Minisymposia Abstracts

Speaker: Jiguo Cao
Simon Fraser University
Title: Parameter Cascading Estimation for Dynamic Models
Abstract: Differential equations describe the rate of change of a process. They are widely used in medicine, engineering, ecology and a host of other applications. One central and difficult problem is how to estimate DE parameters from noisy data. We have developed the parameter cascading method to address this problem. The parameter cascading method approximates DE solutions using nonparametric functions, which are estimated by penalized smoothing with DE-defined penalty. I will demonstrate our method with one extension in genetic mapping, which identifies Quantitative Trait Loci that control the growth dynamics of soybeans.

Speaker: Yanyuan Ma
Texas A&M University
Title: An Semiparametric Approach to Dimension Reduction
Abstract: We provide a novel and completely different approach to dimension reduction problems from the existing literature. We cast the dimension reduction problem in a semiparametric estimation framework and derive estimating equations. Viewing this problem from the new angle allows us to derive a rich class of estimators, and obtain the classical dimension reduction techniques as special cases in this class. The semiparametric approach also reveals that the common assumption of linearity and/or constant variance on the covariates can be removed at the cost of performing additional nonparametric regression. The semiparametric estimators without these common assumptions are illustrated through simulation studies and a data example. This is joint work with Liping Zhu.

Speaker: Siva Tian
University of Houston
Title: A Two-way Regularization Method for MEG Source Reconstruction
Abstract: We propose a two-way regularization (TWR) method to solve the magnetoencephalography (MEG) inverse problem which refers to the reconstruction of the neural activity that results in brain magnetic field. The proposed method is based on the assumptions that only a small number of locations in space are responsible for the measured signals (focality), and each source time course is smooth in time (smoothness). The focality and smoothness of the reconstructed signals are ensured respectively by imposing a sparsity induced penalty and a roughness penalty in the data fitting criterion. A two-stage algorithm is developed for fast computation, where a raw estimate of the source time course is obtained at the first stage and then refined in the second stage by the two-way regularization. The proposed method is shown to be effective on both synthetic and real-world examples.

Speaker: Xiaohong Chen
Yale University
Title: Modeling Spatially Correlated Hierarchical Functional Data
Abstract: Hierarchical functional data are widely seen in complex studies where sub-units are nested within units, which in turn are nested within treatment groups. We propose a general framework of functional mixed effects model for such data: within unit and within sub-unit variations are modeled through two separate sets of principal components; the sub-unit level functions are allowed to be correlated. Penalized splines are used to model both the mean functions and the principal components functions, where roughness penalties are used to regularize the spline fit. An EM algorithm is developed to fit the model, while the specific covariance structure of the model is utilized for computational efficiency to avoid storage and inversion of large matrices. Our dimension reduction with principal components provides an effective solution to the difficult tasks of modeling the covariance kernel of a random function and modeling the correlation between functions. The proposed methodology is illustrated using simulations and an empirical data set from a colon carcinogenesis study.

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