Bayesian Spatial and Functional Data Analysis

Using Gaussian Processes

Alan E. GelfandDuke University

(with contributions from J. Duan, D. Dunson, M. Guindani, A. Kottas, S. MacEachern,

X. Nguyen, S. Petrone, A. Rodriguez)

Outline

• Functional data analysis (FDA) and spatial data analysis (SDA)

• Gaussian Processes

• Dirichlet Processes (DP, DPK)

• Spatial DP (SDP)

• Multivariate Stickbreaking

• Hybrid (HDP, HDPK), Labeling processes, GSDP, GSDPK

Introduction

Algorithmic/deterministic approaches for spatial data

Two approaches

Cartoon of GP, marginally

First consider the atomsThe spatial DP

An Example

True vs. sampled correlations

Now weights driven by GP’sWe switch notation from w’s to p’s

We create a GSDP/HDP

Multivariate stickbreaking

Our modeling world

Progesterone Data (PGD)

PGD Modified