Questions tagged [definition]

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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2
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1answer
332 views

What is the definition of the geometric mean of a random variable?

I haven't found any definition online although searching for hours: So here is the thing: The geometric mean(GM) of an (iid) sample drawn from some random variable is given by: $$\text{GM}(X_1,...,...
28
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18answers
6k views

How to describe statistics in one sentence?

When I first started learning statistics, procedures like the t-test, ANOVA, chi-squared and linear regression each appeared to be very different creatures. But now I realise these procedures each do ...
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2answers
233 views

Does p-value ever depend on the alternative?

Our tag definition of the $p$-value says In frequentist hypothesis testing, the $p$-value is the probability of a result as extreme (or more) than the observed result, under the assumption that the ...
2
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1answer
35 views

What is the difference between embedding in pure math and embedding in ML?

In ML the term "embedding" gets tossed around a lot and the term basically means the construction of a function that takes a high-dimensional vector to a low-dimensional vector in such a way ...
32
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5answers
12k views

Is a time series the same as a stochastic process?

A stochastic process is a process that evolves over time, so is it really a fancier way of saying "time series"?
2
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1answer
245 views

What is the difference between these three concepts: non-experimental design, observational research, correlational study

I'm having a hard time distinguishing the overflowing concepts: non-experimental design, observational research, correlational study. Question is simple: is there any difference between those three ...
2
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1answer
3k views

Inter-cluster variance

Can you please help me understand how is inter-cluster (between clusters) variance defined? As opposed to intra-cluster variance which is pretty straightforward, I have not managed to found a clear ...
5
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2answers
65 views

Exploratory vs. Descriptive Statistical Analysis

Descriptive statistics definition is pretty clear to say that it summarizes data using statistical methods like mean, mode, median, and spread. However, I came across the term 'exploratory' today ...
2
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2answers
22 views

difference between mixed effect logistic regression and logistic regression

Are they different or similar? I read that in SPSS I can't do mixed-effect logistic regression, but I can do logistic regression. So I think they differ.
0
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0answers
14 views

Mean of target values at different time points as predictor in multiple regression

I've received regression model that predicts crop yield based on data collected at 3 time points (years). Input data contains multiple attributes and crop yield in the given year for a given location....
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0answers
29 views

Is the following a GLM?

We know that the standard linear model is a partial case of the GLM scenario by taking the identity link function, i.e. $$g(μ)=μ=η=x_i^Tβ$$ However, in one of our past papers we are asked to ...
2
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1answer
41 views

Difference between the counterfactual mean and average treatment effect

I am new on the causality topic, I don't know the difference between the average treatment effect and counterfactual mean. Can anyone tell me?
28
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2answers
51k views

Is variation the same as variance?

This is my first question on Cross Validated here, so please help me out even if it seems trivial :-) First of all, the question might be an outcome of language differences or perhaps me having real ...
2
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2answers
86 views

statistical use of “relation” vs “relationship”

When describing statistical models such as regression outputs, both terms the relation and relationship seem to be often used interchangeably. Examples include Summaries of papers in Wasserstein et ...
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0answers
20 views

What is 'prototype learning' in computer vision?

I was reading some papers about semantic and instance segmentation (e.g. YOLACT) and often encountered the term 'prototype learning'. Could you please explain this concept?
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3answers
26k views

What exactly is a hypothesis space in machine learning?

Whilst I understand the term conceptually, I'm struggling to understand it operationally. Could anyone help me out by providing an example?
1
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1answer
134 views

How do you call a situation or a point at wich statistics data stops changing?

When I calculate a prediction, for instance I am trying to find out who is going to win elections and I do that by asking people who they voted on. After a certain number of answers my data will stop ...
2
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1answer
46 views

If the KL divergence is not a metric or a measure, what is it?

The KL divergence is not a metric because e.g. it does not satisfy the symmetry property that metrics posses. According to the definition of measure, the KL divergence doesn't seem to be a measure, ...
0
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1answer
788 views

Semi-heavy tailed distribution?

The generalized hyperbolic distribution is said to have semi-heavy tails. I know, that heavy tails means, that the tails are not exponentially bounded, or it has heavier tails than the normal ...
1
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0answers
31 views

Quantile function confusion about $\min\{x \text{ | }F(x) \geq p\}$

I am currently reviewing the quantile function for discrete random variables but I am a bit confused. We use the following definition of the quantile function: $$ \tilde{x}_p = min\{x \in \mathbb{R}...
20
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5answers
106k views

What is the difference between “margin of error” and “standard error”?

Is "margin of error" the same as "standard error"? A (simple) example to illustrate the difference would be great!
3
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1answer
174 views

Why aren't auto-encoders also considered generative models?

Auto-encoders (AEs) are composed of an encoder and a decoder (often represented by a neural network). The encoder produces a vector representation $z$ of its input $x$ (e.g. an image). The decoder ...
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0answers
534 views

What is the definition of the “bias corrected and accelerated” bootstrap confidence interval?

Googling shows several references, but all locked up.
25
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3answers
17k 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 ...
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1answer
24 views

What exactly is a inverse $\chi^2$ distribution?

What exactly is a inverse-chi square distribution?
90
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10answers
13k views

What, precisely, is a confidence interval?

I know roughly and informally what a confidence interval is. However, I can't seem to wrap my head around one rather important detail: According to Wikipedia: A confidence interval does not ...
1
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2answers
568 views

What is the actual definition of endogeneity?

I've been learning about endogeneity but after looking around online I've gotten more and more confused about what the definition is. Most pages say that in a model $y=X\beta+\epsilon$ the definition ...
0
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0answers
13 views

Is *conditional* stationarity (of a stochastic process) a useful concept?

Typical stationarity is defined in terms of some notion of invariance of a stochastic process w.r.t. a time shift operator. I think you could talk about conditional invariance: $ P(X_{t_1}, ... X_{...
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2answers
28 views

Population vs Sample Space

In probability theory, it is my understanding that the sample space $\Omega$ is the set of all possible outcomes of an experiment. In my mind, I am thinking of it as a set of data points such as ...
6
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1answer
49 views

What is the $dF(X)$ in some integrals concerning probability densities?

On multiple occasions I've come across statements about integrals of Considers the problem of minimizing the risk functional (Vapnik's Statistical Learning Theory) $$ R(\alpha ) = \int Q(z, \alpha ...
2
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1answer
72 views

Definition of a simple linear regression model

A while ago I was trying (not entirely successfully) to figure out the definition of a regression model. Now I am narrowing it down to a simple linear regression and trying to identify (loosely ...
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0answers
18 views

Sampling the output of a probabilistic classifier

A probabilistic classifier is a classifier that outputs a probability distribution over classes when provided with an input (feature vector). As stated in the linked wiki page above, a single class ...
0
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0answers
29 views

What is STATISTICS? Generally [duplicate]

What is statistics exactly? Can anyone tell the meaning of statistics in a simplified manner so that even a 5 year old could understand? What would you tell to a 5 year boy when he asks what is stats?...
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0answers
19 views

UMP test equivalence of definitions

I've been revising the past couple of days and have come across $2$ definitions of a UMP test. Suppose we want to test $H_0: \theta=\theta_0$ vs $H_1: \theta>\theta_0$. Then the test is UMP if: ...
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0answers
26 views

Adversarial examples in mixture density networks?

Mixture density networks (MDNs), first introduced by Christopher Bishop in 1994, are a type of neural network that output a probability distribution over categories. I am wondering what an ...
1
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2answers
423 views

Covariance definition

Why is covariance defined the way it is? $$\sigma(x,y)=\mathbb{E}[(X-\mathbb{E}[X])(Y-\mathbb{E}[Y])]$$ How do we know that this definition behaves in the following way? Covariance is a measure ...
9
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2answers
457 views

Why is p-value termed as P(Data | Hypothesis/Model)?

As the title suggests, Why is p-value termed as P(Data | Hypothesis/Model) and not P(Hypothesis | Data)? Shouldn't both be the same? Why is P(Data | Hypothesis) != P(Hypothesis | Data)? Is there any ...
5
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1answer
2k views

From Markov Decision Process (MDP) to Semi-MDP: What is it in a nutshell?

Markov Decision Process (MDP) is a mathematical formulation of decision making. An agent is the decision maker. In the reinforcement learning framework, he is the learner or the decision maker. We ...
0
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1answer
30 views

Is `p` in the formula for adjusted R-square defined for tree models?

Let $R^2$ be the R-squared defined for regression models. Given a vector x, the target, and a vector, y, the prediction of the ...
0
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0answers
18 views

Confusion about several different definitions of continuous random variables [duplicate]

It seems like different books define continuous random variables differently. pdf definition: The random variable X is continuous if a nonnegative function f exists, that is defined for all $x \in (-...
6
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1answer
7k views

What's the difference between binary and binomial data?

I read terms binary data and binomial data in a textbook. What's the difference between them?
3
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2answers
214 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 ...
1
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1answer
27 views

Pearl et al. (2016) definition of cause: circular?; how to improve?

Pearl et al. "Causal Inference in Statistics: A Primer" (2016) p. 26 provides the following definitions of direct cause and cause: A variable $X$ is a direct cause of a variable $Y$ if $X$ appears ...
1
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1answer
37 views

Experimental Design---Definition of treatment

I am learning about Experimental Design and I am confused with an example: 'The following chart displays the burning times of flares of two different type of torch design. The engineers are ...
2
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1answer
117 views

Experimental design definition

I am doing some research on how to analyse experimental data. During the last three weeks, I face the expression "experimental design", I try to google to understand this notion, and how it works. ...
4
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3answers
167 views

Learning a target feature from data

I have a dataset of customers (infos about them, as well as their buying behavior) to whom ads are sent regularly. How can I design a target feature that will result in a good model that predicts when ...
6
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2answers
133 views

What is meant by existence of a (discrete-time) stochastic process?

What is meant by existence of a (discrete-time) stochastic process? How do I know whether a process exists or not? Could anyone offer a simple example of an existent and another of a nonexistent ...
14
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3answers
1k 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 regression ...
20
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5answers
5k views

What does “likelihood is only defined up to a multiplicative constant of proportionality” mean in practice?

I'm reading a paper where the authors are leading from a discussion of maximum likelihood estimation to Bayes' Theorem, ostensibly as an introduction for beginners. As a likelihood example, they ...
3
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1answer
151 views

Is the $t$-test asymptotically nonparametric?

Wikpedia defines "parametric statistics" as: ...a branch of statistics which assumes that sample data comes from a population that follows a probability distribution based on a fixed set of ...

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