Conditional probability under two given variables I am reading the online open textbook called Gaussian Processes for Machine Learning.
In the chapter 2.1, it mentioned the equation 2.5, which is:
$$p(w|y,X) = \frac{p(y|X,w)p(w)}{p(y|X)}$$
where $w$ is parameters; $X$ is design matrix; $y$ is label.
My question is that do we assume random variable $w$ and $X$ here are independent, i.e. $p(w) = p(w|X)$?
Otherwise, based on the source (https://math.stackexchange.com/questions/2613161/conditional-probability-on-two-variables), $p(w)$ should be $p(w|X)$.
Could anyone help me?

Repeating comment so question has an answer:
$p(w)$ is the prior distribution of the "vector of weights (parameters) of the linear model" and would presumably not depend on the input vectors collected into $X$.
