In our daily life, we often need to identify individuals whose longitudinal patterns are different from the patterns of those well-functioning individuals, so that some unpleasant consequences can be avoided. In many such applications, observations of a given individual are obtained sequentially, and it is desirable to have a screening system to give a signal as soon as possible after that individual's longitudinal pattern starts to deviate from the regular pattern so that some adjustments or interventions can be made in a timely manner.
The Statistics Department hosts weekly colloquia on a variety of statistcal subjects, bringing in speakers from around the world.
Type of Event:
Extreme value theory is a branch of statistics that is devoted to studying the phenomena governed by extremely rare events. The modeling and statistics of such phenomena are tail dependent and so we consider a class of heavy-tail distributions, which are characterized by regular variation in the tails. While many articles have considered regular variation at one endpoint (particularly the left endpoint), the idea of regular variation at both endpoints has not be addressed. In this dissertation, we propose extreme value estimators for various non-negative time
Single-nucleotide polymorphisms (SNPs), believed to determine human differences, are widely used to predict risk of diseases and class membership of subjects. In the literature, several supervised machine learning methods, such as, support vector machine, neural network and logistic regression, are available for classification. Typically, however, samples for training a machine are limited and/or the sampling cost is high. Thus, it is essential to determine the minimum sample size needed to construct a classifier based on SNP data.
Evolution is a complex process that involves many sources of variation and interactions that make mathematical modeling a challenge. In nature, evolution is a time dependent process that involves a large number of environmental variables influencing the adaptation of a population and its progress. Environmental effects include the interaction between a population with its physical environment, its interaction with other populations and species, and the within population interactions between its members.
The times of repeated behavioral events can be viewed as a realization of a temporal point process. Rathbun, Shiffman, and Gwaltney (2007) used a Poisson process (Cox 1972) for modelling repeated behavioral events impacted by time-varying covariates. Taking an inspiration from the techniques of Generalized Linear Mixed Models, and the EM algorithm (Dempster et al. 1977) for finite mixture model estimation, we will further extend their models to handel data arising from a heterogeneous population.
TBD Joint seminar with the Department of Epidemiology and Biostatistics.
If the intensity of light radiating from a star varies in a periodic fashion over time, then there are significant opportunities for accessing information about the star's origins, age and structure. For example, if two stars have similar periodicity and light curves, and if we can gain information about the structure of one of them (perhaps because it is relatively close to Earth, and therefore amenable to direct observation), then we can make deductions about the structure of the other. Therefore period lengths, and light-curve shapes, are of significant interest.
We propose a method for evaluating the mean square error (mse) of a possibly biased estimator $\hat\Theta_1$, or, rather, the class of estimators to which it belongs. The method uses confidence intervals c of a corresponding unbiased estimator $\hat\Theta$ and makes its assessment based on the extent to which c includes $\hat\Theta_1$. The method does not require an estimate, implicit or explicit, of the bias of $\hat\Theta_1$, is indifferent to the bias/variance breakdown of $\hat\Theta_1$’s mse, and does not require surety of the model on which $\hat\Theta_1$ is based.
A treatment regime is a rule that assigns a treatment, among a set of possible treatment options, to a patient as a function of his/her individual characteristics, hence \personalizing" treatment to the patient. A goal is to identify the optimal treatment regime; that is, the regime that, if followed by the entire population of patients, would lead to the best outcome on average.
In medical research, it is often interested in finding subgroups in an outlier group. For example, a certain medical condition can be more frequent in a small group that is different from the majority of population. One approach to find groups in a data set is using cluster analysis. Cluster analysis has been widely used tool in exploring potential group structure in complex data and has received greater attention in recent years due to data mining and high dimensional data such as microarrays.