Bayesian Classifiers

What are Bayesian Classifiers?

A Bayesian classifier assigns a probability to each possible outcome class, such as price up versus price down over the next several bars, by applying Bayes' theorem: the posterior probability of a class is proportional to its prior probability multiplied by the likelihood of the observed features under that class. The most common variant in trading tools is naive Bayes, which assumes the features are conditionally independent given the class, so the joint likelihood factorizes into a product of simple per-feature terms that can be estimated from modest amounts of history.

That independence assumption is almost always false for market inputs, since momentum readings, volume measures, and structure flags move together, yet naive Bayes often still ranks outcomes usefully because the violation inflates confidence more than it scrambles ordering. The practical consequence is that posteriors from a naive model tend to be overconfident, pushed toward 0 or 1, so they are better treated as scores to rank and filter with than as literal odds, a concern shared with logistic signal calibration.

How traders use it

• As a directional scorer: several engineered features, such as oscillator zones or order-flow readings, are fused into one posterior probability of an up or down outcome, traded only above a threshold.
• As a filter on another system: an existing signal fires only when the classifier's posterior for the favorable class is high enough, suppressing entries the evidence does not support.
• As an evidence combiner: each feature multiplies the running odds by its historical likelihood ratio, keeping every input's contribution explicit and inspectable.