Session-05

Building a Fraud Detector: Precision Recall and the Cost of Being Wrong

Football goals, website server requests, and traffic accidents all share a common structure: events arrive randomly over time, and whether an event happened in the last minute tells you nothing about the next minute. What mathematical model captures this memoryless, time-homogeneous counting process? Think about why cricket scoring does not fit the same model as football scoring.

A process where events occur independently at a constant average rate $\lambda$ is modelled by the Poisson distribution. The key assumptions are independence of non-overlapping intervals and a constant rate. The next segment derives the Poisson PMF $P(X=k) = e^{-\lambda}\lambda^k/k!$ and applies it with $\lambda = 3$ accidents per day.

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From Fraud Detection to AI Search: How Cascade Classifiers Work