Log Likelihood Ratio

$$\text{LLR}(\mathbf{x})=\log \frac{P(\mathbf{x}\mid s=1)}{P(\mathbf{x}\mid s=2)}$$

Example

A 2-class Bayes classifier is realized by comparing the log-likelihood ratio (LLR) to a fixed threshold value $\theta$ :

$$\text{LLR}(x)\lessgtr \theta$$

Interpret the choice of the threshold value for the cases $\theta =0$ and $\theta =1$

Hint:

$$g(x)=\log \frac{P(x|s=1)}{P(x|s=2)}+\log \frac{P(s=1)}{P(s=2)}$$

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References

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