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Questions tagged [notation]

For questions about statistical notation and mathematical notation used in statistics.

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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 ...
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24 views

what does the notation $X^{(n)}$ mean in the context of matrices? [on hold]

What does the notation $x^{(n)}$ where x is a matrix and n is an integer?
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45 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 ...
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576 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 ...
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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(\...
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15 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 ...
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1answer
49 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 ...
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19 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 ...
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1answer
92 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?
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1answer
72 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 ...
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2answers
43 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 $t$ $Y_{t-1}$: ...
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1answer
32 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?
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1answer
31 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 ...
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31 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 ...
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1answer
56 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: ...
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1answer
56 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 ...
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0answers
10 views

Gradient for deep neural net in matrix notation?

I am used to the notation for gradient that is written explicitly in the individual parameters. What you get is a sum of the derivatives w.r.t each parameter. But is there a way to write this down ...
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78 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 ...
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1answer
18 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/...
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1answer
192 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 ...
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11 views

Statistical notation: At least one vector element satisfies condition

I'm searching for statistical notation to write down "at least one element of vector $\boldsymbol{X}$ satisfies condition Y" (e.g. at least one element of $\boldsymbol{X} = 0$). I know I can write ...
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1answer
61 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 ...
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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 $...
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Notation of Random Variables, samples and estimators

It seems common in the estimators subject to use the following notation: example, (wikipedia estimators) $X$, as a random variable. $x$, as a possible value or single draw from the variable X. $\...
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1answer
74 views

Is an event a subspace of the sample space?

In a lecture today, a professor of mine described an event as being "in" the sample space. When writing on the board, for a sample space $S$ and event $E$, it was denoted: $$E \in S $$ This confused ...
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What does this cross entropy notation $J(o, v_c, U) = CE(y, \hat y)$ mean?

From http://web.stanford.edu/class/cs224n/assignment1/index.html under "complementary written problems" problem $3(a)$: What does $J_{\text{Softmax---CE}}(o, v_c, U) = CE(y, \hat y)$ fully stand for? ...
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1answer
31 views

Clarification on traditional notation for moments

$\newcommand{\E}{\mathrm{E}}$ I have been going over the Hill et al. (1976) paper on Johnson distributions and struggling with some notation that is undefined but I believe might have been considered ...
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1answer
326 views

What notation (symbol) is used to denote correlation between vectors

For publication and/or presentation purposes, is there a symbol to denote the calculation of a correlation between two vectors? Obviously, for the value of the correlation is symbolically represented ...
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1answer
23 views

Is this notation for a lognormally distributed variable misleading?

I have gotten into the habit of notating a lognormally distributed random variable $X$ as: $$X \sim \ln\mathcal{N}(\mu,\sigma^2)$$ I am now starting to question where I picked this habit up and ...
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2answers
250 views

Notation in statistics (parameter/estimator/estimate)

In statistics, it is very important to differentiate between the following three concepts which are often confused and mixed by students. Usually, books denote by $\theta$ an unknown parameter. Then ...
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1answer
33 views

What does ${}^{\mathsf{T}}$ mean in the context of the binomial distribution?

In a presentation of the binomial distribution on this website, the probability of the success of a trial is presented as $\pi=g^{-1}(\eta)$, with $g$ the inverse link function. $\eta=\alpha+\...
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23 views

Little-o/Big-o notation relation

Currently, I am studying kernel regressions. The problem I have is in understanding the relation between big-o and little-o. The following changes (in two different papers) occur: $ \frac{h^{2(j-1)}}{...
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Name and proper notation for multidimensional systematic sampling

I'm trying to find the official name and formulation of the following sampling technique. I believe it is simply referred to as "systematic sampling", but failed to find a reference describing it ...
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3answers
73 views

Converting the beta coefficient from matrix to scalar notation in OLS regression

I've found for my econometrics exams that if I forget the scalar notation, I can often save myself by remembering the matrix notation and working backwards. However, the following confused me. Given ...
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0answers
77 views

Forecasting formula in mathematical notation help please:

Question: is what I have correct? If not what is correct? I am not sure how to correctly write this forecasting model in proper mathematical notation. My attempt is at the bottom, please help fix or ...
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1answer
36 views

What is f in this Neural Gas neighborhood width formula?

I'm implementing the Online Visualization Neural Gas algorithm, as described in the Estévez, Figueroa 2006 paper. I am having trouble interpreting the formula below (Eq. (4) in the paper): $$\lambda(...
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1answer
54 views

Symbol for a discrete domain?

Suppose I have a variable $x\in\mathbb{D}_{X}$, with $\mathbb{D}_{X}$ being its domain. What is the mathematical correct way of expressing "$\mathbb{D}_{X}$ is discrete" (i.e. not continuous)?
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257 views

Why is does the result square root of covariance matrix multiply with its transpose is the covariance matrix itself? [closed]

I think that if $P=\Sigma_u^\frac{1}{2}$, then it should be $PP=\Sigma_u$ instead of $\Sigma_u = PP'$. Then why is it $\Sigma_u = PP'$ (according to some literature)?
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What does $a$ above the tilde mean, when tilde means distributed as?

In statistics notation, the tilde is often used to indicate "has the distribution of," as in $X \sim N(0,1)$, meaning the random variable $X$ follows the distribution of the standard normal ...
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1answer
32 views

probability notation

Part A) I have the following notations : $p(\mu, \sigma^2)$ $N(x)$ $p(x | \mu, \sigma^2)$ I would read them in the following manner: probability function with 2 parameters, namely $\mu$ and $\...
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1answer
56 views

notation conditional normal distribution [duplicate]

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 (...
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1answer
53 views

What is a $\propto$ update in mean-field approximation?

I am trying to understand some notation used in papers about Bayesian variational inference. In some papers that use mean-field approximation to fit a probabilistic model, they describe coordinate ...
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1answer
57 views

Good choice of notation for normal distribution pdf/cdf

Let $\Phi(x)$ be the cumulative distribution function for the standard normal distribution. I have an expression with several terms of the form $$\Phi\left(\frac{\mu-g(x)}{\sqrt{\sigma^2}}\right)$$ ...
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1answer
77 views

Notation to represent the batch-normalised value of x

What notation is used to represent the normalised or z-score value of a vector $x$? Or, given: $? = \dfrac {x - \mu } {\sqrt{\sigma^2}}$ Where $\mu$ and $\sigma$ are calculated across the whole ...
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0answers
20 views

Denominator in pairwise similarities in symmetric SNE

I am trying to understand how symmetric SNE (stochastic neighbour embedding) works while reading the paper of Van der Maaten about t-SNE. However, I am a bit confused about the denominator in the ...
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46 views

Inverse CDF of the survival function

In my course Survival Analysis the following is written: (As an introduction to the Cox-Snell residuals) Inverse CDF: If $T_i$ (the survival time for the $i$th individual) has survivorship ...
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What does 1 with an inequality in the subscript mean? [duplicate]

I have not seen the following notation before (the 1 with a subscript in the density): Consider the problem of sampling from the truncated normal distribution $\mathcal{N}_t (\mu, 1, a)$, given ...
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1answer
42 views

Notation in statistics

I'm reading an old document and I came across a notation I'm unsure of, E.g. the first equation states a uniform distribution given by $\frac{1}{2\pi}$. However, I don't understand the $\mathrm{d}\...
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1answer
34 views

Why do we use superscript notation and asterisks when describing bootstrap samples?

I'm currently reading 'An Introduction to Statistical Learning' and I'm trying to grasp bootstrapping. I am wondering why a superscript * and number value are used to describe a bootstrapped data set,...
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Why is the letter $n$ traditionally used to denote sample size?

Question basically in title. I am just curious if anyone has any historical references that point to the earliest usages of this notation.