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Questions tagged [notation]

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

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Notation to report the measurement of a parameter

The estimation of a parameter ($p$) is customary reported in Physics and other fields with, $ p = \hat{p} \pm \Delta p$, where $\hat{p}$ is an estimator, and $[\hat{p} - \Delta p, \hat{p} + \Delta p]$ ...
Diego Ravignani's user avatar
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103 views

Maximum likelihood for time series notation

I am going over the following slides where the likelihood for time series is formulated as (page 5): $f(y) = \prod_{i=2}^{n} f_{y_i|y_{i-}}(y_i|y_{i-}) f_{y_1}(y_1)$ I am not quite sure what the ...
spie227's user avatar
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11 votes
3 answers
439 views

Expectation conditional on a sigma algebra, what expectation does it refer to?

In a question like Intuition for Conditional Expectation of $\sigma$-algebra a concept like $E[X|\sigma(Y)]$ is used and I am puzzled about what sort of variable this actually is. Say we have a ...
Sextus Empiricus's user avatar
2 votes
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34 views

Errors and residuals in simple exponential smoothing (state space form) in FPP textbook

I am reading Hyndman & Athanasopoulos "Forecasting: Principles and Practice" 2nd edition (FPP2). (I am aware that 3rd edition exists.) In the chapter about exponential smoothing, section ...
Richard Hardy's user avatar
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What is the most common notation to describe cyclostationary stochastic processes?

Can a cyclostationary stochastic process be described as: $\{X_t[i]:i\in\mathbb{N}\}\quad\forall~t\in\{1,2, \dots,T\}$ where variability at the $t^\text{th}$ index across all repetitions/seasons ...
joaocandre's user avatar
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31 views

Conditional Expectation Notation in ARCH Model

I'm new to ARCH models, and I have a question about the correct notation for expressing the conditional expectation of the return at time $t(r_t)$ given the information available up to time t-1. I'd ...
Newbie's user avatar
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15 views

Depicting a Single Equation Error Correction Model in Matrix / Vector notation?

I am trying to express the following single equation error correction model in matrix / vector notation. The original model is: $ \Delta Y = y_{t-1} \delta_0 + \sum_{i=1}^{k}z_{i,t-1} \delta_k + \...
Joe94's user avatar
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What does the apostrophe mean with the explanation of how PLS works?

https://learnche.org/pid/latent-variable-modelling/projection-to-latent-structures/conceptual-mathematical-and-geometric-interpretation-of-pls What does the ' mean with t'? I wasn't 100% sure.
aim6789's user avatar
  • 77
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22 views

Notation that x given z is normally distributed

I am looking for notation stating x given z is normally distributed. The parameters of the normal distribution are unknown/irrelevant and including placeholder parameters in my context will be too ...
Snowy Baboon's user avatar
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23 views

Correct notation for uncertain expectation

I need to write some documentation for a couple of process design options. Ultimately, my organization has to find a way to estimate the values of vector $A$. I have come up with a model to calculate $...
Chechy Levas's user avatar
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1 vote
2 answers
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Meaning of subscript $n$ in sample mean variable

I am reading Wasserman's All of Statistics. In Chapter 13: Linear and Logistic Regression, when deriving the least square estimates for simple linear regression, we have the data $(Y_1, X_1), \dots,(...
Ouroboroski's user avatar
2 votes
0 answers
49 views

Notation for distributions on subspaces

Question What notation should I use for a normal distribution on a subspace $U \subset \mathbb{R}^n$? Motivation I have a geometric intuition for Bessel's correction which goes something like this: A ...
Steven Gubkin's user avatar
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Kendall's Notation for Kelly Networks?

Background Kendall's notation (also see Ciw docs') is a convenience when you work with queues a lot. It not only provides an abbreviation, but its wide use helps make literature searches more specific....
Galen's user avatar
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9 votes
3 answers
743 views

Preferred typography for "z score"

I would like to know if there is a preferred typographic form for the term "z score". A search on Google scholar for "z score" shows six forms no markup: z score hyphenated: z-...
Tristan Fabrini's user avatar
4 votes
1 answer
98 views

Meaning of the notation $ \mathbb{E}_{x\sim \mu_{\text{ref}}, y\sim \mu_D(x)}[\ln y] $ in GAN framework

A very naive question about notations used in mathematical framework for generative adversarial network (GAN). What is precise mathematical definition of terms like $$ \mathbb{E}_{x\sim \mu_{\text{...
user267839's user avatar
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1 answer
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Is the design matrix in a panel regression model a tensor?

In a panel regression model of the form $$Y_{it} = \mathbf{X}_{it} \pmb{\beta} + \epsilon_{it}$$ where $Y_{it}$ is the dependent variable for unit $i$ at time $t$ $\mathbf{X}_{it}$ is a vector of $K$ ...
Peter Jordanson's user avatar
7 votes
4 answers
797 views

Sample notation: When to use capital $N$ vs lowercase $n$?

In statistics and psychological research, what is denoted by capital $N$ vs lowercase $n$? I work in psychological research and I've seen them used in two ways: Capital $N$ represents the entirety of ...
Cameron's user avatar
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2 votes
0 answers
31 views

Stochastic order symbols - Intuition [closed]

I apologize for the following set of questions, which may seem trivial. Let $X_n$ denote a sequence of random variables. Then, $X_n = o_p(1)$ means that $\lim_{{n \to \infty}} X_n = 0$. I can use ...
Dimitru's user avatar
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1 vote
1 answer
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Does the matrix notation for OLS loss function assume that indexing a row from $X$ return a column or row vecotr?

I'm confused about the matrix notation of the loss function in ordinary least squares regression. In matrix form, the expression for a linear model is: $$\hat{y} = Xw$$ Where $\hat{y} \rightarrow$ ...
another_student's user avatar
1 vote
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Partial derivative notation extreme gradient boosting

What is meant by this notation regarding gradient boosting source: $$ g_i = \partial_{\hat{y}_i^{(t-1)}} l(y_i, \hat{y}_i^{(t-1)}) $$ Is it the partial derivative of $l$ w.r.t. $\hat{y}_i^{(t-1)}$ , i....
Herbert's user avatar
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0 answers
25 views

Conditional volatility and notation to express it

I'm taking a risk modelling class, and we're discussing conditional vs unconditional volatility. We have standard volatility $\sigma = \sqrt{\mathbb{E}[r_t - \mathbb{E}(r_t)]^2}$ But what is ...
rudinable's user avatar
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0 answers
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How to interpret the subscript of this equation?

In this paper the authors in equation 18 present $\hat{\sigma_t^2}$ as $$ \hat{\sigma}_{t}^2 = \frac{[X, X]_{t_{i M_n}} - [X, X]_{t_{(i-1)M_n}}}{t_{iM_n} - t_{(i-1)M_n}}. \tag{18} $$ How to read the ...
V013's user avatar
  • 115
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0 answers
22 views

Distribution of the relative range ($R/\sigma$) [duplicate]

Let us assume a $n$-sized random sample $\{ X_1 , \dots, X_n \}$ from a random variable $X \sim N(\mu, \sigma)$. Let $X_\mathrm{min} = \mathrm{min}\{ X_1 , \dots, X_n \}$ $X_\mathrm{max} = \mathrm{...
Vicent's user avatar
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2 votes
1 answer
40 views

Understanding notation for input space

I'm taking the free Caltech machine learning course. I'm having trouble understanding the notation on one of the problems: In this problem, you will create your own target function f and data set D ...
Ben G's user avatar
  • 153
4 votes
1 answer
44 views

The "Multiple Error Terms" notation for hierarchical models

I'm seeking clarification regarding notation for Bayesian hierarchical models, specifically the mixed effects model. Consider the following hierarchical model for the outcome of unit $i \in N$ in ...
socialscientist's user avatar
5 votes
1 answer
351 views

Conditional variance notation

Why does the formula $\operatorname{Var} (Y\mid X)= E \left (\left(Y- E (Y\mid X)\right )^2\mid X\right )$ condition $EY$, but not $Y$, on $X$?
Roman's user avatar
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1 vote
0 answers
18 views

Is the semicolon (;) notation used to indicate operations are performed concurrently in backpropagation algorithm by Bengio?

I am trying to understand the backpropagation algorithm in a multi-layer perceptron environment. Algorithm 6.4 Backward computation for the deep neural network of algorithm 6.3, which uses, in ...
Revolucion for Monica's user avatar
1 vote
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61 views

How borked is my attempted notation for a multilevel gamma regression with AR(1) autocorrelated residuals?

I have no math background and am in way over my head trying to figure out the correct notation for my model: a multilevel random-slopes gamma regression with log link and AR(1) autocorrelated ...
Nick Ballou's user avatar
1 vote
0 answers
37 views

How to mark vector of row sums of a matrix?

We are submitting a paper documenting new statistical model. We have a matrix Fi,t and a vector Fi, defined like this: Thus, the vector Fi contains row sums of matrix Fi,t. Since the definition of Fi ...
Tomas's user avatar
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4 votes
1 answer
65 views

Notation for an ordered pair of stochastic processes

There are two stochastic processes, $\{ Y_{1,t} \}$ and $\{ Y_{2,t}\}$. If I take them as an ordered pair, what notation do I use: $\{(Y_{1,t},Y_{2,t})\}$, $\{(Y_1,Y_2)_t\}$, $(\{Y_{1,t}\},\{Y_{2,t}\}...
Richard Hardy's user avatar
7 votes
3 answers
601 views

What is the cross product of two probability distributions $P \times Q$?

In many papers on machine learning and statistics, I encounter the following notation Let $P$ be a distribution, and let $Q$ be another distribution. Then the author creates an object $P \times Q$ ...
Fraïssé's user avatar
  • 1,590
-1 votes
2 answers
92 views

Purpose of distribution "over" a variable notation

The deep learning book (Goodfellow, Bengio, and Courville, 2016)'s notation section says $\mathcal{N}(\mathbf{x}; \mathbf{\mu}, \mathbf{\Sigma})$ represents a normal distribution over $\mathbf{x}$, ...
Vityou's user avatar
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1 vote
1 answer
92 views

Mathematical/statistical notation of a linear regression model with three-way interaction

I am unsure how to present the equation of a three way interaction linear model (without expanding all the interaction effects). Let me clarify: $y$ is a continuous outcome measured at time $i$ (for $...
Jacob's user avatar
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1 vote
0 answers
58 views

Semantics: Conditional Distribution vs Marginal Distribution

This is something which has always confused me. Suppose we take a standard statistical regression model: \begin{equation} Y_i = \beta_0 + \beta_1 X_i + \epsilon_i \end{equation} where: $Y_i$ is the ...
stats_noob's user avatar
8 votes
4 answers
322 views

iid data (Bayesian) vs iid random variables (Frequentist)?

I've been pondering the differences in notation / language used in some of the resources I've read for statistics / machine learning. Warning: this might be embarrassingly obvious to any decent ...
paul's user avatar
  • 415
1 vote
1 answer
45 views

How to define & mathematically denote "true individual probability"?

The notion of an individual's "true probability" or "true risk" of a certain outcome $Y$ is contested [1, 2, 3]. Nevertheless, it is often discussed and useful for certain kinds of ...
Eike P.'s user avatar
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0 votes
0 answers
24 views

Random variable notation in Gaussian Process

In a number of online articles (e.g. 1, 2) I see the $x$ values over which a Gaussian Process is used written as $X$, e.g. the training points are $X$, test points are $X_*$, and (in the 1D case) the ...
Joseph's user avatar
  • 143
0 votes
1 answer
28 views

How to rewrite a multivariate polynomial term without redundancies?

This is from an exercise found here on page 60. My question is: what is meant by $\sum\limits_{i_1=1}^D\sum\limits_{i_2=1}^{i_1}...\sum\limits_{i_M=1}^{i_{M-1}}w_{i_1i_2...i_M}x_{i_1}x_{i_2}...x_{i_M}$...
user1169080's user avatar
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0 answers
40 views

Terminology / notation for the set of variables associated with a distribution

Suppose I have a conditional (or any) distribution as so: $$ p(A \mid B,C,D) $$ and in the text, I want to refer to the variables $\{A,B,C,D\}$ associated with that density (or mass). Is there a ...
Astrid's user avatar
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2 votes
0 answers
29 views

Notation for calculating $p(v)$ marginalising over $h$ in an Restricted Boltzmann Machine

I am working through equation 22 in Introduction to Boltzmann Machines I am a little confused with the notation, in particular in the line: As I understand it, we want the probability of a specific ...
Joseph's user avatar
  • 143
8 votes
2 answers
2k views

What does Φ mean? [closed]

In the documentation of METAL, a software for meta-analyzing GWAS results, Φ is in the formulas. Intermediate Statistics $Z_i = \Phi^{−1}(P_i/2) * \textrm{sign}(\Delta_i$) Overall P-value $P=2\...
John Smith's user avatar
0 votes
0 answers
36 views

What does this notation mean? $\mathbb{P}_{x\sim \mathcal{D}}$: Clarification in the definition of generalization error $R(h)$

I was reading the book foundations of machine learning by Mehryar Mohri, Afshin Rostamizadeh and Ameet Talwalkar, and I came up with this definition of generalization error: I dont understand what ...
NoetherNerd's user avatar
2 votes
1 answer
98 views

Notational confusion about conditional independence in Pearl 2009

First I read this definition which introduces $X$, $Y$ and $Z$ as sets of random variables. Definition (Pearl 2009) Let $V = \{V_1, V_2, \ldots \}$ be a finite set of variables. Let $P(\cdot)$ be a ...
Galen's user avatar
  • 9,361
2 votes
1 answer
92 views

How to write a Kullback–Leibler divergence in mathematically correct notation?

Let we have random variables $X$, $Y$, $Z$ and a function $q: Z \to \mathbb{R}$. How to write a Kullback–Leibler divergence between $q(Z)$ and $p(Z|X)$ mathematically correct? If we write $D_{\text{...
Oleg S's user avatar
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2 votes
1 answer
95 views

Confused by the notation in DAG depicting structural causal model and corresponding functional equations

Statistical Notations confuses me a lot and I get lost easily in following when the authors are talking about random variables vs observations, probabilities, probability density functions or ...
amsulic's user avatar
  • 61
3 votes
1 answer
965 views

What are balanced and orthogonal designed experiments?

I have recently started studying Designed Experiments and have have come across non-rigorous definitions of "balanced" and "orthogonal" experiments and would be interested in ...
FD_bfa's user avatar
  • 243
13 votes
4 answers
2k views

How should variables in statistics be understood?

I had a slightly basic question about variables (particularly in statistics). We would say that “height” is a variable. In my mind, “height” does not just represent different values, like 2, 45, or 75....
Pranav Jain's user avatar
3 votes
1 answer
205 views

Why do I sometimes see the expectation E, probability P and distributions written in blackboard bold?

For example, $\mathbb{P}(X = 1)$ rather than $P(X=1)$ And for example:
TheFriendlyAsker's user avatar
9 votes
2 answers
1k views

How would you write mathematically that a random variable follows some unknown distribution?

For example, if I had a random variable X and knew it followed a normal distribution, I might write: $X \sim N(5, 10)$ What would I write if I'm trying to say that the distribution is unknown? $X \in \...
TheFriendlyAsker's user avatar
2 votes
0 answers
64 views

What does $\times_i \Sigma_i$ mean?

I cannot for the life of me figure this out. The context is from game theory (source: Game Theory by Fudenberg, Tirole): ... the space of mixed strategy profiles is denoted $\Sigma = \times_i \...
Sarah Hirsch's user avatar

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