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Published byCaroline Thornton Modified over 2 years ago

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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)

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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

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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 atoms The spatial DP

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An Example

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True vs. sampled correlations

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Now weights driven by GPs We switch notation from ws to ps We 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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