Something is behind a door — cat or not-cat, starting at 1 : 1 odds. Five toggleable clue cards each multiply the odds: furry times 4, meows times 10, purrs times 8, barks times one twentieth, huge times one fifth. On a log-odds ruler from minus 6 to plus 6, each active clue lays down a bar segment end-to-end (+1.4, +2.3, +2.1, −3.0, −1.6 points) and a dot marks the net sum; readouts show the odds product, the points sum, and P(cat) = sigmoid(sum) as a probability bar. This invented example assumes clues are independent within each class. Logistic regression uses a similar additive score but fits its weights directly.

The cat detector: evidence adds points

Cat or not-cat? Start at 1 : 1 odds. These invented clues are assumed independent within cat cases and within non-cat cases. Each observed clue multiplies the odds, so its logarithm adds points. A switched-off clue is unobserved, not known to be absent.

The multiplication uses conditional independence given each hypothesis. Logistic regression also adds a weighted score and applies a sigmoid, but learns its weights directly and does not require that independence assumption.