Notation refers to questions about statistical and mathematical notation.
3
votes
0answers
43 views
Simple question about notation
In the context of likelihood-based inference, I've seen some notation concerning the parameter(s) of interest which I've found a little confusing.
For example, notation such as $p_{\theta}(x)$ and ...
-3
votes
1answer
45 views
Denotation of probability symbols
May I kindly clarify if the following mean the same thing?
$$P(AB) = P(A \cap B)$$
Cheers.
2
votes
1answer
94 views
Proof of normal equation in regression using tensor notation
I'm struggling with a proof of the normal equation, so I posted a question which hopefully will get resolved soon. However, I mentioned there that I'm uncomfortable with the proofs dealing with matrix ...
1
vote
1answer
18 views
How to compute y caret
I have been given a data points $x_i,y_i,1\leq i\leq n$. I was asked to compute the standard error of regression coefficients estimates. As in the formula, I have to compute
$\sum_{i=1}^n ...
2
votes
2answers
70 views
Bayesian Inference Notation Confusion
In Bayesian Inference the following notation is quite common:
$P(H|D) = \frac{P(D|H)P(H)}{P(D)}$
where $D$ is data and $H$ is hypothesis. Moreover $P(D)$ is represented as total probability.
$P(D) ...
1
vote
1answer
56 views
Some problems understanding the definition of a function in a maximum likelihood method
I encountered the maximum likelihood method. It says that the common probability density function of sample $X_1,\ldots,X_n$ having distribution $f(x;\theta )$ with observed values $x_1,\ldots,x_n$ is ...
2
votes
0answers
119 views
SVM hyperplane equation
I am trying to understand the hyperplane of the SVM algorithm. My problem is that different sources state different equations.
Which equation is the right one and if both are right, why?
...
0
votes
0answers
47 views
Why is $\rho$ used for both the population correlation and the Spearman estimate?
I am wondering why $\rho$ is used to denote the population correlation whereas it's also used to denote the Spearman correlation estimate. In this wikipedia article it's used to represent the Pearson ...
3
votes
1answer
216 views
Expectation Subscript
What is meant by subscripting the expectation with some distribution, e.g. $\mathrm{E_{f}}[h(X)]$?
If it's any help, here's the context:
In M.C. Simulation, we wanted
$\mathrm{E[h(X)] = ...
0
votes
1answer
29 views
Notation of a resampled mean
For a work that I have to document, at some point I do N resampling of the initial sample and generate N means out of them (some kind of bootstrapping). Pretty easy, however I don't know how to write ...
3
votes
1answer
49 views
Formal way of defining a weighted average
I am looking for a nice and formal way to define moving averages :
$y = \sum_{i=0}^N w_ix_i=<\mathbf{w},\mathbf{x}>$
and especially the fact that weights have to equal one, i.e.
...
3
votes
1answer
81 views
Expectation notations
In Statistical Decision Theory, one often studies the following two measures (from "The Bayesian Choice"):
Average loss (aka the frequentist risk):
$R\left(\theta,\delta\right) = ...
7
votes
2answers
204 views
Why are probability distributions denoted with a tilde?
What is the meaning of the tilde when specifying probability distributions? For example:
$$Z \sim \mbox{Normal}(0,1).$$
1
vote
0answers
61 views
How to understand the notation behind the standarded residuals?
I don't understand my lecture notes. It states that standarded residuals is by definition
$$R_i=\dfrac{y_i-\hat{y}_i}{\sqrt{\dfrac{1}{n-2}\sum_{i=1}^n (y_i-\hat{y}_i)^2 }}$$
I understand that I can ...
1
vote
2answers
115 views
Representation of standard deviation in statistical range
I have computed the mean and standard deviation of a variable in a dataset, and I wish to represent these values in a report. Is the following the correct way to go about this?
$1.23 \pm 0.52 ...
7
votes
2answers
180 views
Terminology for different types of epidemiological variable
If I have a data set with $n$ patients and I have a categorical variable $X$ for each patient, I want to drop all patients whose $x$ is a particular value.
Question 1: what is the term (preferably ...
2
votes
0answers
56 views
What does this formula (to derive the annualized volatility for the VaR) mean?
I'm faced with the formula shown in the image below, which I just don't understand, in part because I've no grounding in stats, and in part because I don't even understand the notation:
What's ...
0
votes
0answers
47 views
Presenting the indexation of a cross-sectional model ($i = 1,…,N$)
Many papers in applied econometrics present the indexation of a cross sectional OLS model as $i = 1,...N$. For example:
$(1) Y_i = a + b X_i + e_i$
$E[e_i] = 0$
$i = 1,...,N$.
Would it be okay to ...
3
votes
0answers
65 views
Is there a standard notation for nested factors?
What is the standard notation for specifying nested factors, for example, if I am estimating a parameter $\large{\beta{{_\text{site}}_i}}$ for the effect of $i=1\ldots m$ sites, and ...
6
votes
2answers
842 views
What is the meaning of the semicolon in $f(x;\Theta)$?
In section 6.2, in the second paragraph of p. 335 (image below) of "Probability and statistical inference 7e" by Hogg and Tanis states:
perhaps it is known that ...
4
votes
2answers
175 views
Correct enunciation of $ \, \sum \big( {Y_{i}}-{ \hat{Y}_{i}} \big)^2$
How can I enunciate this notation correctly, could you show me that, please?
$$ \sum \big( {Y_{i}}-{ \hat{Y}_{i}} \big)^2 $$
Thank you very much.
1
vote
1answer
185 views
How to denote element-wise difference of two matrices
Ok so this may seem like a really stupid question but I'm getting confused by the mathematical notation.
I am calculating the MSE (mean squared error) between two matrices. I know how to compute ...
7
votes
1answer
1k views
Notation of estimators (tilde vs. hat)
1.
Is there any naming convention regarding the hat and the tilde symbol in stats?
I found $\hat{\beta}$ is describing an estimator for $\beta$ ( Wikipedia ) But I also found $\tilde{\beta}$ is ...
1
vote
2answers
216 views
Does “x per y” always refer to the arithmetic mean?
I recognize that there are many types of averages. That said, does "x per y" (e.g. visits per day) always refer specifically to the arithmetic mean?
For some context, I saw this recently where ...
1
vote
2answers
178 views
When should I use $E(X)$ and when to use $\mu$ for the mean?
I see that $E(X)$ and $\mu_x$ are used to refer to the mean of some distribution or variate, but I am not clear on what circumstances each is appropriate.
$E(X)$ seems to always be more often in the ...
4
votes
2answers
516 views
Capitalization of n for sample size
Should the n for sample size be capitalized? Is there a difference between n and N?
4
votes
2answers
367 views
Meaning of probability notations $P(z;d,w)$ and $P(z|d,w)$
What is the meaning between the notation $P(z;d,w)$ and $P(z|d,w)$ which is commonly used in many books and papers?
1
vote
2answers
215 views
Notation of probability matrix corresponding to a contingency table
Contingency tables tables are typically formatted as tables similar to matrices in mathematics, see this example.
Is the equation below an accepted notation of expressing the probabilities of the ...
5
votes
1answer
168 views
What does $d$ mean in this notation of the “usual noninformative prior of $\mu_i$ and $\sigma_i$?”
Samiuddin, (1976) states:
or, typset with $\LaTeX$ as originally posted
We start with the usual noninformative
prior distribution of $\mu_i$ and
$\sigma_i (i = 1,2,\ldots, k)$
...
