Can I use the likelihood to estimate probability of draws I need to estimate $P(data)$ for a Bayesian problem, supposing I have the distribution on which the data are being drawn, can I use the likelihood to estimate that?
I'm asking because as far as I know, likelihood is not a probability, but for discrete rv it's like considering
$$
P(X_1=x_1 \cap X_2=x_2 \cap ... \cap X_n=x_n) \; \;X_i \:iid
$$
But we can't do this for abs. continuous rv right? So in addition to the previous one, how can we estimate $P(data)$ for abs. cont. rv?
I'm referring to:
$$
P(hyp|data) = \frac{P(data|hyp) * P(hyp)}{P(data)}
$$

If $X_1, X_2,\dots, X_n$ are i.i.d., then by the definition of independence
$$
p(X_1, X_2,\dots, X_n) = \prod_{i=1}^n p(X_i)
$$
As for $P(data)$, it is
$$
P(data) = \int P(data|hyp) * P(hyp) \; d \,hyp
$$
by the law of total probability.
