Foundations

Pierre-Simon Laplace

1749 – 1827Bayesian inference
P(θ)θpriorposterior

Théorie analytique des probabilités

Laplace's 1812 treatise was the first comprehensive treatment of probability theory. He unified the work of Pascal, Fermat, Bernoulli, and Bayes into a single coherent framework, developing generating functions, the method of characteristic functions, and the central limit theorem in its modern form.

The rule of succession

Laplace derived the formula for predicting the probability of a future event based on past observations: if an event has occurred s times in n trials, the probability of it occurring next is (s + 1) / (n + 2). This simple rule captures Bayesian reasoning with a uniform prior and remains a useful baseline estimator.

Determinism and probability

Laplace famously argued that probability is a measure of ignorance, not of objective randomness. For a sufficiently powerful intellect (Laplace's demon), the universe is deterministic. Probability theory is the tool we use because we are not omniscient — it quantifies what we do not know.

Why this matters

Laplace's framing of probability as the calculus of uncertainty is our operating philosophy. We do not predict the future — we quantify our uncertainty about it, update as evidence arrives, and allocate capital where the probabilities favour us.