Lately, I have published on various topics in probability, statistical inference, and linear models. Those research topics arose from teaching mostly graduate level, and some undergraduate level, courses.
The Statistics Department hosts weekly colloquia on a variety of statistcal subjects, bringing in speakers from around the world.
Type of Event:
In work carried out with my colleague Pengfei Li, we construct experimental designs for dose-response studies. The designs are robust against possibly misspecified link functions; to this end they minimize the maximum mean squared error of the estimated dose required to attain a response in 100p% of the target population. Here p might be one particular value - p = .5 corresponds to ED50 estimation - or it might range over an interval of values of interest. The maximum of the mean squared error is evaluated over a Kolmogorov neighbourhood of the fitted link.
Additive models have been widely used in nonparametric regression, mainly due to their ability to avoid the problem of the ``curse of dimensionality". When some of the additive components are linear, the model can be further simplified and higher convergence rates can be achieved for the estimation of these linear components. In this paper, we propose a testing procedure for the determination of linear components in nonparametric additive models.
An individual's behaviors may be influenced by the behaviors of friends, such as hours spent watching television, playing sports, and unhealthy eating habits. However, preferences for these behaviors may also influence the choice of friends; for example, two children who enjoy playing the same sport are more likely to become friends. To study the interdependence of social network and behavior, Snidjers et al.
We propose linear discrimination methods which regularize piling of the low dimensional projections for high dimensional, low sample size data. The maximal data piling achieves the extreme regularization by yielding zero scatter within the class while maximizing the separation between the classes. Two different piling regularization methods are studied in this article. Our first attempt to regularize data piling is done by employing linear paths connecting the maximal data piling direction and least data piling direction.
In this talk I will quickly survey some recent progresses on the (conditional) central limit questions for stationary processes. One recent Markov chain example will be focused on, and its analysis is leading to some interesting phenomenon, which apparently we have not understood well yet. In vague terms, the partial sum of this Markov chain has variance growing faster than n, which delivers some challenge to prove the conditional CLT. But when we managed to show a CLT, it was found there is a `mass escaping' --- limiting variance
The use of Bayesian designs and analyses in biomedical and many other applications has burgeoned, even though its use entails additional overhead. Consequently, it is evident that statisticians and collaborators are increasingly ﬁnding the approach worth the bother. To help explain this increase in prevalence, I highlight a subset of the potential advantages of the Bayesian formalism and Bayesian philosophy in study design (“Everyone is a Bayesian in the design phase”), conduct, analysis and reporting.
The theory of Markov jump processes has broad applications in molecular biology and population dynamics modeling. One of the most important practical aspects of analyzing models based on Markov jump processes under the so called “mass-action" kinetics, is the inference on the reaction rate constants. The presentation shall describe some conditions on the data process and the underlying likelihood function which guarantee the identifiability of the process parameters and the consistency of the maximum likelihood estimates.
Variable selection of main effects is often a first step of model building followed by consideration of interactions and nonlinearities. We consider selection of second-order models under various hierarchy restrictions between main effects and second-order terms (squares and interactions) using the FSR approach of Wu et al. (2007, JASA) and Boos et al. (2009, Biometrics). The basic idea is to control the proportion of uninformative variables in the final model.