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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4
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1answer
81 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
144 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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25 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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17 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
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1answer
55 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
66 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
27 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 ...
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0answers
20 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 ...
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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"?
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27 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 ...
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1answer
77 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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18 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 ...
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0answers
44 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 ...
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1answer
47 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 ...
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1answer
14 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 ...
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0answers
42 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 ...
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0answers
19 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 ...
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0answers
40 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\\ ...
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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 ...
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1answer
14 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 ...
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0answers
30 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 $KL$ ...
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0answers
38 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.
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1answer
235 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 ...
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0answers
26 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 ...
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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 ...
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1answer
23 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 ...
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0answers
15 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?
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1answer
170 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, ...
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15 views

Geisser's definition of nonstochastic prediction

Does anyone have Geisser, 1993, "Predictive Inference: An Introduction." Chap- man and Hall, London. MR1252174? I am interested in the definition on page 31 for "nonstochastic prediction," but unable ...
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2answers
174 views

Why is the risk equal to the empirical risk when taking the expectation over the samples?

From Understanding Machine Learning: From theory to algorithms: Let $S$ be a set of $m$ samples from a set $Z$ and $w^*$ be an arbitrary vector. Then $\Bbb E_{S \text{ ~ } D^m}[L_S(w^*)] = L_D(w^*)...
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1answer
114 views

Understanding the definition of a location parameter

In some probability distributions, like normal or (non-standard) t distributions etc, there are location parameters such that a change to this parameter leads to the distribution moving rigidly to the ...
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0answers
16 views

Definition for lifted inference

What is the definition for lifted inference? As per my current knowledge, lifted inference is an inference technique that uses the rules of first-order logic. Is it true?
2
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1answer
83 views

What does it mean to generate a random variable from a distribution when random variable is a function?

I am looking at a reference for sampling from a distribution, and the first step of the so-called algorithm states:http://www.columbia.edu/~ks20/4703-Sigman/4703-07-Notes-ARM.pdf Generate a random ...
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1answer
294 views

Noise and Outliers in DBSCAN

Why are noise and outliers treated as the same concept in DBSCAN (density-based spatial clustering of applications with noise)?
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1answer
72 views

How to call this frequentist interval estimate that is neither a prediction interval nor a confidence interval

This question is inspired by Confidence Interval on a random quantity?. That question introduces an interesting concept for a type of interval that is neither a prediction nor a confidence interval (...
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0answers
27 views

definition of integrated- and- exponential autocorrelation time

I understand them (to an extent) both seperately, but i was reviewing my notes from class and my verbal definition is effectively stating the same thing in different words. I have: integrated: ...
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0answers
20 views

Is there a specific or standard definition for what classes as a peak?

I am working on some peak analysis at present, essentially just a programme that will identify peaks in a histogram and return the graph with those peaks pointed out. My question is, is there a ...
1
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2answers
244 views

What are the predictor variables in a neural network?

In a linear regression model, the predictor or independent (random) variables or regressors are often denoted by $X$. The related Wikipedia article does, IMHO, a good job at introducing linear ...
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3answers
129 views

What comes after the geometric mean?

The geometric mean is a multiplicative alternative to the arithmetic mean, which we could call additive mean, thereby calling the geometric mean multiplicative mean. My question is the following: what ...
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2answers
35 views

What does it mean to condition on a variable B in causal models?

Given the causal model $A \rightarrow B \rightarrow C$, then $A$ and $C$ are independent conditioned on $B$. What does this mean?
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1answer
35 views

What does it mean for a variable to block a path between other two variables?

What does it mean for a variable $Z$ to "block" the path between variables $X$ and $Y$ in a causal model? What is the formal definition of a "block", and how can I intuitively understand this concept? ...
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1answer
70 views

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

I am not sure if my question is a bit stupid but 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 ...
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0answers
74 views

P-value: Fisherian vs. contemporary frequentist definitions

I am trying to see if I understand the definition of $p$-value as used by Sir R. A. Fisher and the one used today by frequentist statisticians (not sure how to call it better). $p$-value according ...
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28 views

Inconsistency between definition of machine learning and popular usage

Wikipedia defines machine learning as "the scientific study of algorithms and statistical models that computer systems use to progressively improve their performance on a specific task". https://en....
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3answers
852 views

What is the precise definition of “performance” in machine learning?

In machine learning, people usually refer to the "performance of a model" or "performance of an optimizer". What is the exact definition of "performance"? What would be the "performance of an ...
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1answer
75 views

Multivariate regression vs. multiple univariate regression models

This is a naive question, but I am a little confused over the term "multivariate" regression. And note this question does not (to my knowledge) pertain to "multiple" regression. When people use the ...
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0answers
52 views

Dot subscript summation notation used in design of experiments

Context I couldn't find a clear explanation of this on this site, and thought that it might be of use. I have provided part of the answer, which anyone is welcome to build from. I'm not sure how to ...
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0answers
18 views

Example of a problem with structured output labels

I'm studying SSVM (Structured SVMs). On my book is stated that Structured SVM is an extension of the SVM, in which Each sample is assigned to a structured output label z ∈ K, e.g. partitions, ...