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

ISBN-13: 9783540133841 / Angielski / Miękka / 1984 / 114 str.

L. Bauwens

Opis

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.

Spis treści

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.2.1. Properties of the posterior density of ?.- III.2.2. Student importance function (STUD).- III.2.3. Poly-t based importance function: Case I (PTFC).- III.2.4. Poly-t based importance function: Case II (PTDC).- III.2.5. Poly-t based importance function: Case III (PTST).- III.2.6. Conclusion.- III.3 The AI(?) approach.- IV. Report and Discussion of Experiments.- IV.1 Report.- IV.1.1. BBM.- IV.1.2. Johnston.- IV.1.3. Klein.- IV.1.4. EX.- IV.1.5. W.- 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 < m ? 2) poly-t distribution.- Appendix B: The Technicalities of Chapter III.- B.I Definition of the parameters of (3.3) and (3.6).- B.II Computation of the posterior mode of ?.- B.III Computation of (3.15).- Appendix C: Plots of Posterior Marginal Densities And of Importance Functions.- Appendix D: The Computer Program.- Footnotes.- References.