The DOI matches its Crossref record; 1 of the 1 references it cites were found in a registry or an index.
Laplace Approximation of High Dimensional Integrals
Abstract
SUMMARY: It is shown that the usual Laplace approximation is not a valid asymptotic approximation when the dimension of the integral is comparable with the limiting parameter n. The formal Laplace expansion for multidimensional integrals is given and used to construct asymptotic approximations for high dimensional integrals. One example is considered in which the dimension of the integral is O(n 1/2) and the relative error of the unmodified Laplace approximation is O(1). Nevertheless, it is possible to construct a valid asymptotic expansion by regrouping terms in the formal expansion according to asymptotic order in n.
Overview
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Integrity signals
Registry
Cites
Statistics
Verification
Claims the paper makes
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
The self-check needs the paper’s full text.
Citations
Cites
McCullagh, P., & Nelder, J. A. (1989) · doi:10.1007/978-1-4899-3242-6 · Cited by 16,836
Self-citation
Cited by
Rue, H., Martino, S., & Chopin, N. (2009) · Journal of the Royal Statistical Society Series B: Statistical Methodology · doi:10.1111/j.1467-9868.2008.00700.x · Cited by 5,279
Smoothing Parameter and Model Selection for General Smooth Models
Wood, S. N., Pya, N., & Säfken, B. (2016) · Journal of the American Statistical Association · doi:10.1080/01621459.2016.1180986 · Cited by 1,312
Bayesian Computing with INLA: A Review
Rue, H., Riebler, A., Sørbye, S. H., Illian, J. B., Simpson, D. P., & Lindgren, F. K. (2017) · Annual Review of Statistics and Its Application · doi:10.1146/annurev-statistics-060116-054045 · Cited by 737
Metadata
- Authors
- Shun, Z., & McCullagh, P.
- Venue
- Journal of the Royal Statistical Society Series B: Statistical Methodology
- Publisher
- Oxford University Press (OUP)
- Published
- 1995-11-01
- Volume
- 57
- Issue
- 4
- Pages
- 749-760
- ISSN
- 1369-7412 (ISSN-L)
- 1467-9868
- OpenAlex
- W2407194592
- Cited by
- 222
- References
- 1
- FWCI
- 4.10
- Type
- journal article
- Language
- en
- Open access
- closed
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
How to cite
Cite CoChat for the checks on this page, and the paper for its own findings.
- This page
- CoChat. (2026). Citation check: Laplace Approximation of High Dimensional Integrals. https://app.cochat.ai/papers/10.1111/j.2517-6161.1995.tb02060.x
- The paper
- Shun, Z., & McCullagh, P. (1995). Laplace Approximation of High Dimensional Integrals. Journal of the Royal Statistical Society Series B: Statistical Methodology. https://doi.org/10.1111/j.2517-6161.1995.tb02060.x
Data sources
Bibliographic data: Semantic Scholar, OpenAlex, Crossref.
Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
