Analyse bayésienne du modèle linéaire avec erreur autocorrélée par échantillonnage de Gibbs : application à la modélisation d'un procédé agroalimentaire à partir de données recueillies sur ligne
Girard, Philippe ; Parent, Eric
Revue de Statistique Appliquée, Tome 48 (2000), p. 5-34 / Harvested from Numdam
Publié le : 2000-01-01
@article{RSA_2000__48_2_5_0,
     author = {Girard, Philippe and Parent, \'Eric},
     title = {Analyse bay\'esienne du mod\`ele lin\'eaire avec erreur autocorr\'el\'ee par \'echantillonnage de Gibbs : application \`a la mod\'elisation d'un proc\'ed\'e agroalimentaire \`a partir de donn\'ees recueillies sur ligne},
     journal = {Revue de Statistique Appliqu\'ee},
     volume = {48},
     year = {2000},
     pages = {5-34},
     language = {fr},
     url = {http://dml.mathdoc.fr/item/RSA_2000__48_2_5_0}
}
Girard, Philippe; Parent, Eric. Analyse bayésienne du modèle linéaire avec erreur autocorrélée par échantillonnage de Gibbs : application à la modélisation d'un procédé agroalimentaire à partir de données recueillies sur ligne. Revue de Statistique Appliquée, Tome 48 (2000) pp. 5-34. http://gdmltest.u-ga.fr/item/RSA_2000__48_2_5_0/

[1] I.V. Basawa and L. Billard. Large-sample inference for a regression model with autocorrelated errors. Biometrika, 76: 283 - 288, 1989. | MR 1016018 | Zbl 0671.62088

[2] C.M. Beach and J.G. Mackinnon. A maximum likelihood procedure for regression with autocorrelated errors. Econometrica, 46: 51- 58, 1978. | MR 464518 | Zbl 0373.62055

[3] J.O. Berger. Statistical decision theory and bayesian analysis. Springer Verlag, New York, 2nd edition, 1980. | MR 804611 | Zbl 0572.62008

[4] J.M. Bernardo and A.F.M. Smith. Bayesian theory. Wiley, Londres, 1 edition 1994. | MR 1274699 | Zbl 0796.62002

[5] G.E.P. Box and G.C. Tiao. Bayesian inference in statistical analysis, Wiley, New York, 1 st edition, 1973. | MR 418321 | Zbl 0850.62004

[6] L.D. Broemeling. Bayesian analysis of linear models. Marcel Dekker, Inc., New York and Basel, 1 edition, 1984. | MR 772380 | Zbl 0564.62020

[7] D. Chalton and C. Troskie. Multiple regression with autocorrelated errors : bayesian analysis with different prior. South African Statistical Journal, 27: 51 -62, 1993. | MR 1242769 | Zbl 0780.62024

[8] S. Chib. Bayes regression with autoregressive errors. Journal of econometrics, 58: 275-294, 1993. | MR 1237737 | Zbl 0775.62068

[9] S. Chib and E. Greenberg. Hierarchical analysis of SUR models with extensions to correlated serial errors and time-varying parameters models. Journal of econometrics, 68: 339-360, 1995. | Zbl 0833.62103

[10] D. Cochrane and G. Orcutt. Application of least square regressions to relationships containing auto-correlated error terms. Journal of the American Statistical Association, 44: 32- 61, 1949. | Zbl 0033.08201

[11] F. Crettaz De Roten and J.-M. Helbling. Données manquantes et aberrantes : le quotidien du statisticien analyste de données. Revue de Statistiques Appliquées, 44: 105-115. | Numdam

[12] M.G. Dagenais. Parameter estimation in regression models with errors in the variables and autocorrelated disturbances. Journal of econometrics, 64: 145-163, 1994. | MR 1310521 | Zbl 0825.62954

[13] P. Dellaportas and D.A. Stephens. Bayesian analysis of error-invariables regression models, Biometrics, 51: 1085-1095, 1995. | Zbl 0867.62013

[14] T.E. Dielman. Regression forecasts when disturbances are autocorrelated. Journal of forecasting, 4: 263-271, 1985.

[15] H. Doran. Applied regression analysis in econometrics. New York Marcel Dekker Inc. edition, 1989. | Zbl 0697.62102

[16] N.R. Draper and H. Smith. Applied Regression Analysis. Wiley, New York, 2nd edition, 1981. | MR 610978 | Zbl 0548.62046

[17] T.B. Fomby and D.K. Guilkey On choosing the optimal level of significance for the Durbin-Watson test and the bayesian alternative. Journal of econometrics, 8: 203-213, 1978. | MR 547141 | Zbl 0394.62065

[18] A. Gelfand and A. Smith. Sampling-based approaches to calculating marginal densities. Journal of the American Statistical Association, 85: 398 -409, 1990. | MR 1141740 | Zbl 0702.62020

[19] A. Gelman and J.B. Carlin and H.S. Stern and D.B. Rubin. Bayesian data analysis, Londres, Chapman and Hall edition, 1995. | MR 1385925

[20] S. Geman and D. Geman. Stochastic relaxation, Gibbs distributions and the bayesian restoration of image. IEEE transactions on Pattern Analysis and Machine Intelligence, 6: 721- 741, 1984. | Zbl 0573.62030

[21] P. Girard. Les mécanismes physico-chimiques responsables de la viscosité du lait concentré sucré - Synthèse bibliographique. Rapport Nestlé, 1997.

[22] A.C. Harvey and G.D.A. Phillips. Maximum likelihood estimation of regression models with autoregressive-moving average disturbances. Biometrika, 66: 49 -58, 1979. | MR 529147 | Zbl 0453.62082

[23] H. Jeffreys. Theory of probability, Oxford University Press, New York, 3rd edition, 1961. | MR 187257 | Zbl 0902.62002

[24] E.L. Lehman. Theory of point estimation, John Wiley and Sons, New York, 1 st edition, 1983. | MR 702834 | Zbl 0522.62020

[25] D.V. Lindley and A.F.M. Smith. Bayes estimates for the linear model- with discussion, Journal of the Royal Statistical Society B, 34: 1-41, 1972. | MR 415861 | Zbl 0246.62050

[26] J. Neter and W. Wasserman and M.H. Kutner. Applied linear statistical model - Regression, analysis of variance and experimental design. IRWIN, Honewood, 2 nd edition, 1985. | Zbl 0347.62043

[27] B.D. Ripley. Stochastic simulation. Wiley, New York, 1 edition, 1987. | MR 875224 | Zbl 0613.65006

[28] C. Robert. Analyse statistique bayesienne. Economica, Paris, 1 st edition, 1992. | Zbl 0827.62006

[29] C. Robert. Méthode de simulation de Monte-Carlo par chaînes de Markov. Economica, paris, economica edition, 1996.

[30] M.A. Tanner. Tools for statistical inference : methods for the exploration of posterior distribution and likelihood functions. Springer Verlag, New York, 3rd edition, 1996. | MR 1396311 | Zbl 0846.62001

[31] S. Weisberg. Applied linear regression. John Wiley, New York, 2 nd edition, 1985. | MR 2112740 | Zbl 0646.62058

[32] A. Zellner, An introduction to Bayesian Inference in econometrics. Krieger Robert E., Londres, 1 st edition, 1971. | MR 610608 | Zbl 0647.62097

[33] A. Zellner and G.C. Tiao. Bayesian analysis of the regression model with autocorrelated errors. Journal of the American Statistical Association, 59: 763-778, 1964. | MR 166886 | Zbl 0141.34703