Timeline for How to interpret this notation with a tilde?

7 events

when toggle format	what		by	license	comment
Dec 27, 2015 at 18:05	comment	added	Did		Even better would be to translate it to English as: "The distribution of $X_n$, conditional on $X_{n-1}$ taking the value $x_{n-1}$, is described by the probability density function $f(\ \mid x_{n-1})$."
Dec 17, 2015 at 9:15	vote	accept	Roman Susi
Dec 17, 2015 at 9:14	comment	added	Matthew Gunn		@RomanSusi No worries. There's a lot of notation around the use of probability. We've all had our confused "uhhh, so what is this?" moments!
Dec 17, 2015 at 9:11	comment	added	Roman Susi		Ok. Those others are of course very familiar, but the version without any "functors" around was confusing.
Dec 17, 2015 at 9:07	comment	added	Matthew Gunn		$X\mid Y$ is standard. For example, $P( X=x \mid Y =y)$, often written $P(X\mid Y)$ is the probability that $X$ takes the value $x$ given $Y$ takes the value $y$. $E[X \mid Y=y]$ is the expectation of $X$ conditional on $Y$ takes value $y$. $X \mid Y $ in general refers to $X$ conditional on $Y$.
Dec 17, 2015 at 9:03	comment	added	Roman Susi		Thanks, could you please also write it in another notation, as I believe the original is just an abbreviation, or is the $X\|Y$ the most used one? (If my guess is right, it should be something with p())
Dec 17, 2015 at 9:01	history	answered	Matthew Gunn	CC BY-SA 3.0