报告题目1：New Classes of Nonseparable Space-Time Covariance Functions
时间：周二（5月20日）下午4点
地点：数学楼二楼学术报告厅
报告人：Tatiyana Apanasovich, Associate Professor, Department of Statistics, George Washington University
报告摘要：Statistical methods for the analysis of space-time data are of great interest for many areas of application. Geostatistical approaches to spatiotemporal estimation and prediction heavily rely on appropriate covariance models. In my talk I will first give an overview of techniques to build valid space-time covariances that must satisfy the positive definiteness constraint. Then, I will discuss the specific properties of covariance functions and how they relate to  spatial and temporal marginal processes as well as their interaction. The highlighted critical aspects to model building will be used to motivate the proposed family of nonseparable space-time covariance structures which have the celebrated Matern family for their spatial margins. I will also describe a simple modification of the new family to address the lack of symmetry. The application of the proposed methodologies will be illustrated on the datasets from environmental science and meteorology.
 
报告题目2：Estimation of Nonlinear Differential Equation Model Using Generalized Smoothing 
时间：周三（5月21日）上午10点
地点：数学楼二楼学术报告厅
报告人：Tatiyana Apanasovich, Associate Professor, Department of Statistics, George Washington University
报告摘要：In this work, we develop an ordinary dierential equations (ODE) model of physiological regulation of glycemia in type 1 diabetes mellitus (T1DM) patients in response to meals and intravenous insulin infusion. Unlike for majority of existing mathematical models of glucose-insulin dynamics, parameters in our model are estimable from a relatively small number of noisy observations of plasma glucose and insulin concentrations. For estimation, we adopt the generalized smoothing estimation of nonlinear dynamic systems of Ramsay et al. (2007).In this framework, the ODE solution is approximated with a penalized spline, where the ODE model is incorporated in the penalty.We propose to optimize the generalized smoothing by using penalty weights that minimize the covariance penalties criterion (Efron, 2004).
The covariance penalties criterion provides an estimate of the prediction error for nonlinear estimation rules resulting from nonlinear and/or non-homogeneous ODE models, such as our model of glucose-insulin dynamics. We also propose to select the optimal number and location of knots for B-spline bases used to represent the ODE solution. The results of the small simulation study demonstrate advantages of optimized generalized smoothing in terms of smaller estimation errors for ODE parameters and smaller prediction errors for solutions of differential equations. Using the proposed approach to analyze the glucose and insulin concentration data in T1DM patients we obtained good approximation of global glucose-insulin dynamics and physiologically meaningful parameter estimates.