Editing Pattern recognition (section)

===Frequentist or Bayesian approach to pattern recognition===
The first pattern classifier – the linear discriminant presented by [[Fisher discriminant analysis|Fisher]] – was developed in the [[Frequentist inference|frequentist]] tradition. The frequentist approach entails that the model parameters are considered unknown, but objective. The parameters are then computed (estimated) from the collected data. For the linear discriminant, these parameters are precisely the mean vectors and the [[covariance matrix]]. Also the probability of each class <math>p({\rm label}|\boldsymbol\theta)</math> is estimated from the collected dataset. Note that the usage of '[[Bayes rule]]' in a pattern classifier does not make the classification approach Bayesian.

[[Bayesian inference|Bayesian statistics]] has its origin in Greek philosophy where a distinction was already made between the '[[A priori and a posteriori|a priori]]' and the '[[A priori and a posteriori|a posteriori]]' knowledge. Later [[A priori and a posteriori#Immanuel Kant|Kant]] defined his distinction between what is a priori known – before observation – and the empirical knowledge gained from observations. In a Bayesian pattern classifier, the class probabilities <math>p({\rm label}|\boldsymbol\theta)</math> can be chosen by the user, which are then a priori. Moreover, experience quantified as a priori parameter values can be weighted with empirical observations – using e.g., the [[Beta distribution|Beta-]] ([[Conjugate prior distribution|conjugate prior]]) and [[Dirichlet distribution|Dirichlet-distributions]]. The Bayesian approach facilitates a seamless intermixing between expert knowledge in the form of subjective probabilities, and objective observations.

Probabilistic pattern classifiers can be used according to a frequentist or a Bayesian approach.