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Volumn 26, Issue 4, 1998, Pages 1215-1241

Bayesian goodness-of-fit testing using infinite-dimensional exponential families

Author keywords

Bayes factor; Consistency; Gaussian process prior; Markov chain Monte Carlo; Nonparametric Bayesian inference; Sieve

Indexed keywords


EID: 0032330376     PISSN: 00905364     EISSN: None     Source Type: Journal    
DOI: 10.1214/aos/1024691240     Document Type: Article
Times cited : (55)

References (67)
  • 1
    • 0038846604 scopus 로고
    • Some inequalities on characteristic roots of matrices
    • ANDERSON, T. W. and DAS GUPTA, S. (1963). Some inequalities on characteristic roots of matrices. Biometrika 50 522-524.
    • (1963) Biometrika , vol.50 , pp. 522-524
    • Anderson, T.W.1    Das Gupta, S.2
  • 3
    • 0000708831 scopus 로고
    • Mixtures of dirichlet processes with applications to non-parametric problems
    • ANTONIAK, C. E. (1974). Mixtures of Dirichlet processes with applications to non-parametric problems. Ann. Statist. 2 1152-1174.
    • (1974) Ann. Statist. , vol.2 , pp. 1152-1174
    • Antoniak, C.E.1
  • 5
    • 0026190366 scopus 로고
    • Minimum complexity density estimation
    • BARRON, A. R. and COVER, T. M. (1991). Minimum complexity density estimation. IEEE Trans. Inform. Theory 37 1034-1054.
    • (1991) IEEE Trans. Inform. Theory , vol.37 , pp. 1034-1054
    • Barron, A.R.1    Cover, T.M.2
  • 6
    • 0000404653 scopus 로고
    • Approximation of density functions by sequences of exponential families
    • Correction (1991) 19 2284
    • BARRON, A. R. and SHEU, C. H. (1991). Approximation of density functions by sequences of exponential families. Ann. Statist. 19 1347-1369. [Correction (1991) 19 2284.]
    • (1991) Ann. Statist. , vol.19 , pp. 1347-1369
    • Barron, A.R.1    Sheu, C.H.2
  • 8
    • 0000303854 scopus 로고
    • Estimating a product of means: Bayesian analysis with reference priors
    • BERGER, J. O. and BERNARDO, J. M. (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
  • 9
    • 0000298252 scopus 로고    scopus 로고
    • The intrinsic Bayes factor for model selection and prediction
    • BERGER, J. O. and PERICCHI, L. (1996). The intrinsic Bayes factor for model selection and prediction. J. Amer. Statist. Assoc. 91 109-122.
    • (1996) J. Amer. Statist. Assoc. , vol.91 , pp. 109-122
    • Berger, J.O.1    Pericchi, L.2
  • 10
    • 0001135785 scopus 로고
    • Sampling and Bayes inference in scientific modeling and robustness
    • Box, G. E. P. (1980). Sampling and Bayes inference in scientific modeling and robustness. J. Roy. Statist. Soc. Ser. A 143 383-430.
    • (1980) J. Roy. Statist. Soc. Ser. A , vol.143 , pp. 383-430
    • Box, G.E.P.1
  • 12
    • 0018116615 scopus 로고
    • Univariate density estimation by orthogonal series
    • BRUNK, H. D. (1978). Univariate density estimation by orthogonal series. Biometrika 65 521-528.
    • (1978) Biometrika , vol.65 , pp. 521-528
    • Brunk, H.D.1
  • 13
    • 0000305870 scopus 로고
    • Estimation of distributions using orthogonal expansions
    • GRAIN, B. (1974). Estimation of distributions using orthogonal expansions. Ann. Statist. 2 454-463.
    • (1974) Ann. Statist. , vol.2 , pp. 454-463
    • Grain, B.1
  • 14
    • 0039652479 scopus 로고
    • More on the estimation of distributions using orthogonal expansions
    • GRAIN, B. (1976). More on the estimation of distributions using orthogonal expansions. J. Amer. Statist. Assoc. 71 741-745.
    • (1976) J. Amer. Statist. Assoc. , vol.71 , pp. 741-745
    • Grain, B.1
  • 15
    • 0005371653 scopus 로고
    • Lower bounds on Bayes factors for multinomial distributions, with application to chi-squared tests of fit
    • DELAMPADY, M. and BERGER, J. O. (1990). Lower bounds on Bayes factors for multinomial distributions, with application to chi-squared tests of fit. Ann. Statist. 18 1295-1316.
    • (1990) Ann. Statist. , vol.18 , pp. 1295-1316
    • Delampady, M.1    Berger, J.O.2
  • 16
    • 0003171807 scopus 로고
    • On the consistency of bayes estimates
    • DIACONIS, P. and FRIEDMAN, D. (1986). On the consistency of Bayes estimates. Ann. Statist. 14 1-67.
    • (1986) Ann. Statist. , vol.14 , pp. 1-67
    • Diaconis, P.1    Friedman, D.2
  • 18
    • 0001244941 scopus 로고
    • Estimation of finite mixture distributions through bayesian sampling
    • DIEBOLT, J. and ROBERT, C. (1994). Estimation of finite mixture distributions through Bayesian sampling. J. Roy. Statist. Soc. Ser. B 56 363-375.
    • (1994) J. Roy. Statist. Soc. Ser. B , vol.56 , pp. 363-375
    • Diebolt, J.1    Robert, C.2
  • 19
    • 0040040083 scopus 로고    scopus 로고
    • New goodness of fit tests and their application to nonparametric confidence sets
    • DÜMBGEN, L. (1998). New goodness of fit tests and their application to nonparametric confidence sets. Ann. Statist. 26 288-314.
    • (1998) Ann. Statist. , vol.26 , pp. 288-314
    • Dümbgen, L.1
  • 20
    • 0030335219 scopus 로고    scopus 로고
    • Specially designed exponential families for density estimation
    • EFRON, B. and TIBSHIRANI, R. (1996). Specially designed exponential families for density estimation. Ann. Statist. 24 2431-2461.
    • (1996) Ann. Statist. , vol.24 , pp. 2431-2461
    • Efron, B.1    Tibshirani, R.2
  • 21
    • 21144481988 scopus 로고
    • Asymptotic comparison Cramér-Von Mises and nonparametric function estimation techniques for testing goodness of fit
    • EUBANK, R. and LARICCIA, V. (1992). Asymptotic comparison Cramér-Von Mises and nonparametric function estimation techniques for testing goodness of fit. Ann. Statist. 20 2071-2086.
    • (1992) Ann. Statist. , vol.20 , pp. 2071-2086
    • Eubank, R.1    Lariccia, V.2
  • 22
    • 0041187177 scopus 로고
    • Distribution theory and inference for polynomial-normal densities
    • EVANS, M. and SWARTZ, T. (1994). Distribution theory and inference for polynomial-normal densities. Comm. Statist. Theory Methods 23 1123-1148.
    • (1994) Comm. Statist. Theory Methods , vol.23 , pp. 1123-1148
    • Evans, M.1    Swartz, T.2
  • 23
    • 0001120413 scopus 로고
    • A Bayesian analysis of some nonparametric problems
    • FERGUSON, T. (1973). A Bayesian analysis of some nonparametric problems. Ann. Statist. 1 209-230.
    • (1973) Ann. Statist. , vol.1 , pp. 209-230
    • Ferguson, T.1
  • 24
    • 0000539315 scopus 로고
    • Bayesian model choice: Asymptotics and exact calculations
    • GELFAND, A. and DEY, D. (1994). Bayesian model choice: asymptotics and exact calculations. J. Roy. Statist. Soc. Ser. B 56 501-515.
    • (1994) J. Roy. Statist. Soc. Ser. B , vol.56 , pp. 501-515
    • Gelfand, A.1    Dey, D.2
  • 25
    • 0000079228 scopus 로고
    • Model determination using predictive distributions with implementation via sampling-based methods
    • with discussion. J. M. Bernardo, J. O. Berger, A. P. Dawid and A. F. M. Smith, eds. Oxford Univ. Press
    • GELFAND, A., DEY, D. and CHANG, H. (1992). Model determination using predictive distributions with implementation via sampling-based methods (with discussion). In Bayesian Statistics 4 (J. M. Bernardo, J. O. Berger, A. P. Dawid and A. F. M. Smith, eds.) 147-167. Oxford Univ. Press.
    • (1992) Bayesian Statistics 4 , vol.4 , pp. 147-167
    • Gelfand, A.1    Dey, D.2    Chang, H.3
  • 26
    • 84950453304 scopus 로고
    • Sampling based approaches to calculating marginal densities
    • GELFAND, A. and SMITH, A. F. M. (1990). Sampling based approaches to calculating marginal densities. J. Amer. Statist. Assoc. 85 398-409.
    • (1990) J. Amer. Statist. Assoc. , vol.85 , pp. 398-409
    • Gelfand, A.1    Smith, A.F.M.2
  • 27
    • 25444484077 scopus 로고    scopus 로고
    • Posterior predictive assessment of model fitness via realized discrepancies
    • GELMAN, A., MENG, X. and STERN, H. (1996). Posterior predictive assessment of model fitness via realized discrepancies. Statist. Sinica 6 733-807.
    • (1996) Statist. Sinica , vol.6 , pp. 733-807
    • Gelman, A.1    Meng, X.2    Stern, H.3
  • 28
    • 0043056438 scopus 로고
    • Modelling with normal polynomial expansions
    • W. A. Bennett, J. Geweke and K. Shell, eds. Cambridge Univ. Press
    • GEWEKE, J. (1989). Modelling with normal polynomial expansions. In Economic Complexity. Chaos, Sunspots and Nonlinearity (W. A. Bennett, J. Geweke and K. Shell, eds.) Cambridge Univ. Press.
    • (1989) Economic Complexity. Chaos, Sunspots and Nonlinearity
    • Geweke, J.1
  • 29
    • 0001561089 scopus 로고
    • A bayesian significance test for multinomial distributions
    • with discussion
    • GOOD, I. J. (1967). A Bayesian significance test for multinomial distributions (with discussion), J. Roy. Statist. Soc. Ser. B 29 399-431.
    • (1967) J. Roy. Statist. Soc. Ser. B , vol.29 , pp. 399-431
    • Good, I.J.1
  • 30
    • 84950429964 scopus 로고
    • The Bayes/non-Bayes compromise: A brief review
    • GOOD, I. J. (1992). The Bayes/non-Bayes compromise: a brief review. J. Amer. Statist. Assoc. 87 597-606.
    • (1992) J. Amer. Statist. Assoc. , vol.87 , pp. 597-606
    • Good, I.J.1
  • 32
    • 21344496537 scopus 로고
    • Comparing nonparametric versus parametric regression fits
    • HÄRDLE, W. and MAMMEN, E. (1993). Comparing nonparametric versus parametric regression fits. Ann. Statist. 21 1926-1947.
    • (1993) Ann. Statist. , vol.21 , pp. 1926-1947
    • Härdle, W.1    Mammen, E.2
  • 34
    • 0001277507 scopus 로고    scopus 로고
    • Bayesian approaches to non-and semiparametric density estimation
    • J. M. Bernardo, J. O. Berger, A. P. Dawid and A. F. M. Smith, eds. Oxford Univ. Press
    • HJORT, N. L. (1996). Bayesian approaches to non-and semiparametric density estimation. In Bayesian Statistics 5 (J. M. Bernardo, J. O. Berger, A. P. Dawid and A. F. M. Smith, eds.) 223-253. Oxford Univ. Press.
    • (1996) Bayesian Statistics 5 , vol.5 , pp. 223-253
    • Hjort, N.L.1
  • 35
    • 0001077759 scopus 로고
    • Nonparametric estimation with a parametric start
    • HJORT, N. L. and GLAD, I. (1995). Nonparametric estimation with a parametric start. Ann. Statist. 23 882-904.
    • (1995) Ann. Statist. , vol.23 , pp. 882-904
    • Hjort, N.L.1    Glad, I.2
  • 36
    • 0030367069 scopus 로고    scopus 로고
    • Locally parametric/nonparametric density estimation
    • HJORT, N. L. and JONES, M. C. (1996). Locally parametric/nonparametric density estimation. Ann. Statist. 24 1619-1647.
    • (1996) Ann. Statist. , vol.24 , pp. 1619-1647
    • Hjort, N.L.1    Jones, M.C.2
  • 37
    • 0030363428 scopus 로고    scopus 로고
    • Asymptotic optimality of data-driven neyman tests for uniformity
    • INGLOT, T. and LEDWINA, T. (1996). Asymptotic optimality of data-driven Neyman tests for uniformity. Ann. Statist. 24 1982-2019.
    • (1996) Ann. Statist. , vol.24 , pp. 1982-2019
    • Inglot, T.1    Ledwina, T.2
  • 40
    • 21844505499 scopus 로고
    • More aspects of Polya tree distributions for statistical modelling
    • LAVINE, M. (1994). More aspects of Polya tree distributions for statistical modelling. Ann. Statist. 22 1161-1176.
    • (1994) Ann. Statist. , vol.22 , pp. 1161-1176
    • Lavine, M.1
  • 41
    • 21844521889 scopus 로고
    • Data-driven version of Neyman's smooth test of fit
    • LEDWINA, T. (1994). Data-driven version of Neyman's smooth test of fit. J. Amer. Statist. Assoc. 89 1000-1005.
    • (1994) J. Amer. Statist. Assoc. , vol.89 , pp. 1000-1005
    • Ledwina, T.1
  • 42
    • 0001742255 scopus 로고
    • The logistic normal distribution for Bayesian, nonparametric, predictive densities
    • LENK, P. J. (1988). The logistic normal distribution for Bayesian, nonparametric, predictive densities. J. Amer. Statist. Assoc. 83 509-516.
    • (1988) J. Amer. Statist. Assoc. , vol.83 , pp. 509-516
    • Lenk, P.J.1
  • 43
    • 0001450917 scopus 로고
    • Towards a practicable bayesian nonparametric density estimator
    • LENK, P. J. (1991). Towards a practicable Bayesian nonparametric density estimator. Biometrika 78 531-543.
    • (1991) Biometrika , vol.78 , pp. 531-543
    • Lenk, P.J.1
  • 44
    • 0000042719 scopus 로고
    • Density estimation, stochastic processes, and prior information
    • LEONARD, T. (1978). Density estimation, stochastic processes, and prior information. J. Roy. Statist. Soc Ser. B 40 113-146.
    • (1978) J. Roy. Statist. Soc Ser. B , vol.40 , pp. 113-146
    • Leonard, T.1
  • 45
    • 0001366850 scopus 로고
    • Exact mean integrated squared error
    • MARRON, J. S. and WAND, M. P. (1992). Exact mean integrated squared error. Ann. Statist. 20 712-736.
    • (1992) Ann. Statist. , vol.20 , pp. 712-736
    • Marron, J.S.1    Wand, M.P.2
  • 46
    • 0042742904 scopus 로고
    • Posterior predictive p-values
    • MENG, X. L. (1994). Posterior predictive p-values. Ann. Statist. 22 1142-1160.
    • (1994) Ann. Statist. , vol.22 , pp. 1142-1160
    • Meng, X.L.1
  • 47
    • 21444451325 scopus 로고    scopus 로고
    • Simulating ratios of normalizing constants via a simple identity: A theoretical exploration
    • MENG, X. and WONG, W. (1996). Simulating ratios of normalizing constants via a simple identity: a theoretical exploration. Statist. Sinica 6 831-860.
    • (1996) Statist. Sinica , vol.6 , pp. 831-860
    • Meng, X.1    Wong, W.2
  • 48
    • 0001765642 scopus 로고
    • "Smooth" test for goodness of fit
    • NEYMAN, J. (1937). "Smooth" test for goodness of fit. Skand. Aktvarietidskr. 20 150-199.
    • (1937) Skand. Aktvarietidskr. , vol.20 , pp. 150-199
    • Neyman, J.1
  • 50
    • 0001857092 scopus 로고
    • Fractional bayes factors for model comparison
    • with discussion
    • O'HAGAN, A. (1995). Fractional Bayes factors for model comparison (with discussion). J. Roy. Statist. Soc. Ser. B 57 99-138.
    • (1995) J. Roy. Statist. Soc. Ser. B , vol.57 , pp. 99-138
    • O'Hagan, A.1
  • 51
    • 0000791208 scopus 로고
    • Asymptotic behavior of likelihood methods for exponential families when the number of parameter tends to infinity
    • PORTNOY, S. (1988). Asymptotic behavior of likelihood methods for exponential families when the number of parameter tends to infinity. Ann. Statist. 16 356-366.
    • (1988) Ann. Statist. , vol.16 , pp. 356-366
    • Portnoy, S.1
  • 52
    • 0000079228 scopus 로고
    • Discussion of, "model determination using predictive distributions with implementation via sampling-based methods"
    • by A. Gelfand, D. Dey and H. Chang. J. M. Bernardo, J. O. Berger, A. P. Dawid and A. F. M. Smith, eds. Oxford Univ. Press
    • RAFTERY, A. (1992). Discussion of, "Model determination using predictive distributions with implementation via sampling-based methods" by A. Gelfand, D. Dey and H. Chang. In Bayesian Statistics 4 (J. M. Bernardo, J. O. Berger, A. P. Dawid and A. F. M. Smith, eds.) 160-163. Oxford Univ. Press.
    • (1992) Bayesian Statistics 4 , vol.4 , pp. 160-163
    • Raftery, A.1
  • 53
    • 0039457366 scopus 로고
    • Smooth tests of goodness of fit: An overview
    • RAYNER, J. C. W. and BEST, D. J. (1990). Smooth tests of goodness of fit: an overview. Internat. Statist. Rev. 58 9-17.
    • (1990) Internat. Statist. Rev. , vol.58 , pp. 9-17
    • Rayner, J.C.W.1    Best, D.J.2
  • 55
    • 0000439370 scopus 로고
    • Bayesianly justifiable and relevant frequency calculations for the applied statistician
    • RUBIN, D. B. (1984). Bayesianly justifiable and relevant frequency calculations for the applied statistician. Ann. Statist. 12 1151-1172.
    • (1984) Ann. Statist. , vol.12 , pp. 1151-1172
    • Rubin, D.B.1
  • 56
    • 0000120766 scopus 로고
    • Estimating the dimension of a model
    • SCHWARZ, G. (1978). Estimating the dimension of a model. Ann. Statist. 6 461-464.
    • (1978) Ann. Statist. , vol.6 , pp. 461-464
    • Schwarz, G.1
  • 58
    • 0001303166 scopus 로고
    • Laplace approximation of high dimensional integrals
    • SHUN, Z. and MCCULLAGH, P. (1995). Laplace approximation of high dimensional integrals. J. Roy. Statist. Soc. B 57 749-760.
    • (1995) J. Roy. Statist. Soc. B , vol.57 , pp. 749-760
    • Shun, Z.1    McCullagh, P.2
  • 60
    • 84950758368 scopus 로고
    • The calculation of posterior distributions by data augmentation
    • TANNER, M. and WONG, W. (1987). The calculation of posterior distributions by data augmentation. J. Amer. Statist. Assoc. 82 528-540.
    • (1987) J. Amer. Statist. Assoc. , vol.82 , pp. 528-540
    • Tanner, M.1    Wong, W.2
  • 62
    • 0011403628 scopus 로고
    • A bayesian approach to density estimation
    • THORBURN, D. (1986). A Bayesian approach to density estimation. Biometrika 73 65-76.
    • (1986) Biometrika , vol.73 , pp. 65-76
    • Thorburn, D.1
  • 63
    • 0000576595 scopus 로고
    • Markov chains for exploring posterior distributions
    • TIERNEY, L. (1994). Markov chains for exploring posterior distributions. Ann. Statist. 22 1701-1762.
    • (1994) Ann. Statist. , vol.22 , pp. 1701-1762
    • Tierney, L.1
  • 64
    • 21844487977 scopus 로고
    • Computing bayes factors by using a generalization of the Savage-Dickey density ratio
    • VERDINELLI, I. and WASSERMAN, L. (1995). Computing Bayes factors by using a generalization of the Savage-Dickey density ratio. J. Amer. Statist. Assoc. 90 614-618.
    • (1995) J. Amer. Statist. Assoc. , vol.90 , pp. 614-618
    • Verdinelli, I.1    Wasserman, L.2
  • 65
    • 0009321339 scopus 로고
    • Data-based optimal smoothing of orthogonal series density estimates
    • WAHBA, G. (1981). Data-based optimal smoothing of orthogonal series density estimates. Ann. Statist. 9 146-156.
    • (1981) Ann. Statist. , vol.9 , pp. 146-156
    • Wahba, G.1
  • 66
    • 0003049326 scopus 로고
    • Modelling with mixtures
    • J. M. Bernardo, J. O. Berger, A. P. Dawid and A. F. M. Smith, eds. Oxford Univ. Press
    • WEST, M. (1992). Modelling with mixtures. In Bayesian Statistics 4 (J. M. Bernardo, J. O. Berger, A. P. Dawid and A. F. M. Smith, eds.) 503-524. Oxford Univ. Press.
    • (1992) Bayesian Statistics 4 , vol.4 , pp. 503-524
    • West, M.1
  • 67
    • 0005394388 scopus 로고
    • On the smoothing of probability density functions
    • WHITTLE, P. (1958). On the smoothing of probability density functions. J. Roy. Statist. Soc. Ser. B 20 334-343.
    • (1958) J. Roy. Statist. Soc. Ser. B , vol.20 , pp. 334-343
    • Whittle, P.1


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