Predictive Likelihood
Open accessAbstract
The likelihood function is the common basis of all parametric inference. However, with the exception of an ad hoc definition by Fisher, there has been no such unifying basis for prediction of future events, given past observations. This article proposes a definition of predictive likelihood which can help to remove some nonuniqueness problems in sampling-theory predictive inference, and which can produce a simple prediction analog of the Bayesian parametric result, posterior $\propto$ prior $\times$ likelihood, in many situations.
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
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.
Claims other papers make about this one
Each is checked against this paper’s own text: does it say what the citing paper says it does?
For models with tens to hundreds of parameters, dense sampling of the parameter space is numerically demanding or infeasible because high-dimensional spaces cannot be sampled densely.
“For models with tens to hundreds of parameters this is numerically demanding or even infeasible because high dimensional spaces cannot be sampled densely.”
From Likelihood based observability analysis and confidence intervals for predictions of dynamic models (2012) · cites this paper as [10]
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
The self-check needs the paper’s full text.
Cited by
Sorted by citations
Profile likelihood in systems biology
Kreutz, C., Raue, A., Kaschek, D., & Timmer, J. (2013) · FEBS Journal · doi:10.1111/febs.12276 · Cited by 179 · 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
Standard Errors of Prediction in Generalized Linear Mixed Models
Booth, J. G., & Hobert, J. P. (1998) · Journal of the American Statistical Association · doi:10.1080/01621459.1998.10474107 · Cited by 133 · see citing works
Likelihood based observability analysis and confidence intervals for predictions of dynamic models
Kreutz, C., Raue, A., & Timmer, J. (2012) · BMC Systems Biology · doi:10.1186/1752-0509-6-120 · Cited by 134 · see citing works
Schneider, N., Wieland, F.-G., Kong, D., Fischer, A., Hörner, M., Timmer, J., Ye, H., & Weber, W. (2021) · Science Advances · doi:10.1126/sciadv.abd3568 · Cited by 123 · see citing works
Predictive Likelihood Inference with Applications
Butler, R. W. (1986) · Journal of the Royal Statistical Society Series B (Statistical Methodology) · doi:10.1111/j.2517-6161.1986.tb01386.x · Cited by 103 · see citing works
Kaminsky, K. S., & Rhodin, L. S. (1985) · Annals of the Institute of Statistical Mathematics · doi:10.1007/bf02481119 · Cited by 101 · see citing works
On the Generalization of the Likelihood Function and the Likelihood Principle
Bjørnstad, J. F. (1996) · Journal of the American Statistical Association · doi:10.1080/01621459.1996.10476947 · Cited by 85 · see citing works
A Simple Predictive Density Function
Lejeune, M., & Faulkenberry, G. D. (1982) · Journal of the American Statistical Association · doi:10.1080/01621459.1982.10477866 · Cited by 85 · see citing works
Data‐based comparison of frequency analysis methods: A general framework
Renard, B., Kochanek, K., Lang, M., Garavaglia, F., Paquet, E., Neppel, L., Najib, K., Carreau, J., Arnaud, P., Aubert, Y., et al. (2013) · Water Resources Research · doi:10.1002/wrcr.20087 · Cited by 74 · see citing works
What is the Likelihood Function?
Bayarri, M. J., DeGroot, M. H., & Kadane, J. B. (1988) · Springer eBooks · doi:10.1007/978-1-4613-8768-8_1 · Cited by 55 · see citing works
Simpson, M. J., & Maclaren, O. J. (2023) · PLoS Computational Biology · doi:10.1371/journal.pcbi.1011515 · Cited by 49 · 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 Techniques for Box-Cox Regression Models
Collins, S. (1991) · Journal of Business and Economic Statistics · doi:10.1080/07350015.1991.10509852 · Cited by 36 · see citing works
Methods to Compute Prediction Intervals: A Review and New Results
Tian, Q., Nordman, D. J., & Meeker, W. Q. (2022) · Statistical Science · doi:10.1214/21-sts842 · Cited by 26 · see citing works
Information criteria for the predictive evaluation of bayesian models
Kitagawa, G. (1997) · Communication in Statistics- Theory and Methods · doi:10.1080/03610929708832043 · Cited by 23 · see citing works
Conformal prediction for uncertainty quantification in dynamic biological systems
Portela, A., Banga, J., & Matabuena, M. (2025) · PLoS Comput. Biol. · doi:10.1371/journal.pcbi.1013098 · Cited by 22 · see citing works
Fast integration-based prediction bands for ordinary differential equation models
Hass, H., Kreutz, C., Timmer, J., & Kaschek, D. (2015) · Bioinformatics · doi:10.1093/bioinformatics/btv743 · 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
Biometrika Centenary: Theory and general methodology
Davison, A. C. (2001) · Biometrika · doi:10.1093/biomet/88.1.13 · Cited by 17 · see citing works
Biometrical Models for Predicting Future Performance in Plant Breeding.
Balzarini, M. (2000) · doi:10.31390/gradschool_disstheses.7178 · Cited by 15 · see citing works
H‐likelihood Predictive Intervals for Unobservables
Lee, Y., & Kim, G. (2015) · International Statistical Review · doi:10.1111/insr.12115 · 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
Introduction to Birnbaum (1962) On the Foundations of Statistical Inference
Bjørnstad, J. F. (1992) · Springer series in statistics · doi:10.1007/978-1-4612-0919-5_31 · Cited by 9 · see citing works
A Note on Priors for the Multinomial Model
Tuyl, F. (2016) · The American Statistician · doi:10.1080/00031305.2016.1222309 · Cited by 9 · see citing works
Discussion of Professor Dawid's Paper
(1979) · Journal of the Royal Statistical Society Series B (Statistical Methodology) · doi:10.1111/j.2517-6161.1979.tb01053.x · Cited by 8 · see citing works
A multivariate frequency-severity framework for healthcare data breaches
Sun, H., Xu, M., & Zhao, P. (2023) · The Annals of Applied Statistics · doi:10.1214/22-aoas1625 · Cited by 8 · see citing works
A family of the adjusted estimators maximizing the asymptotic predictive expected log-likelihood
Ogasawara, H. (2016) · Behaviormetrika · doi:10.1007/s41237-016-0004-6 · Cited by 7 · see citing works
Difficulties and ambiguities in the definition of a likelihood function
Bayarri, M. J., & DeGroot, M. H. (1992) · Statistical Methods & Applications · doi:10.1007/bf02589046 · Cited by 7 · see citing works
Testing for Differences in Path Forecast Accuracy: Forecast-Error Dynamics Matter
Martinez, A. B. (2017) · Working paper · doi:10.2139/ssrn.3064863 · Cited by 7 · see citing works
Likelihood and other approaches to prediction in dynamic models
Cooley, T. F., & Parke, W. R. (1987) · Journal of Econometrics · doi:10.1016/0304-4076(87)90084-4 · Cited by 6 · see citing works
Forecasting dynamic market share relationships
Terui, N. (2000) · Marketing Intelligence & Planning · doi:10.1108/02634500010318610 · Cited by 6 · see citing works
Predictive likelihood for coherent forecasting of count time series
Mukhopadhyay, S., & Sathish, V. (2018) · Journal of Forecasting · doi:10.1002/for.2566 · Cited by 5 · see citing works
Inferential distributions for non-Bayesian predictive fit
Kuboki, H. (1993) · Annals of the Institute of Statistical Mathematics · doi:10.1007/bf00773356 · Cited by 5 · see citing works
Basin-scale relations via conditioning
Troutman, B. M., Karlinger, M. R., & Guertin, D. P. (1989) · Stochastic Environmental Research and Risk Assessment · doi:10.1007/bf01544076 · Cited by 4 · see citing works
Predictive efficiency for simple non-linear models
Cooley, T. F., Parke, W. R., & Chib, S. (1989) · Journal of Econometrics · doi:10.1016/0304-4076(89)90028-6 · Cited by 3 · see citing works
Butler, R. W. (1988) · Springer eBooks · doi:10.1007/978-1-4613-8768-8_3 · Cited by 3 · see citing works
Non-Bayesian predictive approaches
Geisser, S. (1993) · Springer eBooks · doi:10.1007/978-1-4899-4467-2_2 · Cited by 2 · see citing works
A note on the consistency of the modified fisher prediction function
Levy, M. S., & Perng, S. K. (1986) · Journal of Statistical Planning and Inference · doi:10.1016/0378-3758(86)90138-2 · Cited by 2 · see citing works
Measuring delayed and long‐term effects of pricing decisions on market share
Terui, N. (2004) · Marketing Intelligence & Planning · doi:10.1108/02634500410536867 · Cited by 1 · see citing works
Predictive densities and prediction limits based on predictive likelihoods
Vidoni, P. (2010) · Contributions to statistics · doi:10.1007/978-88-470-1386-5_10
Special Problems of Algebraic Regression and Stochastic Estimation
Grafarend, E. W., & Awange, J. L. (2011) · Springer eBooks · doi:10.1007/978-3-642-22241-2_14
On calibration of kullback-leibler divergence via prediction
Keyes, T. K., & Levy, M. S. (1999) · Communication in Statistics- Theory and Methods · doi:10.1080/03610929908832283
Likelihood Prediction for Generalized Linear Mixed Models under Covariate Uncertainty
Alam, M. (2013) · Communication in Statistics- Theory and Methods · doi:10.1080/03610926.2012.657330
A new definition of the predictive likelihood
Chib, S., Jammalamadaka, S. R., & Tiwari, R. C. (1987) · Statistics & Probability Letters · doi:10.1016/0167-7152(87)90065-4
Densidades preditivas no modelo de regressão linear
Rojas, M. D. I. (2000) · doi:10.11606/d.45.2000.tde-20210729-115136
Bjørnstad, J. F. (2005) · Encyclopedia of Statistical Sciences · doi:10.1002/0471667196.ess0707.pub2
Butler, R. W. (2005) · Encyclopedia of Statistical Sciences · doi:10.1002/0471667196.ess3083.pub2
Butler, R. W. (2004) · Encyclopedia of Statistical Sciences · doi:10.1002/0471667196.ess3083
Some Remarks on Generalizations of the Likelihood Function and the Likelihood Principle
Nayak, T. K., & Kundu, S. (2003) · CRC Press eBooks · doi:10.1201/9780203493205.ch14
Bjørnstad, J. F. (2014) · Wiley StatsRef: Statistics Reference Online · doi:10.1002/9781118445112.stat01515
(1994) · Wiley series in probability and statistics · doi:10.1002/9780470316870.refs
Bjørnstad, J. F. (2004) · Encyclopedia of Statistical Sciences · doi:10.1002/0471667196.ess0707
Análise do ajuste do modelo de regressão L1
Rodrigues, K. A. S. (2024) · doi:10.11606/t.45.2024.tde-10042024-202803
Maximum Likelihood Prediction in Software Reliability Assessment
Fujimura, D., Dohi, T., & Okamura, H. (2024) · IEEE Intl Conf on Dependable, Autonomic and Secure Computing, Intl Conf on Pervasive Intelligence and Computing, Intl Conf on Cloud and Big Data Computing, Intl Conf on Cyber Science and Technology Congress (DASC/PiCom/CBDCom/CyberSciTech) · doi:10.1109/dasc64200.2024.00007
- Authors
- Hinkley, D.
- Corresponding author
- Hinkley, David
- Venue
- The Annals of Statistics
- Publisher
- Institute of Mathematical Statistics
- Published
- 1979-07-01
- Volume
- 7
- Issue
- 4
- Pages
- 718-728
- ISSN
- 0090-5364 (ISSN-L)
- 2168-8966
- OpenAlex
- W4236549809
- Cited by
- 56
- References
- 0
- Citations by year
- 2025: 1 · 2024: 2 · 2023: 2 · 2022: 1 · 2021: 1 · 2020: 1 · 2018: 1 · 2017: 1 · 2016: 2 · 2015: 2 · 2014: 1 · 2013: 3 · 2012: 1
- FWCI
- 1.24
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Locations
- The Annals of Statistics (publishedVersion)
- Project Euclid (Cornell University) (submittedVersion)
- University of Minnesota Digital Conservancy (University of Minnesota) (submittedVersion)
- Topics
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Bayesian Inference
- Physical Sciences › Mathematics › Statistics and Probability › Probability and Statistical Research
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Inference
- Keywords
- predictive likelihood, prediction, likelihood function, parametric inference, posterior distribution, Bayesian inference, non-uniqueness
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
