This tag indicates questions about definitions of statistical terms. Use a more general tag [terminology] for questions on statistical parlance that are not specifically about definitions.

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4
votes
1answer
117 views

do(x) operator meaning?

I have seen the $do(x)$ operator everywhere in some literature review I am doing on Causality (see, for instance this wikipedia entry). However, I cannot find a formal and general definition of this ...
10
votes
3answers
515 views

Is there a formula for computing median?

Is there an equivalent of the mean formula: \begin{equation} \mathrm{mean} = \cfrac{1}{N} \sum_{i=1}^{N} X_i \end{equation} for median?
13
votes
5answers
736 views

What's in a name: hyperparameters

So in a Normal distribution, we have two parameters: mean $\mu$ and variance $\sigma^2$. In the book Pattern Recognition and Machine Learning, there suddenly appears a hyperparameter $\lambda$ in the ...
2
votes
2answers
54 views

What is an isotropic covariance matrix?

Could somebody explain to me in simple terms what an isotropic covariance matrix is? I can't find anything online.
0
votes
0answers
13 views

Difference between Discrimination, Calibration, Accuracy and Precision

I have trouble understanding these terms: a.) Discrimination. b.) Calibration. c.) Accuracy. d.) Precision. I really get confused with the books I am reading, ...
5
votes
1answer
75 views

Do we say that the $y_i$'s are i.i.d. if $n_iy_i \sim \text{Binomial}(n_i, \theta)$?

If $y_i$'s are independent and for given $n_i$, $$n_iy_i \sim \text{Binomial}(n_i, \theta)$$ Could we say that $y_i$'s are i.i.d.? If not, then what's the proper way to address such problems?
0
votes
0answers
17 views

What are dynamical process?

Can someone explain to me what are Dynamical processes? It would be helpful if someone can also give me an example/s (if possible, in context of atmospheric or environmental processes) regarding this. ...
0
votes
0answers
28 views

Layman's definition of high-dimensional data

I'm a statistician writing a research proposal to be read by non-statisticians. This will mostly include mathematicians, computer scientists, and engineers, but may also include those in humanities. ...
129
votes
11answers
12k views

What is a data scientist?

Having recently graduated from my PhD program in statistics, I had for the last couple of months began searching for work in the field of statistics. Almost every company I considered had a job ...
0
votes
1answer
15 views

remove the mean over multiple measurements

I have a set of multiple measurements for each subject (i.e. each subject is assessed several days). For each set of measurements (several days of the same subject) I am calculating the mean value of ...
0
votes
1answer
23 views

Ground truth Vs. Baseline [closed]

I was wondering what the difference between ground truth and baseline is? Is it necessary that a system should always be tested ...
1
vote
0answers
14 views

Equivalence of definitions of quantiles

Let us define the concept of quantile of order $\tau$ of a random variable $X\in F$ in two different ways: Definition $1$: $c_\tau$ is said to be a quantile of order $\tau$ if and only if $lim_{x\to ...
2
votes
1answer
66 views

What makes something a “Probability”?

What makes it legitimate to say a set of values are probabilities? (I need an answer for a formalisation reasons.) Let me give a simple example. Let's assume that I have a number of letters and each ...
1
vote
0answers
14 views

Well defineness of the definition of F1 score

The F1 score is defined as the harmonic mean of precision and recall: $$ F_{1}=2\cdot {\frac {\mathrm {precision} \cdot \mathrm {recall} }{\mathrm {precision} +\mathrm {recall} }}.$$ The above ...
0
votes
1answer
60 views

What is $p_i(x_i - \sum_i p_ix_i)$ called?

I was reading a paper (dont have it with me!) on statistics and found a term that I have never encountered before: $p_{i}{(x_{i}-\mu )} = p_i(x_i - \sum_i p_ix_i)$ After some research it seems that ...
11
votes
2answers
322 views

Mathematical definition of Infill Asymptotics

I am writing a paper that uses infill asymptotics and one of my reviewers has asked me to please provide a rigorous mathematical definition of what infill asymptotics is (i.e., with math symbols and ...
0
votes
0answers
84 views

What is a grade-tonnage curve?

What is a grade-tonnage curve ? I cannot find any good online resource, neither wiki, neither any forum... Thanks, PS: sorry if it should be on another website
3
votes
3answers
53 views

Limiting the range of numbers

Suppose that I have the following data set: {0.1, 0.2, 0.5, -0.1, 0.5, 1.1, 0.8} I would like to limit the range of these data to be within the range of [0,1]. ...
2
votes
1answer
32 views

On the definition of covariance matrix

I am having a misunderstanding with the definition of the covariance matrix from the wikipedia page on the covariance matrix. It says the covariance matrix $\sum$ is equivalent to where It ...
1
vote
0answers
31 views

What does error mean in this context?

In the paper: Avrim L. Blum and Pat Langley. 1997. Selection of relevant features and examples in machine learning. Artif. Intell. 97, 1-2 (December 1997), 245-271. are several definitions of the ...
1
vote
1answer
45 views

Defintion of the terms “node weight” and “case weight”

In the literature about decision tress and especially the family of tree approaches that avoid selection bias (conditional inference trees e.g. here: ctree: Conditional Inference Trees by Hothorn, ...
7
votes
1answer
467 views

What is the mathematical definition of location / scale / shape parameters?

I am trying to understand the exact definition of the location / scale / shape parameters (e.g. $a$ is called the shape parameter and $c$ is scale parameter in Pareto Type I). But the books I referred ...
2
votes
1answer
110 views

Confusion about concept of likelihood vs. probability

I've been recently trying to wrap my head around the concept of likelihood, and have made some good progress, but there is one thing that is bugging me, and I think this issue is what makes the ...
3
votes
2answers
68 views

Is $P(X_t=Y_t,\forall\ 0\leq t < \infty )$ well defined?

I have an elementary question about stochastic processes (continuous) and the notion of two processes being indistinguishable. Let $X=(X_t)_{t\geq 0}, Y=(Y_t)_{t\geq 0}$ be two stochastic processes on ...
1
vote
2answers
87 views

Definition and delimitation of regression model

An embarrassingly simple question -- but it seems it has not been asked on Cross Validated before: What is the definition of a regression model? Also a support question, What is not a ...
3
votes
1answer
54 views

Is a random variable taking every rational number or a range of rational numbers discrete or continuous?

My guess would be discrete because such a variable would only take a countable set of values and "continuous" seems to imply the continuum of the real numbers.
2
votes
1answer
69 views

Am I understanding differences between Bayesian and frequentist inference correctly?

Given a sequence of independent experiments, each having as its outcome either success or failure, the probability of success being some number p between 0 and 1: A Bayesian would consider the ...
2
votes
2answers
163 views

How exactly do Bayesians define (or interpret?) probability?

Part of a series of trying to understand Bayesian vs frequentist: 1 2 3 4 5 6 7 I think I get the difference of how Bayesians and frequentists approach choosing between hypotheses, but I'm not quite ...
1
vote
0answers
65 views

What is the difference between a flat and weak prior?

Flat and weak prior distributions are two possible types of prior in Bayesian statistics. In layman's terms, what are the key differences between the two, and why do we use one or the other? ...
1
vote
1answer
65 views

What does 'downward pressure on sample size' mean?

In this article, there is this phrase 'downward pressure on sample size'. This is the paragraph: no matter the approach to collecting this new data, when attempting to ...
1
vote
1answer
37 views

Correlation matrix for uncorrelated parameter esitmates

I have a set of $n$ parameter estimates. How can I understand if they are correlated or uncorrelated? I guess I should calculate the correlation matrix. How is it exactly defined in terms of the ...
0
votes
0answers
39 views

What's a linear aggregate?

A paper I'm reading (Davis-Stober et al, 2014) contains the following statement: A crowd is wise if a linear aggregate, for example a mean, of its members’ judgments is closer to the target ...
1
vote
1answer
274 views

Difference between within-group and between-group covariance matrices in linear discriminant analysis

Could someone explain to me the difference between within-group covariance matrix and between-group covariance matrix in the context of linear discriminant analysis?
2
votes
1answer
148 views

What is the definition of “rare events”? and when it matters for significance testing of differences in a control-case study?

What is the formal definition of "rare events"? and when it matters for significance testing of differences in a control-case study?
2
votes
3answers
463 views

Ground-truth definition

I have found two meanings of how "ground truth" is being used in machine learning: Something to be assumed true Something previously validated as true Although similar in detail the two can ...
1
vote
1answer
86 views

Computing required sample size for paired t-test

I have some paired t-test data (40 pairs) and I would like to use these data to estimate the sample size required if I were to conduct the study again with a new set of requirements. I'm using ...
0
votes
1answer
31 views

Obvious counter examle to the Handshaking Lemma [closed]

The Handshaking Lemma is described thusly in Wikipedia: In graph theory, a branch of mathematics, the handshaking lemma is the statement that every finite undirected graph has an even number of ...
2
votes
1answer
192 views

Is there a difference between on-line learning, incremental learning and sequential learning?

What I mean is the following: Instead of processing all the training data at once and calculating a model or hypothesis, we process one data point at a time and update the model directly afterwards. ...
0
votes
0answers
31 views

What, if any, is the precise definition of “substantively large”?

I am told that while my estimates are not statistically significant, they are "substantively large". Is there a precise definition for the phrase "substantively large"? If I say that my estimates ...
0
votes
0answers
97 views

Homoscedasticity - constant second moment or constant variance

I found the following different definitions of homoscedasticity and I'm wondering which is the correct one. The second moment is constant, i.e. E(X²)=s² (see e.g. p.11 ...
2
votes
1answer
38 views

Reference for definition of multiple-output Gaussian process

Does anyone know any good reference that has a clear and precise definition of multiple-output Gaussian process? Something like the definition of the Gaussian process in the third page of this set of ...
1
vote
1answer
38 views

What is a random variable in the definition of a linear regression model

In wikipedia's definition of a linear regression model: $y_i = \beta_1 x_{i1} + \cdots + \beta_p x_{ip} + \varepsilon_i = \mathbf{x}^{\rm T}_i\boldsymbol\beta + \varepsilon_i, \qquad i = 1, \ldots, ...
5
votes
2answers
649 views

What is a Highest Density Region (HDR)?

In statistical inference, problem 9.6b, a "Highest Density Region (HDR)" is mentioned. However, I didn't find the definition of this term in the book. One similar term is the Highest Posterior ...
4
votes
2answers
215 views

What is a multivariate random variable?

I've been trying to read the Wikipedia article on multivariate random variables but I'm having trouble getting past the math. Is there a more intuitive explanation? I'm assuming that a univariate ...
1
vote
1answer
159 views

Can you reduce the risk involved in an uncertain event?

I'm not sure if this is the right Stack Exchange site but I felt it came closest. Based on Knights 1971 definition of risk uncertainty is defined as a situation where factors exogenous to the ...
1
vote
1answer
93 views

Autocorrelation definition

I am formatting a statistics proof, and I wanted to make sure that I have the definition of autocorrelation correct. Is it the case that the autocorrelation of a continuous variable is the same as ...
12
votes
3answers
346 views

What exactly is a distribution?

Sorry for such a basic question. I know very little of Probability and Statistics, and am wishing to learn. I see the word "distribution" used all over the place in different contexts. For example, ...
1
vote
0answers
65 views

Why are observations from a random variable considered as random sample?

In a couple of books I've read a random sample is defined as a set of $n$ independent identically distributed random variables. And then their behavior is developed based on this definition which I ...
1
vote
0answers
43 views

The most general definition of the Likelihood function for continuous data (including truncation and censoring)

How would you rigorously define the likelihood function for censored/truncated observations? Even in most lifetime/reliability literature (where these types of observations are frequently encountered) ...
2
votes
0answers
47 views

Rigorous definitions of sample and population

I am trying to understand some basic ideas of econometrics (and mathematical statistics) from the precise, mathematical point of view, avoiding vague explanations. I am beginning to learn about these ...