Questions tagged [notation]
For questions about statistical notation and mathematical notation used in statistics.
2
votes
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 ...
0
votes
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, ...
1
vote
0answers
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 ...
0
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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
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-...
1
vote
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 $\...
0
votes
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 ...
0
votes
0answers
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 ...
2
votes
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 ...
2
votes
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^*)...
1
vote
1answer
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 & ...
1
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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 ...
1
vote
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 ...
2
votes
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 ...
1
vote
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
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
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 ...
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
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 ...
0
votes
0answers
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 ...
7
votes
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?
3
votes
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 ...
3
votes
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 $t$
$Y_{t-1}$: ...
2
votes
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?
1
vote
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 ...
0
votes
0answers
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 ...
1
vote
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:
...
0
votes
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 ...
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
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
votes
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 ...
0
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0answers
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
votes
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 ...
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 $...
0
votes
0answers
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.
$\...
5
votes
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 ...
0
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0answers
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?
...
3
votes
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 ...
1
vote
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
votes
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
votes
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 ...
0
votes
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+\...
0
votes
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)}}{...
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 ...
7
votes
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 ...
1
vote
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
votes
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
votes
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)?
1
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0answers
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)?
