摘 要: In this expository talk we will provide an overview on the interface between certain developments in the areas of reliability and multivariate statistics. More specifically, we will illustrate: (a) How the concept of association of random variables, originally motivated by an applied problem in reliability theory, has enhanced the studies of positive dependence and has provided solutions to many interesting problems in statistics. (b) How majorization-related probability inequalities in statistics have been applied to obtain useful results in system reliability theory. Some of the key references and basic ideas will be discussed, and a few theorems will be stated. However, due to the limited time, no mathematical details will be given.
摘 要: In this talk, we introduce a new graph parameter, called t-star-matching number of a graph. We design a polynomial time algorithm to compute the t-star-matching number for any graph. We then relate the 4-star-matching number of a graph to the so called L(2,1)-labeling number of a graph. This leads to a polynomial time algorithm to compute the L(2,1)-labeling numbers of certain classes of graph.
摘 要: When used for modeling longitudinal data generalized estimating equations specify a working structure for the within-subject covariance matrices, aiming to produce efficient parameter estimators. However, misspecification of the working covariance structure may lead to a large loss of efficiency of the estimators of the mean parameters. In this paper we propose an approach for joint modeling of the mean and covariance structures of longitudinal data within the framework of generalized estimating equations. The resulting estimators for the mean and covariance parameters are shown to be consistent and asymptotically Normally distributed. Real data analysis and simulation studies show that the proposed approach yields efficient estimators for both the mean and covariance parameters.
摘 要: In this talk, the speaker shall first introduce the concept of inverse optimization and formulate such problems mathematically. Some applications shall be followed to justify usefulness of the study. Then some general methods shall be discussed. Furthermore, in order to achieve high efficiency, special methods will be given to deal with each type of particular inverse optimization problems. Some extensions and further development, such as system improvement problems and partial inverse optimization problems, shall be mentioned to conclude this talk.
摘 要: A recent study of log-likelihood identity in terms of mutual information yields useful applications in statistical inference. For testing association in a 2 x 2 table (Pearson, 1904; Fisher, 1934), it establishes power analysis using likelihood ratio (LR) test that can not be achieved by other existing methods. An extended identity provides power evaluations for testing inhomogeneous odds ratios of three-way tables. A problem of the celebrated CMH test (1954, 1959) is examined by the geometry of an information identity, and resolved by using an omnibus LR test together with a family of two-step LR tests. In contrast to the hierarchical log-linear models, information identities lead to developing a natural family of linear information models (LIM). Empirical studies of two-way and high-way contingency tables are used to illustrate the new statistical inference at college textbook level.
摘 要: Survey research, broadly conceived as the practice of collecting sample records in order to learn something about an entire population, is likely millennia old. However, the formal systematization of survey research did not begin until shortly after World War II; the effort was spearheaded by three groups: University of Michigan; Columbia University; and the U.S. Census Bureau. Today, survey research constitutes a truly inter-disciplinary endeavor that is fraught with numerous potential complicating factors. Some key issues include how to best design the instrument, conduct the survey, analyze the data, and report the results based on the research questions, the population surveyed, and the type of survey used. As the world's "global economy" (of which China is a major contributor) continues to move towards a "market-based economy", the overall importance of survey-centered, market research is likely to increase. Given the diversity of the survey method landscape and the complexity of the questions asked, it is very important to select "the right tool for the job". In this regard, The Survey System (TSS) 9.5 has been called "the market researcher's surveying package." The question at hand is whether or not TSS 9.5 lives up to its name and more specifically "Should it be our survey software for the FPIL?" The seminar will be organized into three parts: (i) overview of the software; (ii) demonstration of some key features; and (iii) discussion of the strengths and weaknesses of the product.
摘 要: In business, finance, and other endeavors that require constant decision making, effectively combining quantitative information with subjective judgment is critical in achieving success and maintaining competitiveness. Bayesian methodology is ideally suited for this task because it provides a coherent and rigorous probability-based framework for statistical analysis with explicit subjective input via prior specification. The first part of this tutorial demonstrates the modeling aspects of Bayesian Statistics via a couple of examples on airline stocks and insurance mortality. Aided by movies, the second part introduces Markov chain Monte Carlo (MCMC), a general class of simulation methods that have revolutionized the Bayesian Statistics since 1990s because they made it possible to fit many realistic Bayesian models that defeat traditional computational methods.
摘 要: The University of California (UC), home to more than 209,000 students, is "the heart and soul of California, and its future" (Robert Dynes, UC President). In this talk I will give a general description of the higher education system in California, with more detailed information on UC, UCLA, and how to get there. The second part of the talk will give you a peek into the field of biostatistics through the eyes of a biostatistician.
摘 要: In this talk, I will introduce how to select significant variables in semiparametric modeling. Variable selection for semiparametric regression models consists of two components: model selection for nonparametric components and selection of significant variables for the parametric portion. Thus, semiparametric variable selection is much more challenging than parametric variable selection (e.g., linear and generalized linear models) because traditional variable selection procedures including stepwise regression and the best subset selection now require separate model selection for the nonparametric components for each submodel. This leads to very heavy computational burden. In this paper, we propose a class of variable selection procedures for semiparametric regression models using nonconcave penalized likelihood. We establish the rate of convergence of the resulting estimate. With proper choices of penalty functions and regularization parameters, we show the asymptotic normality of the resulting estimate, and further demonstrate that the proposed procedures perform as well as an oracle procedure. A semiparametric generalized likelihood ratio test is proposed to select significant variables in the nonparametric component. We investigate the asymptotic behavior of the proposed test and demonstrate that its limiting null distribution follows a chi-squared distribution, which is independent of the nuisance parameters. Extensive Monte Carlo simulation studies are conducted to examine the finite sample performance of the proposed variable selection procedures.
摘 要: The problem of providing services to a mass of anonymous users whose goals and needs evolve over the time in unpredictable way is common to many application domains of information technology, from web to mobile communication from news broadcasting to advertising. The basic idea of the proposed approach is to use the evolutionary scheme of genetic algorithms in order to dynamically adapt to the audience and service evolution while optimizing the global systems performance.
摘 要: Bayesian Belief Network (BBN) is the currently dominant method for reasoning under uncertainty in Artificial Intelligence. Inferences with BBNs are either optimization, or marginalization, or both on the joint probability space.
We demonstrate that the joint probability distribution of a BBN is a multifractal in its most general form - a random multinomial multifractal. With sufficient asymmetry in individual prior and conditional probability distributions, the joint distribution is not only highly skewed, but also stochastically self-similar and has clusters of high-robability instantiations at all scales. Inspired by the multifractal properties, a sampling-and-search algorithm for finding the Most Probable Explanation (MPE) in BBN is developed and tested. The experimental result shows that these multifractal properties provide good heuristic for solving the NP-hard MPE problem.
- The first Lecture - Statistics for the Community, by Mr. Fung, Hing Wang, Commissioner for Census and Statistics Department, HKSAR. [海报] [演讲稿] [照片]