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Designing the influence diagram

    


tex2html_wrap_inline33790 tex2html_wrap_inline33790 Syntax

  1. BD>grid : tex2html_wrap_inline33712

    BD-B tex2html_wrap_inline33794 ,B tex2html_wrap_inline33798 , ..., B tex2html_wrap_inline37962 tex2html_wrap_inline33712

    BD*X tex2html_wrap_inline33794 ,X tex2html_wrap_inline33798 , ..., X tex2html_wrap_inline37962 tex2html_wrap_inline33712

    BD*Y tex2html_wrap_inline33794 ,Y tex2html_wrap_inline33798 , ..., Y tex2html_wrap_inline37962 tex2html_wrap_inline33712

    BD*R tex2html_wrap_inline33794 ,R tex2html_wrap_inline33798 , ..., R tex2html_wrap_inline37962 tex2html_wrap_inline33712

    BD*C tex2html_wrap_inline33794 ,C tex2html_wrap_inline33798 , ..., C tex2html_wrap_inline37962 tex2html_wrap_inline33712

    BD*U tex2html_wrap_inline33794 ,U tex2html_wrap_inline33798 , ..., U tex2html_wrap_inline37962 tex2html_wrap_inline33712

    BD*V tex2html_wrap_inline33794 ,V tex2html_wrap_inline33798 , ..., V tex2html_wrap_inline37962 tex2html_wrap_inline33712

    BD*A tex2html_wrap_inline38014 ,A tex2html_wrap_inline38016 , ..., A tex2html_wrap_inline38018 tex2html_wrap_inline33712

    BD*A tex2html_wrap_inline38022 ,A tex2html_wrap_inline38024 , ..., A tex2html_wrap_inline38026 tex2html_wrap_inline33712

    BD* tex2html_wrap_inline38030 tex2html_wrap_inline33712

    BD*A tex2html_wrap_inline38034 ,A tex2html_wrap_inline38036 , ..., A tex2html_wrap_inline38038 tex2html_wrap_inline33712

  2. BD>grid : [ @L [(C)] ] tex2html_wrap_inline33712

  3. BD>grid0 : tex2html_wrap_inline33712

    BD-B tex2html_wrap_inline33794 ,B tex2html_wrap_inline33798 , ..., B tex2html_wrap_inline37962 tex2html_wrap_inline33712

    BD*X tex2html_wrap_inline33794 ,X tex2html_wrap_inline33798 , ..., X tex2html_wrap_inline37962 tex2html_wrap_inline33712

    BD*Y tex2html_wrap_inline33794 ,Y tex2html_wrap_inline33798 , ..., Y tex2html_wrap_inline37962 tex2html_wrap_inline33712

    BD*R tex2html_wrap_inline33794 ,R tex2html_wrap_inline33798 , ..., R tex2html_wrap_inline37962 tex2html_wrap_inline33712

    BD*C tex2html_wrap_inline33794 ,C tex2html_wrap_inline33798 , ..., C tex2html_wrap_inline37962 tex2html_wrap_inline33712

    BD*U tex2html_wrap_inline33794 ,U tex2html_wrap_inline33798 , ..., U tex2html_wrap_inline37962 tex2html_wrap_inline33712

    BD*V tex2html_wrap_inline33794 ,V tex2html_wrap_inline33798 , ..., V tex2html_wrap_inline37962 tex2html_wrap_inline33712

  4. BD>grid0 : [ @L [(C)] ] tex2html_wrap_inline33712

where tex2html_wrap_inline37898 are the names of n bases or elements; tex2html_wrap_inline35202 , tex2html_wrap_inline37902 , tex2html_wrap_inline37904 , tex2html_wrap_inline37906 , and tex2html_wrap_inline37908 are real numbers; tex2html_wrap_inline37910 are integers in [1,15]; and tex2html_wrap_inline37912 are integers. L is the name of a label, and C is a valid input channel number: an integer such that tex2html_wrap_inline37914 .

tex2html_wrap_inline33806 tex2html_wrap_inline33806

The GRID:  command is used to define various basic features for the quantities to appear on an influence diagram. Once used, its essential features can be examined by issuing the LOOK:  command with argument grid , and the TESTGRID:  command can be used to test the design. The command typically is spread over tex2html_wrap_inline37916 [B/D] command lines. For the second form of the command an address is given, and the remaining tex2html_wrap_inline37918 lines should then be placed following the given address. The inputs to the command are as follows.

Line 2:
defines a list of bases (or elements in their role as bases containing only one element) which are to be viewed as nodes. If the name of any base or element given here is already defined as a node, the former definition is overwritten and any arcs connecting this node to any other are removed before the new arcs are defined.

Lines 3 and 4:
We consider the coordinate system for the influence diagram as a unit square, with bottom left coordinate (0,0) and top right coordinate (1,1). A location for the centre of each node in this square should be given on lines 3 and 4, such that the centre of node tex2html_wrap_inline37212 locates at tex2html_wrap_inline37920 .

Line 5:
We give the radius of every node to appear on the diagram. That is, tex2html_wrap_inline37922 will be the radius of the node associated with the base tex2html_wrap_inline37924 . It is possible to indicate here, by setting tex2html_wrap_inline37926 , that [B/D] should use it's default radius.

Line 6:
We give the colour to be associated with every node to appear on the diagram. That is, tex2html_wrap_inline35752 will be the colour attached to the node associated with the base tex2html_wrap_inline37924 . Each value of tex2html_wrap_inline35752 is an integer in [1,15], representing a colour. A table showing the colours represented by these integers is shown in Table 11.3. The colour give for the node determines (1) the colour used to draw the node; (2) the colour of any arc leaving the node; (3) the colour used to shade the outer sectors of any nodes to which there is a directed arc connected to this node, and which represent collections which are to be adjusted by this node.

 

Monochrome 4 Colours (UNIX) 8 Colours (Deskjet 500C) 16 Colours (EGA/VGA)
1 black black black darkgray
2 black red red lightred
3 black blue blue lightblue
4 black green green green
5 black red magenta lightmagenta
6 black blue cyan lightcyan
7 black green yellow yellow
8 black red green lightgreen
9 black blue red red
10 black green blue blue
11 black red magenta magenta
12 black blue cyan brown
13 black green yellow darkgray
14 black red green lightgray
15 black blue red cyan
Table 11.3:  Colours available for graphics images

Lines 7 and 8:
We label the nodes by their base or element names. In the same way that we locate the centre of the node, we locate the centre of the node label in the unit square. That is, the centre of the label to be attached to node tex2html_wrap_inline37212 will be located at tex2html_wrap_inline37934 .

Lines 9 to tex2html_wrap_inline37916 :
The remaining n lines are used to define the arcs and their directions. Each tex2html_wrap_inline37938 is an integer between 0 and 31 inclusive which will set the type of the arc drawn from node tex2html_wrap_inline37212 to node tex2html_wrap_inline38122 . The possible values and their meanings are shown in Table 11.4. An arc can consist of (1) a path correlation, if appropriate; (2) a label summarising arc influence; and (3) the arc itself: a directed straight line connecting two nodes. In addition, two further styles may be selected: (4) the arc information can be made to be proportional either to the actual resolution at a destination node, or to the overall uncertainty at the destination node; and (5) arc diagnostic information only might be shown. These possibiliies may be selected separately. An integer in tex2html_wrap_inline37940 is used to set the arc type. The binary representation of this integer is used to determine what possibilities are selected. The integer has a 5 bit binary representation, with a bit equal to 1 if a style is selected, and 0 otherwise. For example, arc style 19 (10011 binary) has the first, second, and fifth style bits set, and consists of a straight line and a label, and the labelling information is primarily diagnostic.

 

Bit Bit value Interpretation
1 0 No arc line drawn
1 Arc line drawn
2 0 No label drawn
1 Label drawn
3 0 No path correlation label drawn
1 Path correlation label drawn
4 0 Arc label information proportional to overall nodal uncertainty
1 Arc label information proportional to overall nodal resolution
5 0 Arc diagnostic information not to cover the entire label.
1 Arc diagnostic information to cover the entire label.
Table 11.4:  Arc styles

Notice that we would define tex2html_wrap_inline37942 and tex2html_wrap_inline37944 to draw an arc from node tex2html_wrap_inline38122 to node tex2html_wrap_inline37212 . If tex2html_wrap_inline37946 then, if appropriate, the information concerning arc influence and a diagnostic quantity will be drawn in the form of a bar overlaying part of the arc.

The real numbers input need not necessarily be in the format suggested. Suppose that there are n nodes being defined. The numeric information following the GRID:  and GRID0:  commands consists of tex2html_wrap_inline37948 and tex2html_wrap_inline37950 real numbers respectively. These numbers must be supplied in the order indicated, 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.

Consider the code given in Figure 11.3 for a fictitious example. This defines three nodes for collections named intelligence, environment, and heredity respectively. The nodes are centred at (0.3,0.5), (0.7,0.7), and (0.7,0.3) respectively; and their names are placed respectively underneath, above, and underneath the nodes. Each node will be drawn with a radius equal to 0.04. There are only two directed arcs, one from the environment node to the intelligence node; and the other connecting the heredity node to the intelligence node. The resulting diagram should resemble Figure 11.4.

  figure13042
Figure 11.3:  Example influence diagram design

  figure13109
Figure 11.4:  A crude influence diagram

The GRID0:  command is identical to the GRID:  command except that no arcs are defined. This is useful when designing the partial correlation diagram, as arcs connecting the nodes on such diagrams are generated according to various other criteria. Notice that the ARC:  command can be used to specify arc connections piecemeal.

  

 


next up previous contents index
Next: Testing the design overall Up: Designing and testing influence Previous: Designing and testing influence

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