Information Technology Reference
In-Depth Information
So from the update-equation we have:
E
n
(H)
=
[(N
−
1)E
n
−
1
(H)
+
E
n
−
1
(H/R
e
)]
If we let N
=
4 so that
(N
−
1)
/
N
=
3/4
=
0.75
and also
1/N = 0.25 for an agent's flexibility then:
Agent
E
n
(H)
Head occurs
Tail occurs
E
n
(H1)
0.75
*
0.8
+
0.25
*
0.67
=
0.77
0.75
*
0.8
+
0.25
*
1.0
=
0
.
85
+
=
+
=
E
n
(H2)
0.75
*
0.2
0.25
*
0.33
0.23
0.75
*
0.2
0.25
*
0.0
0
.
15
Total
1.0
1.0
It is important to note that whereas on a purely Bayesian model the appearance of a
tail could eliminate the belief that the coin is double headed (H2), our model does
not produce this conclusion. This response is not as irrational as it might appear:
it keeps open the possibility of alternative explanations (e.g. that there has been a
switch of the coin, say, for a double-tailed coin, or an observational error). This is
more like what is required for the abductive cycle and for scientific investigation in
general (Tweney
1985
; Matthews
2004
).
6.6
Confidence, Indifference and Change
The number of hypotheses actively considered by scientists varies. During the ex-
ploratory stages of an investigation scientists are rarely in a position to consider just
two well-defined alternative hypotheses. Nevertheless, the tendency is always to re-
duce the number of hypotheses in play, and to make them as specific as possible. This
means that confidence in a particular hypothesis is affected, not only by experiments
and consultations, but also by the number of hypotheses available for consideration.
In order to allow for changing numbers of hypotheses, we introduce a dynamic
threshold, the indifference value. This defines hypotheses that are under active con-
sideration (or are believed to be possibilities). Thus, we have a variable set of
hypotheses that implicates a changing ontology and phenomenology.
To calculate the indifference value we need a function that changes smoothly
between limiting values and is easily to calculate for any number of different hy-
potheses. A quantity that suits our purpose and varies in time as required is the inverse
of entropy.
