BAYESIAN ANALYSIS OF THE ADDITIVE MIXED MODEL FOR RANDOMIZED BLOCK DESIGNS
Summary This paper deals with the Bayesian analysis of the additive mixed model experiments. Consider b randomly chosen subjects who respond once to each of t treatments. The subjects are treated as random effects and the treatment effects are fixed. Suppose that some prior information is available,...
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| Published in | Australian & New Zealand journal of statistics Vol. 48; no. 2; pp. 225 - 236 |
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| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
Melbourne, Australia
Blackwell Publishing Asia
01.06.2006
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| Subjects | |
| Online Access | Get full text |
| ISSN | 1369-1473 1467-842X |
| DOI | 10.1111/j.1467-842X.2006.00436.x |
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| Abstract | Summary
This paper deals with the Bayesian analysis of the additive mixed model experiments. Consider b randomly chosen subjects who respond once to each of t treatments. The subjects are treated as random effects and the treatment effects are fixed. Suppose that some prior information is available, thus motivating a Bayesian analysis. The Bayesian computation, however, can be difficult in this situation, especially when a large number of treatments is involved. Three computational methods are suggested to perform the analysis. The exact posterior density of any parameter of interest can be simulated based on random realizations taken from a restricted multivariate t distribution. The density can also be simulated using Markov chain Monte Carlo methods. The simulated density is accurate when a large number of random realizations is taken. However, it may take substantial amount of computer time when many treatments are involved. An alternative Laplacian approximation is discussed. The Laplacian method produces smooth and very accurate approximates to posterior densities, and takes only seconds of computer time. An example of a pipeline cracks experiment is used to illustrate the Bayesian approaches and the computational methods. |
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| AbstractList | Summary
This paper deals with the Bayesian analysis of the additive mixed model experiments. Consider b randomly chosen subjects who respond once to each of t treatments. The subjects are treated as random effects and the treatment effects are fixed. Suppose that some prior information is available, thus motivating a Bayesian analysis. The Bayesian computation, however, can be difficult in this situation, especially when a large number of treatments is involved. Three computational methods are suggested to perform the analysis. The exact posterior density of any parameter of interest can be simulated based on random realizations taken from a restricted multivariate t distribution. The density can also be simulated using Markov chain Monte Carlo methods. The simulated density is accurate when a large number of random realizations is taken. However, it may take substantial amount of computer time when many treatments are involved. An alternative Laplacian approximation is discussed. The Laplacian method produces smooth and very accurate approximates to posterior densities, and takes only seconds of computer time. An example of a pipeline cracks experiment is used to illustrate the Bayesian approaches and the computational methods. This paper deals with the Bayesian analysis of the additive mixed model experiments. Consider b randomly chosen subjects who respond once to each of t treatments. The subjects are treated as random effects and the treatment effects are fixed. Suppose that some prior information is available, thus motivating a Bayesian analysis. The Bayesian computation, however, can be difficult in this situation, especially when a large number of treatments is involved. Three computational methods are suggested to perform the analysis. The exact posterior density of any parameter of interest can be simulated based on random realizations taken from a restricted multivariate t distribution. The density can also be simulated using Markov chain Monte Carlo methods. The simulated density is accurate when a large number of random realizations is taken. However, it may take substantial amount of computer time when many treatments are involved. An alternative Laplacian approximation is discussed. The Laplacian method produces smooth and very accurate approximates to posterior densities, and takes only seconds of computer time. An example of a pipeline cracks experiment is used to illustrate the Bayesian approaches and the computational methods. |
| Author | Wang, Jenting Hsu, John S.J. |
| Author_xml | – sequence: 1 givenname: Jenting surname: Wang fullname: Wang, Jenting organization: State University of New York – sequence: 2 givenname: John S.J. surname: Hsu fullname: Hsu, John S.J. organization: University of California |
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| CitedBy_id | crossref_primary_10_1080_00949655_2010_491481 |
| Cites_doi | 10.2307/2527668 10.1109/TPAMI.1984.4767596 10.1111/1467-9868.00201 10.1680/iicep.1986.744 10.1111/1467-9884.00117 10.1117/12.302529 10.1214/ss/1177011137 10.1080/01621459.1990.10476213 10.2307/2287731 10.1002/0470867159 10.1023/A:1008932416310 10.1214/aoms/1177704731 10.5006/1.3283991 10.1002/9780470316511 10.1093/biomet/76.3.425 10.2307/3315383 10.1080/01621459.1977.10480998 10.1093/biomet/40.3-4.361 10.1007/978-1-4757-4286-2 10.1080/01621459.1989.10478871 10.1214/ss/1177010123 10.1063/1.1699114 10.1007/BF02294466 10.1023/A:1007665907178 10.1016/0304-4076(84)90007-1 10.1093/biomet/57.1.97 |
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| Notes | ark:/67375/WNG-7JHJDQJC-6 ArticleID:ANZS436 istex:8FA47812B4F4D0146F8C58536C0FA5E7C9C77C96 hsu@pstat.ucsb.edu Department of Mathematical Sciences, State University of New York College at Oneonta, Oneonta, NY 13820, USA. Department of Statistics and Applied Probability, University of California, Santa Barbara, CA 93106, USA. e‐mail |
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| References | Besag, J. & Higdon, D. (1993). Bayesian inference for agricultural field experiments. Bull. Int. Statist. Inst. 55, 121-136. Gelman, A., Carlin, J.B., Stern, H.S. & Rubin, D.B. (1995). Bayesian Inference in Statistical Analysis. New York : Chapman and Hall. Sincich, T. (1995). Business Statistics by Example. Upper Saddle River , NJ : Prentice-Hall. Gelfand, A.E. & Smith, A.F.M. (1990). Sampling-based approaches to calculating marginal densities. J. Amer. Statist. Assoc. 85, 398-409. Metropolis, N., Rosenbluth, A.W., Rosenbluth, M.N., Teller, A.H. & Teller, E. (1953). Equation of state calculations by fast computing machines. Journal of Chemical Physics 21, 1087-1092. Box, G.E.P. & Tiao, G.C. (1973). Bayesian Inference in Statistical Analysis. New York : Wiley. Rubinstein, R.Y. (1981). Simulation and the Monte Carlo Method. New York : Wiley. Hastings, W.K. (1970). Monte Carlo sampling methods using Markov chains and their applications. Biometrika 57, 97-109. Beal, M.J. & Ghahramani, Z. (2003). The variational Bayesian EM algorithm for incomplete data: with application to scoring graphical model structures, in Bayesian Statistics, Vol. 7, eds J.M. Mernardo, M.J. Bayarri, J.O. Berger, A.P. Dawid, D. Heckerman, A.F.M. Smith & M. West, pp. 453-464. New York : Oxford University Press. Wishart, J. & Metakides, T. (1953). Orthogonal polynomial fitting. Biometrika 40, 361-369. Kannappan, S. (1986). Introduction to Pipe Stress Analysis. New York : John Wiley and Sons. Zhang, X.Y., Lambert, S.B., Plumtree, A. & Sutherby, R. (1999). Transgranular stress corrosion cracking of X-60 pipeline steel in simulated ground water. Corrosion 55, 297-305. Berger, J.O. (1985). Statistical Decision Theory and Bayesian Analysis. New York : Springer-Verlag. Besag, J. & Higdon, D. (1999). Bayesian analysis of agricultural field experiments (with discussion). J. R. Statist. Soc. B 61, 691-746. Lu, Y. (1998). Frequency-mode selection for ultrasonic detection and characterization of circumferential cracks in pipelines. Proceedings of SPIE 3398, 18-27. Congdon, P. (2003). Applied Bayesian Modeling. Chichester : Wiley. Brooks, S.P. (1998). Markov chain Monte Carlo method and its application. The Statistician 47, 69-100. Johnson, R.A. & Ladalla, J.N. (1979). The large sample behavior of posterior distributions which sample from multiparameter exponential models, and allied results. Sankyha 41, 196-215. Leonard, T. & Hsu, J.S.J. (1999). Bayesian Methods: An Analysis for Statisticians and Interdisciplinary Researchers. New York : Cambridge University Press. Jordan, M.I., Ghahramani, A., Jaakkola, T.S. & Saul, L.K. (1999). An introduction to variational methods for graphical models. Machine Learning 37, 183-233. Tierney, L., Kass, R.E. & Kadane, J. (1989). Approximate marginal densities of non-linear functions. Biometrika 76, 425-433. Robson, D.S. (1959). A simple method for constructing orthogonal polynomials when the independent variable is unequally spaced. Biometrics 15, 197-191. Harville, D.A. (1977). Maximum-likelihood approaches to variance component estimation and to related problems. J. Amer. Statist. Assoc. 72, 320-340. Geman, S. & Geman, D. (1984). Stochastic relaxation, Gibbs distributions, and the Bayesian restoration of images. IEEE Transactions on Pattern Analysis and Machine Intelligence 6, 721-741. Hsu, J.S.J., Leonard, T. & Tsui, K. (1991). Statistical inference for multiple choice tests. Psychometrika 56, 327-348. Zellner, A. & Rossi, P.E. (1984). Bayesian analysis of dichotomous quantal response models. J. Econometrics 25, 365-393. Leonard, T., Hsu, J.S.J. & Tsui, K. (1989). Bayesian marginal inference. J. Amer. Statist. Assoc. 84, 1051-1057. Thompson, W.A., Jr (1962). The problem of negative estimates of variance components. Ann. Math. Stat. 33, 273-289. Jaakkola, T. & Jordan, M. (2000). Bayesian parameter estimation via variational methods. Statistics and Computing 10, 25-37. Besag, J., Green, P.J., Higdon, D. & Mengersen, K.L. (1995). Bayesian computation and stochastic systems (with discussion). Statist. Sci. 10, 3-66. Hsu, J.S.J. (1995). Generalized Laplacian approximations in Bayesian inference. Canadian J. Statist. 23, 399-410. Cox, B.G. & Kelsall, K.J. (1986). Construction of Cape Peron ocean outlet, Perth, Western Australia. Proceedings of the Institute of Civil Engineers, Part 1 80, 465-491. Geyer, C.J. (1992). Practical Markov chain Monte Carlo (with discussion). Statist. Sci. 7, 473-511. Leonard, T. (1982). Comment on "A simple predictive density function." J. Amer. Statist. Assoc. 77, 657-658. 1989; 84 1991; 56 1984; 25 1995; 10 1982; 77 1973 1995 2003 1999; 61 1962; 33 1998; 47 1970; 57 1999 1998; 3398 1990; 85 1992; 7 1986; 80 1989; 76 1993; 55 2000; 10 2003; 7 1995; 23 1984; 6 1999; 37 1953; 40 1977; 72 1986 1985 1999; 55 1981 1979; 41 1959; 15 1953; 21 e_1_2_5_27_1 e_1_2_5_28_1 e_1_2_5_26_1 e_1_2_5_23_1 e_1_2_5_21_1 e_1_2_5_29_1 Besag J. (e_1_2_5_4_1) 1993; 55 Sincich T. (e_1_2_5_30_1) 1995 e_1_2_5_15_1 Beal M.J. (e_1_2_5_2_1) 2003; 7 e_1_2_5_14_1 e_1_2_5_17_1 e_1_2_5_9_1 Gelman A. (e_1_2_5_12_1) 1995 e_1_2_5_16_1 e_1_2_5_8_1 e_1_2_5_11_1 e_1_2_5_34_1 e_1_2_5_10_1 e_1_2_5_35_1 e_1_2_5_6_1 e_1_2_5_13_1 e_1_2_5_32_1 e_1_2_5_5_1 e_1_2_5_33_1 e_1_2_5_3_1 Johnson R.A. (e_1_2_5_20_1) 1979; 41 Leonard T. (e_1_2_5_25_1) 1989; 84 e_1_2_5_19_1 e_1_2_5_18_1 Leonard T. (e_1_2_5_24_1) 1999 e_1_2_5_31_1 Box G.E.P. (e_1_2_5_7_1) 1973 Kannappan S. (e_1_2_5_22_1) 1986 |
| References_xml | – reference: Zellner, A. & Rossi, P.E. (1984). Bayesian analysis of dichotomous quantal response models. J. Econometrics 25, 365-393. – reference: Zhang, X.Y., Lambert, S.B., Plumtree, A. & Sutherby, R. (1999). Transgranular stress corrosion cracking of X-60 pipeline steel in simulated ground water. Corrosion 55, 297-305. – reference: Sincich, T. (1995). Business Statistics by Example. Upper Saddle River , NJ : Prentice-Hall. – reference: Lu, Y. (1998). Frequency-mode selection for ultrasonic detection and characterization of circumferential cracks in pipelines. Proceedings of SPIE 3398, 18-27. – reference: Tierney, L., Kass, R.E. & Kadane, J. (1989). Approximate marginal densities of non-linear functions. Biometrika 76, 425-433. – reference: Kannappan, S. (1986). Introduction to Pipe Stress Analysis. New York : John Wiley and Sons. – reference: Brooks, S.P. (1998). Markov chain Monte Carlo method and its application. The Statistician 47, 69-100. – reference: Beal, M.J. & Ghahramani, Z. (2003). The variational Bayesian EM algorithm for incomplete data: with application to scoring graphical model structures, in Bayesian Statistics, Vol. 7, eds J.M. Mernardo, M.J. Bayarri, J.O. Berger, A.P. Dawid, D. Heckerman, A.F.M. Smith & M. West, pp. 453-464. New York : Oxford University Press. – reference: Geyer, C.J. (1992). Practical Markov chain Monte Carlo (with discussion). Statist. Sci. 7, 473-511. – reference: Geman, S. & Geman, D. (1984). Stochastic relaxation, Gibbs distributions, and the Bayesian restoration of images. IEEE Transactions on Pattern Analysis and Machine Intelligence 6, 721-741. – reference: Johnson, R.A. & Ladalla, J.N. (1979). The large sample behavior of posterior distributions which sample from multiparameter exponential models, and allied results. Sankyha 41, 196-215. – reference: Cox, B.G. & Kelsall, K.J. (1986). Construction of Cape Peron ocean outlet, Perth, Western Australia. Proceedings of the Institute of Civil Engineers, Part 1 80, 465-491. – reference: Gelfand, A.E. & Smith, A.F.M. (1990). Sampling-based approaches to calculating marginal densities. J. Amer. Statist. Assoc. 85, 398-409. – reference: Leonard, T., Hsu, J.S.J. & Tsui, K. (1989). Bayesian marginal inference. J. Amer. Statist. Assoc. 84, 1051-1057. – reference: Wishart, J. & Metakides, T. (1953). Orthogonal polynomial fitting. Biometrika 40, 361-369. – reference: Besag, J. & Higdon, D. (1999). Bayesian analysis of agricultural field experiments (with discussion). J. R. Statist. Soc. B 61, 691-746. – reference: Congdon, P. (2003). Applied Bayesian Modeling. Chichester : Wiley. – reference: Thompson, W.A., Jr (1962). The problem of negative estimates of variance components. Ann. Math. Stat. 33, 273-289. – reference: Metropolis, N., Rosenbluth, A.W., Rosenbluth, M.N., Teller, A.H. & Teller, E. (1953). Equation of state calculations by fast computing machines. Journal of Chemical Physics 21, 1087-1092. – reference: Gelman, A., Carlin, J.B., Stern, H.S. & Rubin, D.B. (1995). Bayesian Inference in Statistical Analysis. New York : Chapman and Hall. – reference: Robson, D.S. (1959). A simple method for constructing orthogonal polynomials when the independent variable is unequally spaced. Biometrics 15, 197-191. – reference: Hsu, J.S.J., Leonard, T. & Tsui, K. (1991). Statistical inference for multiple choice tests. Psychometrika 56, 327-348. – reference: Jordan, M.I., Ghahramani, A., Jaakkola, T.S. & Saul, L.K. (1999). An introduction to variational methods for graphical models. Machine Learning 37, 183-233. – reference: Besag, J. & Higdon, D. (1993). Bayesian inference for agricultural field experiments. Bull. Int. Statist. Inst. 55, 121-136. – reference: Hastings, W.K. (1970). Monte Carlo sampling methods using Markov chains and their applications. Biometrika 57, 97-109. – reference: Berger, J.O. (1985). Statistical Decision Theory and Bayesian Analysis. New York : Springer-Verlag. – reference: Box, G.E.P. & Tiao, G.C. (1973). Bayesian Inference in Statistical Analysis. New York : Wiley. – reference: Hsu, J.S.J. (1995). Generalized Laplacian approximations in Bayesian inference. Canadian J. Statist. 23, 399-410. – reference: Jaakkola, T. & Jordan, M. (2000). Bayesian parameter estimation via variational methods. Statistics and Computing 10, 25-37. – reference: Harville, D.A. (1977). Maximum-likelihood approaches to variance component estimation and to related problems. J. Amer. Statist. Assoc. 72, 320-340. – reference: Besag, J., Green, P.J., Higdon, D. & Mengersen, K.L. (1995). Bayesian computation and stochastic systems (with discussion). Statist. Sci. 10, 3-66. – reference: Leonard, T. & Hsu, J.S.J. (1999). Bayesian Methods: An Analysis for Statisticians and Interdisciplinary Researchers. New York : Cambridge University Press. – reference: Leonard, T. (1982). Comment on "A simple predictive density function." J. Amer. Statist. Assoc. 77, 657-658. – reference: Rubinstein, R.Y. (1981). Simulation and the Monte Carlo Method. New York : Wiley. – year: 1985 – volume: 6 start-page: 721 year: 1984 end-page: 741 article-title: Stochastic relaxation, Gibbs distributions, and the Bayesian restoration of images publication-title: IEEE Transactions on Pattern Analysis and Machine Intelligence – volume: 57 start-page: 97 year: 1970 end-page: 109 article-title: Monte Carlo sampling methods using Markov chains and their applications publication-title: Biometrika – volume: 55 start-page: 121 year: 1993 end-page: 136 article-title: Bayesian inference for agricultural field experiments publication-title: Bull. Int. Statist. Inst – volume: 56 start-page: 327 year: 1991 end-page: 348 article-title: Statistical inference for multiple choice tests publication-title: Psychometrika – year: 1981 – volume: 84 start-page: 1051 year: 1989 end-page: 1057 article-title: Bayesian marginal inference publication-title: J. Amer. Statist. Assoc – year: 2003 – year: 1973 – volume: 33 start-page: 273 year: 1962 end-page: 289 article-title: The problem of negative estimates of variance components publication-title: Ann. Math. Stat – volume: 80 start-page: 465 year: 1986 end-page: 491 article-title: Construction of Cape Peron ocean outlet, Perth, Western Australia publication-title: Proceedings of the Institute of Civil Engineers, Part 1 – volume: 10 start-page: 25 year: 2000 end-page: 37 article-title: Bayesian parameter estimation via variational methods publication-title: Statistics and Computing – volume: 23 start-page: 399 year: 1995 end-page: 410 article-title: Generalized Laplacian approximations in Bayesian inference publication-title: Canadian J. Statist – year: 1986 – volume: 76 start-page: 425 year: 1989 end-page: 433 article-title: Approximate marginal densities of non‐linear functions publication-title: Biometrika – volume: 61 start-page: 691 year: 1999 end-page: 746 article-title: Bayesian analysis of agricultural field experiments (with discussion) publication-title: J. R. Statist. Soc. B – volume: 7 start-page: 473 year: 1992 end-page: 511 article-title: Practical Markov chain Monte Carlo (with discussion) publication-title: Statist. Sci – volume: 21 start-page: 1087 year: 1953 end-page: 1092 article-title: Equation of state calculations by fast computing machines publication-title: Journal of Chemical Physics – volume: 47 start-page: 69 year: 1998 end-page: 100 article-title: Markov chain Monte Carlo method and its application publication-title: The Statistician – volume: 85 start-page: 398 year: 1990 end-page: 409 article-title: Sampling‐based approaches to calculating marginal densities publication-title: J. Amer. Statist. Assoc – volume: 3398 start-page: 18 year: 1998 end-page: 27 article-title: Frequency‐mode selection for ultrasonic detection and characterization of circumferential cracks in pipelines publication-title: Proceedings of SPIE – volume: 37 start-page: 183 year: 1999 end-page: 233 article-title: An introduction to variational methods for graphical models publication-title: Machine Learning – year: 1995 – volume: 77 start-page: 657 year: 1982 end-page: 658 article-title: Comment on “A simple predictive density function.” publication-title: J. Amer. Statist. Assoc – volume: 10 start-page: 3 year: 1995 end-page: 66 article-title: Bayesian computation and stochastic systems (with discussion) publication-title: Statist. Sci – volume: 25 start-page: 365 year: 1984 end-page: 393 article-title: Bayesian analysis of dichotomous quantal response models publication-title: J. Econometrics – volume: 55 start-page: 297 year: 1999 end-page: 305 article-title: Transgranular stress corrosion cracking of X‐60 pipeline steel in simulated ground water publication-title: Corrosion – volume: 41 start-page: 196 year: 1979 end-page: 215 article-title: The large sample behavior of posterior distributions which sample from multiparameter exponential models, and allied results publication-title: Sankyha – volume: 7 start-page: 453 year: 2003 end-page: 464 article-title: The variational Bayesian EM algorithm for incomplete data: with application to scoring graphical model structures publication-title: Bayesian Statistics – volume: 72 start-page: 320 year: 1977 end-page: 340 article-title: Maximum‐likelihood approaches to variance component estimation and to related problems publication-title: J. Amer. Statist. Assoc – volume: 40 start-page: 361 year: 1953 end-page: 369 article-title: Orthogonal polynomial fitting publication-title: Biometrika – year: 1999 – volume: 15 start-page: 197 year: 1959 end-page: 191 article-title: A simple method for constructing orthogonal polynomials when the independent variable is unequally spaced publication-title: Biometrics – volume-title: Bayesian Inference in Statistical Analysis year: 1973 ident: e_1_2_5_7_1 – ident: e_1_2_5_28_1 doi: 10.2307/2527668 – volume: 55 start-page: 121 year: 1993 ident: e_1_2_5_4_1 article-title: Bayesian inference for agricultural field experiments publication-title: Bull. Int. Statist. Inst – ident: e_1_2_5_13_1 doi: 10.1109/TPAMI.1984.4767596 – ident: e_1_2_5_5_1 doi: 10.1111/1467-9868.00201 – ident: e_1_2_5_10_1 doi: 10.1680/iicep.1986.744 – ident: e_1_2_5_8_1 doi: 10.1111/1467-9884.00117 – volume-title: Introduction to Pipe Stress Analysis year: 1986 ident: e_1_2_5_22_1 – ident: e_1_2_5_26_1 doi: 10.1117/12.302529 – ident: e_1_2_5_14_1 doi: 10.1214/ss/1177011137 – ident: e_1_2_5_11_1 doi: 10.1080/01621459.1990.10476213 – volume: 41 start-page: 196 year: 1979 ident: e_1_2_5_20_1 article-title: The large sample behavior of posterior distributions which sample from multiparameter exponential models, and allied results publication-title: Sankyha – ident: e_1_2_5_23_1 doi: 10.2307/2287731 – ident: e_1_2_5_9_1 doi: 10.1002/0470867159 – ident: e_1_2_5_19_1 doi: 10.1023/A:1008932416310 – ident: e_1_2_5_31_1 doi: 10.1214/aoms/1177704731 – ident: e_1_2_5_35_1 doi: 10.5006/1.3283991 – ident: e_1_2_5_29_1 doi: 10.1002/9780470316511 – volume-title: Business Statistics by Example year: 1995 ident: e_1_2_5_30_1 – volume: 7 start-page: 453 year: 2003 ident: e_1_2_5_2_1 article-title: The variational Bayesian EM algorithm for incomplete data: with application to scoring graphical model structures publication-title: Bayesian Statistics – ident: e_1_2_5_32_1 doi: 10.1093/biomet/76.3.425 – ident: e_1_2_5_17_1 doi: 10.2307/3315383 – volume-title: Bayesian Methods: An Analysis for Statisticians and Interdisciplinary Researchers year: 1999 ident: e_1_2_5_24_1 – ident: e_1_2_5_15_1 doi: 10.1080/01621459.1977.10480998 – ident: e_1_2_5_33_1 doi: 10.1093/biomet/40.3-4.361 – ident: e_1_2_5_3_1 doi: 10.1007/978-1-4757-4286-2 – volume: 84 start-page: 1051 year: 1989 ident: e_1_2_5_25_1 article-title: Bayesian marginal inference publication-title: J. Amer. Statist. Assoc doi: 10.1080/01621459.1989.10478871 – ident: e_1_2_5_6_1 doi: 10.1214/ss/1177010123 – ident: e_1_2_5_27_1 doi: 10.1063/1.1699114 – ident: e_1_2_5_18_1 doi: 10.1007/BF02294466 – volume-title: Bayesian Inference in Statistical Analysis year: 1995 ident: e_1_2_5_12_1 – ident: e_1_2_5_21_1 doi: 10.1023/A:1007665907178 – ident: e_1_2_5_34_1 doi: 10.1016/0304-4076(84)90007-1 – ident: e_1_2_5_16_1 doi: 10.1093/biomet/57.1.97 |
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This paper deals with the Bayesian analysis of the additive mixed model experiments. Consider b randomly chosen subjects who respond once to each of t... This paper deals with the Bayesian analysis of the additive mixed model experiments. Consider b randomly chosen subjects who respond once to each of t... |
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| SubjectTerms | Laplacian approximation Monte Carlo simulation |
| Title | BAYESIAN ANALYSIS OF THE ADDITIVE MIXED MODEL FOR RANDOMIZED BLOCK DESIGNS |
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