What is it about?

We consider an elementary probability problem: given three events, A, B, and C, how can knowledge of A and B be used to predict C? We find a condition that guarantees predictability based on minimal statistical information. The results are useful for analysis of a wide variety of data types.

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Why is it important?

There is a well-known mathematical condition called "conditional independence". When it is satisfied, knowledge of event C simplifies the relationship between events A and B, making their joint occurrence easily predictable. Our main result reveals a symmetry: when conditional independence is satisfied, knowledge of A and B also makes C predictable based on limited information. This finding has important practical applications in the realm of statistical analysis. This is illustrated with four realistic examples.


The results in this paper solved a nagging problem we had in the lab. We studied the performance of human participants when localizing either a sound or a faint visual stimulus, and wanted to know what to expect when they were presented with both stimuli simultaneously. We wanted a prediction based only on their unisensory performance curves and without making any mechanistic assumptions. The search for a solution led us to a general finding with wide applicability.

Emilio Salinas
Wake Forest University School of Medicine

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This page is a summary of: Conditional independence as a statistical assessment of evidence integration processes, PLoS ONE, May 2024, PLOS,
DOI: 10.1371/journal.pone.0297792.
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