Notation refers to questions about statistical and mathematical notation.

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Variance and covariance notation: $\sigma^2 V_1$, $\sigma^2 V_2$

I am reading an internal paper that says: Let $\sigma^2 V_1$ equal the variance of $\sum_{m\in M}Z_m - Z_0$ and $\sigma^2V_2$ equal the covariance of $||M||^{-1}\sum_{m\in M}Z_m - Z_0$ and $Z_m ...
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6 views

Angled brackets in notation (expectation or inner product doesn't seem to make sense)

I am reading an internal paper at my university that refers to volatility (for a variable not explicitly mentioned) as: $\langle X,X\rangle = \int_0^T \sigma_t \, \mathrm{d}t.$ I am unfamiliar with ...
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0answers
10 views

Question on Matrix Operation Notation

I have confused myself in attempt to express a 2-step operation in matrix notation-- The data consists of 2 "chunks" of information--quantity of identical items sold in different stores and their ...
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3answers
325 views

Is the “test statistic” a value or a random variable?

I am a student taking my first Statistics course now. I am confused by the term "test statistic". In the following (I saw this in some textbooks), $t$ seems to be a specific value calculated from a ...
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1answer
124 views

Logit link notation

Here is the whole question: (a)A Simulation Study (Logistic Regression). Assume $y|x \sim \mathrm{Binary}(p)$, where $p= \mathrm{E}(y|x)$, and $\mathrm{logit}(p_i)=-1+5.1x_{1i}-0.3*x_{2i}$. ...
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4answers
1k views

Is it correct to use 'Ln' instead of 'ln' for natural logarithm?

In some research papers, authors use 'Ln' for natural logarithm instead of 'ln'. Is it correct?
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4answers
327 views

Regression residual distribution assumptions

Why is it necessary to place the distributional assumption on the errors, i.e. $y_i = X\beta + \epsilon_{i}$, with $\epsilon_{i} \sim \mathcal{N}(0,\sigma^{2})$. Why not write $y_i = X\beta + ...
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1answer
89 views

Help Translating R GLM Command to Math Notation

I have the following generalized linear model. Object glmDV is modeled as a proportion of successes over total trials. Objects ...
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1answer
55 views

Basic algebra question regarding properties of the summation operator

I admit that my algebra is rusty. Can someone please explain how the middle part of the top equation is transformed to the middle part of the bottom equation (both are highlighted in black).
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0answers
98 views

What is best formula style to write of statistical results in a scientific or medical paper?

I have written a dozen scientific papers and posters about medical trials and psychological trials with a lot of statistical analysis, and a common question "perturbed my certainties": How do I ...
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1answer
80 views

Notation for Random Bernoulli-Like Vector With Fixed Sum

I draw a random vector of dimensionality $k$, each dichotomous element of which taking on a value in $\{0,1\}$. The probability that any element will be $1$ is captured in the $k$-dimensional ...
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1answer
31 views

Expectation of a function of two variables, not with respect to the joint distribution

I am confused by the following expectation which appears within equation (1) of the following paper http://statweb.stanford.edu/~jhf/ftp/trebst.pdf: $E_{X}[E_{Y}[L(Y,F(X))]|X]$ I am confused by the ...
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2answers
72 views

Is it possible for a multinomial sample to be a single number?

I'm reading the Latent Dirichlet Allocation paper trying to understand it. However I got stuck at the very first part! When they sampled from a multinomial distribution and considered the result to be ...
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0answers
25 views

Graphical notation for chaining nodes over time

Is there any plate-notation-like notation used for chaining nodes in a graphical model? For example how to represent a Hidden Markov Models graphically and compactly without using repetitions: ...
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0answers
62 views

What is the meaning of angle brackets?

I have this formula: $\Delta a_{ki} \propto v_k (v_i - \langle v_i \rangle_{recon})$ First, what does $\propto$ mean and second, what is the difference between $v_i$ and $\langle v_i \rangle$?
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0answers
124 views

Why does R use standard deviation instead of variance in normal distribution? [closed]

The title says it all. When working with the normal distribution, we use variance, e.g. $X \sim N(\mu, \sigma^2)$ but working in R, we have to specify the standard deviation: ...
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2answers
206 views

Weird formula for linear regression

I'll try to make the matter as clear as possible given the circumstances. My boss asked me to look at an old report a former employee wrote around a couple of months ago. Apparently the report ...
2
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0answers
165 views

Conditional expectation subscript notation

This should be a relatively simple question. I'm trying to confirm my understanding of the subscript notation on expectations when the subscript denotes a conditioning. In the example ...
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0answers
66 views

Is there any “standard” for statistical model notation?

In, for example, the BUGS manual or the upcoming book by Lee and Wagenmakers (pdf) and in many other places a type of notation is used that to me seems very flexible in that it can be used to ...
3
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1answer
73 views

Notation for random vectors

Random variables are usually denoted with upper-case letters. For example, there could be a random variable $X$. Now, because vectors are usually denoted with a bold lower-case letter (e.g. ...
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0answers
63 views

Notational question about Bayesian prior

This is a simple question about notation. Let $\mathbf{p}$ be a Bayesian prior. Let $\mathbf{x}$ be the data, which is a random vector. Let $\mathbf{S}$ be some indexing set for $\mathbf{x}$. Then ...
3
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1answer
166 views

In statistics what does NA stand for?

I understand that NA means data is missing, null or not present. But what do the letters NA stand for? "Not Available"?
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1answer
549 views

Subscript notation in expectations

What is the exact meaning of the subscript notation $\mathbb{E}_X[f(X)]$ in conditional expectations in the framework of measure theory ? These subscripts do not appear in the definition of ...
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0answers
70 views

How to know whether a vector is a row or a column?

When the text simply says that $X_i$ is a J-dimensional random variable, how do I know that it's supposed to have $1 \times j$ or $j \times 1$ dimension? An example where this matters is Cramer-Wald ...
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2answers
437 views

“Critical value at 5%” or “critical value at 95%”: what is the right way to say it?

I have a quite simple (and not particularly intriguing) question about the way to present a test. I was wondering what is the right expression (or more widespread) when I talk about critical values. ...
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1answer
75 views

How to calculate the weighted covariance?

I'm trying to calculate the weighted co-variance by hand to better understand what is going on. I have read the Wikipeida article and I understand the concept. However, when plugging in numerical ...
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1answer
190 views

Confusion related to expectation notation

I have a confusion regarding notation of the expectation. Consider the following: $$E_x(x^2) = \sum_x x^2p(x)$$ $$E_x(x|y) = \sum_x xp(x|y)$$ So the same notation here is giving different meaning ...
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1answer
176 views

Statistical notation in plain English

I have a very limited understanding of statistics, and am having trouble translating an answer to this question from quant.SE, "Separating the wheat from the chaff", the answer being: Larry Harris ...
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1answer
191 views

Probability notation question [duplicate]

I am reading the Hidden Markov Model note http://cs229.stanford.edu/section/cs229-hmm.pdf from Stanford and have problem finding the meaning of the notation described below. What does the semicolon ...
2
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1answer
68 views

Confused about meaning of rule

What does this mean exactly? Image source I'm a bit confused about the part with z-score. It seems to be important when testing hypothesis.
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66 views

Difference between gamma symbol and betas

I am slightly getting confused at the presentation of regression models. What would be the difference between these two: $y = \beta_0 + \beta_1 x_1 + \beta_2 x_2$ $y = \gamma_0 + \gamma_1 x_1 + ...
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0answers
60 views

Help on expressing a model

I am a complete newbie in statistical modeling and I never got the opportunity to learn how to express a model in algebraic form and its respective matrix notation. I know how to define models in R ...
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68 views

Notation of orthogonality

Consider three random variables $X,Y,Z$, which are jointly normally distributed. I know that $Y$ is orthogonal to $X$ conditional on $Z$, in the sense that $\beta_{YX;Z}=0$ (i.e. the regression ...
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1answer
38 views

Unstandardized beta with an E in it

I have an unstandardized beta of -2.615-E5. What does the E mean? I have never seen this. Thanks!
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1answer
122 views

Notation for sample mean: $\overline{Y}_{\cdot{j}}=\frac{\sum\limits_{i=1}^N Y_{ij}}{N}$

I sometimes see the following notation, e.g., for the mean of the jth variable over N observations: $\overline{Y}_{\cdot{j}}=\frac{\sum\limits_{i=1}^N Y_{ij}}{N}$ My question is: What is this little ...
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1answer
48 views

Little help with notation on estimated functions of random variables

I'm writing something involving random variables and I'm not sure about the notation being right or not, so I'd really appreciate it if someone could take a quick look and confirm. We have a ...
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1answer
51 views

Notation for the sample total variation

Given a sample $x=(x_1, \ldots, x_n)$, what is your favorite notation for the sum of squares $\sum (x_i -\bar x)^2$ ? I like to keep $s^2_x$ for the sample variance, and I wonder whether $ss^2_x$ is a ...
3
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0answers
122 views

Simple question about notation

In the context of likelihood-based inference, I've seen some notation concerning the parameter(s) of interest which I've found a little confusing. For example, notation such as $p_{\theta}(x)$ and ...
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1answer
110 views

Denotation of probability symbols

May I kindly clarify if the following mean the same thing? $$P(AB) = P(A \cap B)$$ Cheers.
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1answer
202 views

Proof of normal equation in regression using tensor notation

I'm struggling with a proof of the normal equation, so I posted a question which hopefully will get resolved soon. However, I mentioned there that I'm uncomfortable with the proofs dealing with matrix ...
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1answer
27 views

How to compute y caret

I have been given a data points $x_i,y_i,1\leq i\leq n$. I was asked to compute the standard error of regression coefficients estimates. As in the formula, I have to compute $\sum_{i=1}^n ...
2
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2answers
91 views

Bayesian Inference Notation Confusion

In Bayesian Inference the following notation is quite common: $P(H|D) = \frac{P(D|H)P(H)}{P(D)}$ where $D$ is data and $H$ is hypothesis. Moreover $P(D)$ is represented as total probability. $P(D) ...
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1answer
92 views

Some problems understanding the definition of a function in a maximum likelihood method

I encountered the maximum likelihood method. It says that the common probability density function of sample $X_1,\ldots,X_n$ having distribution $f(x;\theta )$ with observed values $x_1,\ldots,x_n$ is ...
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0answers
182 views

SVM hyperplane equation

I am trying to understand the hyperplane of the SVM algorithm. My problem is that different sources state different equations. Which equation is the right one and if both are right, why? ...
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0answers
68 views

Why is $\rho$ used for both the population correlation and the Spearman estimate?

I am wondering why $\rho$ is used to denote the population correlation whereas it's also used to denote the Spearman correlation estimate. In this wikipedia article it's used to represent the Pearson ...
5
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3answers
226 views

What is the preferred way to give asymmetric uncertainties?

I have seen something like $4.1^{+2.1}_{-1.5}$ or $4.1 [+2.1, -1.5]$ but I would like to know, what is the preferred way or something like a standard in scientific work (especially in ...
3
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1answer
565 views

Expectation Subscript

What is meant by subscripting the expectation with some distribution, e.g. $\mathrm{E_{f}}[h(X)]$? If it's any help, here's the context: In M.C. Simulation, we wanted $\mathrm{E[h(X)] = ...
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1answer
46 views

Notation of a resampled mean

For a work that I have to document, at some point I do N resampling of the initial sample and generate N means out of them (some kind of bootstrapping). Pretty easy, however I don't know how to write ...
3
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1answer
66 views

Formal way of defining a weighted average

I am looking for a nice and formal way to define moving averages : $y = \sum_{i=0}^N w_ix_i=<\mathbf{w},\mathbf{x}>$ and especially the fact that weights have to equal one, i.e. ...
4
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1answer
112 views

Expectation notations

In Statistical Decision Theory, one often studies the following two measures (from "The Bayesian Choice"): Average loss (aka the frequentist risk): $R\left(\theta,\delta\right) = ...