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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6
votes
2answers
120 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 ...
9
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3answers
23k views

What exactly is a hypothesis space in machine learning?

Whilst I understand the term conceptually, I'm struggling to understand it operationally. Could anyone help me out by providing an example?
13
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3answers
1k views

Definition and delimitation of regression model

An embarrassingly simple question -- but it seems it has not been asked on Cross Validated before: What is the definition of a regression model? Also a support question, What is not a regression ...
1
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0answers
48 views

Definition of a simple linear regression model

A while ago I was trying (not entirely successfully) to figure out the definition of a regression model. Now I am narrowing it down to a simple linear regression and trying to identify (loosely ...
20
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5answers
4k views

What does “likelihood is only defined up to a multiplicative constant of proportionality” mean in practice?

I'm reading a paper where the authors are leading from a discussion of maximum likelihood estimation to Bayes' Theorem, ostensibly as an introduction for beginners. As a likelihood example, they ...
2
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1answer
2k views

Inter-cluster variance

Can you please help me understand how is inter-cluster (between clusters) variance defined? As opposed to intra-cluster variance which is pretty straightforward, I have not managed to found a clear ...
20
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4answers
99k views

What is the difference between “margin of error” and “standard error”?

Is "margin of error" the same as "standard error"? A (simple) example to illustrate the difference would be great!
3
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1answer
127 views

Is the $t$-test asymptotically nonparametric?

Wikpedia defines "parametric statistics" as: ...a branch of statistics which assumes that sample data comes from a population that follows a probability distribution based on a fixed set of ...
48
votes
4answers
15k views

What is a contrast matrix?

What exactly is contrast matrix (a term, pertaining to an analysis with categorical predictors) and how exactly is contrast matrix specified? I.e. what are columns, what are rows, what are the ...
0
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1answer
120 views

Difference between percentage points and percent

Although I am aware that percentage points should be used to describe arithmetical differences between two percent figures, I could not find a satisfying literature reference. Can anyone recommend an ...
6
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2answers
179 views

Does p-value ever depend on the alternative?

Our tag definition of the $p$-value says In frequentist hypothesis testing, the $p$-value is the probability of a result as extreme (or more) than the observed result, under the assumption that ...
1
vote
1answer
28 views

Clarification on the IID assumption in machine learning: who is sampled from where, and who is independent with who?

So there are a couple of questions on IID assumption on this stackexchange, On the importance of the i.i.d. assumption in statistical learning Realistically, does the i.i.d. assumption hold for the ...
2
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1answer
236 views

What is the difference between these three concepts: non-experimental design, observational research, correlational study

I'm having a hard time distinguishing the overflowing concepts: non-experimental design, observational research, correlational study. Question is simple: is there any difference between those three ...
3
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1answer
57 views

Intuition to the Resolution of a fractional factorial design

In design of experiments, is there an intuitive way to understand (and explain) the idea of the "resolution" of the design?
7
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1answer
93 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
44 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: ...
2
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3answers
170 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 ...
1
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1answer
203 views

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

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 random variable is given by: $$\text{GM}(X_1,...,...
2
votes
1answer
93 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 ...
2
votes
2answers
73 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 ...
2
votes
1answer
525 views

In medical statistics, what is usually meant by “internal precision”?

I have come across the term "internal precision" in some books and papers and was wondering what this usually would refer to. Is there a standard definition for this term? Thanks!
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.
1
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1answer
37 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 ...
8
votes
1answer
171 views

Do random variables follow the same algebraic rules as ordinary numbers?

In the comments on my answer to a recent question about the sum of random variables, I came across a link to the Wikipedia article on the ratio distribution, and noticed the following peculiar claim ...
5
votes
4answers
764 views

What exactly is overfitting?

Many people (including me) is thinking or used to think that an overfitted model is the model in which the training error >> the validation error. But after reading this very interesting comment by @...
1
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2answers
403 views

Covariance definition

Why is covariance defined the way it is? $$\sigma(x,y)=\mathbb{E}[(X-\mathbb{E}[X])(Y-\mathbb{E}[Y])]$$ How do we know that this definition behaves in the following way? Covariance is a measure ...
3
votes
1answer
1k views

From Markov Decision Process (MDP) to Semi-MDP: What is it in a nutshell?

Markov Decision Process (MDP) is a mathematical formulation of decision making. An agent is the decision maker. In the reinforcement learning framework, he is the learner or the decision maker. We ...
1
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1answer
128 views

How do you call a situation or a point at wich statistics data stops changing?

When I calculate a prediction, for instance I am trying to find out who is going to win elections and I do that by asking people who they voted on. After a certain number of answers my data will stop ...
1
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3answers
1k views

Why dependent variables are defined to be scalars in definition of linear regression

I was reading about linear regression on wikipedia. It was defined as an approach for modeling the relationship between a scalar dependent variable $y$ and one or more explanatory variables. Later on ...
4
votes
1answer
159 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
500 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
159 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
votes
1answer
356 views

What's the difference between outlier analysis and clustering?

What's the difference between outlier analysis and clustering? When clustering is done isn't that outliers (if exist) are also found?
1
vote
1answer
206 views

Autocorrelation definition

I am formatting a statistics proof, and I wanted to make sure that I have the definition of autocorrelation correct. Is it the case that the autocorrelation of a continuous variable is the same as ...
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 ...
425
votes
22answers
212k views

Why square the difference instead of taking the absolute value in standard deviation?

In the definition of standard deviation, why do we have to square the difference from the mean to get the mean (E) and take the square root back at the end? Can't we just simply take the absolute ...
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) ...
8
votes
4answers
128k views

Degrees of freedom for Chi-squared test

I am facing the following dilemma. I am aware of how to handle the one-sided Chi-squared distribution, but I am falling victim to how to handle degrees of freedom. Let me clarify with an example what ...
1
vote
1answer
31 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 ...
8
votes
3answers
898 views

How exactly do Bayesians define (or interpret?) probability?

Part of a series of trying to understand Bayesian vs frequentist: 1 2 3 4 5 6 7 I think I get the difference of how Bayesians and frequentists approach choosing between hypotheses, but I'm not quite ...
0
votes
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 ...
2
votes
2answers
4k views

Do convolutional neural networks flip the kernel?

After reading various examples of CNNs it doesn't look like the kernel used for convolution is flipped. Can anybody explain why?
1
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4answers
660 views

What is the precise definition of unsupervised learning?

Let's look at a special case: Generative Adversarial Networks (GANs). (For those who don't know what a GAN is: for this purpose they are two neural networks that are trained using user generated ...
0
votes
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 ...
1
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0answers
44 views

What is the sample size when we take repeated measures?

Say we're running an experiment and we have 10 volunteers. From each of these 10 volunteers we take 3 measurements. So we end up with a dataset that has thirty rows. Say we're writing up the results. ...
2
votes
1answer
35 views

Formal definition of a Regression Tree

I am looking for a formal mathematical definition of a Regression Tree. My current idea would look like this: "A Regression Tree is a function $T(X\in\mathbb{R}^n)$ that splits the feature space $\...
0
votes
1answer
73 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.
0
votes
1answer
351 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)??
3
votes
2answers
108 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 ...
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 ...

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