# Questions tagged [notation]

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

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### Partial derivative notation extreme gradient boosting

What is meant by this notation regarding gradient boosting source: $$g_i = \partial_{\hat{y}_i^{(t-1)}} l(y_i, \hat{y}_i^{(t-1)})$$ Is it the partial derivative of $l$ w.r.t. $\hat{y}_i^{(t-1)}$ , i....
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### Conditional volatility and notation to express it

I'm taking a risk modelling class, and we're discussing conditional vs unconditional volatility. We have standard volatility $\sigma = \sqrt{\mathbb{E}[r_t - \mathbb{E}(r_t)]^2}$ But what is ...
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### How to interpret the subscript of this equation?

In this paper the authors in equation 18 present $\hat{\sigma_t^2}$ as $$\hat{\sigma}_{t}^2 = \frac{[X, X]_{t_{i M_n}} - [X, X]_{t_{(i-1)M_n}}}{t_{iM_n} - t_{(i-1)M_n}}. \tag{18}$$ How to read the ...
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### What is the cross product of two probability distributions $P \times Q$?

In many papers on machine learning and statistics, I encounter the following notation Let $P$ be a distribution, and let $Q$ be another distribution. Then the author creates an object $P \times Q$ ...
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### Purpose of distribution "over" a variable notation

The deep learning book (Goodfellow, Bengio, and Courville, 2016)'s notation section says $\mathcal{N}(\mathbf{x}; \mathbf{\mu}, \mathbf{\Sigma})$ represents a normal distribution over $\mathbf{x}$, ...
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### Is a structural VAR method ideal to analyze the effects of the German 9Euro Public transport ticket on CPI?

I am trying to analyse the effects that the German policy to introduce a 9Euro public transport ticket had on German CPI using a VAR model (which, according to my reading, is the most appropriate ...
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### What does this notation mean? $\mathbb{P}_{x\sim \mathcal{D}}$: Clarification in the definition of generalization error $R(h)$

I was reading the book foundations of machine learning by Mehryar Mohri, Afshin Rostamizadeh and Ameet Talwalkar, and I came up with this definition of generalization error: I dont understand what ...
1 vote
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### Notational confusion about conditional independence in Pearl 2009

First I read this definition which introduces $X$, $Y$ and $Z$ as sets of random variables. Definition (Pearl 2009) Let $V = \{V_1, V_2, \ldots \}$ be a finite set of variables. Let $P(\cdot)$ be a ...
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### Notation for uncorrelated random structure in mixed model

I will use the hsb dataset inside descriptr in R as a toy example. In my original dataset variables are different of course, ...
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### Statistical notation question: How do I represent sorting variables, individually and by each other, symbolically?

I'd like to write a formula for a correlation coefficient that involves sorting continuous observations, both within a variable and by another variable. For example, I'd like to say that $r$ is ...
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### Notation confusion regarding Expectation in Kullback-Leibler divergence definition

KL-divergence is often defined as $$D_{KL}(P||Q) = E_{x\sim P} \left[ \log\left(\frac{P(X)}{Q(X)}\right) \right] = \int_{-\infty}^{\infty} P(x) \log\left(\frac{P(X)}{Q(X)}\right)dx$$ I don't quite ...
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### Difference between Greek and Latin letters in OLS

Currently I am learning about the OLS method. In the literature I see different notations for the to be explained variable $y_i$. The different notations have to do with the letters used. In one ...
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### Is Z a random variable of X?

Is Z a random variable of X if it is transformed from X? If Z is a random variable, and therefore a function, of X, could one denoted Z as Zₓ(x)?
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### What does the $t|y(x, \mathbf{w})$ in ${\cal N}(t|y(x, \mathbf{w}), \beta^{-1})$ mean?

I'm starting to work through Bishop's "Pattern Recognition and Machine Learning" book, and have run into unfamiliar statistics notation. In Eq. 160, Bishop writes the PDF for a quantity $t$ ...
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### Mathematical formula for logistic regression mixed effects model

I am unsure how to write these models in mathematical notation when it is a model with nested random effects. This is how the models were created in R: ...
1 vote
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### What is the meaning of this normal distribution?

Following is a normal distribution equation: $$q(\mathbf x_t\mid\mathbf x_{t-1})=\mathcal N(\mathbf x_t;\sqrt{1-\beta_t}\mathbf x_{t-1},\beta_t\mathbf I).$$ I understand there should be mean and ...
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### Issue with the mathematical equation of a Gamma glm with a random intercept

I wanted to write the mathematical equation for my model below. It is a glm that tries to explain the relationship between the sum of observed biomass of several replicas at different observation ...
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### Lost in Fisher information notation

I believe I understand the gist of what Fisher Information is, but I want to be rigorous and I am confused by notation. Also I believe I am masquerading mistakes by ...
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### Accuracy without true negatives

Are there any named metric that calculates TP/(TP+FN+FP)? It is like the accuracy, but disregarding TN In my problem, we have thousand of possible labels. However, the models return a small list of ...
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### Proper notation for Random Matrix and observation

My question is simple, but I could not find any references for this particular case. When we have a random vector, we usually use $\boldsymbol{X}$ to denote the random vector and $\boldsymbol{x}$ to ...
### Meaning of $\uparrow$ in below d-separation algorithm from Koller
In Probabilistic Graphical Models by Koller and Friedman there is an algorithm to find the nodes reachable from node $X$ via trails that are active, given conditioning set $Z$. What is the meaning of &...