notation conditional normal distribution [duplicate]

Question

I'm describing parameter search using a particle filter, for which I use West M. (1993) Approximating Posterior Distributions by Mixture.

On page 8 of the document, he states "and $p(\theta)$ is (approximately) a mixture of multivariate normal distributions,

$p(\theta)=\sum_{j=1}^{n} w_j N_p(\theta \mid m_j, M_j)$."

where $N_p(\mu, \Sigma)$ is a p-variate gaussian distribution.

I.e. he's using a conditional probability inside a Gaussian PDF. Is that notation allowed? I've not seen that anywhere. My professor (i'm a PhD student) says it's incorrect.

Answer 1

OK, after discussing this with some other students, I actually found this is common notation. So I just added the description to my paper:

We use $N_{D}(\vec{x} \mid \vec{\mu}, \Sigma) = (2\pi)^{-D/2} |\Sigma|^{-1/2} \exp \left\lbrace -\frac{1}{2}(\vec{x}-\vec{\mu})^{\text{T}} \Sigma^{-1}(\vec{x}-\vec{\mu}) \right\rbrace$ to denote the probability density function of a D-variate Gaussian distribution with mean vector $\vec{\mu}$ and covariance matrix $\Sigma$.