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Volumn 78, Issue 5, 2016, Pages 1103-1130

A general framework for updating belief distributions

Author keywords

Decision theory; General Bayesian updating; Generalized estimating equations; Gibbs posteriors; Information; Loss function; Maximum entropy; Provably approximately correct Bayes methods; Self information loss function

Indexed keywords


EID: 84959423086     PISSN: 13697412     EISSN: 14679868     Source Type: Journal    
DOI: 10.1111/rssb.12158     Document Type: Article
Times cited : (470)

References (58)
  • 1
    • 0001199215 scopus 로고
    • A general class of coefficients of divergence of one distribution from another
    • Ali, S. M. and Silvey, S. D. (1966) A general class of coefficients of divergence of one distribution from another. J. R. Statist. Soc. B, 28, 131–142.
    • (1966) J. R. Statist. Soc. B , vol.28 , pp. 131-142
    • Ali, S.M.1    Silvey, S.D.2
  • 2
    • 79960993628 scopus 로고    scopus 로고
    • PAC-Bayesian bounds for randomized empirical risk minimizers
    • Alquier, P. (2008) PAC-Bayesian bounds for randomized empirical risk minimizers. Math. Meth. Statist., 17, 279–304.
    • (2008) Math. Meth. Statist. , vol.17 , pp. 279-304
    • Alquier, P.1
  • 3
    • 0020104124 scopus 로고
    • Some teasers concerning conditional probabilities
    • Bar-Hillel, M. and Falk, R. (1982) Some teasers concerning conditional probabilities. Cognition, 11, 109–122.
    • (1982) Cognition , vol.11 , pp. 109-122
    • Bar-Hillel, M.1    Falk, R.2
  • 5
    • 0000626524 scopus 로고
    • Expected information as expected utility
    • Bernardo, J. M. (1979) Expected information as expected utility. Ann. Statist., 7, 686–690.
    • (1979) Ann. Statist. , vol.7 , pp. 686-690
    • Bernardo, J.M.1
  • 7
    • 77954036139 scopus 로고    scopus 로고
    • On Bayesian learning from Bernoulli observations
    • Bissiri, P. G. and Walker, S. G. (2010) On Bayesian learning from Bernoulli observations. J. Statist. Planng Inf., 140, 3520–3530.
    • (2010) J. Statist. Planng Inf. , vol.140 , pp. 3520-3530
    • Bissiri, P.G.1    Walker, S.G.2
  • 8
    • 84865543438 scopus 로고    scopus 로고
    • On Bayesian learning from loss functions
    • Bissiri, P. G. and Walker, S. G. (2012a) On Bayesian learning from loss functions. J. Statist. Planng Inf., 142, 3167–3173.
    • (2012) J. Statist. Planng Inf. , vol.142 , pp. 3167-3173
    • Bissiri, P.G.1    Walker, S.G.2
  • 9
    • 84870253672 scopus 로고    scopus 로고
    • Converting information into probability measures via the Kullback–Leibler divergence
    • Bissiri, P. G. and Walker, S. G. (2012b) Converting information into probability measures via the Kullback–Leibler divergence. Ann. Inst. Statist. Math., 64, 1139–1160.
    • (2012) Ann. Inst. Statist. Math. , vol.64 , pp. 1139-1160
    • Bissiri, P.G.1    Walker, S.G.2
  • 10
    • 33645980911 scopus 로고    scopus 로고
    • Preprint 840, Laboratoire de Probabilités et Modèles Aléatoires, Université Paris 6, Paris
    • Catoni, O. (2003) A PAC Bayesian approach to adaptive classification. Preprint 840. Laboratoire de Probabilités et Modèles Aléatoires, Université Paris 6, Paris.
    • (2003) A PAC Bayesian approach to adaptive classification
    • Catoni, O.1
  • 12
    • 0034566393 scopus 로고    scopus 로고
    • Biclustering of expression data
    • In, (eds, P. Bourne, M. Gribskov, R. Altman, N. Jensen, D. Hope, T. Lengauer, J. Mitchell, E. Scheeff, C. Smith, S. Strande, H. Weissig, Menlo Park, American Association for Artificial Intelligence Press
    • Cheng, Y. and Church, G. M. (2000) Biclustering of expression data. In Proc. 8th Int. Conf. Intelligent Systems for Molecular Biology (eds P. Bourne, M. Gribskov, R. Altman, N. Jensen, D. Hope, T. Lengauer, J. Mitchell, E. Scheeff, C. Smith, S. Strande and H. Weissig), pp. 93–103. Menlo Park: American Association for Artificial Intelligence Press.
    • (2000) Proc. 8th Int. Conf. Intelligent Systems for Molecular Biology , pp. 93-103
    • Cheng, Y.1    Church, G.M.2
  • 14
    • 0000336139 scopus 로고
    • Regression models and life-tables (with discussion)
    • Cox, D. R. (1972) Regression models and life-tables (with discussion). J. R. Statist. Soc. B, 34, 187–220.
    • (1972) J. R. Statist. Soc. B , vol.34 , pp. 187-220
    • Cox, D.R.1
  • 15
    • 31144476037 scopus 로고    scopus 로고
    • Probability matching priors
    • In, (eds, D. Dey, C. R. Rao, Amsterdam, Elsevier
    • Datta, G. S. and Sweeting, T. J. (2005) Probability matching priors. In Handbook of Statistics (eds D. Dey and C. R. Rao), vol. 25, pp. 91–114. Amsterdam: Elsevier.
    • (2005) Handbook of Statistics , vol.25 , pp. 91-114
    • Datta, G.S.1    Sweeting, T.J.2
  • 16
    • 0000093386 scopus 로고
    • Updating subjective probability
    • Diaconis, P. and Zabell, S. L. (1982) Updating subjective probability. J. Am. Statist. Ass., 77, 822–830.
    • (1982) J. Am. Statist. Ass. , vol.77 , pp. 822-830
    • Diaconis, P.1    Zabell, S.L.2
  • 18
    • 0036117466 scopus 로고    scopus 로고
    • Variable selection for Cox's proportional hazards model and frailty model
    • Fan, J and Li, R. (2002) Variable selection for Cox's proportional hazards model and frailty model. Ann. Statist., 30, 74–99.
    • (2002) Ann. Statist. , vol.30 , pp. 74-99
    • Fan, J.1    Li, R.2
  • 19
    • 0032442458 scopus 로고    scopus 로고
    • Bayesian variable selection method for censored survival data
    • Faraggi, D. and Simon, R. (1998) Bayesian variable selection method for censored survival data. Biometrics, 54, 1475–1485.
    • (1998) Biometrics , vol.54 , pp. 1475-1485
    • Faraggi, D.1    Simon, R.2
  • 20
    • 0001918661 scopus 로고
    • La prévision: ses lois logiques, ses sources subjectives
    • de Finetti, B. (1937) La prévision: ses lois logiques, ses sources subjectives. Ann. Inst. H. Poincaré, 7, 1–68.
    • (1937) Ann. Inst. H. Poincaré , vol.7 , pp. 1-68
    • de Finetti, B.1
  • 21
    • 84913730788 scopus 로고
    • Puzzle or paradox?
    • Freund, J. E. (1965) Puzzle or paradox? Ann. Statist., 19, 29–44.
    • (1965) Ann. Statist , vol.19 , pp. 29-44
    • Freund, J.E.1
  • 23
    • 0010899064 scopus 로고
    • Revising previsions: a geometric interpretation
    • Goldstein, M. (1981) Revising previsions: a geometric interpretation. J. R. Statist. Soc. B, 43, 105–130.
    • (1981) J. R. Statist. Soc. B , vol.43 , pp. 105-130
    • Goldstein, M.1
  • 25
    • 84927511887 scopus 로고
    • Direct clustering of a data matrix
    • Hartigan, J. A. (1972) Direct clustering of a data matrix. J. Am. Statist. Ass., 67, 123–129.
    • (1972) J. Am. Statist. Ass. , vol.67 , pp. 123-129
    • Hartigan, J.A.1
  • 27
    • 28044449342 scopus 로고    scopus 로고
    • Bayesian coclustering of Anopheles gene expression time series: study of immune defence response to multiple experimental challenges
    • Heard, N. A., Holmes, C. C., Stephens, D. A., Hand, D. J. and Dimopoulos, G. (2005) Bayesian coclustering of Anopheles gene expression time series: study of immune defence response to multiple experimental challenges. Proc. Natn. Acad. Sci. USA, 102, 16939–16944.
    • (2005) Proc. Natn. Acad. Sci. USA , vol.102 , pp. 16939-16944
    • Heard, N.A.1    Holmes, C.C.2    Stephens, D.A.3    Hand, D.J.4    Dimopoulos, G.5
  • 29
    • 84881224769 scopus 로고    scopus 로고
    • Bayesian sandwich posteriors for pseudo-true parameters
    • Hoff, P. and Wakefield, J. C. (2013) Bayesian sandwich posteriors for pseudo-true parameters. J. Statist. Planng Inf., 143, 1638–1642.
    • (2013) J. Statist. Planng Inf. , vol.143 , pp. 1638-1642
    • Hoff, P.1    Wakefield, J.C.2
  • 30
    • 0003157339 scopus 로고
    • Robust estimation of a location parameter
    • Hüber, P. (1964) Robust estimation of a location parameter. Ann. Math. Statist., 35, 73–101.
    • (1964) Ann. Math. Statist. , vol.35 , pp. 73-101
    • Hüber, P.1
  • 32
    • 0040290583 scopus 로고    scopus 로고
    • What are conditional probabilities conditional upon?
    • Hutchison, K. (1999) What are conditional probabilities conditional upon? Br. J. Philos. Sci., 50, 665–695.
    • (1999) Br. J. Philos. Sci. , vol.50 , pp. 665-695
    • Hutchison, K.1
  • 33
    • 84990894107 scopus 로고    scopus 로고
    • Resolving some puzzles of conditional probability
    • Hutchison, K. (2008) Resolving some puzzles of conditional probability. Adv. Sci. Lett., 1, 212–221.
    • (2008) Adv. Sci. Lett. , vol.1 , pp. 212-221
    • Hutchison, K.1
  • 34
    • 0002083004 scopus 로고    scopus 로고
    • Power prior distributions for regression models
    • Ibrahim, J. G. and Chen, M. H. (2000) Power prior distributions for regression models. Statist. Sci., 15, 46–60.
    • (2000) Statist. Sci. , vol.15 , pp. 46-60
    • Ibrahim, J.G.1    Chen, M.H.2
  • 35
    • 0033266924 scopus 로고    scopus 로고
    • Bayesian variable selection for proportional hazards models
    • Ibrahim, J. G., Chen, M. H. and MacEachern, S. N. (1999) Bayesian variable selection for proportional hazards models. Can. J. Statist., 27, 701–711.
    • (1999) Can. J. Statist. , vol.27 , pp. 701-711
    • Ibrahim, J.G.1    Chen, M.H.2    MacEachern, S.N.3
  • 37
    • 22544479764 scopus 로고    scopus 로고
    • Markov chain Monte Carlo methods and the label switching problem in Bayesian mixture modeling
    • Jasra, A., Holmes, C. C. and Stephens, D. A. (2005) Markov chain Monte Carlo methods and the label switching problem in Bayesian mixture modeling. Statist. Sci., 20, 50–67.
    • (2005) Statist. Sci. , vol.20 , pp. 50-67
    • Jasra, A.1    Holmes, C.C.2    Stephens, D.A.3
  • 38
    • 54349112850 scopus 로고    scopus 로고
    • Gibbs posterior for variable selection in high-dimensional classification and data mining
    • Jiang, W. and Tanner, M. A. (2008) Gibbs posterior for variable selection in high-dimensional classification and data mining. Ann. Statist., 36, 2207–2231.
    • (2008) Ann. Statist. , vol.36 , pp. 2207-2231
    • Jiang, W.1    Tanner, M.A.2
  • 39
    • 0030327756 scopus 로고    scopus 로고
    • The selection of prior distributions by formal rules
    • Kass, R. E. and Wasserman, L. A. (1996) The selection of prior distributions by formal rules. J. Am. Statist. Ass., 91, 1343–1370.
    • (1996) J. Am. Statist. Ass. , vol.91 , pp. 1343-1370
    • Kass, R.E.1    Wasserman, L.A.2
  • 40
    • 0001006927 scopus 로고    scopus 로고
    • Bayesian model choice: what and why (with discussion)?
    • In, (eds, J. M. Bernardo, J. O. Berger, A. P. Dawid, A. F. M. Smith, Oxford, Oxford University Press
    • Key, J. T., Pericchi, L. R. and Smith, A. F. M. (1999) Bayesian model choice: what and why (with discussion)? In Bayesian Statistics 6 (eds J. M. Bernardo, J. O. Berger, A. P. Dawid and A. F. M. Smith), pp. 343–370. Oxford: Oxford University Press.
    • (1999) Bayesian Statistics 6 , pp. 343-370
    • Key, J.T.1    Pericchi, L.R.2    Smith, A.F.M.3
  • 42
    • 21844462365 scopus 로고    scopus 로고
    • Tutorial on practical prediction theory for classification
    • Langford, J. (2005) Tutorial on practical prediction theory for classification. J. Mach. Learn. Res., 6, 273–306.
    • (2005) J. Mach. Learn. Res. , vol.6 , pp. 273-306
    • Langford, J.1
  • 44
    • 84990925478 scopus 로고    scopus 로고
    • Some PAC Bayes theorems
    • In, New York, Association for Computing Machinery
    • McAllester, D. (1998) Some PAC Bayes theorems. In Proc. 11th A. Conf. Computational Learning Theory, pp. 164–170. New York: Association for Computing Machinery.
    • (1998) Proc. 11th A. Conf. Computational Learning Theory , pp. 164-170
    • McAllester, D.1
  • 48
    • 0038107039 scopus 로고    scopus 로고
    • Interpreting statistical evidence by using imperfect models: robust adjusted likelihood functions
    • Royall, R., and Tsou, T.-S. (2003) Interpreting statistical evidence by using imperfect models: robust adjusted likelihood functions. J. R. Statist. Soc. B, 65, 391–404.
    • (2003) J. R. Statist. Soc. B , vol.65 , pp. 391-404
    • Royall, R.1    Tsou, T.-S.2
  • 50
    • 79551481554 scopus 로고    scopus 로고
    • PAC Bayesian analysis of co-clustering and beyond
    • Seldin, Y. and Tishby, N. (2010) PAC Bayesian analysis of co-clustering and beyond. J. Mach. Learn. Res., 11, 3595–3646.
    • (2010) J. Mach. Learn. Res. , vol.11 , pp. 3595-3646
    • Seldin, Y.1    Tishby, N.2
  • 52
    • 11244306358 scopus 로고    scopus 로고
    • Discovering statistically significant biclusters in gene expression data
    • Tanay, A., Sharan, R. and Shamir, R. (2002) Discovering statistically significant biclusters in gene expression data. Bioinformatics, 18, 136–144.
    • (2002) Bioinformatics , vol.18 , pp. 136-144
    • Tanay, A.1    Sharan, R.2    Shamir, R.3
  • 53
    • 0031015557 scopus 로고    scopus 로고
    • The lasso method for variable selection in the Cox model
    • Tibshirani, R. J. (1997) The lasso method for variable selection in the Cox model. Statist. Med., 16, 385–395.
    • (1997) Statist. Med. , vol.16 , pp. 385-395
    • Tibshirani, R.J.1
  • 54
    • 0040007375 scopus 로고    scopus 로고
    • Bayesian model averaging in proportional hazard models: assessing the risk of a stroke
    • Volinsky, C. T., Madigan, D., Raftery, A. E. and Kronmal, R. A. (1997) Bayesian model averaging in proportional hazard models: assessing the risk of a stroke. Appl. Statist., 46, 433–448.
    • (1997) Appl. Statist. , vol.46 , pp. 433-448
    • Volinsky, C.T.1    Madigan, D.2    Raftery, A.E.3    Kronmal, R.A.4
  • 56
    • 84952524259 scopus 로고
    • Optimal information processing and Bayes's theorem
    • Zellner, A. (1988) Optimal information processing and Bayes's theorem. Am. Statistn, 42, 278–284.
    • (1988) Am. Statistn , vol.42 , pp. 278-284
    • Zellner, A.1
  • 57
    • 33847361463 scopus 로고    scopus 로고
    • From ε-entropy to KL-entropy: analysis of minimum information complexity density estimation
    • Zhang, T. (2006a) From ε-entropy to KL-entropy: analysis of minimum information complexity density estimation. Ann. Statist., 34, 2180–2210.
    • (2006) Ann. Statist. , vol.34 , pp. 2180-2210
    • Zhang, T.1
  • 58
    • 33645722194 scopus 로고    scopus 로고
    • Information theoretical upper and lower bounds for statistical estimation
    • Zhang, T. (2006b) Information theoretical upper and lower bounds for statistical estimation. IEEE Trans. Inform. Theor., 52, 1307–1321.
    • (2006) IEEE Trans. Inform. Theor. , vol.52 , pp. 1307-1321
    • Zhang, T.1


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