Discriminant Function Analysis - Discrimination Rules

Discrimination Rules

  • Maximum likelihood: Assigns x to the group that maximizes population (group) density.
  • Bayes Discriminant Rule: Assigns x to the group that maximizes, where represents the prior probability of that classification, and πi represents the population density.
  • Fisher’s linear discriminant rule: Maximizes the ratio between SSbetween and SSwithin, and finds a linear combination of the predictors to predict group.

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    Rules and particular inferences alike are justified by being brought into agreement with each other. A rule is amended if it yields an inference we are unwilling to accept; an inference is rejected if it violates a rule we are unwilling to amend. The process of justification is the delicate one of making mutual adjustments between rules and accepted inferences; and in the agreement achieved lies the only justification needed for either.
    Nelson Goodman (b. 1906)