next up previous contents index
Next: Problems of asymmetry Up: Declaring variances and covariances Previous: Constructing variance matrices from

Direct numerical specification of variance matrices


tex2html_wrap_inline33790 tex2html_wrap_inline33790 Syntax

1a

BD>var : v(S,B tex2html_wrap_inline33794 ,B tex2html_wrap_inline33798 ) tex2html_wrap_inline33712

1b

BD>var : v(S,B tex2html_wrap_inline33794 ) tex2html_wrap_inline33712

2a

BD>var : v(S,B tex2html_wrap_inline33794 ,B tex2html_wrap_inline33798 ) @L tex2html_wrap_inline33712

2b

BD>var : v(S,B tex2html_wrap_inline33794 ) @L tex2html_wrap_inline33712

3a

BD>var : v(S,B tex2html_wrap_inline33794 ,B tex2html_wrap_inline33798 ) @L(C) tex2html_wrap_inline33712

3b

BD>var : v(S,B tex2html_wrap_inline33794 ) @L(C) tex2html_wrap_inline33712

4a

BD>var : v(S,B tex2html_wrap_inline33794 ,B tex2html_wrap_inline33798 ) (C) tex2html_wrap_inline33712

4b

BD>var : v(S,B tex2html_wrap_inline33794 ) (C) tex2html_wrap_inline33712

where tex2html_wrap_inline35086 are the names of bases which may or may not already exist, S is a belief store number, L is the name of a label and tex2html_wrap_inline33870 is a valid input channel number.

tex2html_wrap_inline33806 tex2html_wrap_inline33806

The particular forms for the syntax of the VAR:  command given here all relate to the direct input of a body of numerical variance and covariance specifications. The number of numerical inputs supplied depends upon both the dimensions of the vectors involved and the form of syntax used. The form of the syntax used also establishes the place from which the beliefs will be sought: interactively or from a given macro file address.

Firstly we consider the placing of the numerical inputs. Forms 1a and 1b of the syntax are used when the inputs follow directly afterwrads. Thus, this form of the syntax may be used to obtain beliefs interactively from the keyboard. The remaining forms specify an address where the numeric inputs should be found. If forms 2a and 2b of the command are used, with no channel number being specified, the channel number is deduced - [B/D] does not allow duplicate labels. In forms 4a and 4b of the syntax, the beginning of the file associated with the input channel is indicated. In common with other macro facilities, the channel number can be zero (meaning the keyboard): a label should not be supplied in this case. The channel and label specified or implied must exist at the time the command is issued.

Secondly we consider the formatting of the inputs. The 1a, 2a, 3a, and 4a forms are used to input a rectangular matrix of belief specifications for the covariances between the collections tex2html_wrap_inline35092 and tex2html_wrap_inline35094 . Suppose, for example, that tex2html_wrap_inline35092 consists of the elements tex2html_wrap_inline35202 and that tex2html_wrap_inline35094 consists of the elements tex2html_wrap_inline35206 . (It is possible for tex2html_wrap_inline35094 to be the same as tex2html_wrap_inline35092 .) The belief inputs consist of the following specifications:

displaymath35190

For smaller specifications at least, we recommend that you input the numbers required as an array of n rows each consisting of m columns, with the numbers separated by one or more spaces. However, the real numbers input need not necessarily be in tabular format They must be supplied in the order indicated by reading the matrix above from left to right, top to bottom, but you are free to split the input over several lines, as many numbers per line as you wish (possibly interspersed with blank lines) subject to the usual limitation of no more than 253 characters per physical line. A number must not be split over two or more lines. Any input on the same physical line as the last number required will be ignored. The numbers are to be in standard numerical format; an error message is printed if the number is invalid, and the command is aborted. It is advisable not to input large matrices interactively.

As an example, suppose that tex2html_wrap_inline35224 and that tex2html_wrap_inline35226 and that the following covariance matrix is given on a macro file:

@xybeliefs This is the 3x2 covariance matrix between the x's and the y's tex2html_wrap_inline33712

1.0 -3.2 tex2html_wrap_inline33712

0.5 2.6 tex2html_wrap_inline33712

1.0 -2.2 tex2html_wrap_inline33712

We could now input this covariance matrix into belief store number 2 by issuing the command

BD>var  v(2,B1,B2) @xybeliefs tex2html_wrap_inline33712

We now consider the remaining forms 1b, 2b, 3b, and 4b, which are used to input the lower triangle of the square symmetric variance-covariance matrix specified over the collection tex2html_wrap_inline35092 . Suppose, for example, that tex2html_wrap_inline35092 consists of the elements tex2html_wrap_inline35202 . The belief inputs consist of the following specifications:

displaymath35191

That is there are n rows. The first row has one number, the second row has two numbers, and so forth. For smaller specifications at least, we recommend that you input the tex2html_wrap_inline35246 numbers required as a triangle with n rows, and with the numbers separated by one or more spaces. However, the real numbers input need not necessarily be in this format. They must be supplied in the order indicated by reading the matrix triangle above from left to right, top to bottom, but you are free to split the input over several lines, as many numbers per line as you wish (possibly interspersed with blank lines) subject to the usual limitation of no more than 253 characters per physical line. A number must not be split over two or more lines. Any input on the same physical line as the last number required will be ignored. The numbers are to be in standard numerical format; an error message is printed if the number is invalid, and the command is aborted. It is advisable not to input large matrices interactively.

As an example, suppose that tex2html_wrap_inline35224 and that we interactively input its variance matrix into belief store number 1. The following sequence of commands suffice:

BD>var : v(1,B1) tex2html_wrap_inline33712

BD*5.3 tex2html_wrap_inline33712

BD*0.9 4.6 tex2html_wrap_inline33712

BD*1.1 1.3 7.2 tex2html_wrap_inline33712

Notice that the [B/D] prompt changes from the `>' character to the `-' character when the program is expecting interactive inputs.


next up previous contents index
Next: Problems of asymmetry Up: Declaring variances and covariances Previous: Constructing variance matrices from

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