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A note on Gauss—Hermite quadrature
Abstract
For Gauss—Hermite quadrature, we consider a systematic method for transforming the variable of integration so that the integrand is sampled in an appropriate region. The effectiveness of the quadrature then depends on the ratio of the integrand to some Gaussian density being a smooth function, well approximated by a low-order polynomial. It is pointed out that, in this approach, order one Gauss-Hermite quadrature becomes the Laplace approximationmxHermite quadrature becomes the Laplace approximationmxHermite quadrature becomes the Laplace approximationmxHermite quadrature becomes the Laplace approximation. Thus the quadrature as implemented here can be thought of as a higher-order Laplace approximation.
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Cited by
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Metadata
- Authors
- LIU, Q., & PIERCE, D. A.
- Venue
- Biometrika
- Publisher
- Oxford University Press (OUP)
- Published
- 1994
- Volume
- 81
- Issue
- 3
- Pages
- 624-629
- ISSN
- 0006-3444 (ISSN-L)
- 1464-3510
- OpenAlex
- W2014602125
- Cited by
- 415
- References
- 0
- FWCI
- 2.10
- Type
- journal article
- Language
- en
- Open access
- closed
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- CoChat. (2026). Citation check: A note on Gauss—Hermite quadrature. https://app.cochat.ai/papers/10.1093/biomet/81.3.624
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- LIU, Q., & PIERCE, D. A. (1994). A note on Gauss—Hermite quadrature. Biometrika. https://doi.org/10.1093/biomet/81.3.624
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Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
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