Questions tagged [notation]
For questions about statistical notation and mathematical notation used in statistics.
2
votes
1answer
80 views
Meaning of Bullets within Normal Distribution
I am working through the derivation for a method published in this paper. On page 586 (equation A1) the authors use the notation:
$$ N(\bullet,\bullet) $$
What do the bullets represent? Do they ...
0
votes
0answers
41 views
What does E_n mean
I came across the following symbol in this paper:
I am a little bit confused by the symbol . Does it simply mean population average?
0
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0answers
4 views
Group Minimum in Linear Regression
Let's say for each individual $i$ I have some dependent variable $y_i$ (for example income) and the independent variables $x_i$ and $z_i$ (age and academic degree). $z_i$ is a categorial variable and ...
1
vote
1answer
14 views
How to denote quartiles so as not to be confused with quarterly data
Is there an existing statistical notation convention that can make clear that can only be interpreted as quartiles? To my knowledge, quartile notation is the same with quarterly data notation:
...
8
votes
1answer
284 views
Notation: What does the tilde below of the expectation mean? [duplicate]
I am reading about variational auto encoders, and there is the below loss function:
$$l_i(\Theta,\phi) = - {\mathbb{E}}_{z\sim q} \left[\log p_\phi(x_i|z)\right] + KL(q_{\phi}(z_i|x)||p(z))$$
What ...
0
votes
0answers
9 views
How to properly represent a sum of interactions in ANOVA?
I would like to include an ANOVA-style linear model in my work that shows the main effects but has interactions lumped together in one term for brevity. When I do the analysis I will include the ...
1
vote
2answers
39 views
Convention to denote CDF of “named” distribution
I have found the following convention useful in my own work: If a (family of) distribution(s) has a standard symbol, for example the normal distribution
$$
X \sim \mathcal N (\mu, \sigma^2),
$$
then I ...
0
votes
0answers
15 views
How to denote token length in statistics
I have a vocabulary (V) that includes terms. (e.g., V = ['data mining', 'data', 'machine', 'machine learning'])
I also have a ...
4
votes
2answers
103 views
What is sigma function in the YOLO object detector?
I have gone through the YOLO9000 paper, in that they have mentioned that network predicts 5 coordinates of the bounding box, and from that we find the exact centre coordinates and the width and height....
0
votes
1answer
34 views
Geometric mean and geometric standard deviation
When summarizing normalized data (for example, percentage data), one must use the geometric mean instead of the arithmetic mean. Thus, instead of using the arithmetic standard deviation, one shall use ...
1
vote
1answer
47 views
Expected value notation in GAN loss
I am reading Goodfellow's original paper on GANs.
What I struggle to understand is his notation of the subscript in expected values.
$\mathbb{E}_{\boldsymbol{x} \sim p_{data}(\boldsymbol{x})}$ ....
...
0
votes
0answers
15 views
Unclear “mathematical notation” in a polynomial
Although, the Enigma here is a protocol for enhancing the privacy in blockchain; however, the question is about mathematical notation, where we want to calculate the coefficients in a polynomial. ...
1
vote
1answer
41 views
Brier Score of a Prediction, Mathematical Notation
I am currently working on a logistic regression model that is fitted on the base of a training set ($D_0$) and is used to predict the outcome (0 or 1) of an independent test set ($D_1$). As an ...
2
votes
0answers
30 views
Notation for drawing once from a distribution and reusing values [closed]
Is there a succinct way to denote a one-time draw from a distribution? This is essentially what I want to achieve:
...
0
votes
2answers
211 views
Notation: in general is it ok to think of $p(y|x)$ as $p_x(y)$?
In the notation for the conditional probability, $p(y|x)$, I believe usually we think of this with $x$ having a fixed value and $y$ varying, such that it integrates to one.
In this case, is it ...
2
votes
1answer
41 views
How to write a random variable is not distributed as N(0,1)
I was wondering if the symbol $\not\sim$ (i.e., not tilde) could be used to express that a random variable $X$ is not distributed as a normal distribution with a mean of $0$ and variance of $1$. For ...
0
votes
2answers
68 views
Meaning of $x∈ℝ^d$ notation in matrix approach to regression
How does one interpret the $x ∈ ℝ^d$ in the context of regression, see below
in the following context:
I understand the d refers the dimension of the x vector, ...
1
vote
0answers
75 views
Notation for confidence interval
Since P(lower bound estimate < true parameter < upper bound estimate) = 0.95 means that the series of random bounds contain the true parameter 95 percent of the times, then why not replace the ...
0
votes
0answers
15 views
Notation question for multiplying matrix rows by vector
I have a matrix A and row vector b such that;
$A=\begin{bmatrix}
a_{11} & a_{12} & a_{13} & \dots & a_{1n} \\
a_{21} & a_{22} & a_{23} & \dots & a_{2n} \\
...
1
vote
0answers
25 views
Time series filtering notation
I am looking at some suggested filters for tidal data but am having trouble understanding the notation. For example, Godin (1972) suggests a low-pass filter for tidal data that is a combination of 24-...
1
vote
1answer
32 views
Notation and Transformation Rules of the Normal Distribution
So, I'm wondering. So far I have seen both notations:
(1) $X \sim \mathcal{N}(\mu, \sigma^2)$ and
(2) $X \sim \mathcal{N}(\mu, \sigma)$
where $\mu$ is the mean.
My first questions is directed to $\...
0
votes
1answer
37 views
Understanding random variable notation
Somewhere I read:
$X$ takes values in the set $S$, and $Y$ and $Y'$ are each uniformly distributed over set $T$
Does "take values in the set" mean that $X : S -> ??$?
Does "uniformly ...
0
votes
0answers
16 views
Standard Notation for Gaussian Measure?
There are standard notation for normal PDFs and CDFs, being $\varphi$ and $\Phi$, respectively. I would like to know if there is also standard notation for the Gaussian measure corresponding to a ...
2
votes
1answer
192 views
abusing convergence in distribution notation
If I have $\sqrt{n} (X_n - c) \xrightarrow[]{d} N(0,v) $ does it make any sense at all to say this implies that $X_n \xrightarrow[]{d} N(c, \frac{v}{n})$.
If not, what is the accurate way/notation ...
2
votes
2answers
129 views
Why is the risk equal to the empirical risk when taking the expectation over the samples?
From Understanding Machine Learning: From theory to algorithms:
Let $S$ be a set of $m$ samples from a set $Z$ and $w^*$ be an arbitrary vector. Then $\Bbb E_{S \text{ ~ } D^m}[L_S(w^*)] = L_D(w^*)...
1
vote
1answer
75 views
Machine learning & mathematics - [closed]
I am not from a statistics (or mathematics) major background. Just bachelors in computer science but had learnt algebra, probability, statistics, Integration & Differentiation, Permutation & ...
1
vote
0answers
14 views
Notation in different articles about HMM
I'm studying hidden Markov models, especially the articles by Stamp (2018) and Rabiner (1989). Please let me check with you that I got this right:
Especially the last observation is my own, about the ...
2
votes
1answer
66 views
What does this notation $p(s', r \mid s, a)$ mean in reinforcement learning?
I was reading a book on reinforcement learning, and came across the following notation:
Possibly stupid question, but I cant seem to google how to read this. Is it
A) Probability of (s' and r) GIVEN ...
2
votes
0answers
21 views
Notation for the assumed probabilistic model of our data
The question of best practices for probability notation is a common one on this forum, e.g.here, here, here, and elsewhere, e.g. here, here, here. Despite this, I still have unresolved questions.
As ...
1
vote
2answers
32 views
Denoting random variable $\theta$ with capital $\Theta$?
It is common practice to denote random variables with a capital letter $X$ and the realization with a small $x$. But how about in Bayesian statistics? The parameter $\theta$ is a RV, so shouldn't it ...
1
vote
1answer
46 views
What does $\min_{1 \le i \le n}X_i$ mean?
What does $\min_{1 \le i \le n}X_i$ mean?
In a context:
Show that the distribution function $F$ of $\min_{1 \le i \le n}X_i$ is ...
6
votes
2answers
703 views
What does the angle bracket mean in variance formula?
When I check the formula of variance in Mathworld which is
$$
\sigma^2 \equiv \langle\ (X - \mu)^2 \rangle\
$$
Though I'm more familiar with the other formula, I just wanted to know what does the ...
0
votes
0answers
14 views
Writing down a conditional probability / finding the underlying probability space
This is a notational issue: Let's say we have a partition of $\mathcal X$ given by $\{\Omega,\Sigma\}$ and we define
$P(\omega\in\Omega) = p$,
$P(X(\omega)=x|\omega\in\Omega) = \pi$ and
$P(X(\...
0
votes
0answers
19 views
Shotgun sequence statistics
I trying to understand the statistics behind shotgun sequencing. Below is an excerpt from a book. Can anyone tell what does the below bold sentence mean? I did not understand the interval range and ...
0
votes
1answer
61 views
Cramér-Rao Lower Bound & Fisher information - error in textbook?
I'm currently reading the textbook "Statistics for Mathematician" from Victor Panaretos. On page 65, the author presents the following equation for the Cramér-Rao Lower Bound (Note: I set the ...
0
votes
0answers
36 views
Dot subscript summation notation used in design of experiments
Context
I couldn't find a clear explanation of this on this site, and
thought that it might be of use. I have provided part of the answer, which
anyone is welcome to build from. I'm not sure how to ...
8
votes
1answer
99 views
Who invented the independence notation $\perp \!\!\! \perp$?
This is more of a historical question: who invented the notation $\perp \!\!\! \perp$ for denoting (conditional) independence?
3
votes
1answer
92 views
Expected value notation
I come across the notions $\mathrm{E}[wage]$ and $\mathrm{E}[wage_i]$. I would like to clarify if they have different meanings.
Take the first expression. $\mathrm{E}[wage]$ could represent the ...
3
votes
2answers
60 views
Notation in going from $AR$ and $MA$ to $ARMA$
I'm confused about the notation that leads to an $ARMA$ model.
If, 1: Autoregressive model $AR(p)$ is defined as: $Y_t-\mu=\phi*(Y_{t-1}-\mu)+w_t$
Where,
$Y_t$: observation in time $t$
$Y_{t-1}$: ...
2
votes
1answer
90 views
What do the mu and (.) symbol represent in the deterministic/policy formula?
I am currently going through the OpenAI Spinning Up documents and the following notation puzzled me. What do the mu and . sign mean in the following two formulas?
1
vote
1answer
59 views
Notation for nested multilevel model
I am fitting the following logit model in lme4 (R):
dummy ~ ind_var1 + state_var2 + country_var3 + (1 | country/state)
This specifies varying intercepts for ...
0
votes
0answers
48 views
Notation for Matrix Concatenation
I have an input data matrix $X$. In fact, I have $N$ of these input matrices, so I identify each as $X_i$ using an index $i \in \{1,\ldots,N\}$.
Thinking about something like cross validation, I want ...
1
vote
1answer
95 views
Mathematical notation / formula of a mixed effect model
I am unsure how to define the mathematical notation of a mixed model of R.
I built the model in this way:
...
0
votes
1answer
59 views
Functional form of f
I am reading An Introduction to Statistical Learning with Applications in R by G. James, D. Witten, T. Hastie and R. Tibshiran 2013 after taking a basic statistics course a little while ago.
On ...
2
votes
1answer
143 views
Difference of notation between cross entropy and joint entropy
Although it is clear to me, how the two concepts differs, it has been difficult for me to find a notation that would make it clear, to which type of entropy we refer.
From wikipedia, we can see that ...
1
vote
0answers
79 views
What is the meaning of expression $(X_i−\bar{X})′$?
I came across an expression ($X_i−\bar{X}$)′ while going through covariance matrix calculation.
I know $X_i$ is a random variable and $\bar{X}$ is the mean of all variables, but I cant figure out ...
0
votes
1answer
22 views
Is the inverted pi a standard symbol for d-separation?
I've seen the inverted pi symbol earlier but found it hard to find an explanation for it. Found it again in the context of d-separation between Xu and Xv here: https://en.m.wikipedia.org/wiki/...
3
votes
1answer
197 views
Gini coefficient
I’m learning about inequality measures, there are several ways to calculate it and I understand all but one.
$\kappa = \frac{E|X-X^\prime|}{2E(X)}$
I’m not sure what the second x means in the case ...
6
votes
1answer
68 views
Notation question based on 1950s typesetting
I'm working on a multivariate extension of the Johnson translation family to more accurately generate correlated random variates. In the course of my work, I've run across two separate instances where ...
0
votes
0answers
12 views
Total sum of squares (TSS) terminology for changing average
Consider the setting where there are $n$ nodes each having an initial value $v_{i}(0), i\in [n]$. Over time these values change and at time $t$ the value of node $i\in[n]$ is denoted by $v_i(t)$. Let $...
