Bayes' Theorem-qed

What Would Bayes Say: IRS Scandal? ProPublica, a Pulitzer Prize-winning progressive journalism group, accused the Cincinnati IRS branch of targeting conservative group Not-For-Profit (NFP) groups. If I am a NFP, then a fair question to ask is are the non-conservative companies being audited at the same proportions? This goes directly to Bayes’ theorem and conditional probability. With this concern, I can frame this concern as a question to get my answer.

This is how I will frame this question: What is the probability that since I am a conservative NFP, the IRS has pinned my company as target of audit opportunity?

Translating this into Bayes’ protocol, I can now ask a conditional probability question: What is the probability that the IRS will audit my NFP given I am a conservative (IRS-Target | non-conservative NFP).

Let’s say we assume that out of all conservative and non-conservative NFPs, approximately 10% receive IRS audits. We really do not know what this proportion is but we are using the robustness of using an estimated guess of these proportions.

Let’s assume that of the conservative NFPs, 90% have already been audited and of the non-conservative NFPs, only 10% have been audited. To answer this question, we can apply Bayes’ theorem to determine that the probability of being audited by the IRS given I am a non-conservative NFP is only 1%. If this were just based on random audits, then this percentage would be approximately 50%.

Clearly, if these probabilities are true, then the IRS is actually targeting conservative NFPs.

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