What does the term "proportional to" mean in Bayes Equation?


I don't have a background in maths so I sometimes get confused by basic definitions. Let's for instance consider Bayes Theorem in Bayes Data Analysis:

$P(\theta|\textbf{y}) \propto P(\theta) P(\textbf{y}|\theta)$

How should this equation be understood? What does it mean that the RHS is proportional to LHS?


Posted 2018-04-27T13:45:55.817

Reputation: 11

1I think your expression should change $P(y)$ by $P(\theta)$. – David Masip – 2018-04-27T13:51:51.273

Did I answer your question? – David Masip – 2018-04-28T09:17:20.280



It means that $P(\theta | y ) = kP(\theta) P(y | \theta)$, where $k$ is a constant that does not depend on $\theta$.

In fact, the Bayes Theorem states $P(\theta | y ) = \frac{P(\theta) P(y | \theta)}{P(y)}$. This proportion has to be added in order that $\sum_{\theta}P(\theta | y) = 1$ is satisfied (that is, $P(\theta | y)$ has to be a probability).

David Masip

Posted 2018-04-27T13:45:55.817

Reputation: 5 101