Abstract
It is desired to estimate a real valued function F on the unit square having observed F with error at N points in the square. F is assumed to be drawn from a particular Gaussian process and measured with independent Gaussian errors. The proposed estimate is the Bayes estimate of F given the data. The roughness penalty corresponding to the prior is derived and it is shown how the Bayesian technique can be regarded as a generalisation of variance components analysis. The proposed estimate is shown to be consistent in the sense that the expected squared error averaged over the data points converges to zero as $N\\rightarrow\\infty$. Upper bounds on the order of magnitude of magnitude of the expected average squared error are calculated. The proposed technique is compared with existing spline techniques in a simulation study. Generalisations to higher dimensions are discussed.
Keywords
MathematicsGaussian processStatisticsMean squared errorNonparametric regressionKrigingBayesian probabilityApplied mathematicsGaussianNonparametric statisticsBayes' theorem
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Publication Info
- Year
- 1986
- Type
- article
- Volume
- 14
- Issue
- 3
- Citations
- 72
- Access
- Closed
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Cite This
Daniel Barry
(1986).
Nonparametric Bayesian Regression.
The Annals of Statistics
, 14
(3)
.
https://doi.org/10.1214/aos/1176350043
Identifiers
- DOI
- 10.1214/aos/1176350043