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Activity Number:
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236
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Type:
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Topic Contributed
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Date/Time:
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Tuesday, August 8, 2006 : 8:30 AM to 10:20 AM
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Sponsor:
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Section on Bayesian Statistical Science
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| Abstract - #306827 |
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Title:
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Gaussian Processes and Limiting Linear Models
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Author(s):
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Robert Gramacy and Herbert Lee*+
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Companies:
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University of Cambridge and University of California, Santa Cruz
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Address:
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School of Engineering, Santa Cruz, CA, 95064,
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Keywords:
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Bayesian statistics ; semi-parametric model ; spatial statistics ; nonparametric regression
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Abstract:
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Gaussian processes (GPs) retain the linear model (LM) as either a special case or in the limit. We show how this relationship can be exploited when the data are at least partially linear. However, from the prospective of the Bayesian posterior, the GPs that encode the LM have either probability of nearly zero or are otherwise unattainable without the explicit construction of a prior with the limiting linear model in mind. We develop such a prior and show its practical benefits extend well beyond the computational and conceptual simplicity of the LM. For example, linearity can be extracted on a per-dimension basis or combined with treed partition models to yield a highly efficient nonstationary model. Our approach is demonstrated on synthetic and real datasets of varying linearity and dimensionality.
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