메뉴 건너뛰기




Volumn 4, Issue , 2010, Pages 737-780

Reference priors for exponential families with increasing dimension

Author keywords

Exponential family; Increasing dimension; Mutual information; Objective prior; Posterior normality

Indexed keywords


EID: 84978678945     PISSN: 19357524     EISSN: None     Source Type: Journal    
DOI: 10.1214/10-EJS569     Document Type: Article
Times cited : (14)

References (39)
  • 1
    • 0000303854 scopus 로고
    • Estimating a product of means: Bayesian analysis with reference priors
    • Berger, J. O. and J. M. Bernardo (1989). Estimating a product of means: Bayesian analysis with reference priors. J. Amer. Statist. Assoc. 84, 200-207.
    • (1989) J. Amer. Statist. Assoc , vol.84 , pp. 200-207
    • Berger, J.O.1    Bernardo, J.M.2
  • 2
    • 0000114908 scopus 로고
    • Reference priors in a variance components problem
    • P. Goel and N. Iyengar (Eds.), New York: Springer
    • Berger, J. O. and J. M. Bernardo (1991). Reference priors in a variance components problem. In P. Goel and N. Iyengar (Eds.), Bayesian Inference in Statistics and Econometrics, pp. 177-194. New York: Springer.
    • (1991) Bayesian Inference in Statistics and Econometrics , pp. 177-194
    • Berger, J.O.1    Bernardo, J.M.2
  • 3
    • 0001141391 scopus 로고
    • On the development of reference priors
    • J. M. Bernardo, J. O. Berger, A. Dawid, and A. Smith (Eds.), Oxford: Clarendon Press
    • Berger, J. O. and J. M. Bernardo (1992a). On the development of reference priors. In J. M. Bernardo, J. O. Berger, A. Dawid, and A. Smith (Eds.), Bayesian Statistics IV, pp. 36-60. Oxford: Clarendon Press.
    • (1992) Bayesian Statistics IV , pp. 36-60
    • Berger, J.O.1    Bernardo, J.M.2
  • 4
    • 0002501585 scopus 로고
    • Ordered group reference priors with application to the multinomial
    • Berger, J. O. and J. M. Bernardo (1992b). Ordered group reference priors with application to the multinomial. Biometrika 25, 25-37.
    • (1992) Biometrika , vol.25 , pp. 25-37
    • Berger, J.O.1    Bernardo, J.M.2
  • 6
    • 65349189629 scopus 로고    scopus 로고
    • The formal definition of reference priors
    • Berger, J. O., J. M. Bernardo, and D. Sun (2009). The formal definition of reference priors. Ann. Statist. 37, 905-938.
    • (2009) Ann. Statist , vol.37 , pp. 905-938
    • Berger, J.O.1    Bernardo, J.M.2    Sun, D.3
  • 7
    • 0002183088 scopus 로고
    • Reference posterior distributions for Bayesian inference
    • Bernardo, J. M. (1979). Reference posterior distributions for Bayesian inference. J. Roy. Statist. Soc. B 41, 113-147.
    • (1979) J. Roy. Statist. Soc. B , vol.41 , pp. 113-147
    • Bernardo, J.M.1
  • 8
    • 84869752851 scopus 로고    scopus 로고
    • Integrated objective Bayesian estimation and hypothesis testing
    • J. M. Bernardo, J. O. Berger, A. P. D. Dawid, and A. F. M. Smith (Eds.), Oxford. Clarendon Press
    • Bernardo, J. M. (2010). Integrated objective Bayesian estimation and hypothesis testing. In J. M. Bernardo, J. O. Berger, A. P. D. Dawid, and A. F. M. Smith (Eds.), Bayesian Statistics IX, Oxford. Clarendon Press.
    • (2010) Bayesian Statistics IX
    • Bernardo, J.M.1
  • 9
    • 82655164891 scopus 로고    scopus 로고
    • A Bernstein-von Mises theorem for discrete probability distributions
    • Boucheron, S. and E. Gassiat (2009). A Bernstein-von Mises theorem for discrete probability distributions. Elec. J. Statist. 3, 114-148.
    • (2009) Elec. J. Statist , vol.3 , pp. 114-148
    • Boucheron, S.1    Gassiat, E.2
  • 10
    • 0003369433 scopus 로고
    • Fundamentals of Statistical Exponential Families
    • Hayward, CA: Institute of Mathematical Statistics
    • Brown, L. D. (1986). Fundamentals of Statistical Exponential Families. Vol. 9, Lecture Notes-Monograph Series. Hayward, CA: Institute of Mathematical Statistics.
    • (1986) Lecture Notes-Monograph Series. , vol.9
    • Brown, L.D.1
  • 11
    • 78649533600 scopus 로고    scopus 로고
    • Properties and implementation of Jeffreys’ prior in binomial regression models
    • Chen, M.-H., J. Ibrahim, and S. Kim (2009). Properties and implementation of Jeffreys’ prior in binomial regression models. J. Amer. Stat. Assoc. 103, 1659-1664.
    • (2009) J. Amer. Stat. Assoc , vol.103 , pp. 1659-1664
    • Chen, M.-H.1    Ibrahim, J.2    Kim, S.3
  • 12
    • 0025430804 scopus 로고
    • Information-theoretic asymptotics of Bayes methods
    • Clarke, B. and A. Barron (1990). Information-theoretic asymptotics of Bayes methods. IEEE Trans. Inform. Theory 36, 453-471.
    • (1990) IEEE Trans. Inform. Theory , vol.36 , pp. 453-471
    • Clarke, B.1    Barron, A.2
  • 13
    • 0002138061 scopus 로고
    • Jeffreys’ prior is the reference prior under entropy loss
    • Clarke, B. and A. Barron (1994). Jeffreys’ prior is the reference prior under entropy loss. J. Stat. Planning and Inference 41, 37-60.
    • (1994) J. Stat. Planning and Inference , vol.41 , pp. 37-60
    • Clarke, B.1    Barron, A.2
  • 14
    • 0041378327 scopus 로고    scopus 로고
    • Reference priors under the chi-square distance
    • Clarke, B. and D. Sun (1997). Reference priors under the chi-square distance. Sankhya 59, 215-231.
    • (1997) Sankhya , vol.59 , pp. 215-231
    • Clarke, B.1    Sun, D.2
  • 15
    • 2142717316 scopus 로고    scopus 로고
    • Partial information reference priors: Derivation and interpretations
    • Clarke, B. and A. Yuan (2004). Partial information reference priors: derivation and interpretations. J. Stat. Plann. Inf. 123, 313-345.
    • (2004) J. Stat. Plann. Inf , vol.123 , pp. 313-345
    • Clarke, B.1    Yuan, A.2
  • 16
    • 0043250998 scopus 로고
    • Posterior distributions for multivariate normal parameters
    • Geisser, S. and J. Cornfield (1963). Posterior distributions for multivariate normal parameters. J. Roy. Stat. Soc. Ser. B 25, 368-376.
    • (1963) J. Roy. Stat. Soc. Ser. B , vol.25 , pp. 368-376
    • Geisser, S.1    Cornfield, J.2
  • 18
    • 0013082366 scopus 로고
    • On obtaining invariant prior distributions
    • George, E. and R. McCulloch (1993). On obtaining invariant prior distributions. J. Statist. Plann. Inf. 37, 169-179.
    • (1993) J. Statist. Plann. Inf , vol.37 , pp. 169-179
    • George, E.1    McCulloch, R.2
  • 19
    • 0346244306 scopus 로고    scopus 로고
    • Normal approximation to the posterior distribution for generalized linear models with many covariates
    • Ghosal, S. (1997). Normal approximation to the posterior distribution for generalized linear models with many covariates. Math. Methods Statist. 6, 332-348.
    • (1997) Math. Methods Statist , vol.6 , pp. 332-348
    • Ghosal, S.1
  • 20
    • 0012224228 scopus 로고    scopus 로고
    • Asymptotic normality of posterior distributions in high dimensional linear models
    • Ghosal, S. (1999). Asymptotic normality of posterior distributions in high dimensional linear models. Bernoulli 5, 315-331.
    • (1999) Bernoulli , vol.5 , pp. 315-331
    • Ghosal, S.1
  • 21
    • 0347117630 scopus 로고    scopus 로고
    • Asymptotic normality of posterior distributions for exponential families when the number of parameters tends to infinity
    • Ghosal, S. (2000). Asymptotic normality of posterior distributions for exponential families when the number of parameters tends to infinity. J. Multivariate Anal. 74, 49-68.
    • (2000) J. Multivariate Anal , vol.74 , pp. 49-68
    • Ghosal, S.1
  • 22
    • 0003226396 scopus 로고    scopus 로고
    • Non-informativepriors via sieves and packing numbers
    • S. Panchapakesan and N. Balakrishnan (Eds.), New York: Birkhauser
    • Ghosal, S., J. K. Ghosh, and R. V. Ramamoorthi (1997). Non-informative priors via sieves and packing numbers. In S. Panchapakesan and N. Balakrishnan (Eds.), Advances in Statistical Decision Theory and Applications, pp. 119-132. New York: Birkhauser.
    • (1997) Advances in Statistical Decision Theory and Applications , pp. 119-132
    • Ghosal, S.1    Ghosh, J.K.2    Ramamoorthi, R.V.3
  • 23
    • 0034164796 scopus 로고    scopus 로고
    • Convergencerates of posterior distributions
    • Ghosal, S., J. K. Ghosh, and A. W. van der Vaart (2000). Convergence rates of posterior distributions. Ann. Statist. 30(2), 500-531.
    • (2000) Ann. Statist , vol.30 , Issue.2 , pp. 500-531
    • Ghosal, S.1    Ghosh, J.K.2    Van Der Vaart, A.W.3
  • 24
    • 0001218443 scopus 로고
    • Noninformative priors
    • J. M. Bernardo, J. O. Berger, A. P. D. Dawid, and A. F. M. Smith (Eds.), Oxford, Clarendon Press
    • Ghosh, J. K. and R. Mukerjee (1992). Noninformative priors. In J. M. Bernardo, J. O. Berger, A. P. D. Dawid, and A. F. M. Smith (Eds.), Bayesian Statistics IV, Oxford, pp. 195-210. Clarendon Press.
    • (1992) Bayesian Statistics IV , pp. 195-210
    • Ghosh, J.K.1    Mukerjee, R.2
  • 27
    • 84862296954 scopus 로고    scopus 로고
    • Sparse probabilistic principal component analysis
    • AISTATS
    • Guan, Y. and J. Dy (2009). Sparse probabilistic principal component analysis. In JMLR Workshop and Conference Proceedings Vol. 5: AISTATS, pp. 185-192.
    • (2009) JMLR Workshop and Conference Proceedings , vol.5 , pp. 185-192
    • Guan, Y.1    Dy, J.2
  • 28
    • 85035272808 scopus 로고    scopus 로고
    • Bayesian inference for multinomial group testing
    • Heo, T. and J. Kim (2007). Bayesian inference for multinomial group testing. Korean Communications in Statistics 14, 81-92.
    • (2007) Korean Communications in Statistics , vol.14 , pp. 81-92
    • Heo, T.1    Kim, J.2
  • 30
    • 0001249987 scopus 로고
    • On a measure of the information provided by an experiment
    • Lindley, D. (1956). On a measure of the information provided by an experiment. Ann. Math. Statist. 27, 986-1005.
    • (1956) Ann. Math. Statist , vol.27 , pp. 986-1005
    • Lindley, D.1
  • 32
    • 0000791208 scopus 로고
    • Asymptotic behavior of likelihood methods for exponential families when the number of parameters tends to infinity
    • Portnoy, S. (1988). Asymptotic behavior of likelihood methods for exponential families when the number of parameters tends to infinity. Ann. Statist. 16, 356-366.
    • (1988) Ann. Statist , vol.16 , pp. 356-366
    • Portnoy, S.1
  • 33
    • 84940644968 scopus 로고
    • A mathematical theory of communication, part i
    • Shannon, C. (1948a). A mathematical theory of communication, part i. Bell Syst. Tech. J. 27, 379-423.
    • (1948) Bell Syst. Tech. J , vol.27 , pp. 379-423
    • Shannon, C.1
  • 34
    • 84856043672 scopus 로고
    • A mathematical theory of communication, part ii
    • Shannon, C. (1948b). A mathematical theory of communication, part ii. Bell Syst. Tech. J 27, 623-656.
    • (1948) Bell Syst. Tech. J , vol.27 , pp. 623-656
    • Shannon, C.1
  • 35
    • 84950381139 scopus 로고
    • On a non-informative prior distribution for Bayesian inference of multinomial distribution parameters
    • Sono, S. (1983). On a non-informative prior distribution for Bayesian inference of multinomial distribution parameters. Ann. Inst. Statist. Math. 35(Part A), 167-174.
    • (1983) Ann. Inst. Statist. Math , vol.35 , pp. 167-174
    • Sono, S.1
  • 36
    • 0002902272 scopus 로고    scopus 로고
    • Reference priors with partial information
    • Sun, D. and J. O. Berger (1998). Reference priors with partial information. Biometrika 85, 55-71.
    • (1998) Biometrika , vol.85 , pp. 55-71
    • Sun, D.1    Berger, J.O.2
  • 37
    • 21844496542 scopus 로고
    • Estimation of a covariance matrix using a reference prior
    • Yang, R. and J. O. Berger (1994). Estimation of a covariance matrix using a reference prior. Ann. Statist. 22, 1195-1211.
    • (1994) Ann. Statist , vol.22 , pp. 1195-1211
    • Yang, R.1    Berger, J.O.2
  • 38
  • 39
    • 23844527237 scopus 로고    scopus 로고
    • The counter-intuitive non-informative prior for the Bernoulli family
    • Zhu, M. and A. Lu (2004). The counter-intuitive non-informative prior for the Bernoulli family. J. Stat. Ed. 12, 1-10.
    • (2004) J. Stat. Ed. , vol.12 , pp. 1-10
    • Zhu, M.1    Lu, A.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.