Notation refers to questions about statistical and mathematical notation.

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Hypothesis testing – abusing notation or am I missing something?

In a number of statistics books and references you can find formulas such as: $P\,(result~|~H_0)$ (Bortz, p. 114) $P\,(reject~H_0\;|\;H_0~valid)$ (Wikipedia - Statistical hypothesis testing) and ...
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Are the $\text{P}$ and $\Pr$ operators equivalent?

I have seen both used to represent probability. Are they interchangeable?
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45 views

constant $times$ distribution

I know that if $U\sim\chi^2(k)$ then $aU\sim \Gamma(k/2,2a)$ for $a>0$. But i read about the estimator and its distribution $$\hat{\sigma}_k^2=\frac{1}{2k}\sum_{i=1}^k ...
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86 views

What does it mean 'A random variable is a function'?

I have sometimes seen the formulas such that $\operatorname{Var}(aX+b)=a^2\operatorname{Var} X$ and $EX^2=\sum_{x=0}^nx^2\binom{n}{x}p^x(1-p)^{n-x}$. But how do we define $aX+b$ and $X^2$ if, say ...
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458 views

What does this notation mean?

Could anybody tell me what is this model? What does it mean? $$\Delta Y = C + a(Y_{t-1} + bX_{t-1}) + c\Delta Y_{t-1} + d\Delta X_{t-1} + \varepsilon_t$$ Where $\Delta$ is the differencing operator, ...
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1answer
18 views

Wilcoxon Rank-Sum Test $H_1$ notation

This notation is from Nonparametric Statistical Inference, 5th ed., by Gibbons and Chakraborti. On p. 290, it states: Wilcoxon (1945) proposed a test where we accept the one-sided location ...
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66 views

Notation for constant random variables?

Suppose $X$ is a random variable. Now, suppose I want to add a constant random variable to $X$. Should I denote the constant by a lower- or upper-case letter? So $X+A$ or $X+a$?
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19 views

Notation - gradients

i am reading Friedman's paper on stochastic boosting - and saw as per below the following set of formulas. purely from a notation perspective - why do we write $F(x)$ = $F_{m-1}(x)$ outside the ...
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Meaning of $\psi$ in regard to $p$-value distributions

In Combining dependent P-values by Kost & McDermott, the notation $\psi$ is used in a way that I am not familiar with. Relevant passge: 2.1. Known Variance. Let ...
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1answer
67 views

About the $X\sim \mathcal{N}$ notation

If a random variable $X$ has mean $\mu_{X}$ and variance $\sigma_{X}^{2}$, and follows a normal distribution, it may be written as $X\sim \mathcal{N}(\mu_{X},\sigma_{X}^{2})$. Suppose $Y$ is also ...
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Math notation for bayesian hierarchical models with covariance matrix with LKJ priors

I am fitting a simple hierarchical bayesian gaussian model of the form: $$ Y = b_0 + b_1 X_1 + b_2 X_2 + e $$ $$ b_{0:2} \sim N(\theta_{0:2}, \sigma_{0:2}) $$ $$ \sigma_{0:2} \sim Gamma(.001 , .001) ...
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How is the notation $X\sim N(\mu,\sigma^2)$ read?

How is the notation $X\sim N(\mu,\sigma^2)$ read? Is it $X$ follows a normal distribution? Or $X$ is a normal distribution? Or perhaps $X$ is approximately normal.. What if there are several ...
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105 views

What is the difference between x-bar and X-bar?

I'm reading "Statistics: Principles and Methods" by Johnson and Bhattacharyya (7th edition). I know x-bar is sample mean, mu is population mean, s^2 is sample variance, σ^2 is population variance, s ...
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1answer
24 views

Notation - brackets

How should i interpret the square brackets [] in the third formula per below?
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how can I interpret this notation?

I was wonder if anyone could interpret this in words "Under the Gaussian process prior, these functions depend on the model solely through its predictive mean function ...." Thank you in-advance !
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2answers
64 views

Does ARIMA(0,1,11)4 exist?

I have, without luck, searched to find what an ARIMA model that is differenced once, and has two moving average terms (one at lag 1 and one at lag 4) is called. The equation for what I am asking for ...
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1answer
23 views

Notation - stacked vectors

I am trying to self-study Kevin Murphy's book on machine learning. i am trying to be 100% sure that i understand the notation in the book. . I am however struggling to understand what is meant with ...
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79 views

Notation is confusing me (sufficiency principle)

This example (from a book) illustrates the sufficiency principle and I will write it down so that you get some context : Let $\boldsymbol{X} = (X_1,X_2..,X_n)$ be a sample of independent Bernoulli ...
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1answer
24 views

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
245 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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41 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
37 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
29 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
36 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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30 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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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
25 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. ...
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1answer
60 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 ...
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782 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
55 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
23 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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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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195 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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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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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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35 views

Control chart constants [closed]

When calculating Upper Control Limit (UCL) and Lower Control Limit (LCL) in control charts I use constants from ...
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2answers
170 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
34 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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37 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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51 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 ...
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1answer
58 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 ...
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1answer
111 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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43 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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43 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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59 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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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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144 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 ...
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1answer
49 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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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?