# Questions tagged [notation]

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

562 questions
Filter by
Sorted by
Tagged with
15 views

### Explanation of $X: (\Omega,\mathscr A,P)→(\mathbb R , \mathscr B',\mu)$ [duplicate]

A random variable $X$ is a function with a finite value so that: $X: (\Omega,\mathscr A,P)→(\mathbb R , \mathscr B',\mu)$ I've seen this line but I don't know how to understand it. Can you please ...
147 views

### Mistake in Casella & Berger on page 207?

Page 28: A note on notation: Random variables will always be denoted with uppercase letters and the realized values of the variable (or its range) will be denoted by the corresponding lowercase ...
• 3,180
1 vote
32 views

### What does the (statistical) operator $\mathbb{D}$ usually mean? [closed]

Im reading and trying to understand the following paper on "Disentangled State Space Representations" (https://arxiv.org/pdf/1906.03255.pdf). In the derivation of the KL-loss term the ...
• 11
47 views

### Implied expressions with same probability

Given two variables $a$ and $b$ and two intervals $I$ and $J$, is the following affirmation true? $$\Pr[a\in I]\geq p\ \land\ (a\in I\implies b\in J) \implies \Pr[b\in J]\geq p$$ Of course, $a\in I$ ...
• 217
1 vote
12 views

### Is there an established way to write conditional probability for whole expression?

I am writing a methodological paper and I have expression like this, which is slightly more complicated bayes rule, because everything is conditioned by c: Is ...
• 5,835
1 vote
25 views

### Hierarchical mixed-effects models notation

I have a hierarchical mixed-effects model where observations i, from group S_2 (representing municipalities), are nested inside group S_1 (representing states), which in turn are nested inside N (...
• 255
1 vote
36 views

### conditional expectation of random vectors

For a random vector $X=(X_1, ..., X_n)^\intercal$ the expectation value can be written as $\mathbb{E}[X] = (\mathbb{E}[X_1], ..., \mathbb{E}[X_n])^\intercal$ according to equation 2 in https://en....
• 587
40 views

### What do "Expectation" mean in cost function?

I want to know whether my understanding for expectation of loss function is correct or not. (x,y) means sample data-label distribution from true distribution. And function f which is respect to ...
207 views

• 115
1 vote
39 views

### Weird Term of Log likelihood

Recall the setup of logistic regression: We assume that the posterior probability is of the form $p(Y=1|x) = \frac{1}{1+e^{\beta^Tx}}$ This assumes that Y|X is a Bernoulli Random variable. We now turn ...
• 13
65 views

### What is the meaning of the tilde use in this probability expression? [duplicate]

$$X \sim \mathcal{N}(0,1)$$ $$Y|X = x \sim \mathcal{N}(x,1)$$ I'm familiar with the normal use of tilde in indicating a random variable follows a distribution (such as in the first line of the ...
• 3
50 views

### Regression Notation - does the distribution of $y_i$ refer to the distribution of $(Y|X)$?

The title question is the main focus of what I am trying to understand, but the reasoning behind my asking is more nuanced. I have recently made transition from learning about basic forms of ...
• 61
50 views

### Why is sample variance notated as $\frac{S_{x x}}{n-1}$?

I'm going through my class textbook and it defines sample variance as this: $$s^2 = \frac{\sum (x_i - \bar x)^2}{n-1} = \frac{S_{x x}}{n-1}$$ What exactly does $S_{x x}$ mean? Is it always synonymous ...
• 137
28 views

### Notation used in time series

I found this wikipedia article about the concept of stationarity in stochastic processes. Let $\left\{X_t\right\}$ be a stochastic process and let $F_{X}(x_{t_1 + \tau}, \ldots, x_{t_n + \tau})$ ...
44 views

1 vote
32 views

### Matrix algebra with notation question on $z_{.2}$ [closed]

I am doing some matrix calculations and came across an expression which I don't really understand: $$(z_{i2}-z_{.2})(z_{j2}-z_{.2})$$ As I understand it, those are two integers which are multiplied by ...
27 views

### How to show that $\mathbb E_{X,X'} \left[\sum_{i=1}^m\sum_{j=1}^mk(x_i,x_j) \right] = 2m\mathbb E_{x\sim p} [k(x,x)]$?

I posted a related question also to math.SE. Basically, I would like to know how to show the following, which is part of this paper: \begin{align} &\frac{1}{m} \mathbb E_{X,X'}\left[\sum_{i=1}^m\...
• 3
35 views

### Making predictions with support vector classification

I am reading this book (chapter 8.3 - 8.5) about SVM's, while also trying to work with the ksvm() function from the kernlab ...
• 81
30 views

### What does e+ mean in linear mixed model output? [duplicate]

In my mixed effect model output, the Estimate for Intercept is " 7.141e+00" I know e- but I am not sure what e+ is. Also, df has numbers like 5.461e+01, 1.052e+02, 5.396e+0. If that means ...
1 vote
39 views

### Notation for the summation in unbalanced panel data

Unbalanced panel data, where $i$ stands for sections and $t$ stands for time points, have different numbers of $t$ for every $i$ (or different numbers of $i$ for every $t$, but let me use the first ...
• 53
1 vote
168 views

### What is the difference between a realisation of a random variable and random variable itself?

I am having a hard time distinguishing random variables from their realisations. (Please note that for the sake of simplicity of my question I use discrete values in my example below.) Usually, a ...
• 21
471 views

### Is a tilde or an equals sign correct in linear mixed model formulas?

I know the formula for a linear mixed model (LMM) is often (always?) written with a tilde, rather than an equals sign, between the LHS and RHS. For example, one would write outcome ~ 1 + var1 + (1|...
• 51
64 views

### What does "$\pi$-almost" mean?

I'm reading "Complex Stochastic Systems" edited by Barndorff-Nielsen et al. I found that they use the expression $\pi$-almost consistently throughout Chapter 1. I don't understand what $\pi$-...
1 vote
12 views

### Notation Clarification [duplicate]

Some functions (as an example) are written as $f(\theta;\mu,\sigma^2)$ and other occasions $f(\theta|\mu,\sigma^2)$ might be used. Can anyone clarify the difference in notation between using ';' and '|...
• 153
51 views

• 1,030
59 views

### Rao-Blackwellization in Black Box VI

In the paper, "Black Box Variational Inference," by Ranganath et al. (2013), the authors derive a Rao-Blackwellized estimator of the gradient of the evidence lower bound with respect to a ...
• 41
49 views

### Different equations for linear mixed model

I don't have statistics background but I am studying LMM and trying to understand why different resources have different notation. Based on my reading I tried following as simple model with random ...
• 23
1 vote