Conflict analysis is the activity of detecting, tracing, and
explaining possible conflicts among observations of variable values
(i.e., evidence or data). Inconsistencies among observations are
easily detected (P(evidence) = 0), but also flawed findings should be
detected and traced. For example, in a diagnostic situation a single
flawed test result may take the investigation in a completely wrong
direction.
To understand what conflict analysis is and how it can be used, there
are several issues of interest:
We define two sets of observations e1 and e2 to
be in a possible conflict with one another if they are negatively
correlated.
For positively correlated findings we expect that
P(e1|e2) > P(e1) and
vice versa (i.e., observing e2 makes it more likely to also
observe e1 (and vice versa)). In other words, we expect
that
P(e1,e2) > P(e1)P(e2)
if e1 and e2 are positively correlated,
P(e1,e2) < P(e1)P(e2)
if e1 and e2 are negatively correlated, and
P(e1,e2) = P(e1)P(e2)
if e1 and e2 are independent.
Therefore, given a set of observations (evidence), e =
{e1,...,en}, we define the conflict measure for
e as
If conf(e) is positive, e1,...,en are negatively
correlated, indicating a possible conflict among these pieces of
evidence. (The choice of base for the log function is immaterial.)
Notice, that if conf(e) is negative (i.e., no apparent conflict among
e1,...,en), then this gives you no guarantee
that all of e1,...,en are positively
correlated. It may well happen that there is a local conflict (i.e.,
that conf(e') > 0 for a proper subset e' of e) although
conf(e) < 0.
For more information about detection of local conflict, see the help
page of the junction tree panel.
There are situations in which a positive conflict measure is computed,
where there is no real conflict. These include:
- Rare case: Typical data from a very rare case may
indicate a possible conflict. If
conf(e1,...,en) > 0 and there is a
hypothesis H=h such that
conf(e1,...,en,h) < 0, then h
explains away the conflict. That is, if H=h is the correct hypothesis
(e.g., a diagnosis) in the current situation, then there is no
conflict.
- Missing observation: Basically the same situation, where
conf(e1,...,en) > 0 but
conf(e1,...,en,I=i) < 0, where I=i
is a missing piece of information. That is, there is a local conflict
among e1,...,en, but the observation I=i
explains the conflict.
By activating the button with the
symbol,
one can obtain a list of possible instantiations of currently
uninstantiated variables that can eliminate the current conflict. See
below for an example of the dialog box that appears when this button
is activated.
The dialog box contains a list of possible instantiations in the
form
<CM>: <variable> = <value>
where <CM> is the new conflict measure obtained if <variable> is
instantiated to <value>. Only instantiations (if any) with a resulting
conflict measure less than or equal to 0 get displayed.
The Instantiate button enters the currently selected instantiation (if
any) as evidence.
Whenever a positive conflict has been observed that cannot be
explained as a rare case, it is important to pinpoint the piece (or
pieces) of evidence that is in conflict with the majority of the
pieces of evidence.
Basically, this involves computation of conflict measures for subsets
of the evidence. The junction tree is useful for this purpose; see the
help page for the junction tree panel for more information.
When searching
for a hypothesis or observation that may eliminate the current
conflict it may be desirable to restrict the set of uninstantiated
variables considered in the search. This is done by selecting a set of
hypothesis variables. Any subset of discrete chance nodes may be
selected as hypothesis variables.
Only the selected set of hypothesis variables are considered in the
search for instantiations that may eliminate the current conflict.
So far we have considered data conflict analysis, i.e. how to
identify, resolve, or explain a possible conflict in data. In
hypothesis driven data conflict analysis we investigate how each piece
of evidence impacts a given hypothesis.
In hypothesis driven conflict analysis we investigate the impact of
each piece of evidence on a given hypothesis. For each piece of
evidence (finding) f we compute the prior P(h) of the hypothesis, the
posterior P(h|e) of the hypothesis given the entire set of evidence e
and the posterior P(h|e\f) of the hypothesis given the subset of
evidence where the piece of evidence f under consideration is
retracted.
Hypothesis driven conflict analysis allows the user to investigate how
a single piece of finding impacts the probability of the hypothesis.
A threshold value is applied to reduce the number of findings
considered. Only results for findings where the cost-of-omission is
above the threshold are displayed where cost-of-omission is a measure
of the distance between P(H|e) and P(H|e\f).