1. Bayesian Spatial and Functional Data Analysis Using Gaussian Processes Alan E. Gelfand Duke University (with contributions from J. Duan, D. Dunson, M. Guindani, A. Kottas, S. MacEachern, X. Nguyen, S. Petrone, A. Rodriguez)

2. Outline Functional data analysis (FDA) and spatial data analysis (SDA) Gaussian Processes Dirichlet Processes (DP, DP K ) Spatial DP (SDP) Multivariate Stickbreaking Hybrid (HDP, HDP K ), Labeling processes, GSDP, GSDP K

3. Introduction

6. Algorithmic/deterministic approaches for spatial data

7. Two approaches

9. Cartoon of GP, marginally

20. First consider the atoms The spatial DP

25. An Example

27. True vs. sampled correlations

30. Now weights driven by GPs We switch notation from ws to ps We create a GSDP/HDP

36. Multivariate stickbreaking

43. Our modeling world

50. Progesterone Data (PGD)

52. PGD Modified