The DOI matches its Crossref record; 4 of the 4 references it cites were found in a registry or an index.
On the Asymptotic Behaviour of Posterior Distributions
Abstract
Summary: Let a random sample of size n be taken from a distribution having a density depending on a real parameter θ, and let θ have an absolutely continuous prior distribution with density π(θ). We give a rigorous proof that, under suitable regularity conditions, the posterior distribution of θ will, when n tends to infinity, be asymptotically normal with mean equal to the maximum-likelihood estimator and variance equal to the reciprocal of the second derivative of the logarithm of the likelihood function evaluated at the maximum-likelihood estimator, independently of the form of π(θ).
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Citations
Cites
Note on the Consistency of the Maximum Likelihood Estimate
Wald, A. (1949) · The Annals of Mathematical Statistics · doi:10.1214/aoms/1177729952 · Cited by 1,100
Kiefer, J., & Wolfowitz, J. (1956) · The Annals of Mathematical Statistics · doi:10.1214/aoms/1177728066 · Cited by 1,023
Introduction to Probability and Statistics from a Bayesian Viewpoint
Lindley, D. V. (1965) · Cambridge University Press eBooks · doi:10.1017/cbo9780511662973 · Cited by 760
On the Asymptotic Behavior of Bayes' Estimates in the Discrete Case
Freedman, D. A. (1963) · The Annals of Mathematical Statistics · doi:10.1214/aoms/1177703871 · Cited by 239
Cited by
A practical Bayesian framework for backpropagation networks
MacKay, D. J. C. (1992) · Neural Computation · doi:10.1162/neco.1992.4.3.448 · Cited by 2,917
EFRON, B., & HINKLEY, D. V. (1978) · Biometrika · doi:10.1093/biomet/65.3.457 · Cited by 952
Maximum likelihood estimation in a class of nonregular cases
SMITH, R. L. (1985) · Biometrika · doi:10.1093/biomet/72.1.67 · Cited by 888
A Statistical Model for Positron Emission Tomography
Vardi, Y., Shepp, L. A., & Kaufman, L. (1985) · Journal of the American Statistical Association · doi:10.1080/01621459.1985.10477119 · Cited by 863
Assessing parameter identifiability in phylogenetic models using data cloning
Ponciano, J. M., Burleigh, J. G., Braun, E. L., & Taper, M. L. (2012) · Systematic Biology · doi:10.1093/sysbio/sys055 · Cited by 39
Metadata
- Authors
- Walker, A. M.
- Venue
- Journal of the Royal Statistical Society Series B: Statistical Methodology
- Publisher
- Oxford University Press (OUP)
- Published
- 1969-01-01
- Volume
- 31
- Issue
- 1
- Pages
- 80-88
- ISSN
- 1369-7412 (ISSN-L)
- 1467-9868
- OpenAlex
- W103475893
- Cited by
- 332
- References
- 4
- FWCI
- 2.06
- Type
- journal article
- Language
- en
- Open access
- closed
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- Walker, A. M. (1969). On the Asymptotic Behaviour of Posterior Distributions. Journal of the Royal Statistical Society Series B: Statistical Methodology. https://doi.org/10.1111/j.2517-6161.1969.tb00767.x
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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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