2
$\begingroup$

Suppose we have some random variable $X$ that ranges over some sample space $S$. We also have two probability models $F$ and $G$. Let $f(x)$ and $g(x)$ be the probability density functions for these distributions. Does the following quantity $$ \log \frac{f(x)}{g(x)} = \log \frac{P(F|x)}{P(G|x)}- \log \frac{P(F)}{P(G)}$$ basically tell us how much more likely model $F$ is the true model than model $G$?

  • 0
    What is the difference between $\log\frac{f(x)}{g(x)}$ and the log likelihood ratio (LLR)? The value of the LLR does not depend on the a priori probabilities $P(F)$ and $P(G)$ at all. In other words, there is cancellation on the right side of your displayed equation which makes the a priori probabilities disappear, and the LLR does not have any information about the a priori probabilities.2011-12-20

2 Answers 2