# Questions tagged [notation]

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

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### 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 $X$ ...
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 $p(D|W)$ ...
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 (...
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: $\boldsymbol A$ ...
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 ...
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 $\min_{1\leq n \leq N}$....
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 ...
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 ...
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 ...
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 ...
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 ...
1answer
59 views

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 ...
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(...
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?
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 ...
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, ...
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.
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 ...
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 ...
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 ...
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}? ...
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 ...
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 $F_{i}\left(x_{i}\right)=$...
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 ...
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 ...
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? ...
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 ...
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)....
2answers
100 views

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 ...