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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Definition formule: '∃!α'? [closed]
I'm a rookie with statistics, so I am just very curious about things and very aware of the fact I barely know anything.
I was looking around and found '∃!' which means (please, do correct me if I'm ...
Annie
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1
answer
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Finding a source for the definition of "clustering accuracy"
In papers about unsupervised clustering I see a lot of references to a metric "clustering accuracy" or "unsupervised clustering accuracy" (ACC) which is usually defined as ...
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Example of statistical experiment in which the statistical unit is time
Could you give me some examples of statistical experiment/analysis in which the statistical unit is
the time? If I conduct a study on the number of people who have attended a bachelor degree over time,...
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2
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1
answer
61
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Definition of $\text{“}R^2\text{”}$
I have always taken $\text{“}R^2\text{”}$ to mean the proportion of a sum of squares explained by a model.
The context in which this idea is first encountered is when one explains part of the total ...
- 8,796
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Definition of Uncertainity
I have some confusion regarding Measurement Uncertainty. In some books/articles it is defined wrt true value as "Uncertainty in the average of measurements is the range in which true value is ...
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Strongly vs. weakly stationary ergodic process
I'm reading a paper where a process is assumed as strong stationary ergodic. And I have read some materials where an ergodic process is defined for a weak stationary process, like
$$\lim_{n\rightarrow\...
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4
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Do testability and falsifiability have statistical definitions?
Psychology: the Core Concepts says
Psychology differs from the pseudosciences in that it employs
the scientific method to test its ideas empirically. The scientific
method relies on ...
- 19.1k
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Definition of exponent measure (extreme value theory)
Let $F$ be a distribution function on $\mathbb{R}^2$, and let $U_i$ be the left continuous inverse of $\frac{1}{1-F_i}$, where $F_i$ is the marginal distribution of $F$.
In my textbook, there is the ...
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3
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833
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For a confusion matrix, is there a name for FP / (FP + FN)?
For a confusion matrix, there are a variety of useful rates, ratios and indices. But I cannot find the one I care about:
FP / (FP + FN)
Of course this measure is ...
- 203
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2
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164
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What is a formal and authoritative definition of an 'assumption' in a statistical model?
The description of the tag in this website states that it
Refers to the conditions under which a statistics procedure yields valid estimates and/or inference. E.g., many statistical techniques ...
- 1,375
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Normal distribution in linear regression [duplicate]
There are some references like this that says in linear regression, this is not necessary for variables to have normal distribution.
but I read some books that say otherwise:
Joseph Hilbe in a book ...
11
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2
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Definition of "unpredictable"
How do we rigorously define the term "unpredictable" in cases of point and density prediction?
The term "unpredictable" is employed in various contexts, e.g.
"the outcome of ...
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Clarification: confidence interval of the (slope of the) regression line
When confidence intervals are referenced in the regression context, I often see them mentioned (generally speaking) as "of the slope of the regression line," or as "of the regression ...
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Data vs. Information. What’s the difference between these two terms?
Following are the definitions "representative" of the countless articles I have read about data vs information and yet have nothing to say about them. Can anyone just put some accent upon ...
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Definition of Statistics by Sheldon M. Ross [closed]
Sheldon M. Ross in his book, "Introductory Statistics" states the definition of statistics to be:
"Statistics is the art of learning from data. It is concerned with the collection
of ...
- 11
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2
answers
77
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meaning of independent samples
I am getting confused about the concept of independent samples, which is related to the concept of pseudoreplications. This question is related to this topic. But reading it does not make it clear for ...
- 1,434
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1
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508
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The link between AQL, RQL and the reliability of a process
The problem is to distinguish between the definitions of AQL, RQL and reliability in the field of quality control. Let us just pose the context. We wish to calculate the reliability of a manufacturing ...
- 427
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1
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Questions on what it means when we talk about "overfit"
"Overfit" is a commonly discussed concept in ML community. However, I tend to feel that there might be abuse of using this terminology. I wonder what it means when we talk about overfit, ...
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What's the relationship between these two definitions of martingales?
On wikipedia, the definition of a martingale is given as follows:
A basic definition of a discrete-time martingale is a discrete-time stochastic process (i.e., a sequence of random variables) $X_1, ...
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1
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How to demonstrate amount of virus required to lyse all cells using Poisson distribution?
In a seminal article in virology ('Sur l’unité lytique du bactériophage'
Comptes rendus des séances de la Societé de biologie et de ses filiales, 1939, 130, pp. 904-907) the Nobel prize winner ...
- 211
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Definition p-value and find p-value in practice
I have a problem that I can't solution. Let $\mathbf{X}=\{X_1,X_2,\ldots,X_n\}\sim\mathrm{Uniform}(0,\theta)$ and we have $H_0:\theta=\theta_0$ and $H_1:\theta>\theta_0$. We reject the $H_0$ when $...
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answers
31
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marginal cdf and cdf of marginals
given a joint distribution of 2 variables $P(X,Y)$, is the cdf of the Y-marginal distribution equals to the Y-marginal of the cdf of $P(X,Y)$?
- 325
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14
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Meaning of Conditional Independence Between Sets of Variables
I am reading about the so called "global Markov property" of a Markov random field and this is defined as the conditional independence between two sets of random variables given a third set
$...
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Why are Square Integrable Functions important in Statistics?
I'm reading a paper by Giles Hooker on Functional Decomposition through the use of Functional ANOVA.
In the paper he defines a function:
$$ F(x) : \mathbb{R}^k \rightarrow \mathbb{R} $$
and explicitly ...
- 389
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103
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Is there a connection between the Kernels in Statistics and Linear Algebra?
According to this question, the etymology of the terms is related, and Kernel is used to mean the "core" of something. In general it seems to refer to an unchanging transformation at the ...
- 389
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1
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524
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What are balanced and orthogonal designed experiments?
I have recently started studying Designed Experiments and have have come across non-rigorous definitions of "balanced" and "orthogonal" experiments and would be interested in ...
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vote
1
answer
203
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Relationship between blocks, factors and treatments
I have recently began studying a course on Designed Experiments and am having some trouble understanding some of the terminology. I've looked at some other answers on the site and I think that I am ...
- 223
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0
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14
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Meaning of "distributions with the same value" - context of bootstrapping
In Philip Good's "Permutation, Parametric, and Bootstrap Tests of Hypotheses" (https://dl.acm.org/doi/10.5555/1196379), Good writes, on the topic of "Confidence Intervals Based on the ...
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219
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Is there a difference between out-of-domain and out-of-distribution?
When I research papers on the generalisability of ML models, both terms "Out of Distribution" and "Out of Domain" pop up. Are these essentially the same? In my understanding, yes. ...
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Can we consider the loadings as a proxy for correlation, in a Principal Component Analysis (PCA)?
In a PCA, the loadings can be understood as the weights for each original variable when calculating the principal component, or "how much each variable influence a principal component".
Thus,...
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Questions regarding power of test and type II error
I´m preparing for a lecture in decision theory and I´m a little bit confused by the notation used by my prof.
On the first slide under remark 3.2 point v) its written, that $\beta(\varphi)$ is equal ...
3
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1
answer
376
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What is independent censoring and what are its assumptions?
I'm reading the Introduction to Statistical Learning book. In chapter 11 (Survival Analysis, page 463), the authors state:
In general, we need to assume that the censoring mechanism is
independent: ...
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votes
1
answer
607
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Bounded density function: definition?
What is the correct definition of bounded probability density function:
$\sup_{x} f(x)<\infty$. If this is the correct definition of bounded probability density function, can you give the example ...
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Understanding likelihood vs conditional joint pdf
My course notes (3rd-year module in Bayesian Statistics, unpublished) have a paragraph,
Gaussian data with known variance
Suppose we have $\textbf{x}=\{x_1,\dots,x_n\}$ iid given $\theta$ and $\...
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Rationale behind defining distribution function with strict inequality
A friend from Italy pointed me to a nice Probability Theory book written in Italian by G. Dall'Aglio, a well-known Italian probabilist; Original title: Calcolo delle Probabilità, terza edizione, ...
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1
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Are random variables mathematical functions when dealing with continuous sample spaces?
I'm struggling with some basic concepts regarding the definitions of random variables.
If I'm not mistaken, random variables are functions which aim to "translate" outcomes of a sample space ...
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Definition of Hypothesis Testing in All of Statistics
In the book All of Statistics by Larry Wesserman, the author says "Let $X$ be a random variable and let $\mathcal{X}$ be the range of $X$. We test a hypothesis by finding an appropriate subset of ...
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Regression vs. Classification: Is there a clear, generally accepted definition?
As a mathematician/economist, I am not trained to think in classification and regression tasks. This is why I wonder: is there a clear, widely accepted definition of regression and classification ...
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Provide an example of a dataset where maximum likelihood is inapplicable as third moments and fourth moments "assumptions" do not apply
An additional complication arises with estimation, since maximum likelihood estimation may not be feasible without making unrealistically strong ?????"assumptions"????? about third‐ and ...
user318514
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What is the difference between something being "true" and 'true with probability 1"?
In the beginning of chapter 2 of Information Theory, Inference and Algorithms, the author says that he will refrain from being unnecessarily rigorous and provides the example of saying that something ...
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What is the definition of a non-linear estimator? I heard that ratio of estimators is non-linear
Why don't we consider nonlinear estimators for the parameters of linear regression models?
says that LASSO is a non-linear estimator.
I think LASSO has a solution via matrix multiplication. I don'...
user318514
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2
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When is a statistic not a statistic?
I have a fairly involved ``statistic'' that involves transformation of a set of samples $\mathbf{x}$ by a massive machine-learned matrix and subsequent nonlinear processing into said statistic $\...
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1
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0
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164
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Definition of correlation between events?
I often hear people talk about correlation between events, e.g. event A and event B are positively correlated.
However, unlike correlation between random variables (i.e. $\frac{Cov(X,Y)}{\sigma_X \...
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2
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A Rigorous Definition of Data Generating Process (DGP)
I am trying to find a rigorous mathematical definition of a data generating process (DGP) under a well-defined probability space.
The closest source I have found on Cross Validated is this one, and it ...
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What does 'Parent Distribution' mean in statistics?
I am studying some articles related to statistics and some of them mention the term 'Parent Distribution'. What does that mean? Is it a distribution model that the authors decide to use as a basis of ...
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What is effect size?
It might be silly question-want to have clarity of this concept.I was wondering if someone can elaborate meaning and examples of effect size in clinical research. How to interpret it accurately? How ...
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1
answer
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Can a consensus be reached on the exact meaning of "Cohen's D" and "Hedge's G"?
This question: Difference between Cohen's d and Hedges' g for effect size metrics
shows there are at least two different interpretations each of both Cohen’s D and Hedge’s G, one of them in ...
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Loss function definiton for relabelling
Taken from the appendix to the paper (Yongning Wang & Ruey S. Tsay) of this (2019) paper Clustering Multiple Time Series with Structural Breaks. Appendix to be downloaded her Appendix
To fix label ...
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1
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What does it mean to say that a covariance matrix is a positive definite matrix? [duplicate]
I'm doing a work on covariance matrix and this question came to me that was not very clear.
