What does the notation f(·|θ) mean?

Question

I've been trying to solve a sum where $X$ is a stochastic variable with density $f(\cdot | \theta)$ with density $f$ defined by:

$$f(x|\theta) = \frac{θ}{x^{\theta+1}} \tag{Pareto}$$

I don't really understand what $f(\cdot | \theta)$ means. Can anyone shed some light on this?

Answer 1

For simulation we have to specify the values of parameters; in such a context, the notation $f(x \mid \theta)$ suggests that $\theta$ (may be a vecotr) is "known". For statistical inference the values of parameters are to be investigated via data at hand; in this context, the notation $f(\theta \mid x)$ is preferable, which suggests that the "data" $x$ are known.

I think it will do no harm to read the bar "given".