Multinormal Bayesian Analysis Two Examples

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Multinormal Bayesian Analysis Two Examples
J J James John Martin
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3w, 0. 3w.
12 0. 3w.
(91) 21 22 "--"21 "•-"22 It is clear that, in general, a set of («, w, ^, W22) cannot be found which will satisfy (91) exactly. One possible method of procedure is to choose the set (w, ,, ^1?^ ^22^ ^° ^^ ^° minimize the sum of the squared differences of corresponding elements on the left and right sides of equation (91). Another method is to select three independent equations from the matrix equation (91), solve for the w. . , and, if the variances and covariances of n in^
...lied by this particular set of w. . Are sufficiently close to U use this set. We shall follow ij ' = this latter method for reasons of computational simplicity. For any particular problem, the terminal cost structure will have bearing upon the best way in which to determine V' .
Here, we assume var[a^^] 11 0. 0025 = 0. 9v 44 '14 var[a, ] = 0. 01 '22 0. 3w 22 cov[aj^j^, a22] = 0. 0007 = 0. 2w 12 25 which yields r. -l and 0. 00278 0. 003501 [o. 00350 O. O3333J 4 V' = r415. 0 -43. 6 [_- A3. 6 34 Suppose now that the following data is collected for the years 1955-1958 (details of the way in which this sample was constructed are presented in (92) Appendix B) .


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