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Rejoinder: “Probabilistic integration: a role in statistical computation?”. (English) Zbl 1420.62136
Summary: This article is the rejoinder to the comments [F. J. Hickernell and R. Jagadeeswaran, ibid. 34, No. 1, 23–28 (2019; Zbl 1420.62139); A. B. Owen, ibid. 34, No. 1, 29–33 (2019; Zbl 1420.62145); M. L. Stein and Y. Hung, ibid. 34, No. 1, 34–37 (2019; Zbl 1420.62150)] on the authors’ paper [ibid. 34, No. 1, 1–22 (2019; Zbl 1420.62135)]. We would first like to thank the reviewers and many of our colleagues who helped shape this paper, the Editor for selecting our paper for discussion, and of course all of the discussants for their thoughtful, insightful and constructive comments. In this rejoinder, we respond to some of the points raised by the discussants and comment further on the fundamental questions underlying the paper: (i) Should Bayesian ideas be used in numerical analysis? and (ii) If so, what role should such approaches have in statistical computation?
62G05 Nonparametric estimation
65D30 Numerical integration
65C60 Computational problems in statistics (MSC2010)
Full Text: DOI Euclid
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