By L. Bauwens
In their evaluate of the "Bayesian research of simultaneous equation systems", Dr~ze and Richard (1983) - hereafter DR - convey the subsequent standpoint in regards to the current kingdom of improvement of the Bayesian complete info research of such sys tems i) the tactic permits "a versatile specification of the previous density, together with good outlined noninformative previous measures"; ii) it yields "exact finite pattern posterior and predictive densities". although, they demand additional advancements in order that those densities might be eval uated via 'numerical tools, utilizing an built-in software program packa~e. subsequently, they suggest using a Monte Carlo process, due to the fact van Dijk and Kloek (1980) have confirmed that "the integrations will be performed and the way they're done". during this monograph, we clarify how we give a contribution to accomplish the advancements instructed through Dr~ze and Richard. A simple concept is to exploit recognized houses of the porterior density of the param eters of the structural shape to layout the significance features, i. e. approximations of the posterior density, which are wanted for organizing the integrations.
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Extra info for Bayesian Full Information Analysis of Simultaneous Equation Models Using Integration by Monte Carlo
3) The gain in precision obtained by the 2 round procedures applied to STUD, PTST-l and PTST-2 (see the comments following Table 2) seems worthwhile as is shown by the decrease of the value of the estimated coefficient of variation of the reciprocal of the integrating constant of the posterior density. 73 This is not the case with PTFC and PTDC. 4) The posterior results reported in Table 2 differ slip,htly from those reported by Richard (1973, p. 205). 1 They indicate that our results underestimate Richards's ones, in absolute value.
Moreover, there exist almost certainly values of the points of truncation for which the posterior results will be identical under the two approaches (with the same v o). Clearly, each approach has some degree of arbitrariness: the value of vo' the ranges of the parameters. or In any case, it would be wise to check the sensitivity 44 of the posterior results with respect to these values, if the model were to be used for decision purposes. Table 4 contains the results, in the same presentation as Table 2.
The generation of random drawings from a Student density is discussed in Appendix A. 9) f(o) m n i=l p (Oi I or = dr) where dr is obtained from d, the posterior mode, as 0 i from O. portance function PTFC (for Poly-t, Fixed Conditions). We call this im- It is clearly a product of independent densities for each 0i since the conditioning values are selected once for all. ~ ), for each i. An algorithm to obtain random drawings from 1 - 1 poly-t densities is given in Appendix A. 9), the mode of that density will be usually close to that of p(o), in view of the stated choice of the conditioning values.