Use-case

The Likelihood ratio is another way of writing the Bayes rule. It conveniently allows the use of a threshold which dictates which classification or decision is to be made.

Mathematical Definition

For a two class case,

Variants of the threshold:

  • Maximum Likelihood Decision
  • Bayes Decision
  • Bayes Risk Decision

Note: is the cost of deciding state given state is true, so an and so forth.

![[Pasted image 20240423154225.png|]]

Note: The threshold has same units as the axis.


References

Source