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Activity Number: 246 - Bayesian Nonparametrics
Type: Contributed
Date/Time: Monday, July 29, 2019 : 2:00 PM to 3:50 PM
Sponsor: Section on Bayesian Statistical Science
Abstract #304657
Title: Efficient Bayesian Shape-Constrained Function Estimation
Author(s): Pallavi Ray* and Debdeep Pati and Anirban Bhattacharya
Companies: Texas A&M University - College Station and Texas A&M University and TAMU
Keywords: Circulant embedding; Durbin’s recursion; Elliptical Slice Sampling; Smooth relaxation; Toeplitz

We 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.

Authors who are presenting talks have a * after their name.

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