統計学輪講（第３３回）

日時    2005年 11月 29日(火)  15時〜16時40分
場所    経済学部新棟３階第３教室
講演者  Alan E. Gelfand(Duke University)
演題    Gradient Analysis for Spatial Data Models
概要：
  The topography of spatial surfaces is often of interest to investigate. 
In partic- ular, assuming sufficient smoothness, one can investigate 
gradients to a spatial surface. When the surface is a random realization 
of a spatial process, under suitable conditions for the process covariance 
function, we can, in fact, consider the ensemble of gradients {D_uY(s)} 
where s indexes locations in some spatial region and u indexes directions. 
Banerjee, Gelfand and Sirmans (2003) developed the necessary distribution 
theory and inference in the case of a Gaussian process for Y(s). In this 
talk we will go beyond this work, looking at the following cases: (i) the 
random surface arises as a realization of a mean process which is, itself, 
a linear transformation of a multivariate spatial process, (ii) the random 
surface arises through a nonparametric specification such as the spatial 
Dirichlet process, introduced in Gelfand, Kottas, and MacEachern(2005), 
(iii) the random surface evolves in time say with time discretized so that 
we have a dynamic spatial process model with the ensemble of variables 
{D_u Y(s, t)}. Here we can work with evolving Gaussian processes or spatial 
Dirichlet processes. 

  Theoretical results involving local convergence and formal distribution 
theory will be offered as well as applications to problems involving 
exposure surfaces, land value surfaces and returns on land value investment.

統計学輪講のスケジュールに戻る．

Tokyo University