威尼斯人

//stat.duke.edu/~alan/

Speaker: Alan E. Gelfand, James B Duke Professor, Department of Statistical Science,Duke University

Lecture 1: Geostatistical Modeling

Date:2015.4.27（Monday）9:00-10:00AM

Place:苏州大学本部天元讲堂

Abstract：Collection of spatial data is rapidly increasing. In analyzing such data it is critical to take into account the spatial information in the data. In particular, it is natural to expect spatially structured dependence, i.e., pairs of locations closer to each other are expected to be more associated than those farther apart. Thr setting where spatial data is collected at point referenced locations is usually referred to as geostatistical data. The objective in such settings is usually prediction, so-called kriging at unobserved locations.
To apply full inference to such interpolation requires specifying a probability model over an uncountable set of locations, i.e., a stochastic process, which incorporates suitable dependence behavior. This lecture will focus on the development of such formal processes both theoretically and practically. In particular, we will consider Gaussian processes specified with valid covariance functions and formalize the concept of Gaussian kriging. Examples will be provided to illustrate the theory.

Lecture 2: Inference for Geostatistical Models using Bayesian Hierarchical Models

Date:2015.4.27（Monday）10:00-11:00AM

Place:苏州大学本部天元讲堂

Abstract：Having developed the geostatistical modeling setting, we show that such models are naturally specified using hierarchical models. We also argue that inference for hierarchical models is most satisfyingly implemented within a Bayesian framework in order to avoid inappropriate asymptotics. We clarify the ease with which such models can be fitted using Gibbs sampling/Markov chain Monte Carlo. We illuminate the full inference available through the hierarchical Bayes formulation. We demonstrate how to do fully Bayesian kriging regardless of the nature of the data observed at the locations. We show how to increase the flexibility of the models in order to capture departures from basic assumptions such as homogeneity of variance, Gaussian distributions and isotropic covariance functions. We illustrate the entire approach with several examples.

Lecture 3: Multivariate spatial processes, space time processes, and big space and space-time datasets

Date:2015.4.28（Tuesday）2:00-3:00PM

Place:数学楼二楼学术报告厅

Abstract：Geostatistical data often finds collection of multivariate observations at locations. For instance, at a monitoring station we might collect levels of particulate matter, ozone, and carbon monoxide. Modeling for such data requires multivariate spatial processes incorporating both dependence across locations as well as dependence within locations. We now need to specify a valid cross-covariance function. Then we can proceed with hierarchical Bayesian model fitting. In other geostatistical settings we obtain spatio-temporal data. For example, at a monitoring station, data is collected hourly (or daily). Now, we need to think about space-time dependence, i.e., does the nature of the spatial dependence between locations change as we pass through time?
Both of these settings typically lead to large datasets, creating demanding matrix computation. In order to implement model fitting, we either attempt dimension reduction or sparsity strategies. Here, we will focus dimension reduction approaches. Such approaches can be motivated either through basis representations or suitable Gaussian processes. We show how to introduce the latter into the geostatistical model so that, again, we may proceed with hierarchical Bayes model fitting. Again,we illustrate with examples.

报告人简介：Alan E. Gelfand是美国杜克大学统计系James B杜克教授，Gelfand教授是美国统计协会当选会士，数理统计学院当选会士，国际统计学院当选会士,美国康涅狄格州艺术与科学院院士，是1991-2001年间第10名被引用最多的数学家，他迄今发表了270余篇论文，主要在应用统计，贝叶斯计算，贝叶斯推断领域有重要国际性影响。曾任国际贝叶斯分析学会主席，于2006年因对统计学研究的长期贡献获得Parzen奖。

详见个人网页：//stat.duke.edu/~alan/

About the speaker: Alan E. Gelfand is The James B Duke Professor of Statistical Science, Duke University. Professor Gelfand is an Elected Fellow of the American Statistical Association and the Institute of Mathematical Statistics, an Elected Member of the International Statistical Institute, and Elected member of the Connecticut Academy of Arts and Sciences. Author of more than 270 papers, Gelfand is internationally known for his contributions to applied statistics, Bayesian computation and Bayesian inference.  (An article in Science Watch found him to be the tenth most cited mathematical scientist in the world over the period 1991-2001). He is a former President of the International Society for Bayesian Analysis and in 2006, he received the Parzen Prize for a lifetime of research contribution to Statistics.