Accessing the results of an adjustment

 

Consider the following scenario: Suppose that base has been adjusted by base and that we might observe (otherwise, data-related results are not available).

Adjusted expectation

 

Usage

• aex  operator; one argument N in parenthesis. N is the name of an element.

The value returned is the current evaluation of the adjusted expectation for any newly adjusted element N. For example, suppose that element N is contained in base . Then . See [31, sections 3.1, 4,].  

Adjusted covariance

 

Usage

• ac  operator; two arguments and in parenthesis, and separated by a comma. and are elements.

The value returned is the current adjusted covariance between any two newly adjusted elements and . For example, suppose that and are contained in base . Then

See [31, section 3.3,]. See also the av  operator if only variances are required.

If comprises the elements , and is some k-dimensional vector, and if we define the matrix , then the adjusted variance of is

and is the adjusted belief structure. Note also that

where the 's are the canonical resolutions for the adjustment (these are obtainable using the [B/D] operator ), and where is the corresponding eigenvector (which may be retained using the cd  argument to the KEEP:  command). The diagonal values are what you see if you issue the command SHOW:  (v ).  

Adjusted variance

 

Usage

• av  operator; one argument in parenthesis. is the name of an element.

the value returned is the current adjusted variance for the newly adjusted element . for example, suppose that is contained in base . then . see [31, section 3.3,]. this operator is shorthand for the ac  operator with the same two arguments. that is, is equivalent to .  

Size of the adjustment

 

Usage

• size  operand.

If data is available, the size of an adjustment (the variance of the bearing for the adjustment) is returned, that is . See [31, section 4.4,].  

Discrepancy for the adjustment

 

Usage

• dvsize  operand.

If data is available, the discrepancy for an adjustment (the largest squared change in expectation, relative to the amount of prior variation removed) is returned, that is .  

Last kind of adjustment

 

Usage

• lasttype  operand.

This returns a signed integer according to the last type of adjustment:

-1

An adjustment involving deletion of elements from , with no data observed.

1

An adjustment involving addition of elements to , with no data observed.

-2

An adjustment involving deletion of elements from , with data observed.

2

An adjustment involving addition of elements to , with data observed.

Thus, the sign of the value given indicates whether the command had involved addition to or deletion from ; and the absolute value of the integer indicates whether observations were available or not.  

Rank of prior variance matrix

 

Usage

• rank  operand.

This returns , the rank of the prior variance matrix for the collection being adjusted.  

Maximal resolution matrix rank

 

Usage

• mrmrank  operand.

This returns : the rank of the maximal resolution matrix, being the number of maximal canonical directions corresponding to non-zero maximal canonical resolutions. This quantity is available only when an adjustment involving exchangeable beliefs has been performed.  

Maximal resolution matrix trace

 

Usage

• mrmtr  operand.

This returns , the trace of the maximal resolution matrix, equal to the sum of the maximal canonical resolutions. This quantity is available only when an adjustment involving exchangeable beliefs has been performed.  

Kind of adjustment

 

Usage

• adjhist  operand.

This returns one of three integers according to the type of adjustment performed:

1

is returned if a single adjustment has occurred.

2

is returned if an initial adjustment followed by a partial adjustment has occurred, and where the partial adjustment is null. In such situations, the partial resolution matrix is null.

3

is returned if an initial adjustment followed by a partial adjustment has occurred, and where the partial adjustment is non-null.

 

Resolution matrix rank

 

Usage

• rmrank  operand.

This returns : the rank of the resolution matrix, being the number of canonical directions corresponding to non-zero canonical resolutions. See [31, sections 3.6,3.7,].  

Resolution matrix trace

 

Usage

• rmtr  operand.

This returns , the trace of the resolution matrix, equal to the sum of the canonical resolutions. See [31, sections 3.6, 3.7,].  

Canonical resolutions

 

Usage

• cr  operator; one argument i in parenthesis. i is any valid equation, rounded to the nearest integer.

This returns the ith largest canonical resolution. It is an error if the index i is smaller than one or greater than the rank of the resolution matrix (obtainable as the operand rmrank ). For example, suppose that is the 4th canonical direction for the adjustment of by . Then . See [31, section 3.6,]  

Resolution partition

 

Usage

• rp  operator; two operands, N followed by E, in parenthesis and separated by a comma. N is the name of an element. E is any valid equation. The result of the equation, when rounded, should be a positive integer i.

This returns the contribution to resolution in element N offered by the canonical direction. (See the rp  control for additional information.) It is an error if the index i is smaller than one or greater than the rank of the resolution matrix (obtainable as the operand rmrank ).

An example of the use of the rp  operator is as follows, where Temperature is assumed to be an element in the collection currently being adjusted, and there are at least two canonical directions.

BD>print : (rp (Temperature,2))

 

Sample size for the current adjustment

 

Usage

• obs  operand.

This returns the number of selected data observations (and thus the sample size) for the elements contained in used in the current adjustment. Otherwise, if there is no data available, it returns the fictional sample size being used for the adjustment. Such fictional sample sizes are set using the obs  control.