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Bayesian Spatial and Functional Data Analysis Using Gaussian Processes

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). Outline.

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Bayesian Spatial and Functional Data Analysis Using Gaussian Processes

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  1. Bayesian Spatial and Functional Data AnalysisUsing 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, DPK) • Spatial DP (SDP) • Multivariate Stickbreaking • Hybrid (HDP, HDPK), Labeling processes, GSDP, GSDPK

  3. Introduction

  4. Algorithmic/deterministic approaches for spatial data

  5. Two approaches

  6. Cartoon of GP, marginally

  7. First consider the atomsThe spatial DP

  8. An Example

  9. True vs. sampled correlations

  10. Now weights driven by GP’sWe switch notation from w’s to p’sWe create a GSDP/HDP

  11. Multivariate stickbreaking

  12. Our modeling world

  13. Progesterone Data (PGD)

  14. PGD Modified

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