Likelihood Ratio for Binary Classification

Variants of the threshold:

  • Maximum Likelihood Decision

    Here if the probability greater than the denominator. The threshold has to be greater than one. This is same as choosing making a classification based on which classification has a higher probability.

  • Bayes Decision

    Here we make use of the Priors. Thus if we already know that a particular classification is more probable, we can use this knowledge to essentially weight the threshold .

    Note: Since we define to be greater than , you want it to be smaller for a preferable classification, hence the ratio is flipped.