I'm trying to parse some notation in the following statement. Specifically, what does the "$|\cdot$" refer to?
$\displaystyle\prod^{\tau^*}_{t=0} g_1(B(t)|\cdot)g_2(C(t)|\cdot)g_3(D(t)|\cdot)$
Where $g_1, g_2, g_3$ are the binomial transition density functions described in previous equations and $B(t), C(t), D(t)$ are binomial distributions.
When you have a function with multiple arguments (for example a distribution with some parameter and then the value you want to consider, or some givens) , say $f(x,y,z)$. Then the notation $f(x_0,y_0,\cdot)$ indicates the function $g$ given by the formula $g(z) = f(x_0,y_0,z)$, that is, the function of one argument given by fixing values of the other two.
Edit: The $|$ is there because in whatver you are reading, the arguments or parameters or givens of the distribution are separated by $|$ rather than a comma.
