What does Pr() mean?

Question

What does the expression $Pr(x|y;\theta)$ mean? As in: $$ {\displaystyle {\begin{aligned}L(\theta |x)&=Pr(Y|X;\theta )\\&=\prod _{i}Pr(y_{i}|x_{i};\theta )\\&=\prod _{i}h_{\theta }(x_{i})^{y_{i}}(1-h_{\theta }(x_{i}))^{(1-y_{i})}\end{aligned}}} $$ https://en.wikipedia.org/wiki/Logistic_regression#Model_fitting

I've never been able to figure out what $Pr$ means. What's the difference versus $P$?

It is the probability that Y$_i$=$y_i$ for each i given that $x_i$ for each i and $\theta$ are known. — Michael R. Chernick, Oct 18 '17 at 06:12
Why not $P(x|y;\theta)$ then? And also, does that mean $Pr(a|b;c;d)$ means that it's the probability of $a$ given $b$, $c$, and $d$? — oink, Oct 18 '17 at 06:15

Tim · Answer 1 · 2017-10-18T06:55:24.387

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$\Pr()$ is pretty standard notation used to denote probability. In case of $\Pr(Y|X;\theta)$ it's conditional probability of $Y$ given $X$ and $ \theta$.

See also similar thread Difference between $p(x)$ vs. $\pi(x)$ in literature

edited Oct 18 '17 at 06:55

answered Oct 18 '17 at 06:14

Tim

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Why not just $P(Y|X;\theta)$? – oink Oct 18 '17 at 06:20
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@oink Why $P$ should be "better" then $p$ or $\Pr$? Simply several different notations exist. – Tim Oct 18 '17 at 06:51
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+1 but I vote to close this whole thread as a duplicate of https://stats.stackexchange.com/questions/108441/ – amoeba Oct 18 '17 at 07:11
@amoeba good point, agree. – Tim Oct 18 '17 at 07:30

What does Pr() mean?

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