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Checking the coherence of belief specifications

 


tex2html_wrap_inline33790 tex2html_wrap_inline33790 Syntax

BD>coherence : N1, [N2, ...] tex2html_wrap_inline33712

where N1, N2, ..., are the names of elements or bases.

tex2html_wrap_inline33806 tex2html_wrap_inline33806

The intention of this command is to perform coherence checking prior to carrying out an adjustment of a collection B by a collection D. To use the command, it is necessary first that the collection B be prepared for adjustment. That is, B must be currently defined to be the collection being adjusted. This is the case when you have already performed an adjustment, as in

BD>adjust : [B/F] tex2html_wrap_inline33712

Otherwise, a collection can be prepared for adjustment by issuing the command

BD>adjust : [B/] tex2html_wrap_inline33712

Suppose that we gather the elements and bases supplied as arguments to the command into the collection D. The COHERENCE:  command now checks the coherence of the variance matrix specified over B and D jointly.

The effect of the command is essentially to perform the same kind of preliminary coherence check that is ordinarily made when you issue an ADJUST:  type command. See §6.2 for details of specifying collections for the definition part.

The command will be applied typically to checking the coherence of beliefs expressed about second-order exchangeable sequences as outlined in §16.1. Suppose that tex2html_wrap_inline38802 is the tex2html_wrap_inline38804 observation on the vector D. The variance matrices of interest are tex2html_wrap_inline38806 , tex2html_wrap_inline38808 , and U, the difference between them. Usually, U+G and G are specified directly, rather than U and G being specified.

To use the COHERENCE:  command, you must set the infovar  control to point to the belief store containing U+G and the modelvar  control to point to the belief store containing G. One coherence check then is to check that both G and U are nonnegative definite.

Note that, to use the infinite exchangeability representation, the collection formed by B and the mean components of D must have a nonnegative definite joint variance matrix.

To check that a single variance matrix is nonnegative definite, the COHERENCE:  command can be used in exactly the same way, but with the modelvar  and infovar  controls pointing to the same belief store. In such a case the variance matrix for the collection D in the inidicated belief store has its coherence checked.

Data are not taken into account.  


next up previous contents index
Next: Eigendecomposition of a real Up: Miscellaneous numerical commands Previous: Miscellaneous numerical commands

David Wooff
Wed Oct 21 15:14:31 BST 1998