For questions about statistical notation and mathematical notation used in statistics.
Questions tagged [notation]
561 questions
92
votes
2 answers
Subscript notation in expectations
What is the exact meaning of the subscript notation $\mathbb{E}_X[f(X)]$ in conditional expectations in the framework of measure theory ? These subscripts do not appear in the definition of conditional expectation, but we may see for example in this…
Emile
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35
votes
1 answer
Reference: who introduced the tilde "~" notation to mean "has probability distribution..."?
[Note: although this question has an accepted answer, the investigation is not finished yet. I encourage you to post your findings.]
Who first introduced the notation "$X \sim Q$", meaning that $Q$ is the probability distribution for $X$, and its…
pglpm
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31
votes
4 answers
Meaning of probability notations $P(z;d,w)$ and $P(z|d,w)$
What is the difference in meaning between the notation $P(z;d,w)$ and $P(z|d,w)$ which are commonly used in many books and papers?
Learner
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29
votes
2 answers
Why are probability distributions denoted with a tilde?
What is the meaning of the tilde when specifying probability distributions? For example:
$$Z \sim \mbox{Normal}(0,1).$$
jsj
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27
votes
2 answers
Why there are two different logistic loss formulation / notations?
I have seen two types of logistic loss formulations. We can easily show they are identical, the only difference is the definition of the label $y$.
Formulation/notation 1, $y \in \{0, +1\}$:
$$
L(y,\beta^Tx)=-y\log(p)-(1-y)\log(1-p)
$$
where…
Haitao Du
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27
votes
6 answers
In statistics, should I assume $\log$ to mean $\log_{10}$ or the natural logarithm $\ln$?
I'm studying statistics and often come across formulae containing the log and I'm always confused if I should interpret that as the standard meaning of log, i.e. base 10, or if in statistics the symbol log is generally assumed to be the natural log…
Giuseppe Romagnuolo
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27
votes
2 answers
Should I capitalise the "N" in "Normal Distribution" in British English?
This question is a bit left-field, but I figured that the community here probably has strong views on the subject!
I am writing up my PhD thesis. Consistently, when talking about quantities which are formally related to a Gaussian distribution, I…
Landak
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26
votes
4 answers
What is the difference between $E(X|Y)$ and $E(X|Y=y)$?
Generally, What is difference between $E(X|Y)$ and $E(X|Y=y)$?
Former is function of $y$ and latter is function of $x$? It's so confusing..
신범준
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25
votes
2 answers
What is the meaning of super script 2 subscript 2 within the context of norms?
I am new to optimization. I keep seeing equations that have a superscript 2 and a subscript 2 on the right-hand side of a norm. For instance, here is the least squares equation
min $ ||Ax-b||^2_2$
I think I understand the superscript 2: it means to…
bernie2436
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24
votes
0 answers
What is the meaning of the semicolon in $f(x;\Theta)$?
In section 6.2, in the second paragraph of p. 335 (image below) of "Probability and statistical inference 7e" by Hogg and Tanis states:
perhaps it is known that $f(x;\Theta)=(1/\Theta)e^{x/\Theta}$
where $x$ is data and $\Theta$ is a…
Abe
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24
votes
3 answers
In machine learning, why are superscripts used instead of subscripts?
I'm taking Andrew Ng's course on Machine Learning through Coursera. For equations, superscripts are used instead of subscripts. For example, in the following equation $x^{(i)}$ is used instead of $x_i$:
$J(\theta_0, \theta_1) = \frac{1}{2m}…
entpnerd
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23
votes
1 answer
Notation of estimators (tilde vs. hat)
Is there any naming convention regarding the hat and the tilde symbol in stats?
I found $\hat{\beta}$ is describing an estimator for $\beta$ ( Wikipedia ) But I also found $\tilde{\beta}$ is describing an estimator for $\beta$ (Wolfram ).
Is there…
Sebastian
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21
votes
3 answers
Which notation and why: $\text{P}()$, $\Pr()$, $\text{Prob}()$, or $\mathbb{P}()$
Are these merely stylistic conventions (whether italicized or non-italicized), or are there substantive differences in the meanings of these notations?
Are there other notations meaning "the probability of" that should be considered in this…
Alexis
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18
votes
1 answer
The origin of the Wilkinson-style notation such as (1|id) for random effects in mixed models formulae in R
Model formulae in R such as
y ~ x + a*b + c:d
are based on the so called Wilkinson notation: Wilkinson and Rogers 1973, Symbolic Description of Factorial Models for Analysis of Variance.
This paper did not discuss notations for mixed models (which…
amoeba
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18
votes
4 answers
Why do people use $\mathcal{L}(\theta|x)$ for likelihood instead of $P(x|\theta)$?
According to the Wikipedia article Likelihood function, the likelihood function is defined as:
$$
\mathcal{L}(\theta|x)=P(x|\theta),
$$
with parameters $\theta$ and observed data $x$. This equals $p(x|\theta)$ or $p_\theta(x)$ depending on notation…
danijar
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