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Bayesian Full Information A...

Bayesian Full Information Analysis of Simultaneous Equation Models Using Integration by Monte Carlo

Bauwens, Luc

Springer Berlin Heidelberg 1984

In their review of the "Bayesian analysis of simultaneous equation systems", Dr~ze and Richard (1983) - hereafter DR - express the following viewpoint about the present state of development of the Bayesian full information analysis of such sys- tems i) the method allows "a flexible specification of the prior density, including well defined noninformative prior measures"; ii) it yields "exact finite sample posterior and predictive densities". However, they call for further developments so that these densities can be eval- uated through 'numerical methods, using an integrated software packa~e. To that end, they recommend the use of a Monte Carlo technique, since van Dijk and Kloek (1980) have demonstrated that "the integrations can be done and how they are done". In this monograph, we explain how we contribute to achieve the developments suggested by Dr~ze and Richard. A basic idea is to use known properties of the porterior density of the param- eters of the structural form to design the importance functions, i. e. approximations of the posterior density, that are needed for organizing the integrations

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monografia Rebiun38235998 https://catalogo.rebiun.org/rebiun/record/Rebiun38235998 m o d cr mnu---uuaaa 121227s1984 gw os 000 0 eng 934980633 1255225835 9783642455780 electronic bk.) 3642455786 electronic bk.) 9783540133841 3540133844 10.1007/978-3-642-45578-0 doi AU@ 000051691917 NZ1 14997776 NZ1 15618488 AU@ eng pn AU@ OCLCO OCLCQ GW5XE OCLCF UA@ COO OCLCQ OCLCO EBLCP OCLCQ AU@ LEAUB OCLCQ OCLCO UKAHL OCLCO OCLCQ OCLCO OCLCL OCLCQ KCA bicssc BUS069030 bisacsh 330.1 23 Bauwens, Luc Bayesian Full Information Analysis of Simultaneous Equation Models Using Integration by Monte Carlo by Luc Bauwens Berlin, Heidelberg Springer Berlin Heidelberg 1984 Berlin, Heidelberg Berlin, Heidelberg Springer Berlin Heidelberg 1 online resource (vi, 114 pages) 1 online resource (vi, 114 pages) Text txt rdacontent computer c rdamedia online resource cr rdacarrier Lecture Notes in Economics and Mathematical Systems 0075-8442 232 I. The Statistical Model -- 1.1 Notation -- 1.2 Interpretation -- 1.3 Likelihood function -- II. Bayesian Inference: The Extended Natural-Conjugate Approach -- II. 1 Two reformulations of the likelihood function -- II. 2 The extended natural-conjugate prior density -- II. 3 Posterior densities -- II. 4 Predictive moments -- II. 5 Numerical integration by importance sampling -- III. Selection of Importance Functions -- III. 1 General criteria -- III. 2 The AI approach -- III. 3 The AI approach -- IV. Report and Discussion of Experiments -- IV. 1 Report -- IV. 2 Conclusions -- V. Extensions -- V.I Prior density -- V.2 Nonlinear Models -- Conclusion -- Appendix A: Density Functions: Definitions, Properties And Algorithms For Generating Random Drawings -- A.I The matricvariate normal (MN) distribution -- A. II The inverted-Wishart (iW) distribution -- A. III The multivariate Student distribution -- A. IV The 2-0 poly-t distribution -- A.V The m-1 (0 In their review of the "Bayesian analysis of simultaneous equation systems", Dr~ze and Richard (1983) - hereafter DR - express the following viewpoint about the present state of development of the Bayesian full information analysis of such sys- tems i) the method allows "a flexible specification of the prior density, including well defined noninformative prior measures"; ii) it yields "exact finite sample posterior and predictive densities". However, they call for further developments so that these densities can be eval- uated through 'numerical methods, using an integrated software packa~e. To that end, they recommend the use of a Monte Carlo technique, since van Dijk and Kloek (1980) have demonstrated that "the integrations can be done and how they are done". In this monograph, we explain how we contribute to achieve the developments suggested by Dr~ze and Richard. A basic idea is to use known properties of the porterior density of the param- eters of the structural form to design the importance functions, i. e. approximations of the posterior density, that are needed for organizing the integrations Economics Economics- Statistics Économie politique Économie politique- Statistiques economics. Economics. Statistics. Print version 9783540133841 Lecture notes in economics and mathematical systems 232

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monografia Rebiun38235998 https://catalogo.rebiun.org/rebiun/record/Rebiun38235998 m o d cr mnu---uuaaa 121227s1984 gw os 000 0 eng 934980633 1255225835 9783642455780 electronic bk.) 3642455786 electronic bk.) 9783540133841 3540133844 10.1007/978-3-642-45578-0 doi AU@ 000051691917 NZ1 14997776 NZ1 15618488 AU@ eng pn AU@ OCLCO OCLCQ GW5XE OCLCF UA@ COO OCLCQ OCLCO EBLCP OCLCQ AU@ LEAUB OCLCQ OCLCO UKAHL OCLCO OCLCQ OCLCO OCLCL OCLCQ KCA bicssc BUS069030 bisacsh 330.1 23 Bauwens, Luc Bayesian Full Information Analysis of Simultaneous Equation Models Using Integration by Monte Carlo by Luc Bauwens Berlin, Heidelberg Springer Berlin Heidelberg 1984 Berlin, Heidelberg Berlin, Heidelberg Springer Berlin Heidelberg 1 online resource (vi, 114 pages) 1 online resource (vi, 114 pages) Text txt rdacontent computer c rdamedia online resource cr rdacarrier Lecture Notes in Economics and Mathematical Systems 0075-8442 232 I. The Statistical Model -- 1.1 Notation -- 1.2 Interpretation -- 1.3 Likelihood function -- II. Bayesian Inference: The Extended Natural-Conjugate Approach -- II. 1 Two reformulations of the likelihood function -- II. 2 The extended natural-conjugate prior density -- II. 3 Posterior densities -- II. 4 Predictive moments -- II. 5 Numerical integration by importance sampling -- III. Selection of Importance Functions -- III. 1 General criteria -- III. 2 The AI approach -- III. 3 The AI approach -- IV. Report and Discussion of Experiments -- IV. 1 Report -- IV. 2 Conclusions -- V. Extensions -- V.I Prior density -- V.2 Nonlinear Models -- Conclusion -- Appendix A: Density Functions: Definitions, Properties And Algorithms For Generating Random Drawings -- A.I The matricvariate normal (MN) distribution -- A. II The inverted-Wishart (iW) distribution -- A. III The multivariate Student distribution -- A. IV The 2-0 poly-t distribution -- A.V The m-1 (0 In their review of the "Bayesian analysis of simultaneous equation systems", Dr~ze and Richard (1983) - hereafter DR - express the following viewpoint about the present state of development of the Bayesian full information analysis of such sys- tems i) the method allows "a flexible specification of the prior density, including well defined noninformative prior measures"; ii) it yields "exact finite sample posterior and predictive densities". However, they call for further developments so that these densities can be eval- uated through 'numerical methods, using an integrated software packa~e. To that end, they recommend the use of a Monte Carlo technique, since van Dijk and Kloek (1980) have demonstrated that "the integrations can be done and how they are done". In this monograph, we explain how we contribute to achieve the developments suggested by Dr~ze and Richard. A basic idea is to use known properties of the porterior density of the param- eters of the structural form to design the importance functions, i. e. approximations of the posterior density, that are needed for organizing the integrations Economics Economics- Statistics Économie politique Économie politique- Statistiques economics. Economics. Statistics. Print version 9783540133841 Lecture notes in economics and mathematical systems 232