Consider the following scenario: Suppose that 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 , and then partially by base ; and that represents the complete adjustment by the base . Suppose that the notional sample size is potential observations on each element of .
BD>option cd
switches on standard canonical
direction output.
BD>option cd+
switches on extended canonical
direction output.
BD>show (cd )
displays standard canonical direction output for
the current adjustment.
BD>show (cd+ )
displays extended canonical direction output for
the current adjustment.
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 . The
directions are uncorrelated and are scaled so that each has prior
variance unity. The option is ignored when there is no adjustment.
BD>option cd*
switches on standardised canonical
direction output.
BD>option -cd*
switches off standardised canonical
direction output.
BD>show (cd* )
displays standardised
canonical direction output for the current adjustment.
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 , 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.
The e option is used to display the adjusted expectation for every
element for the current adjustment, . 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.
BD>option e*
switches on standardised adjusted
expectation output.
BD>option -e*
switches off standardised adjusted
expectation output.
BD>show (e* )
displays standardised
adjusted expectation output for the current adjustment.
The e* option is used to display the standardised adjusted
expectation for every element for the current
adjustment, . It is shown as a linear combination of the
standardised elements of the base , 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.
BD>option cde
switches on adjusted expectation
output for the canonical quantities.
BD>option -cde
switches off adjusted expectation
output for the canonical quantities.
BD>show (cde )
displays adjusted
expectation output for the canonical quantities of the current adjustment.
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 . The
cde* option provides the same output in standardised form.
BD>option cde*
switches on standardised adjusted
expectation output for the canonical quantities.
BD>option -cde*
switches off standardised adjusted
expectation output for the canonical quantities.
BD>show (cde* )
displays standardised
adjusted expectation output for the canonical quantities of the current adjustment.
The cde* option is used to display the standardised adjusted
expectation for the canonical quantities for the current
adjustment, . It is shown as a linear combination of the
standardised elements of the base , standardised so
that every element has prior expectation zero and
variance unity. The cde option
provides similar output.
BD>option bases
enable the display of base
titling for adjustments.
BD>option -bases
disable the display of base
titling for adjustments.
BD>show (bases )
displays the names
of the elements and bases involved in the current
adjustment.
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
switches on standard maximal canonical
direction output.
BD>option mcd+
switches on extended maximal
canonical direction output.
BD>option -mcd
switches off maximal canonical
direction output.
BD>show (mcd )
displays standard maximal canonical direction
output for the current adjustment.
BD>show (mcd+ )
displays extended maximal canonical direction
output for the current adjustment.
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 . The directions
are uncorrelated and are scaled so that each has prior variance unity.
The option is ignored when there is no maximal adjustment.
BD>option mcd*
switches on standardised maximal
canonical direction output.
BD>option -mcd*
switches off standardised maximal
canonical direction output.
BD>show (mcd* )
displays standardised
maximal canonical direction output for the current adjustment.
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 ,
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.
BD>option -mrm
switches off maximal resolution matrix
output.
BD>show (mrm )
displays the maximal resolution matrix for
the current adjustment.
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
switches on standard partial canonical
direction output.
BD>option pcd+
switches on extended partial
canonical direction output.
BD>option -pcd
switches off partial canonical
direction output.
BD>show (pcd )
displays standard partial
canonical direction output for the current adjustment.
BD>show (pcd+ )
displays extended partial
canonical direction output for the current adjustment.
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 . The directions are uncorrelated and are scaled
so that each has prior variance unity. The option is ignored when there
is no partial adjustment.
BD>option pcd*
switches on standardised partial
canonical direction output.
BD>option -pcd*
switches off standardised partial
canonical direction output.
BD>show (pcd* )
displays standardised
partial canonical direction output for the current adjustment.
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 ,
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.
BD>option -prm
switches off partial
resolution matrix output.
BD>show (prm )
displays the partial resolution matrix for
the current partial adjustment.
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
switches on partial adjustment variance
output.
BD>option -pv
switches off partial adjustment
variance output.
BD>show (pv )
displays partial adjustment
variance output for the current adjustment.
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 the output consists of the
element's name ; the adjustment variance for the initial
adjustment: ; the adjustment variance following the
additional adjustment by : ; the difference between
these two quantities, being ; the partial resolution
; and finally a term amounting to the resolution for the
adjusted version of given for an adjustment by :
that is, . (See [48][section 13]).
Additionally, analagous results for the entire structure are
shown. These consist of the the name of the structure: ; the
uncertainty in unresolved after the initial adjustment:
; the uncertainty in unresolved after the full
adjustment: ; the difference between these two uncertainties,
being ; the partial system resolution ; and
the resolution for the adjusted version for the adjustment by
, being .
For every element 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 and that the canonical resolutions are
. Then we can write
and we take the quantity 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.
BD>option lccd
switches on element/canonical
quantity covariance output.
BD>option -lccd
switches off
element/canonical quantity covariance
output.
BD>show (lccd )
displays the
element/canonical
quantity
covariance
output for the current adjustment.
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 resolution 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.
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
switches on standard adjustment variance
output.
BD>option v+
switches on extended adjustment
variance output.
BD>show (v )
displays standard adjustment
variance output for the current adjustment.
BD>show (v+ )
displays extended
adjustment variance output for the current adjustment.
The v and v+ options display information about the variances for the current
adjustment. For each element the standard output displays
the name of the element and its current adjusted variance, .
The extended output also displays its resolved variance,
; and its resolution .
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].)
In addition various uncertainties for the overall belief structure
are presented. These are the name of the structure being
adjusted; its prior, unresolved and resolved uncertainty respectively
( , , and ); and its current system
resolution, . In the case of exchangeability, also shown is
the system maximal resolution, . (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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