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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11 views

Symbol interpretation in non-constant power law density

I am reading Barabasi book on network science. I am struggling to interpret the density formula for a power-law degree distribution with low-degree saturation and high-degree cut-off (http://...
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21 views

Probability distribution over a variable? What does it mean?

In this document http://legacydirs.umiacs.umd.edu/~xyang35/files/understanding-variational-lower.pdf at the very first page, it says: Moreover, uppercase P(X) denotes the probability distribution over ...
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What does “autocorrelation/heteroscedasticity of the errors” mean?

When learning clustering error, from this discussion In general, you should look to cluster-adjust standard errors at the level in which you believe there exists autocorrelation/heteroscedasticity of ...
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37 views

Null hypothesis definition

why do we use H0: μ ≥ μ0 in a left tailed test and try to reject H0 rather than using H0: μ ≤ μ0 and trying to prove H0 is true? thanks
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20 views

Definition of the word “embedding”

The mathematical definition of the word "embedding" requires the mapping to be injective, so in that context one speaks of, for example, embedding real numbers in complex numbers (ie, ...
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18 views

Can the distribution of a pivot depend on known parameters?

I have a question about the distribution of a pivot. Different sources give slightly different definitions of a pivot. Some of them define it as a random variable $Q(\mathbf{X}, \theta)$ whose ...
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79 views

Decision Theory: Why is it called a “least favorable prior”?

I'm currently reading the chapter on Statistical Decision Theory in Larry Wasserman's "All of Statistics". Reading the section 13.4 about Minimax Rules he introduces the so called Least ...
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15 views

What is a Figure of Merit in statistics?

Papers published on the arXiv often mention the notion of Figure of Merit (FOM). Can you explain what a Figure of Merit is, how it is used and what are its relations to statistics?
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30 views

For a generative model, how is modelling p(X,Y) equivalent to modelling P(X|Y=y)?

On the Wikipedia page for generative models it gives the following definitions of a generative model: (X is an observable variable, Y is the target variable) 1) A generative model is a model of the ...
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Clarification regarding comonotonic random variables

According to wikipedia, an equivalent definition of a comonotonic random vector is: A $\mathbb{R}^n$-valued vector is comonotonic iff it agrees in distribution with a random vector where all ...
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3answers
96 views

What are Global minima and Local minima in Machine Learning?

What are Global minima and Local minima in Machine Learning? How is it used?
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22 views

Can I define a random sample as a collection of random variables?

I have been reading a few posts like this one (What is the difference between random variable and random sample?) on the subject so I'd like to make sure my understanding is correct. Let us say I ...
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1answer
60 views

What is meant by divergence in statistics?

I have learned about the Intuition on the Kullback-Leibler (KL) Divergence as how much a model distribution function differs from the theoretical/true distribution of the data. The two most important ...
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2answers
76 views

Likelihood $L(\theta; \mathbf{y})$: Is $\theta$ a vector of parameters or is it a single parameter?

I have the following definition of likelihood: Let $y_1, \dots, y_n$ be a sample of observations taken on corresponding random variables $Y_1, \dots, Y_n$ whose distribution depends on the parameter(...
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1answer
56 views

Definition of statistical significance

Consider the following definition of statistical significance: Statistical significance is a characteristic of a statistic viewed in light of an (implicit or explicit) null hypothesis and a given ...
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2answers
590 views

Is a spline interpolation considered to be a nonparametric model?

I am aware of the basic differences between nonparametric and parametric statistics. In parametric models, we assume the data follows a distribution and fit it onto it using a fixed number of ...
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22 views

Should I say “copula” or “copula function”? Is the latter superfluous?

I am writing a paper involving copulas and have been thinking of whether I should say "copula function" or just "copula", as I am not sure whether the term "copula" ...
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1answer
125 views

Splines: relationship of knots, degree and degrees of freedom

Could one explain how these three parameters change the behaviour of this "wiggle curve" In particular, I am trying to understand b-splines and m-splines. My limited understanding is as ...
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1answer
35 views

Seeking clarity regarding kernels

With regards to Bayesian statistics, I understand the kernel of a probability density function (pdf) or probability mass function (pmf) to be the form of the pdf or pmf in which any factors that are ...
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1answer
46 views

Need help with understanding random variables/the data generating distribution

Lets say we want to predict a persons weight using their height and gender. We always assume there is a data generating distribution $P_{X×Y}$, and all output and input pairs are generated i.i.d from $...
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20 views

Specificity and Sensitivity vs. Confidence and Power

Specificity (True Negative Rate) and Sensitivity (True Positive Rate) seem to be conceptually similar to Confidence (Probability of True Negative) and Power (Probability of True Positive). What are ...
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1answer
43 views

Why sample complexity must be polynomial for PAC learning?

I'm reading up on Probably Approximately Correct (PAC) learning and most sources require that the sample complexity must be polynomial in $\frac{1}{\epsilon}$ and $\frac{1}{\delta}$, where ${\epsilon}$...
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16 views

What about the covariance formula makes it obvious that it is about 'linear' associations? [duplicate]

The covariance (and correlation) are described as the strength of a linear association between variables. Is there a way to see where the 'linear' part comes from in the formula?
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39 views

What is a sepset in a probabilistic graphical model?

The terminology sepset is used quite often in the Probabilistic graphical models and causality. What does it mean and what is its relevance ?
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Learning Event Order of Non-ordered Events from Already Ordered Events

Is there a name for the problem of taking ordered and non-ordered nodes, and creates an ordering of the non-ordered nodes based on the ordered nodes, with the requirement that preexisting ordering be ...
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27 views

Are invariant and stationary distribution the same thing?

I am reading a material about Markov chains and in it the author works on the Markov chains part discrete the invariant distribution of the process. However, when addressing the part of continuous ...
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45 views

Two conflicting definitions of AR(1)

I've been starting to learn about AR(1) processes but I have come across two different definitions of them. The different definitions lead to different conclusions about stationarity and I'm not sure ...
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2answers
132 views

Is the following textbook definition of $p$-value correct?

I have found the following definition of $p$-value in an introductory statistics textbook (not in English, so I am translating it): $p$-value is the probability of getting a result that is at least ...
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1answer
166 views

In reinforcement learning, what is the correct definition of “value function”?

This is a follow up to: In reinforcement learning, what is the correct mathematical definition of the discounted reward? I discovered that there seems to exist an extremely large and disparate ...
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2answers
52 views

Does the distribution $f(x) \propto (1-x^2)^{n/2}$ have a name?

The distribution $f(x) \propto (1-x^2)^{n/2}$ for $-1 \leq x \leq 1$ It occurs in a problem like Law of the norm of the empirical mean of uniforms on the sphere? It relates to intersections of high ...
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0answers
105 views

Formal definition of a latent variable model

Wikipedia says that: A latent variable model is a statistical model that relates a set of observable variables (so-called manifest variables) to a set of latent variables. I am wondering how to ...
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1answer
17 views

What is meant by a “sweep” in Reinfocement Leraning?

what is meant by a sweep in value iteration or policy iteration in RL. please try to give a nice explanation because I am new to RL.
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1answer
67 views

Why is the Hyndman and Fan 1996 recommendation for sample quantile definition to standardize on not more accepted? [closed]

The 1996 paper Sample quantiles in statistical packages is often cited as the comprehensive source of sample quantile definitions and many a software package refers to the paper in the description of ...
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40 views

What are the characteristics of a comparison distribution?

In my introductory statistics course I have been offered a definition of a comparison distribution that honestly leaves me quite confused. Any help would be greatly appreciated. On a practice ...
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13 views

Why the definition of a discrepancy or objective fit function does not require monotonicity?

In the context of covariance structure models (as used in SEM), we have $\Sigma$ a population covariance structure, and $\Sigma(\cdot)$, a function of a parameter vector that returns a model-implied ...
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1answer
364 views

Terminology: unconditional heteroskedasticity

I have seen mentions of both unconditional and conditional heteroskedasticity. The latter is fine with me but I am struggling to uderstand the former. It appears I am not the only one to question ...
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39 views

Degrees of Freedom as Defined by Discipline

I've just begun a machine learning course and I've been confused over my professors use of the degrees of freedom terminology. I've picked up that while in statistics talking about degrees of freedom ...
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66 views

What is the difference between brokerage and betweenness?

This link describes betweenness: "Betweenness centrality measures the extent to which a vertex lies on paths between other vertices." This link describes brokerage: "Brokerage is a ...
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1answer
49 views

In reinforcement learning, what is the correct mathematical definition of the discounted reward?

I'm seeing several different definitions of discounted reward/return as it is used in MDP based RL. I am wondering which one is correct. Let $r_t$ be the scalar-valued immediate reward at time $t$, $...
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19 views

What does this mean? ($\boldsymbol{I}_{\theta, \infty}(x_i)$) [duplicate]

In my studies I came across this There is some more to this answer but for the purpose of this question lets leave it at that. I can't figure out what $\boldsymbol{I}_{\theta, \infty}(x_i/i)$ is and ...
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81 views

What is it called when a random variable is weakly greater than another for all elements of the sample space?

Suppose I have random variables $(X_1,X_2)$ defined on a probability space $(\Omega, \mathcal{F},P)$ such that for any element $\omega \in \Omega$, $X_1(\omega) \geq X_2(\omega)$. I'm looking to work ...
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18 views

How is an 'ogival function' defined?

Reading on a paper on factor analysis and measurement invariance I find the description of some functions as 'ogival' functions. In Google I find it referenced mostly in papers from the '70s and '80s....
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1answer
882 views

What is the formula for the standard error of Cohen's d

I found different answers to the question how to calculate the standard error (SE) of Cohen's d. First formula is (see here, here or here): $$ SE_d = \sqrt{\frac{n_1 + n_2}{n_1 n_2} + \frac{d^2}{2(n_1+...
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1answer
30 views

Does MAD/MAV have a name?

mean(abs(pred - true)) / mean(abs(true)) I defined above metric that works well for measuring reconstruction error for zero-mean signal data (1D); does it have a ...
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1answer
38 views

(Apparently) Different Definitions of Statistical Independence

I am reading John Mandel's book " The Statitical Analysis of Experimental Data). In it, in Ch 5, p. 52, he describes Statistical Independence of two RVs $X,Y$ in terms of independence in the ...
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20 views

What is the name of this type of testing?

I am trying to find information on this type of testing but I don't know what it's called... I have 7 samples that I am using to interpolate over a geographic area using Spline. I am curious to the ...
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1answer
50 views

Definition of Partial Autocovariance Function

The most interpretable definition of the Partial Autocovariance of a $(L^2)$ time series $\{X_t\}$ that I have seen is the following: $$ \phi_{hh} = \mathrm{Cov} (X_{t+h}, X_t | X_{t+h - 1}, \cdots,X_{...
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19 views

Defining statistical significance under methods: using alpha or p?

Two options: Statistical significance was defined as alpha = 0.05, and all tests were 2-sided. Statistical significance was defined as p < 0.05, and all tests were 2-sided. Are both of them ...
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107 views

What is gradient correlation?

I came to cross a type of correlation that I haven't heard before --- what is gradient correlation? Does the gradient correlation function range from 0 to 1 just like the regular Pearson's correlation?...
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1answer
632 views

What is Asymptotic Independence

What does it mean if two random variables are asymptotically independent? And how would you prove that they are?

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