The DOI matches its Crossref record; 36 of the 36 references it cites were found in a registry or an index.
A General Framework for Updating Belief Distributions
Open accessAbstract
Summary: We propose a framework for general Bayesian inference. We argue that a valid update of a prior belief distribution to a posterior can be made for parameters which are connected to observations through a loss function rather than the traditional likelihood function, which is recovered as a special case. Modern application areas make it increasingly challenging for Bayesians to attempt to model the true data-generating mechanism. For instance, when the object of interest is low dimensional, such as a mean or median, it is cumbersome to have to achieve this via a complete model for the whole data distribution. More importantly, there are settings where the parameter of interest does not directly index a family of density functions and thus the Bayesian approach to learning about such parameters is currently regarded as problematic. Our framework uses loss functions to connect information in the data to functionals of interest. The updating of beliefs then follows from a decision theoretic approach involving cumulative loss functions. Importantly, the procedure coincides with Bayesian updating when a true likelihood is known yet provides coherent subjective inference in much more general settings. Connections to other inference frameworks are highlighted.
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Cites
Regression Models and Life-Tables
Cox, D. R. (1972) · Journal of the Royal Statistical Society Series B: Statistical Methodology · doi:10.1111/j.2517-6161.1972.tb00899.x · Cited by 39,793
The Elements of Statistical Learning
Hastie, T., Tibshirani, R., & Friedman, J. (2009) · Springer Series in Statistics · doi:10.1007/978-0-387-84858-7 · Cited by 25,970
On Information and Sufficiency
Kullback, S., & Leibler, R. A. (1951) · The Annals of Mathematical Statistics · doi:10.1214/aoms/1177729694 · Cited by 20,193
Robust estimation of a location parameter
Huber, P. J. (1964) · The Annals of Mathematical Statistics · doi:10.1214/aoms/1177703732 · Cited by 7,228
Prediction, Learning, and Games
Cesa-Bianchi, N., & Lugosi, G. (2006) · Cambridge University Press eBooks · doi:10.1017/cbo9780511546921 · Cited by 3,162
Bernardo, J. M., & Smith, A. F. M. (1994) · Wiley Series in Probability and Statistics · doi:10.1002/9780470316870 · Cited by 2,178
Biclustering of expression data.
Cheng, Y., & Church, G. M. (2000) · PubMed · Cited by 2,098
Huber, P. J., & Ronchetti, E. M. (2009) · Wiley Series in Probability and Statistics · doi:10.1002/9780470434697 · Cited by 1,718
La prévision : ses lois logiques, ses sources subjectives
de Finetti, B. (1937) · French digital mathematics library (Numdam) · Cited by 1,642
The Selection of Prior Distributions by Formal Rules
Kass, R. E., & Wasserman, L. (1996) · Journal of the American Statistical Association · doi:10.1080/01621459.1996.10477003 · Cited by 1,308
A General Class of Coefficients of Divergence of One Distribution from Another
Ali, S. M., & Silvey, S. D. (1966) · Journal of the Royal Statistical Society Series B: Statistical Methodology · doi:10.1111/j.2517-6161.1966.tb00626.x · Cited by 1,205
Direct Clustering of a Data Matrix
Hartigan, J. A. (1972) · Journal of the American Statistical Association · doi:10.1080/01621459.1972.10481214 · Cited by 1,165
Ibrahim, J. G., Chen, M.-H., & Sinha, D. (2001) · Springer Series in Statistics · doi:10.1007/978-1-4757-3447-8 · Cited by 938
Discovering statistically significant biclusters in gene expression data
Tanay, A., Sharan, R., & Shamir, R. (2002) · Bioinformatics · doi:10.1093/bioinformatics/18.suppl_1.s136 · Cited by 855
The Analytics of Uncertainty and Information
Hirshleifer, J., & Riley, J. G. (1992) · Cambridge University Press eBooks · doi:10.1017/cbo9781139167635 · Cited by 842
Approximate Bayesian computational methods
Marin, J.-M., Pudlo, P., Robert, C. P., & Ryder, R. J. (2012) · Statistics and Computing · doi:10.1007/s11222-011-9288-2 · Cited by 818
Power prior distributions for regression models
Chen, M.-H., & Ibrahim, J. G. (2000) · Statistical Science · doi:10.1214/ss/1009212673 · Cited by 732
Markov Chain Monte Carlo Methods and the Label Switching Problem in Bayesian Mixture Modeling
Jasra, A., Holmes, C. C., & Stephens, D. A. (2005) · Statistical Science · doi:10.1214/088342305000000016 · Cited by 670
Self-citationVariable Selection for Cox's proportional Hazards Model and Frailty Model
Fan, J., & Li, R. (2002) · The Annals of Statistics · doi:10.1214/aos/1015362185 · Cited by 602
Expected Information as Expected Utility
Bernardo, J. M. (1979) · The Annals of Statistics · doi:10.1214/aos/1176344689 · Cited by 568
Merhav, N., & Feder, M. (1998) · IEEE Transactions on Information Theory · doi:10.1109/18.720534 · Cited by 438
Updating Subjective Probability
Diaconis, P., & Zabell, S. L. (1982) · Journal of the American Statistical Association · doi:10.1080/01621459.1982.10477893 · Cited by 303
Optimal Information Processing and Bayes's Theorem
Zellner, A. (1988) · The American Statistician · doi:10.1080/00031305.1988.10475585 · Cited by 273
Goldstein, M., & Wooff, D. A. (2007) · Wiley series in probability and statistics · doi:10.1002/9780470065662 · Cited by 197
From ɛ-entropy to KL-entropy: Analysis of minimum information complexity density estimation
Zhang, T. (2006) · The Annals of Statistics · doi:10.1214/009053606000000704 · Cited by 162
Some teasers concerning conditional probabilities
Bar‐Hillel, M., & Falk, R. (1982) · Cognition · doi:10.1016/0010-0277(82)90021-x · Cited by 132
Interpreting Statistical Evidence by using Imperfect Models: Robust Adjusted Likelihood Functions
Royall, R. M., & Tsou, T. (2003) · Journal of the Royal Statistical Society Series B (Statistical Methodology) · doi:10.1111/1467-9868.00392 · Cited by 117
Gibbs posterior for variable selection in high-dimensional classification and data mining
Jiang, W., & Tanner, M. A. (2008) · The Annals of Statistics · doi:10.1214/07-aos547 · Cited by 98
Bayesian variable selection for proportional hazards models
Ibrahim, J. G., Chen, M., & MacEachern, S. N. (1999) · Canadian Journal of Statistics · doi:10.2307/3316126 · Cited by 73
Heard, N. A., Holmes, C. C., Stephens, D. A., Hand, D. J., & Dimopoulos, G. (2005) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.0408393102 · Cited by 66
Self-citationBayesian Variable Selection Method for Censored Survival Data
Faraggi, D., & Simon, R. M. (1998) · Biometrics · doi:10.2307/2533672 · Cited by 63
PAC-Bayesian bounds for randomized empirical risk minimizers
Alquier, P. (2008) · Mathematical Methods of Statistics · doi:10.3103/s1066530708040017 · Cited by 50
Revising Previsions: A Geometric Interpretation
Goldstein, M. (1981) · Journal of the Royal Statistical Society Series B (Statistical Methodology) · doi:10.1111/j.2517-6161.1981.tb01160.x · Cited by 42
What Are Conditional Probabilities Conditional Upon?
Hutchison, K. (1999) · The British Journal for the Philosophy of Science · doi:10.1093/bjps/50.4.665 · Cited by 41
Bayesian Model Choice: What and Why?
Key, J. T., Pericchi, L. R., & Smith, A. F. M. (1999) · doi:10.1093/oso/9780198504856.003.0015 · Cited by 29
Tibshirani (1997) · doi:10.1002/(sici)1097-0258(19970228)16:4<385::aid-sim380>3.0.co;2-3
Cited by
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Fournier, R., Tsangalidou, Z., Reich, D., & Palamara, P. F. (2023) · Nature Communications · doi:10.1038/s41467-023-43522-6 · Cited by 49
Metadata
- Authors
- Bissiri, P. G., Holmes, C. C., & Walker, S. G.
- Venue
- Journal of the Royal Statistical Society Series B: Statistical Methodology
- Publisher
- Oxford University Press (OUP)
- Published
- 2016-02-23
- Volume
- 78
- Issue
- 5
- Pages
- 1103-1130
- ISSN
- 1369-7412 (ISSN-L)
- 1467-9868
- OpenAlex
- W2243651912
- Cited by
- 285
- References
- 36
- FWCI
- 11.04
- Type
- journal article
- Language
- en
- Open access
- hybrid
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