Bayesian Spatial and Functional Data Analysis Using Gaussian Processes

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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)

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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

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Introduction
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Algorithmic/deterministic approaches for spatial
data
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Two approaches
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Cartoon of GP, marginally
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First consider the atomsThe spatial DP
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An Example
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True vs. sampled correlations
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Now weights driven by GPsWe switch notation
from ws to psWe create a GSDP/HDP
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Multivariate stickbreaking
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Our modeling world
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Progesterone Data (PGD)
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PGD Modified
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