Published posthumously in 1763, Bayes' essay addressed the inverse probability problem: given observed data, what can we infer about the underlying probability that generated it? His theorem provides a precise formula for updating prior beliefs in light of new evidence.
Bayes' theorem states that the posterior probability is proportional to the prior probability multiplied by the likelihood of the observed data. This simple formula is the mathematical basis of learning from experience — every observation shifts our beliefs toward the truth, weighted by how surprising it is.
Modern machine learning, spam filters, medical diagnostics, and signal processing all rely on Bayesian updating. The framework is especially powerful when data arrives sequentially, as it does in financial markets — each new filing, each earnings report, each price movement is evidence to be incorporated.
Our systems continuously update beliefs as new filings, news, and market data arrive. Bayesian reasoning is not a metaphor in our work — it is the literal mechanism by which our models learn and adapt.