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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7
votes
1answer
87 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 ...
0
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0answers
12 views

Are all rate parameter the same? [closed]

Is the following definition correct? $\lambda = $ rate parameter $=$ average amount of y-value per x-axis unit. $Poisson(\lambda), Gamma(\alpha, \lambda), Exponential(\lambda)$ have the same ...
2
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2answers
57 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 ...
0
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0answers
12 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.
0
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1answer
33 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 ...
4
votes
1answer
157 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 ...
9
votes
3answers
484 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"). ...
2
votes
1answer
100 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 ...
0
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0answers
36 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: ...
1
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0answers
66 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) ...
3
votes
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 ...
1
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1answer
29 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 ...
0
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0answers
20 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 ...
0
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0answers
25 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 ...
0
votes
1answer
63 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.
3
votes
2answers
69 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 ...
0
votes
1answer
276 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)??
11
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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
votes
1answer
160 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 ...
4
votes
1answer
89 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 ...
4
votes
3answers
155 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 ...
0
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0answers
27 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 ...
0
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0answers
22 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?...
2
votes
1answer
62 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 ...
0
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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 ...
11
votes
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 ...
3
votes
2answers
70 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 ...
-1
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1answer
32 views

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 ...
0
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0answers
23 views

Dimension of a probability distribution function

Consider the following statement We want to sample from a complex high dimensional distribution which is intractable. What is meant by a dimension of distribution here? Does each random variable ...
1
vote
1answer
19 views

What does it mean to have “groups” and “levels” of variables?

Using this website, a user can find a correct statistical test for their project. However, what do they mean when they write "2+ groups" or "2+ levels"?
0
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0answers
35 views

What is a sparse Gaussian process?

In the paper Junction Tree Variational Autoencoder for Molecular Graph Generation, section 3.2, the authors state that they train a sparse Gaussian process to predict a chemical property, $y(m)$, of a ...
2
votes
1answer
101 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 ...
0
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0answers
19 views

How does the rejection sampling method work in layman's terms?

Suppose that I have no knowledge of sampling methods and that I have some knowledge of probability theory (e.g. probability distribution and marginal distribution). How would you explain the ...
4
votes
0answers
45 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 ...
2
votes
1answer
82 views

Targeted Maximum Likelihood Estimation for dummies?

I have tried to get my head around the concept of TMLE, but most references seem to be written by people who despise being understood (or maybe I am just hebetudinous). I have tried to read the paper ...
1
vote
1answer
16 views

What exactly is “fundamental data” and “technical data?”

I'm not sure if this question is appropriate for this community, and if so please feel free to let me know by down voting or closing. I'm currently working on projects that use machine learning/deep ...
2
votes
0answers
43 views

Name/definition of $\int \log F(x) \cdot g(x)dx$?

We know that: $$-\int \log f(x) \cdot g(x)dx,$$ where $f$ and $g$ are density functions, is known as the cross entropy. Does $$-\int \log F(x) \cdot g(x)dx,$$ where $F$ is the cumulative ...
0
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0answers
25 views

What is the difference between “paired” and “unpaired” versions in Wilcoxon's test?

Statistical tests can e.g. be used to decide whether to accept, reject or fail to reject the null hypothesis (the status quo). There are (apparently) two variants of this Wilcoxon's test: paired and ...
1
vote
0answers
43 views

Trouble with copulas: how do we justify its definition?

A bivariate function $C(u,v)$ that maps $[0,1]^{2}$ to $[0,1]$ is a copula if it satisfies the following two conditions: (i) Boundary conditions: \begin{align*} C(u,0) = 0\\ C(0,v) = 0\\ C(u,1) = u\\ ...
0
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0answers
8 views

Correct definition of prospective repeatability study for study protocol

I'm going to submit a protocol at my local IRB for a prospective single centre study which is a repeatability study. In this study we will perform an additional sequence in magnetic resonance. How ...
0
votes
1answer
15 views

Word for data-series comprised from resampled, interpolated and merged data-series

Two series of data-points for a specific curve are given: $x$ as a function of $y$ (high resolution, low range) $y$ as a function of $x$ (low resolution, high range) The two series are merged and ...
0
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0answers
33 views

When do these two definitions of KL-divergence match?

Suppose $P$ and $Q$ are two distributions on a space ${\cal H}$ (could be a subset of an infinite dimensional function space) with p.d.fs denoted by the same letter then one can define the $KL$ ...
0
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0answers
41 views

What is Ergodic Variance

I am curious as to the definition of ergodic variance in relation to an estimate of some parameter. It was mentioned to me by a teacher although I have not been able to find any references to it.
2
votes
1answer
472 views

Defining fixed effect and random effect in a model

I'm unconfident that whether my understanding on fixed effect and random effect is correct: Fixed effect= variable that make inferences about the specific levels. Random effect= variable that make ...
0
votes
0answers
34 views

How do you explain 'explained variance'?

What is the best definition of 'explained variance' from a teaching perspective? I quite like this one: "Explained variance (also called explained variation) is used to measure the discrepancy ...
14
votes
2answers
2k views

Examples of a statistic that is not independent of sample's distribution?

This is the definition for statistic on wikipedia More formally, statistical theory defines a statistic as a function of a sample where the function itself is independent of the sample's ...
1
vote
1answer
24 views

Definition of curvature

Kay (Fundamentals of Statistical Signal Processing) defines the curvature of a log-likelihood function to be the "negative of the second derivative of the logarithm of the likelihood function at its ...
0
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0answers
17 views

ARMA is there any relationship/implication between uniqueness and invertibiliity? [duplicate]

ARMA is there any relationship/implication between uniqueness and invertibiliity? Does one implies an other or not?
3
votes
1answer
308 views

Are the law of iterated expectation and the law of total expectations the same?

On the Wikipedia page of the Law of total expectations it is said that The proposition in probability theory known as the law of total expectation, the law of iterated expectations, the tower rule, ...
0
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0answers
27 views

Geisser's definition of nonstochastic prediction

Does anyone have Geisser, 1993, "Predictive Inference: An Introduction." Chapman and Hall, London. MR1252174? I am interested in the definition on page 31 for "nonstochastic prediction," but unable ...