Normalized Product

Can be useful when multiple two distributions of the same random variable together. Keeps it a distribution adding to 1.

$$p(\mathbf{x}|{\mathbf{y}}_1,{\mathbf{y}}_2)=\eta p(\mathbf{x}|{\mathbf{y}}_1)p(\mathbf{x}|{\mathbf{y}}_2)$$ $$\eta =\frac{p({\mathbf{y}}_1)p({\mathbf{y}}_2)}{p({\mathbf{y}}_1,{\mathbf{y}}_2)p(\mathbf{x})}$$

This can be derived from Bayes’ Theorem #probability