Conditional Probability Tables
Whereas the arcs connecting the nodes constitute the qualitative part of the network by indi
cating the direct probabilistic dependences, conditional probability distributions represent th
e quantitative part (type and strength of the probabilistic relations). The most commonly use
d representation models to describe these distributions are the conditional probability
tables.
The reading of a conditional probability table in BayesiaLab is carried out in the following
way:
zone 1 corresponds to the value combinations of the parents of the node. Of course, t
his zone exists only if the node has at least one entering arc. When a node has paren
ts, it is possible to change the order of the parents by dragging the name of the parent
s inside the header of the zone 1. When a parent is moved, the conditional probability
table is reorganized to take the modification into account.
zone 2 corresponds to the probability distributions, conditionally to each case describ
ed by zone 1, or to the a priori probability distribution in the absence of entering arc. If
the network has a database and the states of the node are not modified, a tool tip dis
plays, for each probabilities, the number of corresponding cases in the database (taki
ng into account the smoothing factor, if any) and the rep- resented percentage of
the database.
Example
The interpretation of the first line of this table is thus:
the probability of having Dyspnea is 10% when TbOrCa is False and Bronc
hitis is False
Table Edition
The main problem with conditional probability tables is the exponential growth of the numbe
r of lines with respect to the number of parents. Their data acquisition can then quickly bec
ome a tedious task. When databases exist, it is possible to fill them automatically (learning
of the parameters). It is also possible to use equations to describe more concisely the
probability distributions.
The probability acquisition can also be alleviated by using the cut & paste facilities, inside t
he same table, between different tables or with external applications.
These tables also come with the classical cell selection tools, either by directly clicking on t
he cells, or by clicking on the line/column headers. Whereas a click on a header with the
key pressed allows making an OR with the previous selection, the same click with the
key makes an AND. A click with the
key on a cell allows selecting/unselecting the cell without changing the set of selected cells.
This is then the way to edit a cell that belongs to a selection and to set this edit to all the oth
er selected cells. A click on a cell with the
key pressed selects form the active cell to the pointed cell.
Probabilities can be copied and pasted to other tables or to external applications.
Complete
This operation consists in equally distributing the residual probability, defined as being equ
al to 100 - the sum of the probabilities already defined on the line. If there are blank cells, th
is residual probability is distributed on these cells. Otherwise, if the residual probability is po
sitive, this operation works as the Normalization one over all the cells of the line.
Normalize
Depending on probability probabilities are reduced or augmented in such way that relative
weight of each remains unchanged there at least a blank cell and if residual is positive this
operation corresponds to the complete one.
Randomize
All the cells of the Conditional Probability Table, or just the selected cells, are randomly
filled.
Assessment
When experts are associated with the network, a button Assessment is displayed and is a
ctivated when a cell is selected. The border of the cells with assessments becomes green
and the icon
displayed in the cell indicates how important is the disagreement between the experts for
this cell.