Talk:Probability Theory

Bayes' theorem

The way I have understood Bayes' theorem is:

$D(y|x) = \frac{D(x,y)}{D(x)}\,$

$D(x|y) = \frac{D(x,y)}{D(y)}\,$

$D(x|y)D(y) = D(x,y) = D(y|x)D(x)\,$

And the Bayes' theorem is:

$D(x|y) = \frac{D(y|x)D(x)}{D(y)}\,$ ,

where eg., $y\,$ can denote a measurement, and $x\,$ a model, or model parameter.

If we ignore the normalization constant $D (y)$ we can use a more simple form:

$D(x|y) \propto D(x,y) = D(y|x)D(x)$ ,