Many data sets in the sciences (broadly defined) deal with multiple sets of multivariate time series. The case of a single univariate time series is very well developed in the literature; and single multivariate series though less well studied have also been developed (under the rubric of vector time series). A class of matrix time series models is introduced for dealing with the situation where there are multiple sets of multivariate time series data.
The Statistics Department hosts weekly colloquia on a variety of statistcal subjects, bringing in speakers from around the world.
Type of Event:
Dynamic treatment regimen is emerging as a new strategy for treatment which takes individual heterogeneity in disease severities, background characteristics and related clinical measurements into consideration. In this work, we propose a strategy to select variables with qualitative interactions to get the optimal treatment regime based on sequential advantage. We will demonstrate the proposed method with extensive numerical results and a real data analysis.
Semiparametric regression models have been wildly applied into the longitudinal data. In this dissertation, we model generalized longitudinal data from multiple treatment groups by a class of semiparametric analysis of covariance models, which take into account the parametric effects of time dependent covariates and the nonparametric time effects. In these models, the treatment effects are represented by nonparametric functions of time and we propose a generalized quasi-likelihood ration (GQLR) test procedure to test if these functions are the same.
In the large cohorts typically used for genome-wide association studies (GWAS), it is not economically feasible to sequence all cohort members. A cost-effective strategy is to sequence subjects with extreme values of quantitative traits or those with specific diseases. By imputing the sequencing data from the GWAS data for the cohort members who are not selected for sequencing, one can dramatically increase the number of subjects with information on rare variants.
We propose trace pursuit for model-free variable selection under the sufficient dimension reduction paradigm. Two distinct algorithms are proposed: stepwise trace pursuit and forward trace pursuit, both of which can be combined with many existing sufficient dimension reduction methods. Stepwise trace pursuit achieves selection consistency with fixed dimension p, and is readily applicable in the challenging p>n setting. Forward trace pursuit can serve as an initial screening step to speed up the computation in the case of ultrahigh dimensionality.
The usefulness and popularity of nonlinear models have spurred a large literature on data analysis, but research on design selection has not kept pace. One complication in studying optimal designs for nonlinear models is that information matrices and optimal designs depend on unknown parameters. Besides the popular locally optimal designs strategy, another common approach is to use Bayesian optimal design approach, which typically means an optimality problem has to be solved through numerical approaches. However, very few algorithm approaches are available for Bayesian optimal design.
Functional magnetic resonance imaging (fMRI) is one of the leading brain mapping technologies for studying brain activity in response to mental stimuli. For neuroimaging studies utilizing this pioneering technology, there is a great demand of high-quality experimental designs that help to collect informative data to make precise and valid inference about brain functions. In this talk, I provide a survey on some recently developed analytical and computational results on fMRI design selection.
In this talk we will give a quick overview of some of the strengths and challenges in Bayesian variable selection as it evolved over the last two decades. We will then discuss two specific problems in linear regression with strong multicollinearity among the covariates.
Finding optimal designs for generalized linear models is a challenging problem. Recent research has identified the structure of optimal designs for generalized linear models with a single or multiple independent explanatory variables that appear as first-order terms in the predictor. We consider generalized linear models with a single-variable quadratic polynomial predictor under a popular family of optimality criteria.
Gene duplication is the key mechanism for evolutionary change. To infer the timing and nature of gene duplication, the 'data' used are the end result of various pipelines. In this talk, I will summarize how the 'data' are obtained, explore the shortcomings of analyses in the literature, and end with current work on overcoming these shortcomings. The interesting statistical problems are that the 'data' are maximum likelihood estimates, and that the biological process (saturation effects) present complications in data modeling.