Questions tagged [notation]

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

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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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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 ...
johnf42's user avatar
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56 views

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
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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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1 answer
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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
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1 answer
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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
328 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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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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59 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
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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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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
5 votes
3 answers
315 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
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2 answers
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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 $\mathbf{x}$, ...
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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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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
6 votes
4 answers
204 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
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1 answer
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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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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
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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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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 ...
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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
1k 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
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Is a structural VAR method ideal to analyze the effects of the German 9Euro Public transport ticket on CPI?

I am trying to analyse the effects that the German policy to introduce a 9Euro public transport ticket had on German CPI using a VAR model (which, according to my reading, is the most appropriate ...
Niko Busch's user avatar
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35 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
1 vote
1 answer
78 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
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2 votes
1 answer
74 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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1 answer
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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
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2 votes
1 answer
524 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
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13 votes
4 answers
1k 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
2 votes
1 answer
118 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
924 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
53 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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0 answers
73 views

In the Bernoulli distribution $P(x^{(i)} ; \theta)=\theta^\color{red}{x^{(i)}}(1-\theta)^{(1-\color{red}{x^{(i)}})}$ what does $x^{(i)}$ stand for?

I am trying to understand the Bernoulli example for the biais given in Deep Learning by Bengo et. al. in 5.4.2: Consider a set of samples $\{\color{red}{x^{(1)}, . . . , x^{(m)}}\}$ that are ...
Revolucion for Monica's user avatar
0 votes
1 answer
66 views

Help resolving apparent ambiguity: P(A|B,C) = P(A|(B,C)) or P((A|B), C)?

Per title, it always confuses me than not, specially when more random variables are used. There is more than one way to get confused imho: (As in title) P(A|B,C) = P(A|(B,C)) or P((A|B), C)? P(A,B|C) ...
StatStudent's user avatar
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1 answer
42 views

What does $R(G:X)$ mean in Rao's book?

I was reading Rao's chapter 4 of his Linear Statistical Inference, 2nd ed. He uses the notation $R(G:X)$ in section 4.i (p. 294, formula (e), p. 296 formula (4i.1.21)) and that notation appears again ...
William M.'s user avatar
2 votes
2 answers
62 views

Does a random sample $X_1, \dots, X_n$ imply $n > 1$? [closed]

I am calculating the variance for an estimator which is a function of a random sample $X_1, \dots, X_n$. However, if $n=1$, then $E(\theta^2) = \infty$ and the variance is infinite. Can I assume $n &...
s5s's user avatar
  • 665
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0 answers
21 views

Notation for uncorrelated random structure in mixed model

I will use the hsb dataset inside descriptr in R as a toy example. In my original dataset variables are different of course, ...
Unai Vicente's user avatar
3 votes
2 answers
58 views

Statistical notation question: How do I represent sorting variables, individually and by each other, symbolically?

I'd like to write a formula for a correlation coefficient that involves sorting continuous observations, both within a variable and by another variable. For example, I'd like to say that $r$ is ...
virtuolie's user avatar
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3 votes
1 answer
317 views

Notation confusion regarding Expectation in Kullback-Leibler divergence definition

KL-divergence is often defined as $$D_{KL}(P||Q) = E_{x\sim P} \left[ \log\left(\frac{P(X)}{Q(X)}\right) \right] = \int_{-\infty}^{\infty} P(x) \log\left(\frac{P(X)}{Q(X)}\right)dx$$ I don't quite ...
Soltius's user avatar
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4 votes
3 answers
290 views

Difference between Greek and Latin letters in OLS

Currently I am learning about the OLS method. In the literature I see different notations for the to be explained variable $y_i$. The different notations have to do with the letters used. In one ...
Tim's user avatar
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2 votes
1 answer
76 views

Is Z a random variable of X?

Is Z a random variable of X if it is transformed from X? If Z is a random variable, and therefore a function, of X, could one denoted Z as Zₓ(x)?
Joseph_and_Betty's user avatar
0 votes
1 answer
29 views

What does the $t|y(x, \mathbf{w})$ in ${\cal N}(t|y(x, \mathbf{w}), \beta^{-1}) $ mean?

I'm starting to work through Bishop's "Pattern Recognition and Machine Learning" book, and have run into unfamiliar statistics notation. In Eq. 160, Bishop writes the PDF for a quantity $t$ ...
Jolyon's user avatar
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0 answers
155 views

Mathematical formula for logistic regression mixed effects model

I am unsure how to write these models in mathematical notation when it is a model with nested random effects. This is how the models were created in R: ...
psych_student's user avatar
1 vote
1 answer
65 views

What is the meaning of this normal distribution?

Following is a normal distribution equation: $$q(\mathbf x_t\mid\mathbf x_{t-1})=\mathcal N(\mathbf x_t;\sqrt{1-\beta_t}\mathbf x_{t-1},\beta_t\mathbf I).$$ I understand there should be mean and ...
Jing Gu's user avatar
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1 vote
1 answer
59 views

Issue with the mathematical equation of a Gamma glm with a random intercept

I wanted to write the mathematical equation for my model below. It is a glm that tries to explain the relationship between the sum of observed biomass of several replicas at different observation ...
Florian B.'s user avatar
2 votes
0 answers
77 views

Lost in Fisher information notation

I believe I understand the gist of what Fisher Information is, but I want to be rigorous and I am confused by notation. Also I believe I am masquerading mistakes by ...
Fred Guth's user avatar
  • 193
1 vote
1 answer
300 views

Accuracy without true negatives

Are there any named metric that calculates TP/(TP+FN+FP)? It is like the accuracy, but disregarding TN In my problem, we have thousand of possible labels. However, the models return a small list of ...
Jonathan alis's user avatar
4 votes
1 answer
258 views

Proper notation for Random Matrix and observation

My question is simple, but I could not find any references for this particular case. When we have a random vector, we usually use $\boldsymbol{X}$ to denote the random vector and $\boldsymbol{x}$ to ...
Renato Fernandes's user avatar
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0 answers
32 views

Looking for help unpacking a NHST notation using probabilities

In brief, I am used to a definition of the P-value as: the probability of observing our sample data (or something more extreme) if the null hypothesis is true. Consequently, seeing null hypotheses of ...
Gregg H's user avatar
  • 5,364
2 votes
1 answer
41 views

Meaning of $\uparrow$ in below d-separation algorithm from Koller

In Probabilistic Graphical Models by Koller and Friedman there is an algorithm to find the nodes reachable from node $X$ via trails that are active, given conditioning set $Z$. What is the meaning of &...
Anirban Chakraborty's user avatar

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