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Questions tagged [notation]

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

2
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1answer
38 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 ...
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2answers
65 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, ...
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52 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 ...
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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} \\ ...
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24 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-...
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1answer
31 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 $\...
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1answer
35 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 ...
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13 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 ...
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1answer
189 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 ...
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2answers
111 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^*)...
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73 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 & ...
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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 ...
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1answer
56 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 ...
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0answers
20 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 ...
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2answers
28 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
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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 ...
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2answers
637 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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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(\...
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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 ...
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1answer
52 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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25 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
94 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
87 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
50 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
64 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
48 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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34 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
69 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
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
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1answer
19 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
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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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12 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 ...
6
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1answer
62 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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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 $...
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20 views

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
83 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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25 views

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
34 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
801 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 ...
0
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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 ...
5
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2answers
286 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
34 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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0answers
27 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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0answers
23 views

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
89 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
78 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 ...
3
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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(...
2
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1answer
61 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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349 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)?