joint likelihood

Let there be a generative model $m$ describing measured data $y$ using model parameters $\theta$ and a prior distribution on $\theta$ .

$$p(y,\theta \mid m)=p(y\mid \theta ,m)p(\theta \mid m)$$

Then, the joint likelihood is equal to the product of likelihood function and prior density:

Related

• law of conditional probability

References

• https://statproofbook.github.io/P/jl-lfnprior.html