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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The posterior predictive distribution maximizes the expected log-likelihood of hypothetical future observations when averaged over the data-generating distribution.
“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)
Cites
Handbook of Mathematical Functions
McQuarrie, D. A. (1966) · American Journal of Physics · doi:10.1119/1.1972842 · Cited by 40,433 · see citing works
On Information and Sufficiency
Kullback, S., & Leibler, R. A. (1951) · The Annals of Mathematical Statistics · doi:10.1214/aoms/1177729694 · Cited by 20,193 · see citing works
An Introduction to Multivariate Statistical Analysis
Muirhead, R. J., & Anderson, T. W. (1986) · Journal of Business and Economic Statistics · doi:10.2307/1391399 · Cited by 9,209 · see citing works
Introduction to Multivariate Statistical Analysis.
Madow, W. G., & Anderson, T. W. (1959) · American Mathematical Monthly · doi:10.2307/2308777 · Cited by 3,914 · see citing works
BMD : biomedical computer programs
Dixon, W. J. (1965) · University of California Press eBooks · Cited by 2,670 · see citing works
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 · see citing works
Estimation of Error Rates in Discriminant Analysis
Lachenbruch, P. A., & Mickey, M. R. (1968) · Technometrics · doi:10.1080/00401706.1968.10490530 · Cited by 1,508 · see citing works
Statistical Prediction Analysis
Aitchison, J., & DUNSMORE, I. R. (1975) · Cambridge University Press eBooks · doi:10.1017/cbo9780511569647 · Cited by 839 · see citing works
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 · see citing works
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 · see citing works
Posterior Odds for Multivariate Normal Classifications
Geisser, S. (1964) · Journal of the Royal Statistical Society Series B (Statistical Methodology) · doi:10.1111/j.2517-6161.1964.tb00540.x · Cited by 168 · see citing works
Principles, practice and performance in decision-making in clinical medicine
Aitchison, J., & Kay, J. (1975) · ENLIGHTEN (Jurnal Bimbingan dan Konseling Islam) · Cited by 29 · see citing works
Self-citationThe Choice of the Degree of a Polynomial Model
Hager, H. W., & Antle, C. E. (1968) · Journal of the Royal Statistical Society Series B (Statistical Methodology) · doi:10.1111/j.2517-6161.1968.tb00745.x · Cited by 17 · see citing works
Flagged first, then by citations
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 · see citing works
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 · see citing works
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 · see citing works
Akaike, H. (1985) · Springer eBooks · doi:10.1007/978-1-4613-8560-8_1 · Cited by 373 · see citing works
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 · see citing works
Rissanen, J. (1987) · Journal of the Royal Statistical Society Series B (Statistical Methodology) · doi:10.1111/j.2517-6161.1987.tb01694.x · Cited by 342 · see citing works
Jeffreys' prior is asymptotically least favorable under entropy risk
Clarke, B. S., & Barron, A. R. (1994) · Journal of Statistical Planning and Inference · doi:10.1016/0378-3758(94)90153-8 · Cited by 291 · see citing works
Bayesian stochastic search for VAR model restrictions
George, E. I., Sun, D., & Ni, S. X. (2007) · Journal of Econometrics · doi:10.1016/j.jeconom.2007.08.017 · Cited by 261 · see citing works
Logistic-normal distributions:Some properties and uses
ATCHISON, J., & SHEN, S. M. (1980) · Biometrika · doi:10.1093/biomet/67.2.261 · Cited by 197 · see citing works
Frequentist prediction intervals and predictive distributions
Lawless, J. F., & Frédette, M. (2005) · Biometrika · doi:10.1093/biomet/92.3.529 · Cited by 187 · see citing works
Analysis of Variance, Design, and Regression: Applied Statistical Methods
Christensen, R. (1996) · Cited by 179 · see citing works
A significance test for cyclic trends in incidence data
Roger, J. (1977) · Biometrika · doi:10.1093/biomet/64.1.152 · Cited by 155 · see citing works
Generalizing the derivation of the schwarz information criterion
Cavanaugh, J. E., & Neath, A. A. (1999) · Communication in Statistics- Theory and Methods · doi:10.1080/03610929908832282 · Cited by 138 · see citing works
On asymptotic properties of predictive distributions
Komaki, F. (1996) · Biometrika · doi:10.1093/biomet/83.2.299 · Cited by 129 · see citing works
Chatterjee, S., Lahiri, P., & Li, H. (2008) · The Annals of Statistics · doi:10.1214/07-aos512 · Cited by 118 · see citing works
A new look at the Bayes procedure
Akaike, H. (1998) · Springer series in statistics · doi:10.1007/978-1-4612-1694-0_22 · Cited by 114 · see citing works
Information Measures in Perspective
Ebrahimi, N. B., Soofi, E. S., & Soyer, R. (2010) · International Statistical Review · doi:10.1111/j.1751-5823.2010.00105.x · Cited by 109 · see citing works
Predictive Fit for Natural Exponential Families
Harris, I. R. (1989) · Biometrika · doi:10.1093/biomet/76.4.675 · Cited by 109 · see citing works
A Critical Comparison of Two Methods of Statistical Discrimination
Aitchison, J., Habbema, J. D. F., & Kay, J. (1977) · Journal of the Royal Statistical Society Series C (Applied Statistics) · doi:10.2307/2346863 · Cited by 102 · see citing works
Self-citationOn Resolving the Controversy in Statistical Inference
Wilkinson, G. N. (1977) · Journal of the Royal Statistical Society Series B (Statistical Methodology) · doi:10.1111/j.2517-6161.1977.tb01613.x · Cited by 100 · see citing works
Hartigan, J. A. (1998) · The Annals of Statistics · doi:10.1214/aos/1024691462 · Cited by 94 · see citing works
Improved minimax predictive densities under Kullback–Leibler loss
George, E. I., Liang, F., & Xu, X. (2006) · The Annals of Statistics · doi:10.1214/009053606000000155 · Cited by 93 · see citing works
Stochastic complexity and the mdl principle
Rissanen, J. (1987) · Econometric Reviews · doi:10.1080/07474938708800126 · Cited by 92 · see citing works
The Mahalanobis Distance and Elliptic Distributions
Mitchell, A. F. S., & Krzanowski, W. J. (1985) · Biometrika · doi:10.1093/biomet/72.2.464 · Cited by 86 · see citing works
A shrinkage predictive distribution for multivariate Normal observables
Komaki, F. (2001) · Biometrika · doi:10.1093/biomet/88.3.859 · Cited by 78 · see citing works
Exact Minimax Strategies for Predictive Density Estimation, Data Compression, and Model Selection
Liang, F., & Barron, A. R. (2004) · IEEE Transactions on Information Theory · doi:10.1109/tit.2004.836922 · Cited by 75 · see citing works
A Note on the Estimation of Probability Density Functions
Murray, G. D. (1977) · Biometrika · doi:10.2307/2335788 · Cited by 74 · see citing works
Statistical modeling methods: challenges and strategies
Henley, S. S., Golden, R. M., & Kashner, T. M. (2019) · Biostatistics & Epidemiology · doi:10.1080/24709360.2019.1618653 · Cited by 70 · see citing works
Application of Nonlinear Models with Random Coefficients to Growth Data
Palmer, M. J., Phillips, B. F., & Smith, G. T. (1991) · Biometrics · doi:10.2307/2532151 · Cited by 65 · see citing works
Predictive Inference, Sufficiency, Entropy and an Asymptotic Likelihood Principle
Larimore, W. E. (1983) · Biometrika · doi:10.1093/biomet/70.1.175 · Cited by 64 · see citing works
Bayesian MIDAS penalized regressions: Estimation, selection, and prediction
Mogliani, M., & Simoni, A. (2020) · Journal of Econometrics · doi:10.1016/j.jeconom.2020.07.022 · Cited by 64 · see citing works
A Generalized Bayes Rule for Prediction
Corcuera, J. M., & Giummolè, F. (1999) · Scandinavian Journal of Statistics · doi:10.1111/1467-9469.00149 · Cited by 61 · see citing works
Akaike, H. (1985) · Springer series in statistics · doi:10.1007/978-1-4612-1694-0_30 · Cited by 60 · see citing works
Order selection of autoregressive models
Djurić, P. M., & Kay, S. (1992) · IEEE Transactions on Signal Processing · doi:10.1109/78.165674 · Cited by 49 · see citing works
Admissible predictive density estimation
Brown, L. D., George, E. I., & Xu, X. (2008) · The Annals of Statistics · doi:10.1214/07-aos506 · Cited by 48 · see citing works
Prediction with confidence—A general framework for predictive inference
Shen, J., Liu, R. Y., & Xie, M. (2017) · Journal of Statistical Planning and Inference · doi:10.1016/j.jspi.2017.09.012 · Cited by 47 · see citing works
Bayesian forecasting of recurrent earthquakes and predictive performance for a small sample size
Nomura, S., Ogata, Y., Komaki, F., & Toda, S. (2011) · Journal of Geophysical Research Atmospheres · doi:10.1029/2010jb007917 · Cited by 46 · see citing works
Statistical Diagnosis When Basic Cases are Not Classified with Certainty
Aitchison, J., & Begg, C. B. (1976) · Biometrika · doi:10.1093/biomet/63.1.1 · Cited by 42 · see citing works
Self-citationBayesian nonparametric model selection and model testing
Karabatsos, G. (2005) · Journal of Mathematical Psychology · doi:10.1016/j.jmp.2005.07.003 · Cited by 41 · see citing works
On the Estimation of Parametric Density Functions
Ng, V. M. (1980) · Biometrika · doi:10.1093/biomet/67.2.505 · Cited by 41 · see citing works
Meta-learned models of cognition
Binz, M., Dasgupta, I., Jagadish, A. K., Botvinick, M., Wang, J. X., & Schulz, E. (2024) · Behavioral and Brain Sciences · doi:10.1017/s0140525x23003266 · Cited by 38 · see citing works
Discrimination, Allocatory and Separatory, Linear Aspects
Geisser, S. (1977) · Elsevier eBooks · doi:10.1016/b978-0-12-714250-0.50015-2 · Cited by 39 · see citing works
An Optimal Prediction Function for the Normal Linear Model
Levy, M. S., & Perng, S. K. (1986) · Journal of the American Statistical Association · doi:10.2307/2287989 · Cited by 39 · see citing works
Prediction Limits for the Inverse Gaussian Distribution
Chhikara, R. S., & Guttman, I. (1982) · Technometrics · doi:10.1080/00401706.1982.10487794 · Cited by 37 · see citing works
Lane, D. A., & Sudderth, W. D. (1982) · University of Minnesota Digital Conservancy (University of Minnesota) · Cited by 37 · see citing works
Simultaneous prediction of independent Poisson observables
Komaki, F. (2004) · The Annals of Statistics · doi:10.1214/009053604000000445 · Cited by 36 · see citing works
Asymptotic Prediction Analysis
DUNSMORE, I. R. (1976) · Biometrika · doi:10.1093/biomet/63.3.627 · Cited by 36 · see citing works
The Curve Fitting Problem: A Bayesian Rejoinder
Bandyopadhyay, P. S., & Boik, R. J. (1999) · Philosophy of Science · doi:10.1086/392740 · Cited by 34 · see citing works
On Parametric Density Estimation
El-Sayyad, G. M., SAMUDDIN, M., & Al-Harbey, A. A. (1989) · Biometrika · doi:10.1093/biomet/76.2.343 · Cited by 34 · see citing works
Approximate Tolerance Intervals, Based on Maximum Likelihood Estimates
Atwood, C. L. (1984) · Journal of the American Statistical Association · doi:10.1080/01621459.1984.10478072 · Cited by 33 · see citing works
Reference priors in multiparameter nonregular cases
Subhashis Ghosal, B. (1997) · Test · doi:10.1007/bf02564432 · Cited by 33 · see citing works
How Should We Quantify Uncertainty in Statistical Inference?
Lele, S. R. (2020) · Frontiers in Ecology and Evolution · doi:10.3389/fevo.2020.00035 · Cited by 31 · see citing works
Estimation, prediction and the Stein phenomenon under divergence loss
Ghosh, M., Mergel, V., & Datta, G. S. (2008) · Journal of Multivariate Analysis · doi:10.1016/j.jmva.2008.02.002 · Cited by 30 · see citing works
An objective use of Bayesian models
Akaike, H. (1977) · Annals of the Institute of Statistical Mathematics · doi:10.1007/bf02532770 · Cited by 30 · see citing works
Bootstrap prediction and Bayesian prediction under misspecified models
Fushiki, T. (2005) · Bernoulli · doi:10.3150/bj/1126126768 · Cited by 29 · see citing works
Decisionmetrics: A decision-based approach to econometric modelling
Skouras, S. (2006) · Journal of Econometrics · doi:10.1016/j.jeconom.2006.03.012 · Cited by 39 · see citing works
On improved predictive density estimation with parametric constraints
Fourdrinier, D., Marchand, É., Righi, A., & Strawderman, W. E. (2011) · Electronic Journal of Statistics · doi:10.1214/11-ejs603 · Cited by 28 · see citing works
Simultaneous prediction of independent Poisson observablesPreprint
Komaki, F. (2004) · Cited by 28 · see citing works
Bayesian predictive density operators for exchangeable quantum-statistical models
Tanaka, F., & Komaki, F. (2005) · Physical Review A · doi:10.1103/physreva.71.052323 · Cited by 25 · see citing works
Nonparametric bootstrap prediction
Fushiki, T., Komaki, F., & Aihara, K. (2005) · Bernoulli · doi:10.3150/bj/1116340296 · Cited by 25 · see citing works
A Bayesian nonparametric meta‐analysis model
Karabatsos, G., Talbott, E., & Walker, S. G. (2014) · Research Synthesis Methods · doi:10.1002/jrsm.1117 · Cited by 24 · see citing works
Decisions with Estimation Uncertainty
Klein, R. W., Rafsky, L. C., Sibley, D. S., & Willig, R. D. (1978) · Econometrica · doi:10.2307/1913834 · Cited by 24 · see citing works
Universality of Bayesian Predictions
Sancetta, A. (2012) · Bayesian Analysis · doi:10.1214/12-ba701 · Cited by 23 · see citing works
A derivation of the information criteria for selecting autoregressive models
Bhansali, R. J. (1986) · Advances in Applied Probability · doi:10.1017/s0001867800015809 · Cited by 23 · see citing works
Improved prediction for a multivariate normal distribution with unknown mean and variance
Kato, K. (2008) · Annals of the Institute of Statistical Mathematics · doi:10.1007/s10463-007-0163-z · Cited by 22 · see citing works
Model selection based on Bayesian predictive densities and multiple data records
Djurić, P. M., & Kay, S. (1994) · IEEE Transactions on Signal Processing · doi:10.1109/78.298276 · Cited by 22 · see citing works
Goodness of Prediction Fit for Multivariate Linear Models
Keyes, T. K., & Levy, M. S. (1996) · Journal of the American Statistical Association · doi:10.1080/01621459.1996.10476676 · Cited by 22 · see citing works
Asymptotic redundancies for universal quantum coding
Krattenthaler, C., & Slater, P. B. (2000) · IEEE Transactions on Information Theory · doi:10.1109/18.841164 · Cited by 23 · see citing works
On the Sample Information About Parameter and Prediction
Ebrahimi, N. B., Soofi, E. S., & Soyer, R. (2010) · Statistical Science · doi:10.1214/10-sts329 · Cited by 21 · see citing works
Fushiki, T. (2009) · Journal of Statistical Planning and Inference · doi:10.1016/j.jspi.2009.06.007 · Cited by 21 · see citing works
On efficient probability forecasting systems
Skouras, K. (1999) · Biometrika · doi:10.1093/biomet/86.4.765 · Cited by 21 · see citing works
Induction and polynomial networks
Elder, J. F., & Brown, D. E. (2002) · Conference proceedings/Conference proceedings - IEEE International Conference on Systems, Man, and Cybernetics · doi:10.1109/icsmc.1995.537877 · Cited by 20 · see citing works
Decisionmetrics: A Decision-Based Approach to Econometric ModellingPreprint
Skouras, S. (2001) · SSRN Electronic Journal · doi:10.2139/ssrn.291921 · Cited by 19 · see citing works
Closed Form Prediction Intervals Applied for Disease Counts
Wang, H. (2010) · The American Statistician · doi:10.1198/tast.2010.09125 · Cited by 19 · see citing works
Nonsubjective priors via predictive relative entropy regret
Sweeting, T. J., Datta, G. S., & Ghosh, M. (2006) · The Annals of Statistics · doi:10.1214/009053605000000804 · Cited by 18 · see citing works
Bayesian prediction of a density function in terms of -mixture
Yanagimoto, T., & Ohnishi, T. (2009) · Journal of Statistical Planning and Inference · doi:10.1016/j.jspi.2009.02.005 · Cited by 19 · see citing works
From Minimax Shrinkage Estimation to Minimax Shrinkage Prediction
George, E. I., Liang, F., & Xu, X. (2012) · Statistical Science · doi:10.1214/11-sts383 · Cited by 19 · see citing works
On Efficient Point Prediction Systems
Skouras, K., & Dawid, A. P. (1998) · Journal of the Royal Statistical Society Series B (Statistical Methodology) · doi:10.1111/1467-9868.00153 · Cited by 19 · see citing works
Bhandari, S. K., Basu, A., & Sarkar, S. (2006) · Australian & New Zealand Journal of Statistics · doi:10.1111/j.1467-842x.2006.00428.x · Cited by 18 · see citing works
Exact minimax estimation of the predictive density in sparse Gaussian models
Mukherjee, G., & Johnstone, I. M. (2015) · The Annals of Statistics · doi:10.1214/14-aos1251 · Cited by 17 · see citing works
Biometrika Centenary: Theory and general methodology
Davison, A. C. (2001) · Biometrika · doi:10.1093/biomet/88.1.13 · Cited by 17 · see citing works
Maruyama, Y., & Strawderman, W. E. (2012) · Institute of Mathematical Statistics collections · doi:10.1214/11-imscoll803 · Cited by 17 · see citing works
Taper, M. L., Lele, S. R., Ponciano, J. M., Dennis, B., & Jerde, C. L. (2021) · Frontiers in Ecology and Evolution · doi:10.3389/fevo.2021.679155 · Cited by 16 · see citing works
The Estimation of Multivariate Normal Density Functions Using Incomplete Data
Murray, G. D. (1979) · Biometrika · doi:10.1093/biomet/66.2.375 · Cited by 16 · see citing works
On predictive density estimation for location families under integrated squared error loss
Kubokawa, T., Marchand, É., & Strawderman, W. E. (2015) · Journal of Multivariate Analysis · doi:10.1016/j.jmva.2015.07.013 · Cited by 15 · see citing works
Tran, M., Nott, D. J., & Leng, C. (2011) · Statistics and Computing · doi:10.1007/s11222-011-9279-3 · Cited by 15 · see citing works
Bayesian prediction based on a class of shrinkage priors for location-scale models
Komaki, F. (2007) · Annals of the Institute of Statistical Mathematics · doi:10.1007/s10463-006-0102-4 · Cited by 15 · see citing works
Robust Predictive Distributions for Exponential Families
Basu, A., & Harris, I. R. (1994) · Biometrika · doi:10.1093/biomet/81.4.790 · Cited by 15 · see citing works
Minimaxity in predictive density estimation with parametric constraints
Kubokawa, T., Marchand, É., Strawderman, W. E., & Turcotte, J. (2013) · Journal of Multivariate Analysis · doi:10.1016/j.jmva.2013.01.001 · Cited by 14 · see citing works
Bayesian predictive densities based on latent information priors
Komaki, F. (2011) · Journal of Statistical Planning and Inference · doi:10.1016/j.jspi.2011.06.009 · Cited by 14 · see citing works
Parametric boostrap and objective Bayesian testing for heteroscedastic one-way ANOVA
Zhang, G., Christensen, R., & Pesko, J. C. (2021) · Statistics & Probability Letters · doi:10.1016/j.spl.2021.109095 · Cited by 14 · see citing works
On Parametric Bootstrapping and Bayesian Prediction
Fushiki, T., Komaki, F., & Aihara, K. (2004) · Scandinavian Journal of Statistics · doi:10.1111/j.1467-9469.2004.02_127.x · Cited by 14 · see citing works
An information criterion for likelihood selection
Yuan, A., & Clarke, B. S. (1999) · IEEE Transactions on Information Theory · doi:10.1109/18.749003 · Cited by 14 · see citing works
A maximum likelihood prediction function for the linear model with consistency results
Levy, M. S., & Perng, S. K. (1984) · Communication in Statistics- Theory and Methods · doi:10.1080/03610928408828753 · Cited by 14 · see citing works
On predictive density estimation for location families under integrated absolute error loss
Kubokawa, T., Marchand, É., & Strawderman, W. E. (2017) · Bernoulli · doi:10.3150/16-bej842 · Cited by 13 · see citing works
Statistical Pattern Recognition
Golden, R. M. (2015) · Elsevier eBooks · doi:10.1016/b978-0-08-097086-8.43093-x · Cited by 13 · see citing works
A General Framework for Distributed Inference With Uncertain Models
Hare, J. Z., Uribe, C. A., Kaplan, L., & Jadbabaie, A. (2021) · IEEE Transactions on Signal and Information Processing over Networks · doi:10.1109/tsipn.2021.3085127 · Cited by 12 · see citing works
Empirical Bayes predictive densities for high-dimensional normal models
Xu, X., & Zhou, D. (2011) · Journal of Multivariate Analysis · doi:10.1016/j.jmva.2011.05.008 · Cited by 12 · see citing works
On predictive density estimation with additional information
Marchand, É., & Sadeghkhani, A. (2018) · Electronic Journal of Statistics · doi:10.1214/18-ejs1493 · Cited by 12 · see citing works
Mourtada, J., & Gaïffas, S. (2019) · arXiv (Cornell University) · doi:10.48550/arxiv.1912.10784 · Cited by 12 · see citing works
- 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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