How to apply the bayes theorem with probability density functions?

322 Views Asked by At

I'm trying to implement the agent based model presented on the following paper in Python:

https://www.nature.com/articles/s41598-018-25558-7 (Method section)

In the model each agent updates its belief in a particular hypothesis in a bayesian manner

$$ P(H|E) = P(H) ∗ \frac{P(E|H)}{P(E)} $$

The paper states that both $P(E)$ and $P(E|H)$ are obtained from a probability density function using a set of parameters related to each agent: evidence, belief (mean) and confidence (variance). $P(H)$ is the prior belief, so it should be a value between $0$ and $1$.

The problem is that, if $P(E)$ and $P(E|H)$ are obtained from a probability density function, their values can be $>1$ thus generating a $P(H|E)$ larger than $1$.

Is there something here that I'm not understanding? Should I integrate the output of those probability density functions?

Thanks and sorry if I'm not clear enough