An investment thesis is a belief you hold with some probability and revise as evidence arrives. You don't reach it once, like a verdict. Bayes' theorem is the mathematically correct rule for that revision. In words, your posterior belief, after seeing evidence, is proportional to your prior belief before it, times the likelihood of seeing that evidence if your belief were true. Formally, for a hypothesis H (say, "my thesis is right") and evidence E:
P(H | E) = P(E | H) × P(H) / [ P(E | H) × P(H) + P(E | not H) × P(not H) ]
The denominator is just the total probability of seeing the evidence E under all hypotheses, and it normalises the answer into a proper probability. You need three inputs: your prior P(H), the likelihood of the evidence if the thesis is true, P(E | H), and the likelihood of the same evidence if it's false, P(E | not H). Evidence moves your belief a lot when it's much more likely under one hypothesis than the other. It barely moves it when it's roughly as likely either way. So "confirming" news that any company would have produced tells you almost nothing.
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Worked example: updating belief in a durable moat
A worked update on a thesis. You believe a company has a durable cost moat, and your prior is P(H) = 0.60. Then new evidence E arrives. During an input-cost spike, the company held gross margins flat while a smaller rival's collapsed. If the moat is real, that's likely, say P(E | H) = 0.80. If it isn't, and the margin hold was luck or temporary hedging, the evidence is less likely, say P(E | not H) = 0.30. Then:
P(H | E) = (0.80 × 0.60) / [ (0.80 × 0.60) + (0.30 × 0.40) ] = 0.48 / (0.48 + 0.12) = 0.48 / 0.60 = 0.80
Your belief in the moat rationally rises from 60% to 80%. Now suppose disconfirming evidence D arrives a quarter later. The company cut prices to defend share, which suggests weaker pricing power. Take your 80% as the new prior. If P(D | H) = 0.20 and P(D | not H) = 0.70:
P(H | D) = (0.20 × 0.80) / [ (0.20 × 0.80) + (0.70 × 0.20) ] = 0.16 / (0.16 + 0.14) = 0.16 / 0.30 = 0.53
and the belief falls from 80% back to 53%. That's how a thesis should breathe. It updates in both directions as evidence lands, never leaps to certainty on one data point and never ignores data that cuts against you. Your decision journal works as a Bayesian instrument. You record the prior and "what would change my mind" before the outcome, then update explicitly as evidence arrives. That improves the decision, and over many decisions it calibrates you (competency C9). The disposition Bayes formalises is "strong opinions, weakly held": enough conviction to act and size, and enough humility to revise when the likelihoods say so.
What is base-rate neglect?
Base-rate neglect, the trap Bayes exposes. The most common Bayesian error is ignoring the prior, which is the base rate, and over-reacting to the evidence. It ties straight back to the outside view and to the forensic screens. Here's a vivid case. A quality-of-earnings screen, say the Beneish M-Score, flags a company as a possible manipulator. The test is decent. Suppose it catches 80% of true manipulators (P(flag | manipulator) = 0.80) and has a 10% false-positive rate (P(flag | clean) = 0.10). Your gut screams "manipulator." But the base rate of accounting manipulators is low, say 5% of companies. Then:
P(manipulator | flag) = (0.80 × 0.05) / [ (0.80 × 0.05) + (0.10 × 0.95) ] = 0.04 / (0.04 + 0.095) = 0.04 / 0.135 ≈ 0.30
Even after a flag from a good test, there's only about a 30% chance the company is actually a manipulator. Clean companies are so much more common that the 10% false-positive rate throws up more false alarms than the 5% base of true positives produces real ones. So a screen flag is a reason to investigate, never a verdict, the same rule the forensic screens taught you. It's also why intuition, which neglects base rates, is so badly miscalibrated on rare events. Carry the habit into everything. What was the prior before this evidence, and how strong is the evidence really?