On Suspicious Coincidences and Pointwise Mutual Information.

Area of Science:

• Statistics
• Data Analysis
• Probability Theory

Background:

• The concept of
• suspicious
• co-occurrence of events A and B was proposed by Barlow (1985) when P(A,B) is significantly greater than the product of their individual probabilities P(A)P(B).
• Classical measures of association for 2 × 2 contingency tables are essential for quantifying relationships between binary variables.

Purpose of the Study:

• To review and compare classical measures of association for 2 × 2 contingency tables.
• To analyze the behavior of mutual information (MI) and pointwise mutual information (PMI) as measures of association.
• To evaluate the suitability of PMI for flagging suspicious coincidences, considering its sensitivity to marginal probabilities.

Main Methods:

• Review of established statistical measures like Yule's Y.
• Analysis of mutual information (MI) and pointwise mutual information (PMI) based on probability ratios.
• Comparison of MI and PMI behavior with Yule's Y after accounting for marginal effects.

Main Results:

• Yule's Y is independent of marginal probabilities, depending solely on the odds ratio (λ).
• Mutual information (MI) and pointwise mutual information (PMI) are functions of the ratio P(A,B)/P(A)P(B).
• After controlling for marginal effects, MI and PMI exhibit similar functional behavior to Yule's Y concerning the odds ratio (λ).

Conclusions:

• Pointwise mutual information (PMI) is widely used for identifying suspicious coincidences.
• The sensitivity of PMI to marginal probabilities can lead to inflated scores for sparse events.
• Careful consideration of marginal effects is crucial when using PMI to assess event co-occurrence.