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.

中文翻译：

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约束高斯过程先验的有效贝叶斯形状受限函数估计

鉴于最近开发的近似高斯过程，本文重新审视了贝叶斯形状受限的推理问题，该过程接受了基于基本系数的等效形状约束公式。我们提出了一种通过吸收可能性的平稳松弛并利用循环嵌入技术从无约束的修改后的样本中有效地从产生的后约束的后样本中采样的策略。我们还特别注意减轻因更新高斯过程的协方差内核中的超参数而引起的计算复杂性。在模拟和真实数据示例中，开发的算法被证明是准确且高效的。