Data Conflict Analysis

What is Data Conflict Analysis?

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:

Definition of Data Conflict: How do we define data conflict?
Conflict Measure: How do we define an appropriate measure of data conflict?
Tracing Conflicts: How do we identify the piece(s) of evidence that contribute to a data conflict?
Conflict Resolution: How do we distinguish between a conflict and a rare case?

Definition of Data Conflict

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.

Conflict Measure

Therefore, given a set of observations (evidence), e = {e₁,...,e_n}, we define the conflict measure for e as

If conf(e) is positive, e₁,...,e_n 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,...,e_n), then this gives you no guarantee that all of e₁,...,e_n 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.

Conflict Resolution

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,...,e_n) > 0 and there is a hypothesis H=h such that conf(e₁,...,e_n,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,...,e_n) > 0 but conf(e₁,...,e_n,I=i) < 0, where I=i is a missing piece of information. That is, there is a local conflict among e₁,...,e_n, 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. An example of the dialog box that appears when this button is activated can be seen below.

The dialog box contains a list of possible instantiations in the form

where <RM> is a measure indicating the ability of the instantiation to resolve the conflict. An instantiation with an <RM> value of 100 will reduce the conflict measure to 0. Thus, only instantiations with an <RM> value greater than or equal to 100 get displayed. The higher the <RM> value of the selected instantiation (if any), the larger the negative value of the resulting conflict measure.

The Instantiate button enters the currently selected instantiation (if any) as evidence.

Tracing Conflicts

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.