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

• 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
• ISSN: 0960-3174; 1573-1375
• DOI: 10.1007/s11222-020-09922-0

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.