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Some Ongoing Projects in Statistics, Probability and Mathematical Finance Some ongoing projects in Statistics, Probability and Mathematical Finance Department of Statistics and Applied Probability John Hsu Department of Statistics and Applied Probability 10 Faculty: 5.5 Statisticians & 4.5 Probabilists: Statistics: Carter, Hsu, Jammalamadaka, Meiring, Wang, Holmes (0.5) Probability: Feldman, Fouque, Ichiba, Ludkovski, Holmes (0.5) Research Interests include: actuarial statistics, asymptotic statistical inference, Bayesian inference, Bayesian networks, biostatistics, data mining, directional data analysis, environmental statistics, financial mathematics, linear models and generalized linear models, Markov Chain Monte Carlo (MCMC) methods, microarray data analysis, nonparametric curve fitting, nonparametric inference, resampling methods, smoothing spline methods, spatial data analysis, stochastic processes, stochastic control, stochastic differential equations, stochastic partial differential equations, and time series. Undergraduate Majors: BA in Statistical Science BS in Statistical Science BS in Actuarial Science BS in Financial Mathematics and Statistics (jointly with Math) Graduate Majors: MA in Statistics MS in Actuarial Science Five-Year Combined BS and MS in Actuarial Science PhD in Statistics --- Optional PhD emphasis in Financial Mathematics and Statistics (FMS) --- Optional PhD emphasis in Quantitative Methods in the Social Sciences (QMSS) 900 800 700 600 500 400 300 200 100 0 90 91 92 93 94 95 96 97 98 99 00 01 02 03 04 05 06 07 08 09 10 11 12 13 14 S. Rao Jammalamadaka: Statistical Methodology Bayesian Meta-analysis for the Evaluation of a Test Treatment Placebo-controlled trials are the ideal for evaluating medical treatment efficacy. It is inappropriate and unethical to use a placebo control by treating a patient with placebo, while witholding an effective drug, may lead to death or irreversible morbidity. Given the large number of proven effective treatments, placebo-controlled trials are often unethical. In the absence of placebo-controlled trials, the efficacy of a test treatment can be alternatively examined by showing its non-inferiority to a standard (existing) control by borrowing information from a network of historical trials. Their model can predict the effect of the test treatment over placebo. Test Treatment Standard Control Placebo John Hsu: Bayesian Methods Bayesian Recommendation Systems for Social Networks Who uses them? Website Avergage Rating Personalized Rating Jean-Pierre Fouque, Michael Ludkovski & Tomoyuki Ichiba: Probability & Financial Mathematics Number of bank failures 600 500 400 300 200 100 0 36 40 44 48 52 56 60 64 68 72 76 80 84 88 92 96 00 04 08 12 34 38 42 46 50 54 58 62 66 70 74 78 82 86 90 94 98 02 06 10 14 * The FDID was created in 1933 * The Great Depression * Savings and Loan Crisis * Housing Bubble bursted Jean-Pierre Fouque, Michael Ludkovski & Tomoyuki Ichiba: Probability & Financial Mathematics What are important probabilistic aspects of large financial markets? What kind of stochastic mechanisms generated the financial crisis in 2007? What is the optimal trading strategy in emerging financial markets where many market participants trade assets electronically by some computer algorithms? For example, in order to understand the systemic risk of large, complicated, financial network or inter-bank lending market, they propose some probabilistic, dynamical models that are described in the form of stochastic differential equations. They examine various aspects of such models, in particular, they characterize mechanism of systemic risk events as mean-field type phenomena. They also propose measures of such financial risk and financial health indicators for such systems. Mean Feild Theory: In physics and probability theory, mean field theory studies the behavior of large and complex stochastic models by studying a simpler model. Such models consider a large number of small interacting individual components which interact with each other. The effect of all the other individuals on any given individual is approximated by a single averaged effect, thus reducing a many-body problem to a one-body problem. Yuedon Wang: Biostatistics He is involved in research on end stage renal disease (ESRD). He is collaborating with researchers from Renal Research Institute and is one of the founding members of the MONitoring Dialysis Outcomes (MONDO) Initiative. The MONDO Initiative is an international consortium of eight worldwide dialysis providers. The goal of MONDO is to understand and improve outcomes in patients with end stage renal disease. Currently the MONDO database comprises longitudinal data from over 128,000 hemodialysis (HD) patients in 26 countries on five continents. They are doing research on many aspects of the patient case including prediction models for high risk patients. Wendy Meiring: Environmental & Ecology Statistics She works in the area of environmental and ecology statistics, studying processess that change in space and time. Collaborating with an interdisciplinary group of Statisticians, Biologists, engineers and environmental scientists to develop a life-history model for the endangered Delta Smelt fish that lives in the San Francisco Delta. Much remains unknown about this fish species in the wild. Studying the nature of biases when using the traditional April 1 snow pack measurements as proxies of maximum snow accumulation in the Sierra Nevada. They study how biases in both the magnitude and in the timing of peak snow accumulation, vary with topographical factors such as elevation, as well as with atmospheric and oceanic dynamics. It is very important that we improve our understanding of these biases, since they may impact the interpretation of long-term trend studies of the snow pack accumulation in the Sierra Nevada. Much of California’s water arises from this snow-pack. Raya Feldman & Ian Duncan: Probability & Actuarial Statistics Assess the premiums charged for patients with diabetes They are doing this research project with the Sansum Diabetes Research Institute. They are interested in knowing how CA hospitals compare with respect to the length of stay for patients with elective procedures (knee; hip and spinal surgeries) who also have diabetes. The objective is to determine the extend to which the presence of a diabetes diagnosis adds to the length of hospital stay. Raya Feldman & Ian Duncan: Probability & Actuarial Statistics Jean-Pierre Fouque, Michael Ludkovski & Tomoyuki Ichiba: Probability & Financial Mathematics John Hsu: Bayesian Methods S. Rao Jammalamadaka: Statistical Methodology Wendy Meiring: Environmental & Ecology Statistics Yuedon Wang: Biostatistics Drew Carter: Asymptotic Statistical Inference Dawn Holmes: Bayesian Networks http://www.pstat.ucsb.edu/ .
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