Notation refers to questions about statistical and mathematical notation.

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3
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1answer
24 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 $p(\beta, \mu|y)$?
2
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0answers
19 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". ...
1
vote
1answer
38 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?
1
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1answer
40 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 ...
0
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0answers
29 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 ...
5
votes
1answer
138 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
27 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
votes
1answer
22 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 ...
7
votes
4answers
239 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..
5
votes
2answers
79 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 ...
1
vote
1answer
68 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
votes
1answer
86 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
votes
3answers
69 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 ...
0
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0answers
91 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: ...
2
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2answers
135 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
votes
1answer
159 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
votes
1answer
38 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 ...
3
votes
2answers
28 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 ...
6
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2answers
97 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 ...
1
vote
2answers
44 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
votes
1answer
98 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 ...
0
votes
1answer
43 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. ...
2
votes
1answer
63 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 ...
1
vote
1answer
54 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 ...
1
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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)) = ...
3
votes
1answer
81 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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0answers
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
2
votes
1answer
138 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 ...
2
votes
3answers
96 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 ...
1
vote
1answer
123 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 ...
0
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0answers
21 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
15 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 ...
12
votes
3answers
523 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 ...
-1
votes
1answer
139 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 $\mathrm{logit}(p_i)=-1+5.1x_{1i}-0.3*x_{2i}$. ...
8
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4answers
2k 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?
9
votes
4answers
380 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 + ...
4
votes
1answer
139 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
120 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).
2
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0answers
130 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
votes
1answer
127 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 ...
0
votes
1answer
46 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 ...
0
votes
2answers
84 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 ...
0
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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
174 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
191 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
218 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
365 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 ...
2
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0answers
99 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
votes
1answer
158 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
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 ...