Seminar at SMU Delhi
January 17, 2012 (Tuesday) ,
3:30 PM at Webinar
(PCM lecture)
Speaker:
Alan Gelfand,
Duke University
Title:
Analyzing Spatial Directional Data through the use of Gaussian Processes
Abstract of Talk
Circular data arise in oceanography (wave directions) and meteorology
(wind directions), and, more generally, with periodic measurements
recorded in degrees or angles on a circle. In this talk we introduce a
fully model-based approach to handle circular data in the case of
measurements taken at spatial locations, anticipating structured
dependence between these measurements. We formulate a wrapped Gaussian
spatial process model for this setting, induced from a customary {\em
inline} Gaussian process. We look at the properties of this process,
including the induced correlation structure.
We build a hierarchical model to handle this situation and show how
to fit this model straightforwardly using Markov chain Monte Carlo
methods. Our approach enables spatial interpolation and can
accommodate measurement error. We illustrate with a set of angular
wave direction data from the Adriatic coast of Italy, generated
through a complex computer model.
Then, we consider the projected normal spatial process built from a
bivariate Gaussian process model. Such models are more flexible than
usual wrapped or von Mises models and easily handle regression.
However, they are more challenging to fit. We illustrate with a
butterfly dataset.