Notation refers to questions about statistical and mathematical notation.

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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 ...
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1answer
69 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 ...
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3answers
64 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
83 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: ...
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2answers
118 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. ...
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1answer
131 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 ...
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1answer
25 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
27 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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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
41 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 ...
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1answer
94 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 ...
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1answer
38 views

Correct notation wrt. uniform distribution

Assume that I have a discrete set $L$ and a transformation $\phi: L \rightarrow [0,1]$ that normalizes set $L$ such that now values belonging $L$ are uniformly distributed among the unit interval. ...
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1answer
61 views

Random variable as a function

I'm reading Schaum's outline of probability, random var. and random processes. In the second chapter they make it clear that a random variable $X$ is not a variable in the traditional sense but ...
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1answer
53 views

Correct way to write values which have a certainty of 95 percent?

Instead of perusing through many more textbooks, I thought it's easier to ask here. Say I would like to express the mean for a variable with a certainty of 95 percent, how exactly do ("should") I do ...
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0answers
27 views

What's the proper notation for a formula that includes values sampled from a distribution?

I'm trying to write an equation for a time series $\text{TS}$ containing noisy and unevenly sampled data from a function $m(t)$. Here's what I've come up with: $$\text{TS}(t \in \mathcal{U}(0, 1)) = ...
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1answer
79 views

dG(y) in expected value integral

I am wondering what exactly the notation dG(y) inside an integral means, what it's called and where I can read more about it: $$E[B_1]=\int_0^{\infty}E[B_1 \vert Y_1 = y] dG(y)$$
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28 views

How to simplify equation without using backshift notation and with “Yt” expression alone on left side?

I have three equations and don't understand why I missed points. All that was said was "simplify." B^4Yt = c + et (B-0.6B^3)Yt=(2+5B+0.8B^2)et Yt=(1+B^3/B)et
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1answer
132 views

What does the | in |Z| mean in mathematical expressions for distribution statistics

I am doing some self study on statistics and noticed that in the notes that I was using the $|Z|$ expression as attached in the photos below. I am confused with the "$|$" that is being used. The only ...
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3answers
95 views

Can I write estimate $\pm$ its standard error?

Suppose I have an MLE estimate $\hat{\theta}$ for a parameter $\theta$, and $\hat{\sigma}$ is the sqrt of the inverse of the negative of the Hessian of the log likelihood at $\hat{\theta}$. Can I ...
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1answer
83 views

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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0answers
18 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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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
426 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
131 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
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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
359 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
120 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
96 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
118 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 ...
3
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1answer
114 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
44 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
81 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
136 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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163 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: ...
2
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2answers
213 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 ...
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0answers
299 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
90 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
127 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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71 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 ...
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1answer
229 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
989 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
74 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
955 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
96 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
312 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
223 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
315 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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77 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 + ...