Statistics and Probability
Tuncay Alparslan
My main research interests are in the theory of stochastic processes, applied probability, and statistics. I focus on non-standard models, where heavy-tails or long-range dependence (or long memory) is present. In heavy-tailed models the probability of observing an extreme value is relatively high. In the presence of long-range dependence, long periods of high values or long periods of low values are observed.
My contributions have been primarily in the study of the asymptotic analysis of the probability of a random walk with negative drift exceeding a threshold ("ruin probability") as the threshold tends to infinity, where the steps of the random walk constitue a stationary ergodic a-stable process with finite expectation and infinite variance. The concept of ruin probabilities finds applications in many fields of applied probability including actuarial science, queuing theory, and dam/storage models.
Tomasz Kozubowski
My main research interests include theory and applications of stable, geometric stable, and other heavy-tail 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 when the number of variables n is itself a random variable and/or or when the variables are combined by operations other than adding. A heavy-tail random variable is one that has a non-negligible probability of resulting in 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, as well as other areas. My other research interests include computational statistics, characterizations of probability distributions, and stochastic simulation.
Anna Panorska
My research interests include probability, statistics, stochastic modeling and interdisciplinary work. In particular, I study the limit theory for random and deterministic sums of random quantities and estimation for heavy tailed distributions. Stochastic modeling and interdisciplinary work cover finance and insurance, hydrology and water resources, atmospheric science and climate, environmental science and biostatistics. Current research projects include statistical estimation for heavy tailed hydrology data, climate and hydrological extremes in the US, and clean water issues in Nevada and California.
Do-Hwan Park
My research includes developing semiparametric and nonparametric methods for the analysis of longitudinal data (repeated measurements over time). Statistical analysis of longitudinal data is receiving more and more attention in a number of applied fields including epidemiology, medicine, and public health due to the great development of data collection techniques in such fields. The common approaches in these situations have been generalized estimating equations (GEE) or else multivariate approaches, which may ignore some correlated data structure. To overcome this drawback, my research includes adopting the stochastic processes in the data structure and apply it for modelling and estimating procedures. The methods have been applied to various cancer studies.
Ilya Zaliapin
My research focuses on theoretical and applied statistical analysis of complex (non-linear) dynamical systems, with emphasis on spatio-temporal pattern formation and development of extreme events. Specifically, I work on multiscale methods of time series analysis, heavy-tailed random processes, and spatial statistics. This choice is predicated by the essential common properties of the observed complex systems: they tend to evolve in multiple spatio-temporal scales; and have observables that exhibit absence of characteristic size, long-range correlations in space-time, and not-negligible probability of assuming extremely large values. The underlying methods of analysis include those of hierarchical aggregation and its inverse – branching processes.
Examples of the observed systems relevant to my research include the Earth's lithosphere which generates destructive earthquakes, its atmosphere that produces El-Ninos, stock-markets subject to financial crashes, etc. My current applications and ongoing collaborations are in Solid Earth geophysics (seismology, geodynamics), climate dynamics, computational finance, biology, and hydrology.