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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29
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3answers
1k 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
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1answer
11 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
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1answer
15 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
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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
64 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 ...
0
votes
1answer
39 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
259 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
62 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
51 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
26 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
29 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
31 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
342 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
95 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
65 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 ...
0
votes
1answer
33 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
51 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
62 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
142 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
41 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? ...
0
votes
0answers
51 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
28 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
35 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
162 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
77 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
249 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
82 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
29 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
91 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
29 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
80 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
35 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
35 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, ...
4
votes
2answers
297 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
200 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
151 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
88 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
341 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
49 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
41 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) ...
1
vote
0answers
42 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 ...
2
votes
1answer
147 views

Two different definitions of a median

I read from the book "Introduction to the Practice of Statistics", The International Seventh Edition, page 31 that "The $\textbf{median $M$}$ is the midpoint of a distribution. Half the observations ...
2
votes
2answers
125 views

In the definition of probability density function, does it matter if the interval is open or closed?

I can find two definitions of Probability Density Functions in the sources I have checked: $$P(a < X < b) = \int^b_a f(x)dx$$ Ref: Hogg & Tanis, Probability and Statistical Inference and ...
6
votes
2answers
140 views

Why is the standard deviation defined using differences^2 instead of differences^4? [duplicate]

I've read some post about why to take the std. deviation and its benefits, here's one of them: Why square the difference instead of taking the absolute value in standard deviation?, and another by ...
1
vote
0answers
43 views

What is industrial statistics?

We have a course titled "Industrial Statistics". But I don't understand what is industrial statistics? What I have understood after searching some sites is only that Industrial statistics ...
0
votes
1answer
28 views

What is intervention?

An intervention is strategy to produce change among individuals or entire population. Is the definition of intervention correct ?
4
votes
1answer
55 views

Is there a basic definition of Significant result and Non-significant result?

Is there a basic or widely accepted definition of Significant Result and Non-Significant Result? Seems that every where I look they want to get into problem solving without defining what those terms ...
1
vote
0answers
42 views

Is a model including a square root of a variable linear in the parameters? [duplicate]

Is the model $$ y = \gamma_0 + \gamma_1 + \sqrt x + \varepsilon $$ linear in parameters? ( $\varepsilon$ is the error term.)
3
votes
0answers
40 views

How to construct “reference priors”?

I have been reading about noninformative priors. Two of the most popular priors of this kind seem to be the Jeffreys prior and the reference prior. The Jeffreys prior has a clear construction, being ...
5
votes
2answers
58 views

Short term for Probability of Type I error

When comparing statistical tests, one often compares the probability of committing a Type 1 error, and the probability of not committing a Type 2 error. While (2) can be concisely termed 'power', ...