Notation refers to questions about statistical and mathematical notation.

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Correct notation for unbiased estimate of population variance

I've seen the notation $s^2$, ${s}_{n}^2$, and ${s}_{n-1}^2$ used to represent the unbiased estimate of population variance. Is there a standard notation?
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1answer
236 views

What does the number E mean? [closed]

When I do some computation, I get a number as follows. I cannot use this in my further computations as it requires it to a number and not have characters in between. How can I expand this number to an ...
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0answers
31 views

How do you use mathematical notation to write out an equation for a GLM with a gamma distribution and a log link?

Basically, I'm trying to estimate a GLM in Stata with a log link function and a gamma distribution and I need the mathematical notation behind the data analysis. My model has a price variable as its ...
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1answer
33 views

A question on notation in the least squares method

I am reading some nice lecture notes on basic statistics, learning some basic topics on estimation of parameters. Reading the chapter about the method of least squares estimation I meet the following ...
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1answer
22 views

Notation for multi-level hierarchical model

I'm having a hard time understanding how to write a multi-level hierarchical linear regression model in mathematical language. Suppose, for example, that our independent variable is x, our dependent ...
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2answers
34 views

Notation: covariance on scalars?

I've recently seen the degrees-of-freedom for K-nearest neighbors regression specified like so: $\frac{1}{\sigma^2}\sum_{i=1}^NCov(y_i,\hat{y}_i)$ But what does $Cov(y_i,\hat{y}_i)$ mean? ...
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1answer
27 views

Accepted notation for sparsity/density of a network

Is there an accepted notation in the study of network structure for the measure of network sparsity and/or density? For example, I see $\rho$ is typically used for spectral radius, $\alpha$ for leak ...
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0answers
28 views

What does the notation $\chi_{(V\ge1)}$ mean in probability / statistics? [duplicate]

I reading Benjamini and Hochberg's paper on controlling the FDR, and I came across this notation "$\chi_{(V\ge1)}$" in section 2.1 paragraph (b), and I'm guessing from context that: $$ \chi_{(V\ge1)} ...
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1answer
24 views

Robinson's Geometric Mean Test

I am reading this book: Ending Spam: Bayesian Content Filtering and the Art of Statistical Language Classification by Jonathan A. Zdziarski page 78 is about the Robinsons Geometric Mean Test. ...
5
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1answer
55 views

Foundational sufficient statistics

I've been reading through Casella and Berger's Statistical Infererence and have am having a little trouble understanding something in their explanation of sufficient statistics. Here is the passage ...
5
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2answers
760 views

What does capital letter I mean in this formulas?

Hello I don't understand meaning of the symbol represented by a capital letter "I" in the formulas below. There is a link to the paper with the formulas. At the beginning I thought it mean "where c ...
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2answers
49 views

Lag polynomial coefficients for integrated stationary processes

I'm following http://faculty.chicagobooth.edu/john.cochrane/research/papers/time_series_book.pdf to ramp up on time series (my background is Elec Eng). I'm having confusion about the meaning of some ...
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1answer
22 views

Clarification on Notation

I'm using Andrew Gelman's 3rd edition of Bayesian Data Analysis and am going through the exercises. For one of the exercises, he supposes that if $\theta = 1$, then $y$ has a normal distribution with ...
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0answers
20 views

Notation question about the plus in marginal distribution symbol when calculating independence

I'm just looking at independence in a joint distribution, and understand conceptually that the distributions are independent if the joint distribution is the product of its marginal distributions; ...
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2answers
180 views

Different CDF Notations

I understand that $F_X(x)$ is the CDF of the random variable X and $F_Y(y)$ is the CDF of the random variable Y. What do these mean? 1. $F_X(y)$ 2. $F_X(X)$ 3. $F_x(Y)$
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0answers
26 views

What is the Big O of rejection sampling from large sets of weighted items (like billions of records)?

On average, how many "rejections" will I get before I get an acceptance (for large sets using weights)? This answer suggested O(log n)?
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2answers
45 views

Definition of $X_t$ in the context of Stochastic process and Time Series

In the book An Introduction to Stochastic Modeling , Stochastic process is defined as : A stochastic process is a family of random variable(s) , $X_t$ , where $t$ is a parameter running over a ...
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0answers
30 views

Control chart constants [closed]

When calculating Upper Control Limit (UCL) and Lower Control Limit (LCL) in control charts I use constants from ...
2
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2answers
154 views

Which notation should be used for the mean, SD, and median: mean±SD or mean (SD)?

I usually use mean±SD notation for reporting values. I know that many people use mean (SD) notation and I understand why. Right now in the document I am writing I am also reporting medians but I ...
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1answer
32 views

Names for standard error equations

The equation for a standard error of the mean can be written like this: $\sqrt{\frac{s^2}{n}}$ or like this $\sqrt{\frac{\left(\frac{\sum (X - \bar{X}) ^2}{n-1}\right)}{n}}$ They both say the same ...
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0answers
34 views

Notation for a random vector whose length depends on another random variable?

I have the following process that I'm trying to describe with random variables. First, I have a random variable $X$ that takes on values drawn from a Poisson distribution with parameter ...
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0answers
48 views

Correctness proof of bayesian networks

I want something simple and my brain is getting in my way. Assume I have three different coins - C1 is fair, C2 has p(Heads)=0.6 and C3 has P(haeds)=0.8 I want to draw a bayes network for the ...
2
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1answer
55 views

Question about notation in Introduction to Statistical Learning

I've been working my way through the problems in the book "Introduction to Statistical Learning". I have a question about the notation in Question 5 from Chapter 3 (screenshot below). What does ...
2
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1answer
107 views

Bayesian linear regression question

I am doing a problem on Bayesian regression but I'm having a lot of trouble with it. Here is the question: Consider $f=w^Tx$, $p(w)\sim N(w|0,\Sigma)$. Show that $p(f|x)$ is Gaussian. Find the mean ...
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0answers
42 views

Question about notation of expectation operators over multiple random processes

My question is what are suitable or accepted notations for taking expectations over multiple random processes in the same equation. Let a model for variable $y$ be given by $$y_{i ...
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1answer
41 views

What does posterior “over” parameters $\alpha$ exactly mean? [closed]

From my understanding the posterior "over" parameters $\alpha$ is $$p(D|\alpha)$$ and not $$p(\alpha|D),$$ is it correct?
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0answers
54 views

How can the output from a Cox proportional hazards model be mathematically translated into a log regression model? [closed]

I would like to write down the log-regression model associated with the formula: coxph(Surv(time, status) ~ rx + cluster(litter), rats) I am not interested in ...
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2answers
126 views

What does $\{x|x = 7\} = \emptyset$ mean? (Probability)

To my understanding $\{x|x = 7\} = \emptyset$ means that the number seven is a not allowed value. But I do not understand the meaning of "$x|x$". Can anybody please explain $\{x|x = 7\} = \emptyset$ ...
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1answer
134 views

Understanding the error term

I am trying to figure out the meaning of these different "hatted" terms in regression analysis. Here is my basic understanding: $Y$ the original of population/sample values $\hat{Y}$ regression ...
3
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1answer
48 views

Posterior of a simple Bayes linear regression

In the context of simple linear Bayesian regression, why or when is it appropriate to define the posterior as $p(\beta, \sigma^2|y)$ and not $p(\beta, \mu|y)$?
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0answers
27 views

Is it a well-established convention that pdf is lower case but CDF is upper case?

I'm wondering if the Wikipedia page for "probability density function" is wrong in having the acronym be all lower-case "pdf". The page for "cumulative distribution function" has all upper case "CDF". ...
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1answer
49 views

Why do some parameters not appear in the matrix equation for an ANOVA model?

Here is the question I have been working on and this is the answer of it I realised $\beta_3$ is not in the $\beta$ matrix. I don't understand why. Can anyone please explain this?
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1answer
55 views

Does a Bayesian network include the CPTs?

I'm preparing slides for a lecture, and I require some guidance. I'm only talking about discrete variables. How would you formally define the concepts surrounding Bayesian networks? A Bayesian ...
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0answers
32 views

$L_p$ norms for vector valued function in econometrics

What is meant in econometrics by $\|\mathbb{y}\|_p$, where $y$ is an $d$-dimensional random variable? Namely, is it true that $$\|\mathbb{y}\|_p = (E\|y\|^p)^{1/p},$$ where $\| \cdot \|$ denotes the ...
6
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1answer
191 views

What is the meaning of $\oplus$ and $\otimes$?

I am struggling to fully understand some notation in a book where they use a "crosshair" symbol - first like $\bigoplus\limits_{i=1}^n{} Z_j $ where the $Z_j$ are matrices and second like $I_n \otimes ...
2
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0answers
44 views

Standard error notation

Dealing with a standard error of a mean $$ \widehat{SE}_{\bar x} = \hat \sigma_{\bar x} = \frac{s_x}{\sqrt{n}}$$ $$ SE_{\bar x} = \sigma_{\bar x} = \frac{\sigma_x}{\sqrt{n}}$$ Is this the ...
2
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1answer
40 views

Symbol to indicate normalized or standardized variables

Is there a symbol to indicate that variables have been standardized? For example, if I have 2 different scoring functions Score1 and Score2. Let's say I want to form a combo score and show that the ...
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4answers
297 views

What is the difference between $E(X|Y)$ and $E(X|Y=y)$?

Generally, What is difference between $E(X|Y)$ and $E(X|Y=y)$? Former is function of $y$ and latter is function of $x$? It's so confusing..
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3answers
109 views

What is the correct notation for stating that random variables X and Y are independent?

Often people put down $X\perp\ Y$ as independence, but this merely means that the expectation of X and Y is zero and does not have any implication on correspondence between their joint PDF, CDF and ...
2
votes
1answer
111 views

Random Forest proof notation

I am having a bit of difficulty understanding the notation in equation (1) on page 4 of the following paper: https://escholarship.org/uc/item/35x3v9t4#page-4 Specifically, what do $E_{X,Y}$ and ...
2
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1answer
137 views

Best statistical notation for expected probability density

Assume that we have two multivariate normal distributions $\mathcal{N}_1 = \mathcal{N}(\mu_1, \Sigma_1)$ and $\mathcal{N}_2 = \mathcal{N}(\mu_2, \Sigma_2)$. We do these two steps: Pick a point, say ...
4
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3answers
81 views

What is the correct notation if two random variables belong to the same distribution?

I want to explain that both the real and imaginary part of a complex variable follow a zero-mean complex Gaussian distribution. How can I write that? For one variable I'd write $a \sim ...
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0answers
100 views

Did I write down my model correctly using matrix algebra and LaTex?

Model is essentially a seemingly unrelated regression estimation of the two following equations: ...
3
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2answers
172 views

What does the notation $(\textbf{X} \perp \textbf{Y} , \textbf{W}\mid \textbf{Z})$ mean?

I was reading Koller's and Friedman's Probabilistic Graphical Models book and became confused about some of its notation because of a set of notes that either contradict it or express it differently. ...
3
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1answer
500 views

What do vertical bars mean in statistical distributions?

What do the vertical bars mean in the first and third formulae? $$v_i|z_i=k,\mu_k\sim\mathcal{N}(\mu_k, \sigma^2)$$ $$P(z_i=k)=\pi_k$$ $$\pi|\alpha\sim \text{Dir}(\alpha/K1_K)$$ $$\mu_k\sim ...
3
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1answer
85 views

Notation: Deterministic Variable, Random Variable, Realization of Random Variable, Function

Is there a standard notation for distinguishing between the following: Random Variables Realizations of Random Variables Deterministic Variables (not random) Functions I am familiar with using ...
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2answers
36 views

X vs x Notation in law of large numbers

This may be a silly question, but I can't find a concise answer. I've been studying Convergence of Random Variables in Wasserman's All of Statistics, which starts out by explaining: $X_n$ is a ...
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2answers
115 views

Which notation and why: $\text{P}()$, $\Pr()$, $\text{Prob}()$, or $\mathbb{P}()$

Are these merely stylistic conventions, or are there substantive differences in the meanings of these notations? Are there other notations meaning "the probability of" that should be considered in ...
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2answers
60 views

Mixed variable, joint distribution, How do we know which one is continuous distribution, which one is discrete

If we have one continuous r.v. $x$ and a discrete r.v. $y$ which takes one of the two values $y_1$ and $y_2$. Let's say we know the prior probabilities $P(y_1)$ and $P(y_2)$. From Bayes theorem we ...
3
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1answer
109 views

Squared random variable $X^2$ vs $X\times X$

As I understand a random variable represents all possible outcomes of an experiment with their associated probabilities. Why $X^2$ is understood as squaring outcomes of experiments instead of as ...