Efficient Bayesian shape-restricted function estimation with constrained Gaussian process priors

This article revisits the problem of Bayesian shape-restricted inference in the light of a recently developed approximate Gaussian process that admits an equivalent formulation of the shape constraints in terms of the basis coefficients. We propose a strategy to efficiently sample from the resulting...

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Bibliographic Details
Published in:Statistics and computing 2020-07, Vol.30 (4), p.839-853
Main Authors: Ray, Pallavi, Pati, Debdeep, Bhattacharya, Anirban
Format: Article
Language:English
Subjects:
Algorithms
Artificial Intelligence
Bayesian analysis
Computer simulation
Constraints
Covariance
Gaussian process
Mathematics and Statistics
Probability and Statistics in Computer Science
Statistical Theory and Methods
Statistics
Statistics and Computing/Statistics Programs
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Summary:This article revisits the problem of Bayesian shape-restricted inference in the light of a recently developed approximate Gaussian process that admits an equivalent formulation of the shape constraints in terms of the basis coefficients. We propose a strategy to efficiently sample from the resulting constrained posterior by absorbing a smooth relaxation of the constraint in the likelihood and using circulant embedding techniques to sample from the unconstrained modified prior . We additionally pay careful attention to mitigate the computational complexity arising from updating hyperparameters within the covariance kernel of the Gaussian process. The developed algorithm is shown to be accurate and highly efficient in simulated and real data examples.
ISSN:0960-3174
1573-1375
DOI:10.1007/s11222-020-09922-0