All Questions
Tagged with notation statistics
184
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Is there any way to compact the propagation of uncertainty formula in terms of vectors?
The uncertainty associated to $\xi=f(\mathbf x)$ with $\mathbf x\in\mathbf R^n$ is
$$\delta\xi=\sqrt{\sum_{i=1}^n\left(\frac{\partial \xi}{\partial x_i}\delta x_i\right)^2}$$
What I was wondering was ...
- 2,648
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Weird syntax in MIT Statistic For Applications course
I'm new to statistics and I'm completely stuck on the first question from an online MIT course.
The full question is here (first question):
https://github.com/hoangnguyen7699/...
- 29
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Notation for residual sum of squares $\sum_{i=1}^{n} (y_i - f(x_i))^2$
I’m reading the The Data Science Design Manual by Skiena and I need help with the notation on page 270.
Linear regression seeks the line $y = f(x)$ which minimizes the sum of the squared errors over ...
- 2,362
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47
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Interpreting notation for binary loss function
I am taking a advanced machine learning class, and in the class notes I noticed a notation that I did not recognize. It is the notation for binary loss function (Please note that it is not binary ...
- 151
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69
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What is the notation for the null and alternative hypotheses in an ANOVA?
An analysis of variance test (ANOVA) tests for a difference in means between two or more groups. In the case where there are more than two groups, the null hypothesis is written as the following:
$$
{...
- 129
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2
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125
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What is a difference between g(Y) and g(y)?
Say you have a random variable, X.
Suppose g(x) = x+3 for all x. In this case, g(X) is a random variable that takes a value g(x) when X=x.
I am a bit confused with this. g(X) is a function of X, and g(...
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26
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Moment and Cumulant Notation
I recently started working with moments and cumulants for some statistical analysis and among my research I can’t figure out some of the notation.
It will be written as:
M2,1 and C4,3
I know M ...
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97
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True value of a parameter in statistics
Let us consider a statistics model
$X_1,X_2,\cdots,X_n\sim^{i.i.d} f(x,\theta)$,
where $f(x,\theta)$ is a probability density function with a parameter $\theta$.
Let $\theta_0$ be a true value of $\...
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2
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80
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Notation for Convergence in Probability
I am struggling with intuitively understanding convergence in probability, and I think my difficulty lies in understanding the notation of the definition. I was unable to find other questions/answers ...
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121
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Is there a mathematical symbol for "among all"?
Let there be a set C of discrete values, and a function f be defined for all values belonging to C.
Say we define the dependent variable t as:
t = xₖ such that f(xₖ) is maximum among all values of f(...
- 3
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61
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Meaning of notation in Bayes' theorem
My lecture notes state Bayes' theorem, for data $\mathcal D$ of distribution parametrised by unknown parameters $\mathbf w$, as follows:
$$p(\mathbf w | \mathcal D)=\frac{p(\mathcal D | \mathbf w)p(\...
- 197
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1
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79
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Conditional PDF notation when conditioning on variable falling within certain range
I understand that the conditional PDF of some RV $X$, given some variable $Y$, is written as $f_{X|Y}(x|y)$. Also, I understand that if I want to describe general features of that function, I am to ...
- 705
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45
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What does underbar y in distribution notation mean?
I was wondering what $\underline y$ means in a distribution notation like this: "The distribution cost y is distributed on $[\underline y, \bar y]$". I know that $\bar y$ could mean the mean ...
- 103
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Ran into this paraphrasing of the definition of a sequence of probabilities, what does this notation mean? [closed]
The problem looks like the following:
$$\mathsf{P}\left( A_n \text{ i.o}\right) \;=\; \mathsf{P}\left(\bigcap_{n \ge1} \bigcup_{m\ge n } A_m\right)$$
- 15
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Partial differentiation becomes regular differentiation?
I am reading a book on the Fundamentals of Statistical Signal Processing by Steven M. Kay. Chapter 3 discusses the Cramér-Rao Lower Bound (CRLB) which places a lower bound of the variance of any ...
