Questions tagged [notation]
For questions about statistical notation and mathematical notation used in statistics.
525
questions
4
votes
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 $X$ ...
1
vote
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 $p(D|W)$ ...
0
votes
0answers
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 (...
1
vote
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: $\boldsymbol A$
...
6
votes
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
votes
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 $\min_{1\leq n \leq N}$....
2
votes
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 ...
0
votes
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 ...
1
vote
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 ...
0
votes
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 ...
0
votes
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 ...
0
votes
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\...
2
votes
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 ...
3
votes
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) ...
0
votes
0answers
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:
...
0
votes
0answers
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'} \...
2
votes
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 ...
0
votes
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(...
1
vote
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?
1
vote
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 ...
1
vote
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, ...
0
votes
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.
1
vote
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 ...
0
votes
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 ...
0
votes
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 ...
0
votes
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}? ...
0
votes
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 ...
0
votes
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 $F_{i}\left(x_{i}\right)=$...
0
votes
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 ...
5
votes
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 ...
0
votes
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?
...
6
votes
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 ...
0
votes
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)....
2
votes
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 $...
1
vote
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
$EPE(f) = E(Y - f(x))^{2}$
...
1
vote
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 ...
-1
votes
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 ...
1
vote
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 ...
0
votes
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.
1
vote
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 ...
0
votes
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}...
1
vote
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 ...
1
vote
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 ...
0
votes
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
votes
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 ...
1
vote
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 ...
2
votes
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 ...
1
vote
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
vote
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
votes
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 ...
