The DOI matches its Crossref record; 13 of the 13 references it cites were found in a registry or an index.
Goodness of prediction fit
Abstract
Fitting a parametric model or estimating a parametric density function plays an important role in a number of statistical applications. Two widely-used methods, one replacing the unknown parameter by an efficient estimate and so termed estimative and the other using a mixture of the possible density functions and commonly termed predictive, are compared. On a general criterion of closeness of fit based on a discriminating information measure the predictive method is shown to be preferable. Explicit measures of the relative closeness of predictive and estimative fits are obtained for gamma and multinomial models.
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“It states that the posterior predictive distribution is the distribution (from the set of all possible distributions Q ) that maximizes the log-likelihood of hypothetical future observations when averaged over the data-generating distribution p ( µ, x 1: t +1 ) = p ( µ ) p ( x 1: t +1 | µ ):”
From Meta-learned models of cognition (2024) · cites this paper as Aitchison (1975)
Citations
Cites
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On Information and Sufficiency
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Madow, W. G., & Anderson, T. W. (1959) · American Mathematical Monthly · doi:10.2307/2308777 · Cited by 3,908
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Dixon, W. J. (1965) · University of California Press eBooks · Cited by 2,673
INADMISSIBILITY OF THE USUAL ESTIMATOR FOR THE MEAN OF A MULTIVARIATE NORMAL DISTRIBUTION
Stein, C. M. (1956) · doi:10.1525/9780520313880-018 · Cited by 1,875
Estimation of Error Rates in Discriminant Analysis
Lachenbruch, P. A., & Mickey, M. R. (1968) · Technometrics · doi:10.1080/00401706.1968.10490530 · Cited by 1,560
Statistical Prediction Analysis
Aitchison, J., & DUNSMORE, I. R. (1975) · Cambridge University Press eBooks · doi:10.1017/cbo9780511569647 · Cited by 839
Self-citationThe Use of the Concept of a Future Observation in Goodness-Of-Fit Problems
Guttman, I. (1967) · Journal of the Royal Statistical Society Series B (Statistical Methodology) · doi:10.1111/j.2517-6161.1967.tb00676.x · Cited by 210
Spline Transformations: Three New Diagnostic Aids for the Statistical Data-Analyst
Boneva, L., Kendall, D. G., & Stefanov, I. (1971) · Journal of the Royal Statistical Society Series B (Statistical Methodology) · doi:10.1111/j.2517-6161.1971.tb00855.x · Cited by 190
Cited by
Sorted by citations
A Predictive Approach to Model Selection
Geisser, S., & Eddy, W. (1979) · Journal of the American Statistical Association · doi:10.1080/01621459.1979.10481632 · Cited by 1,079
39 Dimensionality and sample size considerations in pattern recognition practice
Jain, A. K., & Chandrasekaran, B. (1982) · Handbook of statistics · doi:10.1016/s0169-7161(82)02042-2 · Cited by 560
Information-theoretic asymptotics of Bayes methods
Clarke, B. S., & Barron, A. R. (1990) · IEEE Transactions on Information Theory · doi:10.1109/18.54897 · Cited by 429
Akaike, H. (1985) · Springer eBooks · doi:10.1007/978-1-4613-8560-8_1 · Cited by 373
Laud, P. W., & Ibrahim, J. G. (1995) · Journal of the Royal Statistical Society Series B (Statistical Methodology) · doi:10.1111/j.2517-6161.1995.tb02028.x · Cited by 351
Metadata
- Authors
- AITCHISON, J.
- Affiliations
- University of Glasgow (GB)
- Corresponding author
- AITCHISON, J.
- Venue
- Biometrika
- Publisher
- Oxford University Press (OUP)
- Published
- 1975
- Volume
- 62
- Issue
- 3
- Pages
- 547-554
- ISSN
- 0006-3444 (ISSN-L)
- 1464-3510
- OpenAlex
- W2034517627
- Cited by
- 256
- References
- 13
- Citations by year
- 2026: 2 · 2025: 8 · 2024: 5 · 2023: 6 · 2022: 2 · 2021: 11 · 2020: 12 · 2019: 10 · 2018: 5 · 2017: 8 · 2016: 3 · 2015: 5 · 2014: 9 · 2013: 9 · 2012: 8
- FWCI
- 8.61
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Biometrika (publishedVersion)
- Topics
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Distribution Estimation and Applications
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Bayesian Inference
- Physical Sciences › Computer Science › Artificial Intelligence › Bayesian Methods and Mixture Models
- Keywords
- goodness of fit, parametric density estimation, predictive density, discriminant information, gamma distribution, multinomial distribution, model fitting
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