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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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31 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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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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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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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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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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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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135 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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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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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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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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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?
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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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178 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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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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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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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 ...
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2answers
137 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
109 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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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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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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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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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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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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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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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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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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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, ...
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Definition of a 'design adaptive' fit?

When studying non-parametric regression, I've been told that local linear fitting is often better than local constant fitting at the job of estimating regression functions because local linear fitting ...
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1answer
50 views

Typo or change of interpretation in loss function in the Bayesian Choice textbook?

In the proof of the following proposition, the posterior loss depends on a prior distribution $\pi$, while in the derivation it depends on the parameter $\theta$. Should the posterior loss function be ...
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253 views

What is the name for the complement of accuracy?

I have a metric that is defined as $1 - Accuracy$ and I need a name for it. Is there a scientific name for the complement of accuracy?
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What is the definition of layer in neural network?

What is the precise definition of layer in neural network? Are things like concatenate functions, activations, batch normalizations, skip connections considered as layers?
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Name of functional part of a pdf after removing proportionality constants?

Let $f(x;\theta)$ be probability density function. Suppose that this pdf contains a proportionality constant $c$, so that $f(x;\theta) = c\cdot g(x;\theta)$, where $g$ is an integrable function. Is ...
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Frequentist definition of probability and prediction?

The frequentist definition of probability states that: The probability of an event is the ratio of the number of cases favorable to it, to the number of all cases possible when nothing leads us to ...
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301 views

VC dimension of sine family is infinite?

From what I understand, the VC dimension of an hypothesis class is given by the maximum number of points in general position (or random) on the domain space that can be arbitrarily labeled by the ...
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132 views

The definitions of estimator and estimate

This example demonstrates the difference between a theoretical observation and a realized observation. A theoretical observation is a random variable with a probability distribution, while its ...
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Sampling from a finite sequence without replacement yields exchangeable sequences?

I have read (and re-read) the wikipedia article on Exchangeability https://en.wikipedia.org/wiki/Exchangeable_random_variables . The disconnect for me is that : after having sampled without ...