Questions tagged [notation]

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

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2answers
62 views

Lowercase $x$ vs Uppercase $X$ in statistics

There are many definitions online but they do not seem to align, or at least do not clearly correspond to, the usages I see elsewhere. For example: this website defines the difference is being $X$ ...
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1answer
18 views

Notation of the Likelihood Term in Bayesian Neural Networks

I see that in Bayesian neural networks likelihood function is defined in two ways: $p(W|D) = Z^{-1} p(D|W)p(W)$ or $p(W|y,x)=Z^{-1}p(y|x,W)p(W)$ Are there a slight difference in interpreting $p(D|W)$ ...
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6 views

Why is the set of parents written as a random variable in Zuk 2012?

There is a convention in statistics to write random variables in capital form, and their instantiations (realizations) in lowercase form. In a given Bayesian network each node will have a given (...
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1answer
36 views

How to express the notion of a vector, where every element inside is matrix?

I met a question when I tried to express a vector, where every element inside is a matrix. We know the notion usually works like this: scalar: $a$ vector: $\boldsymbol{a}$ matrix: $\boldsymbol A$ ...
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1answer
348 views

How to interpret Pearl's do notation?

I'm going through the Dragonnet paper (slides available here), and the authors use Pearl's do notation to make this claim: How can I interpret the do notation? Is the author claiming that the average ...
5
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1answer
37 views

What does the syntax $\min_{1\leq n \leq N}$ mean in $\min_{1\leq n \leq N} y_n(\mathbf w^{*T}\mathbf x_n)$?

I'm working through a machine learning problem and it uses the following syntax: $$\rho=\min_{1\leq n \leq N} y_n(\mathbf w^{*T}\mathbf x_n)$$ I am not familiar with the syntax $\min_{1\leq n \leq N}$....
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2answers
124 views

Estimated linear model: notation, properties of residuals

Let us say we have a linear model $$ Y=\beta_0+\beta_1X+\varepsilon, \quad \varepsilon|X\sim i.i.N(0,\sigma^2). $$ Suppose estimation yields $(\hat\beta_0,\hat\beta_1,\hat\sigma^2)=(5,2,9)$. Question ...
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1answer
39 views

How to write a multilevel GLM poisson model in mathematical notation?

I have constructed a Poisson GLM (modeling it Bayesian in brms) as a part of a social network analysis, predicting counts of outgroup/ingroup connections over two different cohorts/years of a study ...
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1answer
121 views

Derivation of Hessian for multinomial logistic regression in Böhning (1992)

This question is basically about row/column notation of derivatives and some basic rules. However, I couldn't figure out where I'm wrong. For multinomial logistic regression, I'm trying to get the ...
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0answers
18 views

Notation in Variational Inference models

Using VAEs to perform approximate inference, most often I see notation akin to this where the network parameters are written in the index and the conditioning notation is preserved for actual random ...
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0answers
40 views

comment on: semicolon notation in joint and conditional probability

This question is really a comment on: what is the semicolon notation in joint probability?. I attached a short version of this comment on it -- written as a rhetorical question -- but then was asked ...
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1answer
59 views

Why does $\pm$ mean two different things in statistics?

In statistics, why do we sometimes use the symbol $\pm$ to mean interval of numbers, for example in confidence intervals, and sometimes to mean two numbers, for example in the formula $x=\frac{-b\pm\...
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0answers
68 views

Use of lowercase letters for random variables in machine learning

In statistics/probability, a random sample from a distribution $D$ is a set of i.i.d. random variables denoted by $X_1, X_2, \dots, X_n$, each with distribution $D$. A realization of a random sample ...
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1answer
36 views

Equation notation for crossed-effect mixed models

I have conducted a crossed-effect logistic regression using Stata's meqrlogit command and have been asked to provide the equation notation. I have participants (ID) who each rated 8 activities (act) ...
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20 views

Mathematical expression for a cross-correlation matrix

Given the matrices $A_{p\times q}$ and $B_{p\times q}$ with $p>q$ the cross-correlation matrix in R is calculated as: cor(A,B) The underlaying code for this is: ...
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8 views

Notation for counterfactual conditional independencies

What is the standard way to express the conjunction of the following 4 counterfactual conditional independencies with dichotomous $X \in \{x, x'\}$? $Y_x \perp \!\!\! \perp Z_{x'} | Z_x$ $Y_{x'} \...
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2answers
70 views

Notation for ECDF

I'm reviewing statistical functionals and U-statistics, trying to make notes, and I am tripping on notation. From my understanding, $X$ is used to denote a random variable and $x$ is used to denote an ...
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2answers
74 views

Likelihood $L(\theta; \mathbf{y})$: Is $\theta$ a vector of parameters or is it a single parameter?

I have the following definition of likelihood: Let $y_1, \dots, y_n$ be a sample of observations taken on corresponding random variables $Y_1, \dots, Y_n$ whose distribution depends on the parameter(...
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1answer
31 views

How is this given distribution specified? What is the PDF?

If you say that $$ Y \sim \sigma^2 \chi^2(n-1) / (n-1) $$ what does that mean then? Is it just a scaled version of the expression of the pdf?
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1answer
32 views

Understanding math notation in infoGAN paper

I'm reading this paper about mutual information in infoGAN infoGAN_paper_link and already have the code to run it. I pretty much found code for it which is fine and dandy except for the fact that I ...
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1answer
19 views

AR model notation for non-consecutive PACF values?

I am fairly new to time series analysis, and I was learning from this tutorial on AR. The process's PACF has non-zero values at lag t-1, ...
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0answers
8 views

How to define data within a 1D matrix as categorical

Is there any way to clearly delineate that the data contained within a matrix is categorical to the reader? Ie: is there a symbol that I can use to mark the data as qualitative and not quantitative.
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0answers
59 views

Bayesian inference - Pi notation

I often see people use $\pi(\theta|y)$ and $\pi(\theta)$ for posterior distribution and prior, respectively. e.g. $\pi(\theta|y) \propto f(y|\theta)*\pi(\theta)$ sometime, the notation is simply ...
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1answer
58 views

Induced Likelihood Function for Max Likelihood Estimators

A small doubt on the notation for the induced likelihood function and invariance properties of maximum likelihood estimators - It says in a textbook I am reading that: Let $X = {X1, X2,..., Xn}$ be a ...
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1answer
48 views

Different notations for cutoff values in statistical tests ($z_{\frac{\alpha}{2}}$ and $t_{\frac{\alpha}{2}}$)

I realize that this question is most likely not too interesting and challenging to discuss here, it's rather a matter of different notations, but I would like to clarify that if possible. When ...
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0answers
15 views

The successor state and action with different notation in Reinforcement Learning

I am currently writing a summary of what I understand from the bellman equation, Value- and Q-functions. I am getting different ways of writing the Bellman equation: Does a' mean the same as a_{t+1}? ...
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0answers
63 views

Sampling notation

I have a question regarding the notation in two papers (these two papers are not related and are simply meant to illustrate the notation): In Auto-encoding Variational Bayes Kingma and Welling sample ...
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1answer
49 views

Way to define marginal probabilities

I found this notation in one paper that focuses on copulas: Consider a $d$ -dimensional continuous random vector $X=\left\{X_{1}, X_{2}, \cdots X_{d}\right\}$ with marginals $F_{i}\left(x_{i}\right)=$...
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0answers
8 views

Common notation of a time series variable that is aggregated to another time frame to differentiate from itself measured in another time frequency

Just a very general question I am interested in. Assume I have a variable that measures sth on a monthly basis and I aggregate it to another time scale, say ...
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2answers
138 views

Should you introduce new notation for every regression?

I am currently writing an empirical paper which reports on the results from estimating a number of regression models. Question: is it standard to introduce new notation for each of these models, or ...
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0answers
23 views

Help with the appropriate mathematical notation for the zero inflated negative binomial model in brms

Can someone please help me with the appropriate mathematical notation for the zero inflated negative binomial model below? ...
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4answers
537 views

Why is entropy sometimes written as a function with a random variable as its argument?

Why do people sometimes write the entropy as a function on a random variable? For example, in some class notes I am seeing: $$ \sum_X Q(X) \log Q(X) = - H_Q(X) $$ I realize this is not to be taken as ...
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1answer
44 views

Symbol for 'equally likely/probable'

I'm looking for the 'mathematical' symbol, if it exists, that denotes 'equally likely'. For example, one has two potential outcomes from a present state, both of which are equally likely (or probable)....
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2answers
100 views

Intuitively understanding $F_X(X)$ (r.v. as argument) [duplicate]

When considering some cdf $F_X(x)$ — e.g. from here — I’m having a hard time trying to understand what $F_X(X)$ really means. Expanding gives $P(X \leq X)$, which at first glance should always equal $...
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1answer
29 views

Derivation of expected loss ESL (integrating over conditional expectation confusion)

I am trying to understand the derivation of expected loss (equation 2.11 in Elements of Statistical learning) and there is a specific step I do not understand. We start with $EPE(f) = E(Y - f(x))^{2}$ ...
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1answer
32 views

auto.arima and Arima equations in R

(First of all, sorry if my English isn't perfect) I'm new in R and with ARIMA models, and I am trying to understand the equations under Arima or ...
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2answers
292 views

$f(\{Y \vert X = x\})$ vs $f(Y) \vert X = x$

This is probably a question with a simple answer, but the reason is likely to be more technical. Suppose $Y$ and $X$ are random variables and $f$ is a function of single variable (it is not to mean ...
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1answer
35 views

$O_p$ and orders in probability

How can we relate the notions of the order of some term with his expectation and variance? I was reading a paper which aims to find the order of some random sequence $X_n$ and it says (it doesn't ...
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0answers
35 views

Trouble Understanding Statistics Notation

I'm specifically having trouble understanding this paragraph and most of the notation. If someone could explain what $EX$, $X$ bar, and the whole quantile definition meant that would be great.
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1answer
27 views

Correct notation for the probability of an event in entropy

I am looking at the formula of entropy on Wikipedia, where $P(X)$ is a probability mass function. \begin{equation} H(X) = -\sum_{i=1}^{n}P(x_i)log_bP(x_i) \end{equation} I got curious why they use ...
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0answers
6 views

Simplify notation of composite variables

Is it possible to simplify the notation of the 'composite' variables (the explanatory variables expressed using a sum) in the regression that follows: $$y_{t}= \alpha+\beta_{-1} N_{t+1}+\beta_{1} N_{t}...
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0answers
22 views

Difference of the indices i and j in binary response models

I am currently trying to get the hang of binary probit and logit models as well as multinomial models, but I struggle to see the difference in the indices i and j respectively the difference in their ...
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0answers
23 views

In confirmatory factor analysis, what is the notation for the modification index?

What symbol or abbreviation can we use to refer to the modification index? Say you were writing an article about a CFA that was performed and inside of the article you want to list several ...
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1answer
40 views

Mixed Model / Wilkinson Notation for Interaction Effects

I'm a bit confused about the various notations that are used to describe effects and coefficients in mixed models. I have 2 main effects and included the 2-way interaction effect in my model. The ...
0
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1answer
33 views

How to formally write a VAR model including an exogenous variable?

I fitted a Vector Auto-Regressive models of order 2 VAR(2) with two variables "V1" and "V2" plus an exogenous one "EX". How can I formally write the equations of the ...
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2answers
50 views

Residual Subscript in Time Series

I am familiar with the following notation for a simple AR1 model: $ x_t = x_{t-1} + \epsilon_t $. However, I recently came across a very well known paper in my area of research, in which the authors ...
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1answer
50 views

Notation for expected value [duplicate]

I often find the following notation in ML Papers, with $k$ as kernel: $E_{x, y \sim p} [ k(x, y ) ]$ I am not familiar with it. Is it the expected value with $x$ and $y$ as a random variable with ...
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0answers
15 views

Appropriate notation for denoting a multivariate student's t distribution?

Suppose, we have a vector variable $\mathbf{Y}=[y_1,y_2]$, such that $\mathbf{Y}\sim N(0,I)$, where $I$ is the identity matrix. Then the bivariate distribution $P[y_1\leq Y_1,y_2\leq Y_2]$ can be ...
1
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1answer
41 views

Summation notation

I am reading a statistics book which says: " If $ X \sim N ( \mu, \sigma^2)$, it is verified that: $ \sum_{i=1}^{n}X \sim N ( n\mu, n\sigma^2) $ My doubt is if it should have been written as $ ...
2
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1answer
163 views

Mathematical (matrix) notation for a regression model with several dummy variables

I have spent a significant amount of time on this, but my knowledge in Matrix Algebra is still limited. So, I am not sure ... I have a linear regression model based on $n$ observations. The dependent ...

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