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Accessing the results of adjustments and partial adjustments

 

Consider the following scenario: Suppose that the base tex2html_wrap_inline40230 has been adjusted by the base tex2html_wrap_inline40232 . Occasionally we will be concerned with partial adjustments, and to this purpose for the partial adjustment results we suppose that we adjust initially by the base tex2html_wrap_inline40234 , and then partially by base tex2html_wrap_inline40236 ; and that tex2html_wrap_inline35840 represents the complete adjustment by the base tex2html_wrap_inline40240 . Suppose that the notional sample size is tex2html_wrap_inline40242 potential observations on each element of tex2html_wrap_inline35840 .

Canonical directions
   
tex2html_wrap_inline33790 tex2html_wrap_inline33790 Usage

tex2html_wrap_inline33806 tex2html_wrap_inline33806

The cd  and cd+  options yield the canonical resolutions and directions for the current adjustment. (See [31][section 3.6].) The standard output consists of the resolutions only; and the extended output of the resolutions with the corresponding directions represented as linear combinations of the elements of tex2html_wrap_inline34520 . The directions are uncorrelated and are scaled so that each has prior variance unity. The option is ignored when there is no adjustment.    

Standardised canonical directions
 


tex2html_wrap_inline33790 tex2html_wrap_inline33790 Usage

  • BD>option  cd*  tex2html_wrap_inline33712 switches on standardised canonical direction output.

  • BD>option  -cd*  tex2html_wrap_inline33712 switches off standardised canonical direction output.

  • BD>show  (cd* ) tex2html_wrap_inline33712 displays standardised canonical direction output for the current adjustment.

tex2html_wrap_inline33806 tex2html_wrap_inline33806

The cd*  option yields the standardised canonical resolutions and directions for the current adjustment. The directions are ouput as linear combinations of the elements of tex2html_wrap_inline34520 , standardised such that each element has prior expectation zero and prior variance unity. The directions are uncorrelated and are scaled so that each direction has prior variance unity. The option is ignored when there is no adjustment.  

Adjusted expectations
 


tex2html_wrap_inline33790 tex2html_wrap_inline33790 Usage

  • BD>option  e  tex2html_wrap_inline33712 switches on adjusted expectation output.

  • BD>option  -e  tex2html_wrap_inline33712 switches off adjusted expectation output.

  • BD>show  (e ) tex2html_wrap_inline33712 displays adjusted expectation output for the current adjustment.

tex2html_wrap_inline33806 tex2html_wrap_inline33806

The e  option is used to display the adjusted expectation for every element tex2html_wrap_inline40674 for the current adjustment, tex2html_wrap_inline40676 . It is shown as a linear combination of the elements of the base tex2html_wrap_inline40232 . (See [31][sections 3.1, 3.2].) It is one of the options usable with the VARYSIZE:  command. The e*  option provides the same output in standardised form.  

Standardised adjusted expectations
 


tex2html_wrap_inline33790 tex2html_wrap_inline33790 Usage

  • BD>option  e*  tex2html_wrap_inline33712 switches on standardised adjusted expectation output.

  • BD>option  -e*  tex2html_wrap_inline33712 switches off standardised adjusted expectation output.

  • BD>show  (e* ) tex2html_wrap_inline33712 displays standardised adjusted expectation output for the current adjustment.

tex2html_wrap_inline33806 tex2html_wrap_inline33806

The e*  option is used to display the standardised adjusted expectation for every element tex2html_wrap_inline40674 for the current adjustment, tex2html_wrap_inline40676 . It is shown as a linear combination of the standardised elements of the base tex2html_wrap_inline40232 , standardised so that every element tex2html_wrap_inline40686 has prior expectation zero and variance unity. (See [31][sections 3.1, 3.2].) It is one of the options usable with the VARYSIZE:  command. The e  option provides similar output.  

Adjusted expectations for canonical quantities
 


tex2html_wrap_inline33790 tex2html_wrap_inline33790 Usage

  • BD>option  cde  tex2html_wrap_inline33712 switches on adjusted expectation output for the canonical quantities.

  • BD>option  -cde  tex2html_wrap_inline33712 switches off adjusted expectation output for the canonical quantities.

  • BD>show  (cde ) tex2html_wrap_inline33712 displays adjusted expectation output for the canonical quantities of the current adjustment.

tex2html_wrap_inline33806 tex2html_wrap_inline33806

The cde  option is used to display the adjusted expectation for every canonical quantity for the current adjustment. It is shown as a linear combination of the elements of the base tex2html_wrap_inline40232 . The cde*  option provides the same output in standardised form.  

Standardised adjusted expectations for the canonical quantities
 


tex2html_wrap_inline33790 tex2html_wrap_inline33790 Usage

  • BD>option  cde*  tex2html_wrap_inline33712 switches on standardised adjusted expectation output for the canonical quantities.

  • BD>option  -cde*  tex2html_wrap_inline33712 switches off standardised adjusted expectation output for the canonical quantities.

  • BD>show  (cde* ) tex2html_wrap_inline33712 displays standardised adjusted expectation output for the canonical quantities of the current adjustment.

tex2html_wrap_inline33806 tex2html_wrap_inline33806

The cde*  option is used to display the standardised adjusted expectation for the canonical quantities for the current adjustment, tex2html_wrap_inline40676 . It is shown as a linear combination of the standardised elements of the base tex2html_wrap_inline40232 , standardised so that every element tex2html_wrap_inline40686 has prior expectation zero and variance unity. The cde  option provides similar output.  

Bases subject to the adjustment
 


tex2html_wrap_inline33790 tex2html_wrap_inline33790 Usage

  • BD>option  bases  tex2html_wrap_inline33712 enable the display of base titling for adjustments.

  • BD>option  -bases  tex2html_wrap_inline33712 disable the display of base titling for adjustments.

  • BD>show  (bases ) tex2html_wrap_inline33712 displays the names of the elements and bases involved in the current adjustment.

tex2html_wrap_inline33806 tex2html_wrap_inline33806

The bases  option is used to provide titling and an indication of the base being adjusted and the current fit. It is one of the options usable with the VARYSIZE:  command.  

Maximal canonical directions
   


tex2html_wrap_inline33790 tex2html_wrap_inline33790 Usage

  • BD>option  mcd  tex2html_wrap_inline33712 switches on standard maximal canonical direction output.

  • BD>option  mcd+  tex2html_wrap_inline33712 switches on extended maximal canonical direction output.

  • BD>option  -mcd  tex2html_wrap_inline33712 switches off maximal canonical direction output.

  • BD>show  (mcd ) tex2html_wrap_inline33712 displays standard maximal canonical direction output for the current adjustment.

  • BD>show  (mcd+ ) tex2html_wrap_inline33712 displays extended maximal canonical direction output for the current adjustment.

tex2html_wrap_inline33806 tex2html_wrap_inline33806

The mcd  and mcd+  options yield the maximal canonical resolutions and directions for the current maximal adjustment. The standard output consists of the resolutions only; and the extended output of the resolutions with the corresponding directions represented as linear combinations of the elements of tex2html_wrap_inline34520 . The directions are uncorrelated and are scaled so that each has prior variance unity. The option is ignored when there is no maximal adjustment.    

Standardised maximal canonical directions
 


tex2html_wrap_inline33790 tex2html_wrap_inline33790 Usage

  • BD>option  mcd*  tex2html_wrap_inline33712 switches on standardised maximal canonical direction output.

  • BD>option  -mcd*  tex2html_wrap_inline33712 switches off standardised maximal canonical direction output.

  • BD>show  (mcd* ) tex2html_wrap_inline33712 displays standardised maximal canonical direction output for the current adjustment.

tex2html_wrap_inline33806 tex2html_wrap_inline33806

The mcd*  option yields the standardised maximal canonical resolutions and directions for the current adjustment. The directions are ouput as linear combinations of the elements of tex2html_wrap_inline34520 , standardised such that each element has prior expectation zero and prior variance unity. The directions are uncorrelated and are scaled so that each direction has prior variance unity. The option is ignored when there is no adjustment.  

Maximal resolution matrix
 


tex2html_wrap_inline33790 tex2html_wrap_inline33790 Usage

  • BD>option  mrm  tex2html_wrap_inline33712 switches on maximal resolution matrix output.

  • BD>option  -mrm  tex2html_wrap_inline33712 switches off maximal resolution matrix output.

  • BD>show  (mrm ) tex2html_wrap_inline33712 displays the maximal resolution matrix for the current adjustment.

tex2html_wrap_inline33806 tex2html_wrap_inline33806

The mrm  option is available in the case of exchangeability to display the maximal resolution matrix for the full adjustment. For the full rank case, this is equal to

displaymath40646

 

Partial canonical directions
   


tex2html_wrap_inline33790 tex2html_wrap_inline33790 Usage

  • BD>option  pcd  tex2html_wrap_inline33712 switches on standard partial canonical direction output.

  • BD>option  pcd+  tex2html_wrap_inline33712 switches on extended partial canonical direction output.

  • BD>option  -pcd  tex2html_wrap_inline33712 switches off partial canonical direction output.

  • BD>show  (pcd ) tex2html_wrap_inline33712 displays standard partial canonical direction output for the current adjustment.

  • BD>show  (pcd+ ) tex2html_wrap_inline33712 displays extended partial canonical direction output for the current adjustment.

tex2html_wrap_inline33806 tex2html_wrap_inline33806

The pcd  and pcd+  options yield the partial canonical resolutions and directions for the current partial adjustment. (See [31][section 5.3].) The standard output consists of the resolutions only; and the extended output of the resolutions with the corresponding directions represented as linear combinations of the elements of tex2html_wrap_inline34520 . The directions are uncorrelated and are scaled so that each has prior variance unity. The option is ignored when there is no partial adjustment.    

Standardised partial canonical directions
 


tex2html_wrap_inline33790 tex2html_wrap_inline33790 Usage

  • BD>option  pcd*  tex2html_wrap_inline33712 switches on standardised partial canonical direction output.

  • BD>option  -pcd*  tex2html_wrap_inline33712 switches off standardised partial canonical direction output.

  • BD>show  (pcd* ) tex2html_wrap_inline33712 displays standardised partial canonical direction output for the current adjustment.

tex2html_wrap_inline33806 tex2html_wrap_inline33806

The pcd*  option yields the standardised partial canonical resolutions and directions for the current adjustment. The directions are ouput as linear combinations of the elements of tex2html_wrap_inline34520 , standardised such that each element has prior expectation zero and prior variance unity. The directions are uncorrelated and are scaled so that each direction has prior variance unity. The option is ignored when there is no adjustment.  

Partial resolution matrix
 


tex2html_wrap_inline33790 tex2html_wrap_inline33790 Usage

  • BD>option  prm  tex2html_wrap_inline33712 switches on partial resolution matrix output.

  • BD>option  -prm  tex2html_wrap_inline33712 switches off partial resolution matrix output.

  • BD>show  (prm ) tex2html_wrap_inline33712 displays the partial resolution matrix for the current partial adjustment.

tex2html_wrap_inline33806 tex2html_wrap_inline33806

The prm  option is used to display the partial resolution matrix for a partial adjustment. For the full rank case, this is equal to

displaymath40647

 

Variances for a partial adjustment
 


tex2html_wrap_inline33790 tex2html_wrap_inline33790 Usage

  • BD>option  pv  tex2html_wrap_inline33712 switches on partial adjustment variance output.

  • BD>option  -pv  tex2html_wrap_inline33712 switches off partial adjustment variance output.

  • BD>show  (pv ) tex2html_wrap_inline33712 displays partial adjustment variance output for the current adjustment.

tex2html_wrap_inline33806 tex2html_wrap_inline33806

The pv  option is only available when there is both a previous and a current adjustment, and is not available for the iterative algorithm. It displays the effects of the partial adjustment on several variance and uncertainty quantities. It is one of the options usable with the VARYSIZE:  command.

For every element tex2html_wrap_inline40674 the output consists of the element's name tex2html_wrap_inline35430 ; the adjustment variance for the initial adjustment: tex2html_wrap_inline40730 ; the adjustment variance following the additional adjustment by tex2html_wrap_inline36456 : tex2html_wrap_inline40734 ; the difference between these two quantities, being tex2html_wrap_inline40736 ; the partial resolution tex2html_wrap_inline40738 ; and finally a term amounting to the resolution for the adjusted version of tex2html_wrap_inline35430 given tex2html_wrap_inline34518 for an adjustment by tex2html_wrap_inline40744 : that is, tex2html_wrap_inline40746 . (See [48][section 13]).

Additionally, analagous results for the entire structure tex2html_wrap_inline40748 are shown. These consist of the the name of the structure: tex2html_wrap_inline40748 ; the uncertainty in tex2html_wrap_inline40748 unresolved after the initial adjustment: tex2html_wrap_inline40754 ; the uncertainty in tex2html_wrap_inline40748 unresolved after the full adjustment: tex2html_wrap_inline40758 ; the difference between these two uncertainties, being tex2html_wrap_inline40760 ; the partial system resolution tex2html_wrap_inline40762 ; and the resolution for the adjusted version tex2html_wrap_inline40764 for the adjustment by tex2html_wrap_inline40744 , being tex2html_wrap_inline40768 .  

Resolution partition
 


tex2html_wrap_inline33790 tex2html_wrap_inline33790 Usage

  • BD>option  rp  tex2html_wrap_inline33712 switches on resolution partition output.

  • BD>option  -rp  tex2html_wrap_inline33712 switches off resolution partition output.

  • BD>show  (rp ) tex2html_wrap_inline33712 displays the resolution partition for the current adjustment.

tex2html_wrap_inline33806 tex2html_wrap_inline33806

For every element tex2html_wrap_inline40674 the output given by the rp  option shows the contribution made by each canonical direction to the resolution of tex2html_wrap_inline35430 . That is, suppose that there are g canonical directions tex2html_wrap_inline40774 and that the canonical resolutions are tex2html_wrap_inline40776 . Then we can write

displaymath40648

and we take the quantity tex2html_wrap_inline41052 to be the contribution in the tex2html_wrap_inline34732 direction. The rp  control can be used to limit the number of contributory directions. The rp  operator can be used to access individual contributions.  

Element with canonical quantity covariances
 


tex2html_wrap_inline33790 tex2html_wrap_inline33790 Usage

  • BD>option  lccd  tex2html_wrap_inline33712 switches on element/canonical quantity covariance output.

  • BD>option  -lccd  tex2html_wrap_inline33712 switches off element/canonical quantity covariance output.

  • BD>show  (lccd ) tex2html_wrap_inline33712 displays the element/canonical quantity covariance output for the current adjustment.

tex2html_wrap_inline33806 tex2html_wrap_inline33806

The lccd  option is used to display covariances between the elements of the collection B being adjusted, and the canonical quantities for the adjustment.  

Adjustment summary
 


tex2html_wrap_inline33790 tex2html_wrap_inline33790 Usage

  • BD>option  ru  tex2html_wrap_inline33712 switches on adjustment summary output.

  • BD>option  -ru  tex2html_wrap_inline33712 switches off adjustment summary output.

  • BD>show  (ru ) tex2html_wrap_inline33712 displays the adjustment summary for the current adjustment.

tex2html_wrap_inline33806 tex2html_wrap_inline33806

The ru  option is used to display a one-line summary of the current fit. The potential sample size is reported together with the resolved uncertainty for the system, tex2html_wrap_inline38364 ; the resolution for the system, tex2html_wrap_inline37648 (expressed as a percentage); and the initial uncertainty for the system, tex2html_wrap_inline40794 . It is one of the options usable with the VARYSIZE:  command.  

Resolution matrix
 


tex2html_wrap_inline33790 tex2html_wrap_inline33790 Usage

  • BD>option  rm  tex2html_wrap_inline33712 switches on resolution matrix output.

  • BD>option  -rm  tex2html_wrap_inline33712 switches off resolution matrix output.

  • BD>show  (rm ) tex2html_wrap_inline33712 displays the resolution matrix for the current adjustment.

tex2html_wrap_inline33806 tex2html_wrap_inline33806

The rm  option is used to display the (generally asymmetric) resolution matrix for the full adjustment. For the full rank case, this is equal to

displaymath40649

 

Variances for the adjustment
   


tex2html_wrap_inline33790 tex2html_wrap_inline33790 Usage

  • BD>option  v  tex2html_wrap_inline33712 switches on standard adjustment variance output.

  • BD>option  v+  tex2html_wrap_inline33712 switches on extended adjustment variance output.

  • BD>option  -v  tex2html_wrap_inline33712 switches off adjustment variance output.

  • BD>show  (v ) tex2html_wrap_inline33712 displays standard adjustment variance output for the current adjustment.

  • BD>show  (v+ ) tex2html_wrap_inline33712 displays extended adjustment variance output for the current adjustment.

tex2html_wrap_inline33806 tex2html_wrap_inline33806

The v  and v+  options display information about the variances for the current adjustment. For each element tex2html_wrap_inline40674 the standard output displays the name of the element and its current adjusted variance, tex2html_wrap_inline40734 . The extended output also displays its resolved variance, tex2html_wrap_inline40808 ; and its resolution tex2html_wrap_inline40810 . In the case of exchangeability, also given is the maximal resolution for tex2html_wrap_inline35430 , tex2html_wrap_inline40814 (representing the maximum resolution possible with an essentially infinite sample size). (See [31][section 3.3].)

In addition various uncertainties for the overall belief structure tex2html_wrap_inline40748 are presented. These are the name of the structure being adjusted; its prior, unresolved and resolved uncertainty respectively ( tex2html_wrap_inline40794 , tex2html_wrap_inline40758 , and tex2html_wrap_inline38364 ); and its current system resolution, tex2html_wrap_inline37648 . In the case of exchangeability, also shown is the system maximal resolution, tex2html_wrap_inline40826 . (See [31][section 3.7] and [48][section 10.3].)

The v  option can be used in both standard and extended modes as one of the options usable with the VARYSIZE:  command.    


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Next: Accessing the results of Up: Output options Previous: Setting options

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