By J.-A. Morales (auth.)

ISBN-10: 3540054170

ISBN-13: 9783540054177

ISBN-10: 3642651968

ISBN-13: 9783642651960

Read or Download Bayesian Full Information Structural Analysis: with an Application to the Study of the Belgian Beef Market PDF

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Extra resources for Bayesian Full Information Structural Analysis: with an Application to the Study of the Belgian Beef Market

Sample text

33. will converge if e > max (2p +n -1, 2q +n -3). e > a' +n -1, since 2p + 2q This condition is fulfilled if = a'e 7. The results above can be generalized for the case m > 2. Those generalizations are shown below with the normalization rule ~ .. l. i = l,2, ••• ,m. The argument is similar for other norma- lizations. "'Ym) is the number of transpositions required to change (1,2, ••• ,p) into (y l ,y 2 , ••• ,Y p ). 1 The determinant IBI expression of degree with power at at can be expanded in a polynomial in the elements of b.

1 6. 31. is dominated by lSee Appendix, section A for the properties of the Wishart density function. ) m+l since -}2 1'I'-1 1 {~. l. 32. 33. will converge if e > max (2p +n -1, 2q +n -3). e > a' +n -1, since 2p + 2q This condition is fulfilled if = a'e 7. The results above can be generalized for the case m > 2. Those generalizations are shown below with the normalization rule ~ .. l. i = l,2, ••• ,m. The argument is similar for other norma- lizations. "'Ym) is the number of transpositions required to change (1,2, ••• ,p) into (y l ,y 2 , ••• ,Y p ).

00, l. l. = o~l. 0k for k ~ i. l. lroximately Normal, with mean t~o. l. 15. ' _ ~(t-t ° )'(8 -~ II' )( t-t ° ) denotes "approximately proportional" and t and to denote the column expansions of T' and TO I respectively. 16. t33 ••••• tmm/tik- tik cr = 0. 2 •••• ,m, i~k) 1 E - s ij (t .. °. )'Mo.. ( t .. -t ° exp - -2 .. )• . 17. t22 ••••• tmm' with means t~1't~2 ••••• t~, and covariance - 0 -1 • matr1x y • This completes the argument. 4. is a proper density function. 1. This lemma allows us also to represent the integral of the density of the parameters in B as a mixture of marginal moments of B, provided that they exist.