science, where I use tools from stochastic analysis and econometrics. I’m also interested in other uses of statistics and probability, especially biology and ecology.
My research interests are driven by interdisciplinary problems, often in the biomedical field. Recently, I have helped develop statistical computing tools that enable clinical researchers to interpret molecular data on the scale of individual patients (with the aim of performing precision medicine). The common themes of these projects include large-scale hypothesis testing, high dimensionality, massively parallel computing, knowledge database integration, multivariate statistics, Bayesian analysis, and clustering.
My research is driven by the desire to understand the role of stochastics, structure, and evolution in shaping the dynamics of biological systems. I develop and analyze mathematical models by combining methods from probability and statistics, dynamic systems and random graph theory to shed light on biological questions and to generate new mathematical questions. In particular, I study stochastic processes in networks with applications in neuroscience and stochastic models in genetics.
I am currently working on optimal reduction techniques for complex ion channel gating models, which can be represented as a stochastic (Markov) process in a graph. I also look at the relative contributions of network structure and nodal dynamics in determining the collective dynamics of a network, thinking in particular of neural networks involved in sleep-wake regulation. Finally, I am generally interested in mathematical and statistical applications in population and evolutionary genetics.
My research focuses on the theoretical and applied statistical analysis of complex (non-linear) dynamic systems, with a focus on spatiotemporal pattern formation and the development of extreme events. Specifically, I deal with multi-scale methods of time series analysis, heavy-tailed random processes and spatial statistics. This choice is determined by the essential common properties of the observed complex systems: They tend to develop on several spatiotemporal scales; and have observables that have the lack of a characteristic quantity, far-reaching correlations in space-time, and a non-negligible probability of taking on extremely large values. The underlying analysis methods include hierarchical aggregation and its inverse branching processes.
Examples of observed systems that are relevant to my research are the Earth’s lithosphere, which creates destructive earthquakes, its atmosphere, which produces El-Ninos, exchanges that are subject to financial crashes, etc. My current applications and ongoing collaborations are in geophysics solid earth (seismology, geodynamics), climatic dynamics, computational finance, biology and hydrology.