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

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.