 
  
  
  
  
 
Consider the following scenario: Suppose that the base   has
been adjusted by the base
  has
been adjusted by the base   . 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
 . 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
  , and then partially by base
 , and then partially by base   ; and that
 ; and that   represents the complete adjustment by the base
 
represents the complete adjustment by the base   . Suppose
that the notional sample size is
 . Suppose
that the notional sample size is   potential observations on each
element of
  potential observations on each
element of   .
 .
 
 
  Usage
  Usage BD>option  cd 
  BD>option  cd+ 
  BD>show  (cd )
  BD>show  (cd+ )
  
 
 
  
 
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   
 
 BD>option  cd* 
  BD>option  -cd* 
  BD>show  (cd* )
  
 
 
  
 
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   
 
 
 
  
 
The e  option is used to display the adjusted expectation for every
element   
 
 BD>option  e* 
  BD>option  -e* 
  BD>show  (e* )
  
 
 
  
 
The e*  option is used to display the standardised adjusted
expectation for every element   
 
 BD>option  cde 
  BD>option  -cde 
  BD>show  (cde )
  
 
 
  
 
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   
 
 BD>option  cde* 
  BD>option  -cde* 
  BD>show  (cde* )
  
 
 
  
 
The cde*  option is used to display the standardised adjusted
expectation  for the canonical quantities for the current
adjustment,   
 
 BD>option  bases 
  BD>option  -bases 
  BD>show  (bases )
  
 
 
  
 
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.
 
 
 
 BD>option  mcd 
  BD>option  mcd+ 
  BD>option  -mcd 
  BD>show  (mcd )
  BD>show  (mcd+ )
  
 
 
  
 
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   
 
 BD>option  mcd* 
  BD>option  -mcd* 
  BD>show  (mcd* )
  
 
 
  
 
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   
 
 BD>option  -mrm 
  BD>show  (mrm )
  
 
 
  
 
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
 
   
 
 BD>option  pcd 
  BD>option  pcd+ 
  BD>option  -pcd 
  BD>show  (pcd )
  BD>show  (pcd+ )
  
 
 
  
 
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   
 
 BD>option  pcd* 
  BD>option  -pcd* 
  BD>show  (pcd* )
  
 
 
  
 
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   
 
 BD>option  -prm 
  BD>show  (prm )
  
 
 
  
 
The prm  option is used to display the partial resolution matrix
for a partial adjustment. For the full rank case, this is equal to
   
 
 BD>option  pv 
  BD>option  -pv 
  BD>show  (pv )
  
 
 
  
 
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   
Additionally, analagous results for the entire structure   
 
 
 
  
 
For every element   
   
 
and we take the quantity   
 
 BD>option  lccd 
  BD>option  -lccd 
  BD>show  (lccd )
  
 
 
  
The lccd  option is used to display covariances between the
elements of the collection B being adjusted, and the canonical
quantities for the adjustment.
 
 
 
 
 
  
 
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,   
 
 
 
  
 
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
 
   
 
 BD>option  v 
  BD>option  v+ 
  BD>show  (v )
  BD>show  (v+ )
  
 
 
  
 
The v  and v+  options display information about the variances for the current
adjustment. For each element   
In addition various uncertainties for the overall belief structure
  
The v  option can be used in both standard and extended modes as
one of the options usable with the VARYSIZE:  command.
 
 
 
  switches on standard  canonical
direction output.
  switches on standard  canonical
direction output.
 switches on extended canonical
direction output.
  switches on extended canonical
direction output.
 displays standard canonical direction output for
the current adjustment.
  displays standard canonical direction output for
the current adjustment.
 displays extended canonical direction output for
the current adjustment.
  displays extended canonical direction output for
the current adjustment.
 
    
   . The
directions are uncorrelated and are scaled so that each has prior
variance unity. The option is ignored when there is no adjustment.
 . The
directions are uncorrelated and are scaled so that each has prior
variance unity. The option is ignored when there is no adjustment.
   
 
  
 
  Usage
  Usage  switches on standardised canonical
direction output.
  switches on standardised canonical
direction output.
 switches off  standardised canonical
direction output.
  switches off  standardised canonical
direction output.
 displays  standardised
canonical direction output for the current adjustment.
  displays  standardised
canonical direction output for the current adjustment.
 
    
   , 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.
 , 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.
 
 
  
 
  Usage
  Usage  
    
   for the current adjustment,
  for the current adjustment,   . It is shown
as a linear combination of the elements of the base
 . It is shown
as a linear combination of the elements of the base   . (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.
 . (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.
 
 
  
 
  Usage
  Usage  switches on standardised adjusted
expectation output.
  switches on standardised adjusted
expectation output.
 switches off standardised adjusted
expectation output.
  switches off standardised adjusted
expectation output.
 displays standardised
adjusted expectation output for the current adjustment.
  displays standardised
adjusted expectation output for the current adjustment.
 
    
   for the current
adjustment,
  for the current
adjustment,   . It is shown as a linear combination of the
standardised elements of the base
 . It is shown as a linear combination of the
standardised elements of the base   , standardised so
that every element
 , standardised so
that every element   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.
  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.  
 
  
 
  Usage
  Usage  switches on adjusted expectation
output for the canonical quantities.
  switches on adjusted expectation
output for the canonical quantities.
 switches off adjusted expectation
output for the canonical quantities.
  switches off adjusted expectation
output for the canonical quantities.
 displays adjusted
expectation output  for the canonical quantities of the current adjustment.
  displays adjusted
expectation output  for the canonical quantities of the current adjustment.
 
    
   . The
cde*  option provides the same output in standardised form.
 . The
cde*  option provides the same output in standardised form.
 
 
  
 
  Usage
  Usage  switches on standardised adjusted
expectation output for the canonical quantities.
  switches on standardised adjusted
expectation output for the canonical quantities.
 switches off standardised adjusted
expectation output for the canonical quantities.
  switches off standardised adjusted
expectation output for the canonical quantities.
 displays standardised
adjusted expectation output  for the canonical quantities of the current adjustment.
  displays standardised
adjusted expectation output  for the canonical quantities of the current adjustment.
 
    
   . It is shown as a linear combination of the
standardised elements of the base
 . It is shown as a linear combination of the
standardised elements of the base   , standardised so
that every element
 , standardised so
that every element   has prior expectation zero and
variance unity. The cde  option
provides similar output.
  has prior expectation zero and
variance unity. The cde  option
provides similar output.  
 
  
 
  Usage
  Usage  enable the display of base
titling for adjustments.
  enable the display of base
titling for adjustments.
 disable the display of base
titling for adjustments.
  disable the display of base
titling for adjustments.
 displays the names
of the elements and bases involved in the current
adjustment.
  displays the names
of the elements and bases involved in the current
adjustment.
 
    
  
 
  
 
  Usage
  Usage  switches on standard maximal canonical
direction output.
  switches on standard maximal canonical
direction output.
 switches on extended maximal
canonical direction output.
  switches on extended maximal
canonical direction output.
 switches off maximal canonical
direction output.
  switches off maximal canonical
direction output.
 displays standard maximal canonical direction
output for the current adjustment.
  displays standard maximal canonical direction
output for the current adjustment.
 displays extended maximal canonical direction
output for the current adjustment.
  displays extended maximal canonical direction
output for the current adjustment.
 
    
   . The directions
are uncorrelated and are scaled so that each has prior variance unity.
The option is ignored when there is no maximal adjustment.
 . The directions
are uncorrelated and are scaled so that each has prior variance unity.
The option is ignored when there is no maximal adjustment.  
 
 
  
 
  Usage
  Usage  switches on standardised maximal
canonical direction output.
  switches on standardised maximal
canonical direction output.
 switches off  standardised maximal
canonical direction output.
  switches off  standardised maximal
canonical direction output.
 displays  standardised
maximal canonical direction output for the current adjustment.
  displays  standardised
maximal canonical direction output for the current adjustment.
 
    
   ,
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.
 ,
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.  
 
  
 
  Usage
  Usage  switches off maximal resolution matrix
output.
  switches off maximal resolution matrix
output.
 displays the maximal resolution matrix for
the current adjustment.
  displays the maximal resolution matrix for
the current adjustment.
 
    
   
 
 
  
 
  Usage
  Usage  switches on standard partial canonical
direction output.
  switches on standard partial canonical
direction output.
 switches on extended partial
canonical direction output.
  switches on extended partial
canonical direction output.
 switches off partial canonical
direction output.
  switches off partial canonical
direction output.
 displays standard partial
canonical direction output for the current adjustment.
  displays standard partial
canonical direction output for the current adjustment.
 displays extended partial
canonical direction output for the current adjustment.
  displays extended partial
canonical direction output for the current adjustment.
 
    
   . The directions are uncorrelated and are scaled
so that each has prior variance unity. The option is ignored when there
is no partial adjustment.
 . The directions are uncorrelated and are scaled
so that each has prior variance unity. The option is ignored when there
is no partial adjustment.    
 
  
 
  Usage
  Usage  switches on standardised partial
canonical direction output.
  switches on standardised partial
canonical direction output.
 switches off  standardised partial
canonical direction output.
  switches off  standardised partial
canonical direction output.
 displays  standardised
partial canonical direction output for the current adjustment.
  displays  standardised
partial canonical direction output for the current adjustment.
 
    
   ,
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.
 ,
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.  
 
  
 
  Usage
  Usage  switches off partial
resolution matrix output.
  switches off partial
resolution matrix output.
 displays the partial resolution matrix for
the current partial adjustment.
  displays the partial resolution matrix for
the current partial adjustment.
 
    
   
 
 
  
 
  Usage
  Usage  switches on partial adjustment variance
output.
  switches on partial adjustment variance
output.
 switches off partial adjustment
variance output.
  switches off partial adjustment
variance output.
 displays partial adjustment
variance output for the current adjustment.
  displays partial adjustment
variance output for the current adjustment.
 
    
   the output consists of the
element's name
  the output consists of the
element's name   ; the adjustment variance for the initial
adjustment:
 ; the adjustment variance for the initial
adjustment:   ; the adjustment variance following the
additional adjustment by
 ; the adjustment variance following the
additional adjustment by   :
 :   ; the difference between
these two quantities, being
 ; the difference between
these two quantities, being   ; the partial resolution
 ; the partial resolution
  ; and finally a term amounting to the resolution for the
adjusted version of
 ; and finally a term amounting to the resolution for the
adjusted version of   given
  given   for an adjustment by
  for an adjustment by   :
that is,
 :
that is,   . (See [48][section 13]).
 . (See [48][section 13]).
 are
shown. These consist of the the name of the structure:
  are
shown. These consist of the the name of the structure:   ; the
uncertainty in
 ; the
uncertainty in   unresolved after the initial adjustment:
  unresolved after the initial adjustment:
  ; the uncertainty in
 ; the uncertainty in   unresolved after the full
adjustment:
  unresolved after the full
adjustment:   ; the difference between these two uncertainties,
being
 ; the difference between these two uncertainties,
being   ; the partial system resolution
 ; the partial system resolution   ; and
the resolution for the adjusted version
 ; and
the resolution for the adjusted version   for the adjustment by
  for the adjustment by
  , being
 , being   .
 .
 
 
  
 
  Usage
  Usage  
    
   the output given by the rp 
option shows the contribution made by each canonical direction to the
resolution of
  the output given by the rp 
option shows the contribution made by each canonical direction to the
resolution of   . That is, suppose that there are g canonical
directions
 . That is, suppose that there are g canonical
directions   and that the canonical resolutions are
  and that the canonical resolutions are
  . Then we can write
 . Then we can write
 
  to be
the contribution in the
  to be
the contribution in the   direction. The rp  control can
be used to limit the number of contributory directions. The rp 
operator can be used to access individual contributions.
  direction. The rp  control can
be used to limit the number of contributory directions. The rp 
operator can be used to access individual contributions.
 
 
  
 
  Usage
  Usage  switches on element/canonical
quantity covariance output.
  switches on element/canonical
quantity covariance output.
 switches off
element/canonical quantity covariance
output.
  switches off
element/canonical quantity covariance
output.
 displays the
element/canonical
quantity
 covariance
output for the current adjustment.
  displays the
element/canonical
quantity
 covariance
output for the current adjustment.
 
    
  
 
  
 
  Usage
  Usage  
    
   ; the resolution for
the system,
 ; the resolution for
the system,   (expressed as a percentage); and the initial
uncertainty for the system,
  (expressed as a percentage); and the initial
uncertainty for the system,   . It is one of the options usable with the VARYSIZE:  command.
 . It is one of the options usable with the VARYSIZE:  command.
 
 
  
 
  Usage
  Usage  
    
   
 
 
  
 
  Usage
  Usage  switches on standard adjustment variance
output.
  switches on standard adjustment variance
output.
 switches on extended adjustment
variance output.
  switches on extended adjustment
variance output.
 displays standard adjustment
variance output for the current adjustment.
  displays standard adjustment
variance output for the current adjustment.
 displays extended
adjustment variance output for the current adjustment.
  displays extended
adjustment variance output for the current adjustment.
 
    
   the standard output displays
the name of the element and its current adjusted variance,
  the standard output displays
the name of the element and its current adjusted variance,   .
The extended output also displays its resolved variance,
 .
The extended output also displays its resolved variance,
  ; and its resolution
 ; and its resolution   .
In the case of exchangeability, also given is the maximal resolution for
 .
In the case of exchangeability, also given is the maximal resolution for
  ,
 ,   (representing
the maximum resolution possible with an essentially infinite sample
size). (See [31][section 3.3].)
  (representing
the maximum resolution possible with an essentially infinite sample
size). (See [31][section 3.3].)
 are presented. These are the name of the structure being
adjusted; its prior, unresolved and resolved uncertainty respectively
(
  are presented. These are the name of the structure being
adjusted; its prior, unresolved and resolved uncertainty respectively
(  ,
 ,   , and
 , and   ); and its current system
resolution,
 ); and its current system
resolution,   . In the case of exchangeability, also shown is
the system  maximal resolution,
 . In the case of exchangeability, also shown is
the system  maximal resolution,   . (See [31][section 3.7] and
[48][section 10.3].)
 . (See [31][section 3.7] and
[48][section 10.3].)
 
  
  
  
 