Questions tagged [notation]

For questions about statistical notation and mathematical notation used in statistics.

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Question about conventions for notation of random and regular variables in this regression example

I’m trying to follow some lectures notes on regression I found online and want to make sure I’m interpreting the notations correctly. On page 4 here, we have $\mu(x) = E[Y | X = x]$. Is it correct ...
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61 views

Is it correct to write $\Bbb E[X]$ or $\Bbb E_{\theta}[X]$?

Suppose that we observe the discrete random variable $ X = (X_1, \dotsc , X_n)$ with state space S, whose distribution we do not know but we are assuming that its joint p.m.f. belongs to a known ...
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What does X²(1, N=100) =6.83, p =0.009 mean?

I am reading scientific research (Link) and stumbled upon the following notation: X²(1, N=100)=6.83, p =0.009. An explanation is given as follows: ...
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Prediction model clarification

I have the following formula and I'm trying to understand whether the square root, Rˆ2 the coefficient of determination is and whether sdev(y) the standard deviation of the outcome variable is. Please ...
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25 views

Clarification of Notation

I am learning some new statistics concepts, and I am having a bit of difficulty discerning certain notation. How does $\hat{\sigma}$ differ from $\sigma$ in the description below: CLT: If $X_1,...,...
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54 views

Notation and meaning of a general probability distribution

I had two questions regarding the meaning and notation of a probability distribution when it is not specifically specified. For example, some papers jump right into their approach with notation like (...
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24 views

Confusion over the notation of REINFORCE algorithm in Reinforcement Learning

From this paper, https://arxiv.org/pdf/1806.09460.pdf, page 9 I am confused by the line "sample $z_k \sim p(z;\theta_k)$" It seems that $z_k$ is a random variable, as explained here Why are ...
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What is the history of the vertical bar symbol |

The vertical bar symbol is used for the conditional probability. For example $$P (A|B) = \frac {P (\text {$A $ and $B $})}{P (B)}$$ The symbol is also used in describing likelihood $$L (\theta | x) =...
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81 views

How do I write a mixed-effect regression model (MRM)?

So I am trying to write a MRM with both random intercept and random slope. I know the general model is as follows, yij = b0 + b1xij + vi0 + vi1xij + eij However, I want to actually write my ...
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1answer
36 views

Parameter in expectation subscript

There are a few questions/answers out there about subscripts involving a random variable ($E_X[...]$) or a density ($E_{f(X)}[...]$) in expectations. I like this one. But today I ran into a ...
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24 views

Understanding average treatment effect estimator notation

I want to check that I understand the notation for the average treatment effect (ATE) estimator correctly, and hopefully some of you can double check this. I often try to understand formulas through ...
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1answer
25 views

In ordinal classification, how can adjacent accuracy be expressed mathematically?

Say that we have an ordinal classification problem where we have an ordered set of classes $\mathbb{C} = \{ C_0, C_1, \ldots, C_{K-1} \}$. We have $N$ samples, where the true and predicted classes of ...
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Parsing and understanding plate notation for topic modeling example?

I'm trying to understand the following plate notation which is used a lot as an example of topic model to introduce variational methods, etc. I wanted to ask if my understanding is correctly depicted ...
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1answer
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Notation for conditional density

Are $p(\mu \mid \sigma)$ and $p(\mu ; \sigma)$ equivalent? I've seen the notation $p(b_i \mid T_i, \delta_i, y_i ; \theta)$ used to represent the posterior distribution for $b_i$. I am assuming that ...
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1answer
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Compact notation for one-hot indicator vectors?

Many machine learning approaches use one-hot vectors to represent categorical data. This is sometimes called using indicator features, indicator vectors, regular categorical encoding, dummy coding, or ...
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53 views

Mathematical notation (or formula) of mixed effect models

I am unsure how the correct mathematical notation of two mixed model I've estimated in R should look like. The data consists of test scores of students that were in different classes. Some of the ...
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Could someone please translate this lme code into mathematical equation?

ekte4.1 <- lme(sqrt(LRcongruence) ~ wrclmch2 + gndr + agea2 + hinctnta2, data = dfComplete, method = "ML", na.action = "na.omit", random = ~1|...
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473 views

How to mathematically denote common elements

I have 5 lists collected over 5 years as follows. year1 = [8, 1, 5, 6] year2 = [6, 8] year3 = [8, 5, 6] year4 = [9, 2, 8, 1, 6] year5 = [8, 1, 6] I extracted the ...
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38 views

Information Entropy - Ambiguous Notation

I'm constantly confused by the ambiguous notation when discussing Entropy (H) and Mutual Information (I). For example, here's a formula from "Elements of Information Theory": $$ I(X;Y|Z) = H(X|Z) − H(...
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43 views

Spline basis function notation to include constraint for continuity at the knots

I know splines use basis functions to approximate a function locally, so that the function in one region is approximated with a weighted sum of these basis functions. Suppose the input is one-...
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1answer
53 views

The $\|x\|$ inside Generalized Gaussian distribution [closed]

The density of generalized Gaussian distribution is $$ f(x) = c_0\exp\left(-\frac{\|x\|^s}{s}\right), \quad x\in \mathbb{R}^m, $$. So, why we are writing $\|x\|$. Is that norm?
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How to describe a split-plot ordinal logistic regression

I am having difficulties reporting a split-plot ordinal logistic regression. I get the concept of ordinal logistic regression involving a categorical representation of a latent continuous variable, ...
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Notation for skewness and kurtosis

Traditionally (see Johnson et al., 2005, for instance), the (population) standardised skewness and kurtosis can be denoted as $\sqrt{\beta_1}= \frac{\mu_3}{\sigma^3}\;\;$ and $\;\;\beta_2= \frac{\...
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29 views

Set Notation in probability

My problem is below, however the notation is confusing me. Consider an experiment where you throw two three-sided dice. Let $F_n$ be the event “The first die rolls an $n$” and $S_n$ be “The second die ...
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34 views

Notation for Pearson residual vs Pearson correlation coefficient

From my book, the Pearson residual is defined as: $R = \frac{Observed - Expected}{\sqrt{Expected}}$ And from wikipedia, the Pearson correlation coefficient is defined as: $r_{xy}={\frac {\sum _{i=1}...
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366 views
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157 views

What does the symbol for pi with a lower perpendicular mean?

What does mean in context of the equation
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Joint expectation subscript when we only have single random variable

As a follow-up to these two questions, Subscript notation in expectations and Double expectation (Not law of iterated expectation) If we have $E_{XY}[X]$, what is the correct integral expression? i....
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1answer
87 views

Ambiguity with math notation

I was just solving several problems and get stuck into the one with some weird notation. I wasn't able to understand it, though I know the meaning behind the character (angle bracket) in more broader ...
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How to separate Matrix indices? (notation wise)

I just wanted to know what you guys think of this matter or if there are any styleguides for this. I usually refer to elements of a matrix $X\in\mathbb{R}^{n\times m}$ as $x_{kl}$. For a concrete ...
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89 views

Correct mathematical notation for subscripts in regression equation

For the first time in a paper I am going to attempt to write out the equation for my model using mathematical notation, but I am a little unclear about how best to do it for the particular model I am ...
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3answers
654 views

Why are flat priors said to be proportional to a constant?

I'm a little confused why everyone writes a flat prior as $f(\theta) \propto c$. In this instance couldn't they just write $f(\theta)=c$? A uniform distribution always a has a constant density ...
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204 views

Notation for leads and lags in difference-in-differences

I was hoping someone could help clarify a notational discrepancy. For example, Lord Pischke uses the following sigma notation in two different lecture notes published on the web, yet refers to the ...
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Greek Symbol To Denote the Posterior Mean

What symbol is commonly accepted to denote the mean of the posterior distribution generally speaking?
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What is meaning of different symbols in image?

I am learning about Deep Generative Models, tutorials all over the places use symbols and no one actually explaining the meaning of it. Can you please suggest the meaning of these terms?
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1answer
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Logistic regression log-likelihood - meaning of μ

I'm trying to implement my own logistic regression, but I'm not sure I understand some of the notation. In Machine Learning : A Probabilistic Perspective (Murphy, 2012), the negative log-likelihood is ...
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1answer
31 views

Notation for conditional probability when the conditioned event is observed

I am trying to understand proper notation for functions related to state transition models (e.g., a HMM). There are two indexing variables $t$ (time step) and $i$ (state). Such that it matters, in my ...
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Multi-dimensional Lebesgue integral applied to probability measures

I have a question on multi-dimensional Lebesgue integral when applied to probability measures. In particular, consider the random variables $Y,X,\epsilon,T,V$, with supports $\mathcal{Y},\mathcal{X},...
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Formula for expectation that works both for the continuous and discrete cases

Consider a random variable $X$ with support $\mathcal{X}$ and probability distribution $P$. I want to write down the formula for the expectation of $X$ (other than $E(X)$) that generically works for ...
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Basic CDF / CDF Notation Question

The following is copied from some old course notes: $F_{X-\theta}(x)=P(X-\theta < x) = P(X<x+\theta)=F_\theta(x+\theta)=F_0(x+\theta-\theta)=F_0(x)$ Is anyone able to explain the $P(X<x+\...
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1answer
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Notation in definition of a quantity involving uncertainty and posterior probability

As a probs & stats noob, I'm still getting confused by notation. I would appreciate if someone could elaborate a bit on what's going on here, on p12 of Settles' Active Learning survey (2012). He ...
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85 views

Notation for unevenly-spaced to evenly-spaced time series conversion

I have an unevenly-spaced time series. To make it evenly-spaced, I resample the time series to a larger timespan (e.g. day) and sum up all values within this time frame. In Python (and pandas) it is ...
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1answer
62 views

Linear Regression - Vector Notation

I'm a bit confused about the vector notation of the linear regression vector notation. We have this: $X : n\times p$ matrix of data we have obtained; $\beta: p\times 1$ matrix of coefficients I ...
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Question regarding notation for F-distribution

Apologies for the basic question; I don't have a very deep or broad background in statistics. I am reading this paper on phase transitions in the existence of maximum likelihood estimators for ...
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518 views

What does this notation mean: $F$ at the matrix norm and $Q$ under the $\arg\min$

I am trying to figuring out what is meant by Q and F in the 4th equation mentioned in this paper: Diachronic Word Embeddings ...
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Conditional probability formula for continuous random variables [duplicate]

Let $V,T$ be two random variables with supports $\mathcal{V},\mathcal{T}$, respectively. Let $P_{V|T}$ denote the probability distribution of $V$ coditional on $T$ $P_{V,T}$ denote the probability ...
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70 views

Application of law of total probability for continuous random variables

Consider 3 random variables $Y,V,T$, with supports $\mathcal{Y},\mathcal{V},\mathcal{T}$, respectively. Let $P_{Y,V}$ denote the probability distribution of $(Y,V)$ $P_{V}$ denote the probability ...
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Formula for expected value of continuous random variable without using density

I'm looking for some correct notation. Consider the random variable $V$ with support $\mathcal{V}$ and probability distribution $P_V$. Consider a function $u:\mathcal{V}\rightarrow \mathbb{R}$. Let $...
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2answers
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Does this notation in the context of reinforcement learning have an unambiguous measure-theoretic interpretation?

In the context of reinforcement learning, I have seen the formula $$V^\pi(s)=\mathbb E_{\tau \sim \pi}[R(\tau)|s_0=s]$$ and $$V^\pi(s)=\mathbb E_{a\sim \pi}[Q^\pi(s,a)]$$ Does this notation have ...
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2answers
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What is the meaning of × in statistics?

What is the meaning of the symbol × in an ANOVA context? More specifically what is the meaning of × in the following table? ...