From Evidence to Source: Using Bayes' Theorem to Trace a False News Report

This record contains a one-page teaching poster, in Chinese, that illustrates Bayes’ theorem through a journalism example. It was prepared for Data Analysis: A Network Approach, taught by Junbin Su at the School of Journalism and Communication, Xiamen University.

The poster asks a practical question: if a reposted report on a public account turns out to be false, which media outlet is it more likely to have come from? Using a hypothetical set of 10,000 reposted articles, it assumes that 65% come from outlet A1 and 35% from outlet A2, with false-report rates of 2% and 5%, respectively. These assumptions yield 130 and 175 false reports, or 305 in total.

Working with natural frequencies, the poster moves through three steps: the prior (the share of each source), the evidence (a report is false), and the posterior (the share of each source among false reports only). The probability that a false report came from A2 rises from the prior of 35% to a posterior of about 57.4%, whereas the probability for A1 falls from 65% to about 42.6%.

The poster also addresses a common error in interpreting conditional probability, the confusion of P(F|A2) = 5% with P(A2|F) ≈ 57.4%, and shows that the posterior depends on both the prior shares and the conditional probabilities. All figures are illustrative and do not describe actual media outlets.

More course materials are available at:
https://sujunbin.github.io/Data-Analysis-with-Junbin-Su/