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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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 ...
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1answer
37 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?
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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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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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19 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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1answer
37 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, ...
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27 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}...
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1answer
23 views

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

What exactly is a inverse-chi square distribution?
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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
27 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 ...
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1answer
47 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 ...
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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 ...
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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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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 ...
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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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2answers
455 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 ...
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1answer
28 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 ...
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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 (-...
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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 ...
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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 ...
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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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2answers
214 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 ...
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1answer
47 views

Clarification on the IID assumption in machine learning: who is sampled from where, and who is independent with who?

So there are a couple of questions on IID assumption on this stackexchange, On the importance of the i.i.d. assumption in statistical learning Realistically, does the i.i.d. assumption hold for the ...
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1answer
134 views

Reverse causality opposite definitions

I have three sources, and all of them describe different DAG structures, and yet all claim that exactly their structure is the reverse causality: From s0: From s1 (page 84): From s2: Which of ...
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2answers
407 views

What is a latent space?

In the context of machine learning, I often hear the term latent space, sometimes qualified with the word "high dimensional" or "low dimensional" latent space. I am a bit puzzled by this term (as it ...
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22 views

Exposed vs Unexposed Group?

I am new to statistics and I don't quite get what are exposed and unexposed groups? I have not found clear definition on the Internet. Any useful links would be very appreciated.
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1answer
50 views

Confounder real definition

In this video, I can see that confounding variable is a variable that is correlated with two other variables: But this image tells that confounding variables is causally related to other two ...
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1answer
163 views

What does “the denominator does not contain any theta dependence” mean in Bayes' Rule? [duplicate]

Every lecture and book says that the denominator in Bayes' Rule does not depend on the parameter $\theta$. However, the denominator also includes $\theta$ in the formula of Bayes' Rule. I just cannot ...
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3answers
551 views

Random variable vs Statistic? [duplicate]

What's the difference between a random variable and a statistic? It seems that formally, a random variable is simply any real-valued function (and its domain is a set that we call a "sample space"). ...
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1answer
415 views

what means to be outside unit circle?

I am trying to study time series without a great math background and I came across the next problem: When checking for stationarity I check the roots, and if they are not on the unit circle, then it ...
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113 views

Definition of Statistical Rigor

Is there an accepted definition for "statistical rigor" in the statistics literature? Perhaps in historic works by pioneers in the field such as the Pearsons, Cohen or Fisher? I found a commentary: ...
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68 views

Non-uniqueness of a CDF in N >= 2

Peacock in his paper on 'Two-dimensional goodness-of-fit testing in astronomy', http://adsabs.harvard.edu/full/1983MNRAS.202..615P, described the issue with the non-uniqueness of CDF in higer (N >= 2) ...
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3answers
2k views

What is the “opposite” of a random variable?

I am learning about random variables with all of their different types of distributions for discrete and continuous types. However, before knowing about random variables, I am not sure what would be a ...
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1answer
32 views

What is the name for n dimensional data sampled at regular intervals in n-1 dimensions?

I'm looking for a word to describe n-dimensional data sampled at regular intervals in n-1 dimensions. For example, a 3d dataset would have data sampled at regular intervals on a 2d grid. A 4d dataset ...
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23 views

Why does the denominator of the likelihood ratio change for simple hypotheses?

My understanding is that when we are considering composite hypotheses (one-sided or two-sided), we often want to use the likelihood ratio as part of a test statistic. In this case, the likelihood ...
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27 views

Is term “metric” for evaluating machine learning model misnomer?

Term "metric" is used in many popular machine learning articles [1, 2] for describing an evaluation criterium of the performance of a model. Although, mathematically is the term defined as: In ...
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1answer
175 views

What is the definition of a aperiodic Markov chain?

I understand the definition of a state being aperiodic or periodic with period d. But what does it mean for a chain to be aperiodic / periodic with period d? Thanks.
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2answers
550 views

What is the conceptual difference between posterior and likelihood? [duplicate]

I have trouble discerning conceptually between these two notions. I am aware of their formal relations, proprieties and what not, but I just can't wrap my head around what they "mean", if that even ...
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1answer
593 views

when to say that an algorithm is a learning algorithm?

If I have an algorithm that deals with data, and the result of this algorithm is binary classes, When can i say that this algorithm is a classification algorithm ( machine learning algorithm)??
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2answers
1k views

Is population size a parameter, or sample size a statistic?

The definitions of a parameter and statistic pretty much agree: parameters and statistics are numerical characteristics or numerical summaries of a population and sample, respectively, for a given ...
4
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1answer
178 views

Provide a precise and concise statement on what a simple linear model is

I have recently commenced a 2nd-year course on linear models and have been a little overwhelmed by either the abuse of notation or the lack of clarity behind what a linear model is. I've read multiple ...
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1answer
90 views

Reconciling alternative definitions of parametric vs. nonparametric

In the thread Is there any statistical test that is parametric and non-parametric?, @JohnRos gives an answer saying that Parametric is used in (at least) two meanings: A - To declare you ...
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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 ...
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0answers
30 views

Usefulness and validity of Alternative definitions of “quantile”

According to textbook, the $p\,$th quantile of a random variable $X$ is any real value $x$ satisfying $P(X \geq x)\geq 1-p$ and $P(X \leq x) \geq p$. Why isn't the alternative definition, a $p\,$th ...
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26 views

Is survival analysis is a time series models

I would like to apply a quantile regression model on lung cancer (survival). My question is, does survival analysis is a time series models. Or can I fit linear quantile regression models to this data?...
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1answer
65 views

Interpretation of the technical requirement on a random variable

I found a slide where there is the definition of a random variable and after a technical requirement difficult to understand for me. Can you explain it by using a counterexample please? What happens ...
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0answers
12 views

The function machine learning is trying to approximate

Consider a random experiment E with sample space S and the probability measure P. Assume that all events are measurable. Let X1, X2, X3,...., Xn are random variables over S. Now machine learning ...
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2answers
2k views

Definition of “percentile”

I'm now reading a note on Biostatistics written by PMT Education, and notice the following sentences in Section 2.7: A baby born at the 50th percentile for mass is heavier than 50% of babies. A ...
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2answers
72 views

Does $P(X>x, Y>x)= P(X>x)P(Y>y)$ implies independence?

We know, by definition, that two random variables are independent if $$P(X\leq x, Y\leq y)= P(X\leq x)P(Y\leq y).$$ If, insted, I have that $$P(X>x, Y>y)= P(X>x)P(Y>y),$$ does this also ...
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1answer
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In the context of predicting customer churn, what is “small effect size?” [closed]

One research paper says an example of "effect size" is the difference in the average age of churners vs. non-churners (31 vs 40). A different paper says "effect size" is the difference in the area ...

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