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Mean-parameterizable models that have invariant concentration functions, but that aren't translation-invariant?

Definitions: Sorry for the ad hoc terminology -- comments or answers that provide pointers to standard terminology would be much appreciated. For simplicity I'd like to restrict discussion to real-...
hasManyStupidQuestions's user avatar
24 votes
7 answers
5k views

Statistical fallacy from a Japanese light novel

The following is a snippet of dialogue from the first volume of the Japanese light novel series Combatants Will Be Dispatched: "Listen here, number 6. This teleportation machine hasn't failed ...
夏目漱石's user avatar
12 votes
2 answers
848 views

Does the use of OLS imply the model is linear in parameters?

I used to say that OLS is an estimation technique and should never be confused with the type of model on which it is applied. Thus a phrase like "I have an OLS model" would not make sense to ...
Richard Hardy's user avatar
1 vote
0 answers
42 views

On the naming of two different median estimators

Assume that $X \sim \mathcal{E}(\lambda)$ is, for example, exponential with $\lambda > 0$. Given a data sample $X_1, \ldots, X_n$, assume that I want to estimate the median of $X$. Consider these ...
runr's user avatar
  • 672
2 votes
1 answer
204 views

Who proposed the reflective correlation coefficient?

The Wikipedia page for the Pearson product-moment correlation coefficient has a section on variants of the idea. This includes the reflective correlation coefficient, which has had a citation needed ...
Galen's user avatar
  • 9,680
3 votes
1 answer
1k views

Can the sample equal the population?

I came across this test question from an introductory statistics course for undergraduates in biology. The solutions are in square brackets. Which cases are possible? The sample is larger than the ...
rokamama's user avatar
  • 199
2 votes
1 answer
74 views

Statistical model for quantities that add up to 1

I want to create a model for quantities $z$ that live in a probability simplex, that is, they are nonnegative and always add up to 1: $$ S = \left\{z \in \mathbb{R}^{k} : z_1 + \dots + z_{k} = 1, z_i \...
dhasson's user avatar
  • 123
2 votes
0 answers
224 views

What is the "lower bound average gain" metric used in GMM stopping criterion used in Scikit learn?

In Scikit Learn's GMM class, it says that GMM training algorithm stops according to the "lower bound average gain" https://scikit-learn.org/stable/modules/generated/sklearn.mixture....
Fraïssé's user avatar
  • 1,630
4 votes
2 answers
423 views

In optimization, is there a distinction between "implicit/natural" and "explicit/designed" constraints?

For example, I wish to optimization a function which has a log term $\log(x)$ Now the very presence of the log term induces a constraint which says $x > 0$. The case $x = 0 $ might be a bit ...
Norman's user avatar
  • 357
6 votes
1 answer
636 views

How should one call the complement of the critical / rejection region?

In null hypothesis statistical testing, the critical region (also known as the rejection region) is A set of values for the test statistic for which the null hypothesis is rejected. i.e. if the ...
B.Liu's user avatar
  • 1,402
9 votes
4 answers
847 views

The fallacy of correlating some time series values with specific time points: is there a specific name for it or are there references?

Intro / Background / Example A recent article connecting pollen with covid-19 has gone viral this week. Higher airborne pollen concentrations correlated with increased SARS-CoV-2 infection rates, as ...
Sextus Empiricus's user avatar
1 vote
0 answers
944 views

What is the difference between FPN(Feature Pyramid Network), FPNlite and SSDlite?

I came across this when I used MobileNet v2 from tensorflow hub. I know that FPN means feature pyramid network and it's better at identifying smaller objects in the frame. However I still don't know ...
t T s's user avatar
  • 141
1 vote
0 answers
162 views

Who invented the concept of over-fitting?

I list the references that I found so far. Shortly, the first appearance of the term was in 1670, first appearance in in close meaning was in 1827, first appearance in a biological paper was in 1923 ...
DaL's user avatar
  • 4,732
5 votes
0 answers
458 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 ...
doubled's user avatar
  • 5,047
8 votes
0 answers
347 views

How do we call a more extreme case of fat tails than a power law?

According to Wikipedia the most extreme case of a fat tail follows a power law: The most extreme case of a fat tail is given by a distribution whose tail decays like a power law. That is, if the ...
Sextus Empiricus's user avatar
3 votes
1 answer
102 views

Term for the error in machine learning as a direct result of incorrectly labelled data?

Is there a term for the inaccuracy that results from an ML model being trained on imperfectly labelled data? For example, if humans label a training set, they could make occasional human errors. In ...
stevec's user avatar
  • 303
16 votes
1 answer
477 views

What is the "direct likelihood" point of view in statistics?

I am reading a Springer title from 1997 called Applied Generalized Linear Models by James K. Lindsey. In the preface, Lindsey writes For this text, the reader is assumed to have knowledge of basic ...
Hugo's user avatar
  • 263
1 vote
2 answers
2k views

What does residual mean in the context of minimizing a function?

equation 1.2 in PRML: pattern recognition and machine learning denotes the sum of the squares of the errors between the predictions $y(x_n,w)$ and the corresponding target values $t_n$. $w^*$ ...
JJJohn's user avatar
  • 2,005
4 votes
2 answers
114 views

Learning from multiple very varied data sets?

Suppose we have a set of objects $X$ (e.g. individual humans). Suppose also that humans can be described by a set of (potentially very high-dimensional) variables $V_i$, (e.g. $V_1$ is a picture of ...
user56834's user avatar
  • 2,987
2 votes
1 answer
73 views

Learning problem when we have data from distributions $(p_i)$ when we care about (known) distribution $p^*$?

Suppose we have a dataset $D$ or multiple datasets $(D_i)$, with distributions $p_i:X\to \mathbb R$. Suppose there is another distribution $p^*$. All distributions are known, including $p^*$, but the $...
user56834's user avatar
  • 2,987
3 votes
0 answers
495 views

Signal-to-noise-ratio, Fisher information and and "estimability"

Given a parametric statistical model, is it common to study the quantity $$ Q_{\theta} = \theta^2 I_{\theta} \, ,$$ where $I_{\theta}$ is the Fisher information? (I focus on a single parameter for ...
0 votes
0 answers
44 views

What is a "surface" and the "likelihood"?

On Neyman & Pearson, 1933, page 302, Then the family of surfaces of constant likelihood, $\lambda$, appropriate for testing a simple hypothesis $H_0$ is defined by $$ p_0 = \lambda p(\...
nalzok's user avatar
  • 1,817
7 votes
1 answer
431 views

Name and interpretation of "$h(x)$" in exponential family

The exponential family is defined (in many sources) as: $$p(x | \theta) = h(x) \exp\{\theta^TT(x) - A(\theta)\}$$ where: $T(x)$ is a sufficient statistic, $\theta$ is a canonical parameter, and $A(...
Bryan Glazer's user avatar
1 vote
1 answer
298 views

Terminology for a "studentized" random variable?

Let $X_{1}, \dots, X_{n}$ be i.i.d. ramdom variables having mean $\mu$ and standard deviation $\sigma$. I wonder if the "studentized" $X_{i}$, the sample version of standardized $X_{i}$ where $\mu$ is ...
Yes's user avatar
  • 478
1 vote
0 answers
11 views

Is there an informative term for calling the random elements conditional on which a PDF of a random element is defined?

Let $X_{1}, \dots, X_{n}$ be i.i.d. random elements; suppose the conditional PDF $f_{X_{1} \mid X_{2} , \dots, X_{n}}$ exists. Then I wonder if there is already in literature an informative name for $...
Yes's user avatar
  • 478
7 votes
3 answers
540 views

Can "cross-validation" be used to choose a prior?

To be clear, I doubt I am using the term "cross-validation" correctly here; what I am suggesting also seems similar to "boot-strapping" and "hyperparameter tuning". ...
Chill2Macht's user avatar
  • 6,479
0 votes
0 answers
67 views

Statistics? Data Science? [duplicate]

Is there a generally acknowledged "fine" line between the meanings of the two terms "statistics" and "data science"? If not, why is "data science" seen nearly everywhere? Just want to learn about the ...
Yes's user avatar
  • 478
3 votes
1 answer
59 views

Name for an expectation of this form $\mathbb{E}X 1_{A}$?

Let $(\Omega, \mathscr{F}, \mathbb{P})$ be a probability space; let $X: \Omega \to \mathbb{R}$ be a random variable; let $A \in \mathscr{F}$; let $1_{A}$ be the indicator function of $A$. Now is there ...
Yes's user avatar
  • 478
1 vote
0 answers
466 views

What is the standard definition of a non-parametric machine learning algorithm?

According to my experience, the non-parametric term usually refers to algorithms complying the following definition from a clasic textbook [1]: A learning model that summarizes data with a set of ...
Daniel López's user avatar
7 votes
2 answers
22k views

What is a strict definition of U-shaped relationship?

I now have seen several papers that analyze U-shaped or inverse U-shaped relations among variables (in a regression framework). The general understanding I have from there is that it is a specific ...
Neznajka's user avatar
  • 223
7 votes
1 answer
2k views

Machine learning models that combine sequences and static features?

I'm working with a classification problem where the data points include both sequential (time series) data and "static" features - attributes that don't change. An analogy could be a datapoint ...
jmully's user avatar
  • 91
2 votes
1 answer
563 views

What is the distribution of $X'AX$ when $A$ is not necessarily a symmetric matrix?

Assume that $X$ is a multivariate normal random variable($n$-vector) with known mean $\mu$ and covariance matrix $\sigma^2 I_n$. What is the distribution of $X'AX$ when $A$ is not necessarily a ...
Henry.L's user avatar
  • 2,490
1 vote
0 answers
28 views

Is there a term that encompasses all the different classifiers which do not consider the order of features?

Some time ago I read a term (or compact expression) used to encompass all the different classification algorithms that do not consider the ordering or spatial relation of features (eg SVMs, Multilayer ...
Daniel López's user avatar
8 votes
2 answers
4k views

In online convex optimization, what is a leader in FTL algorithm?

I am currently reading into online convex optimization. Can someone please explain me what exactly is a leader in the Follow-The-Leader algorithm and its variants? Why is it called Follow-The-Leader?...
Fraïssé's user avatar
  • 1,630
3 votes
0 answers
52 views

PLS between error and negative loglikelihood in classification models?

Consider a large but finite output space $\mathcal{Y}$. Let $\Delta$ denote a loss function between $y^*$ and $\hat{y}$, i.e. $\Delta : \mathcal{Y} \times \mathcal{Y} \rightarrow \mathbb{R_{+}}$. One ...
Pushpendre's user avatar
1 vote
0 answers
269 views

Periodic Cross-Correlation vs Aperiodic Cross-Correlation

I am doing research in spread spectrum communication, and many papers frequently use the terms Periodic Cross-Correlation and Aperiodic Cross-Correlation. However, I cannot find a clear definition of ...
Dimitris S's user avatar
2 votes
0 answers
60 views

Non-random parameter estimation, alternative terminology?

I have a book Navigation Signal Processing for GNSS [sic, global navigation satellite system] Software Receivers" by Thomas Pany (2010) that describes non-random parameter estimation as a fundamental ...
Tyler Durden's user avatar
1 vote
2 answers
2k views

What is the name for this iterative regression method? [duplicate]

What's the correct term for regression where you first regress on one input variable (feature), take the errors, regress on the next feature, etc.? In what specific cases is this useful? Are there any ...
Baron Yugovich's user avatar
3 votes
0 answers
120 views

Name of an $f$-divergence

The term divergence means a function $D$, which, given two probability distributions $P,Q$, assigns a non-negative real number $D(P,Q)$ such that $D(P,Q) = 0$ iff $P(x)=Q(x) \forall x$. The relative ...
Ashok's user avatar
  • 1,181
2 votes
0 answers
235 views

Comprehensive list of misnomers in machine learning

Are there any reference document(s) that give a comprehensive list of misnomers in machine learning? I would like to have a list and simple explanation if needs be that I could go through easily (vs. ...
Franck Dernoncourt's user avatar
1 vote
1 answer
2k views

Multifactorial analysis of variance with repeated measurements-literature

What is the difference between multivariate and multifactor ANOVA? Does anybody have any pointers to downloadable literature about multifactorial analysis of variance with repeated measurements?
M Maric's user avatar
  • 11
1 vote
2 answers
390 views

Lifetime or Failure Time

Lifetime / Survival time / Failure time : the time to the occurrence of event (always nonnegative) . Lifetime and Survival time can be synonymous . But ...
ABC's user avatar
  • 1,705
3 votes
3 answers
3k views

Is there any difference between Random and Probabilistic?

It seems i can't directly say probabilistic and random are identical . But this is telling : random experiment is a probabilistic experiment. Is there any difference between Random and ...
time's user avatar
  • 1,617
1 vote
1 answer
9k views

What is the difference (if any) between 'harmonized' and 'standardized data? [closed]

I am trying to describe the process of combining multiple datasets into a common format - e.g. a single database that enforces a common vocabulary, scale, and structure. However, I am unclear if I ...
David LeBauer's user avatar
3 votes
2 answers
2k views

Mathematical Modeling and Statistical Modeling

What is the difference between mathematical modeling and statistical modeling? I only know that a mathematical model is deterministic while a statistical model is stochastic. Is that all to answer ...
time's user avatar
  • 1,617
3 votes
1 answer
693 views

What is industrial statistics?

We have a course titled "Industrial Statistics". But I don't understand what is industrial statistics? What I have understood after searching some sites is only that Industrial statistics measure ...
time's user avatar
  • 1,617
21 votes
3 answers
1k views

Why are “time series” called such?

Why are “time series” called such? Series means sum of a sequence. Why is it time Series, not time sequence? Is time the independent variable?
user 31466's user avatar
  • 1,427
0 votes
1 answer
129 views

Confidence interval violating physical boundaries

A model is supposed to predict a value that represents proportion, namely, the predicted value should be in [0,1]. However, model is just a linear regression, producing confidence intervals violating ...
John Zi's user avatar
0 votes
1 answer
927 views

Population Projection, Forecast, Prediction

I am frequently reading some terminology But not understanding their difference . Those are : $\bullet$Difference between ...
user 31466's user avatar
  • 1,427