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Partial adjustment of beliefs

Suppose that we intend to adjust our beliefs about a collection tex2html_wrap_inline3600 by observation of two further collections tex2html_wrap_inline3598 and tex2html_wrap_inline4368 of quantities. We adjust B by the collection tex2html_wrap_inline4370 (i.e. the collection tex2html_wrap_inline4372 ) but separate the effects of the subsets of data. Therefore, we adjust B in stages, first by D, then adding F. We may show that the additional adjustment of B by F, given that we have already adjusted by D, is the same as the adjustment of B by tex2html_wrap_inline4374 , the belief structure tex2html_wrap_inline4376 adjusted by tex2html_wrap_inline3968 :

  equation881

(This relation follows as adjusting F by D removes the `common variability' between F and D.) We call

displaymath4362

the (partial) adjustment of B by F given D. Note the following properties of partial adjustment.

  1. equation894

  2. equation898

  3. equation906

  4. eqnarray908



David Wooff
Thu Oct 15 11:56:54 BST 1998