Tagged Questions

Notation refers to questions about statistical and mathematical notation.

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Is my notation here reasonable? (basic probability)

Disclaimer: this is a homework problem, but I'm not asking for the answer I already have it. What I'm wondering is if a specific way of writing part of the problem is correct or not. I have other ways ...
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What description fits this this learning scenario, is this a form of active learning?

A system is involved in dialog with a human partner. The system has a model of a problem domain and knows mappings between words an concepts. The human has its own model of the problem domain and ...
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Is it okay to write the square of expectation of a random variable $X$ as $\mathbb{E}^2(X)$?

Is this notation accepted when I write $\text{Var}(X)=\mathbb{E}(X^2)-\mathbb{E}^2(X)$?
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Scaling parameters to lie in unit hypercube — how to understand this notation?

I am attempting to emulate a simulation in a paper I am reading. The model includes two parameters $\theta_1,\theta_2$. These parameters are scaled to lie in the unit hypercube. That is, where the ...
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Question on Kernel function notation and rationale

Say I have the following kernel function: $$K(u) = \frac{15}{16}(1-u^2)^2\ 1_{(|u|\leq1)}$$ As I understand, $u$ denotes some absolute distance parameter for each observation $x_i$ from a given ...
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What does $S$ mean in this standard deviation estimate

What does $S$ mean in estimates like $$s^2 = \frac{S(x_1^2)}{n} - \left(\frac{S(x_1)}{n}\right)^2 = \frac{S(x_1^2)}{n} - \frac{S(x_1^2)}{n} - 2\frac{S(x_1 x_2)}{n^2}$$ (for context look "The probable ...
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Terminology: Vector, attributes, and matrices in a dataset

I am confused about the terms "vectors", "attributes", and "matrix" when applied to a dataset. I know that attributes are the features or columns of the dataset, and the matrix is $N \times M$ data ...
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What do the angular parentheses in $\langle g_n \rangle^2$ mean?

I am reading this paper. At the first part it says $\langle g_n \rangle=0$ and $\langle g_{n} \rangle ^2=1$. I know that $\langle x \rangle$ is used in physics to refer to the mean. So, the second ...
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Why is F used for an unspecified distribution?

I'm taking a linear regression course in university right now, and my professor often uses the notation F to refer to a generic, unspecified distribution with the given mean and variance. For example, ...
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Maximum Likelihood Formulation for Linear Regression

I have seen the following for maximum likelihood estimation (MLE) for linear regression in multiple sources, e.g. here: $$\mathcal{D} \equiv \{(x_1, y_1), ..., (x_n, y_n)\}$$ I do not understand ...
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What is the mathematical symbol for a predicted value?

Take a simple linear regression $y = ax + b$. Here, $y$ is predicted. In my analysis I need to compare the predicted $y$s to the actual $y$s from my data set upon which the regression was built. What ...
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In machine learning, why are superscripts used instead of subscripts?

I'm taking Andrew Ng's course on Machine Learning through Coursera. For equations, superscripts are used instead of subscripts. For example, in the following equation $x^{(i)}$ is used instead of $x_i$...
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Should the arithmetic mean of a subset of population data be annotated as sample mean?

If I have population data, and I want to calculate the arithmetic mean of a subset of the population data (e.g. for a certain category of values within a certain range of $n$ observations), is the ...
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Notation in Markov Chain and MCMC literature

In the MC and MCMC literature one commonly finds statements of the following form (see e.g. Roberts & Rosenthal, 2004): $$\int_{x \in \mathcal X} \pi(dx)P(x, dy) = \pi(dy).$$ What is the ...
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Express Normal Distributions with Integral Notation?

If possible, how would I be able to express some Normal Distribution using Integral notation if I had a distribution such that $$\mu = 188 \text{ units}$$ $$\sigma = 41 \text{ units}$$ And we ...
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Trouble plotting probability

I have a density function that can be written as follows: $$f(r) = \frac{(1-r^2)^{\frac{n-4}{2}}}{\mathbf{B}\left(\frac{1}{2}, \frac{n-2}{2}\right)}$$ Where $\mathbf{B}$ is the beta function. I got ...
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Notation for CDF of the binomial distribution

The CDF for $X \sim \operatorname{Bin}(n,p)$ is $I_{1-p}(n-k,1+k)$. What does the $I$ mean?
Does $S$ and $s$ mean different things in statistics regarding standard deviation?
In some contexts when denoting sample standard deviation, I notice a capital $S$ and sometimes a small $s$. I also notice this in the same standard textbook. Do they mean different things in context ...
I'm trying to obtain an estimator $f(x)=y$ where $x \in \mathbb{R}^{D_1}$ and $y \in \mathbb{R}^{D_2}$, both are column vectors. So my training set $X$ and $Y$ are data matrices of size \$D_1 \times ...