Questions tagged [history]

Questions about the history of statistics.

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A misspecification error with linear models that can complete reverse the direction of an effect, has this been described, has this a name?

Linear models are ubiquitous in economic, social, health and nutritional sciences and the starting point for much research and many articles. However, there is a problem with linear models. When the ...
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29 votes
4 answers
2k views

What important ideas came since Nelder and McCullagh's book Generalized Linear Models (a 40 year old book)?

I read not too long ago Nelder and McCullagh's book Generalized Linear Models and thought the book was fantastic and I consider it a useful manual on the subject. Not surprising that's the case, ...
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1 vote
1 answer
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Who originally defined leverage scores to be the diagonal elements of $X(X^TX)^{-1}X^T$?

A nice description of leverage in the sense that I am using it is given here so I will not repeat it. Who originally defined leverage scores to be the diagonal elements of $X(X^TX)^{-1}X^T$?
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5 votes
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When using ROC curves for WWII Radars, what was the TN?

One of the origins of ROC curves seems to be to compare radar systems in WWII (source). How did they actually compute the False Positive Rate when they didn't have an estimate for True Negatives? If I ...
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4 votes
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Were Many (Famous) Theoretical Laws in Science Based on "Regression"? [closed]

In a essay about the meaning of life, the famous scientist Schrodinger once said "Physical laws rest on atomic statistics and are therefore only approximate" (http://www.whatislife.ie/...
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What exactly is the history of Dynamic Time Warping? Where can I find information?

I am writing a thesis comparing some methods of time series classification, part of which is DTW combined with K-NN algorithm. I'd love to know (and write, backed by reliable references) something ...
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52 views

History of Regularization and Shrinkage [duplicate]

Can anyone recommend any research papers where the undesirable effects of overfitting on statistical models were first observed? In the context of regression, at what point did researchers begin to ...
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13 votes
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What is the original derivation of the Poisson distribution?

I am learning the Poisson distribution. I understand it, but its probability mass function is not natural to me. I think its probability mass function seems to be derived from somewhere with more ...
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0 votes
1 answer
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How to forecast a rental weekly sales demand using a 4 year history data?

I need to estimate the weekly demand required for a specific product in a specific week at a specific location. I have the past 4 years daily data of each product at each location. For example: number ...
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1 vote
1 answer
50 views

Why is it called the ‘error’ term?

In econometrics, why is the error term called the ‘error’ term? The myriad things it captures that influence the independent variable are not errors. They are valid real life phenomena. Is there any ...
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7 votes
1 answer
201 views

Who first coined the phrase "correlation does not imply causation"?

Reading Galton and Wright has indicated to me that even from the early days of considering correlation, there was some awareness that correlation is not synonymous with causation. However, who was the ...
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5 votes
3 answers
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What is the history of $p < 0.05$ or 95% confidence?

I'm wondering what the history of $p < 0.05$ or using a 95% confidence interval is. I know that more nuanced reasoning would argue that there is nothing special about 0.05 or 95% (I think decision ...
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8 votes
1 answer
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Intuition about the coupon collector problem approaching a Gumbel distribution

The coupon collector's problem Let there be $n$ different types of coupons and we try to collect all of the types. We do this by independent random draws of coupons in which each type of coupon has an ...
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4 votes
1 answer
91 views

When was a random variable first called a "random variable"? And why is it called as such?

From measure theoretic foundations, it is clear that a random variable is neither random nor a variable. It is a deterministic function developed as follows: Construct probability space: $(\Omega, \...
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1 vote
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Relationship between conjoint measurement and conjoint analysis

The wikipedia page "Cojoint Analysis" says that conjoint analysis originated in mathematical psychology (without a reference) but also that it was developed by marketing professor Paul Green....
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2 votes
4 answers
339 views

Why didn't $\Pr \left( A \rightarrow B \right)$ catch on?

Students are conditioned to thinking in terms of IF-THEN statements even before high school, and courses offered at the university level often lead to the formalization of material implication. ...
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35 votes
1 answer
508 views

Reference: who introduced the tilde "~" notation to mean "has probability distribution..."?

[Note: although this question has an accepted answer, the investigation is not finished yet. I encourage you to post your findings.] Who first introduced the notation "$X \sim Q$", meaning ...
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Who came up with time course experiments?

Time course experiments are extremely popular choice of experimental design in empirical sciences in part because it (1) allows for some understanding of system dynamics by measuring at different ...
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7 votes
1 answer
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History of the term "early stopping"

Who first used "early stopping" to refer to a form of regularization by stopping training before convergence? I have attempted to search myself but I am not sure how to find the answer. Was ...
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3 votes
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Did Auguste Bravais really derive the mathematical definition of Pearson's product-moment correlation coefficient?

The wikipedia pages on Auguste Bravais,Karl Pearson, the Pearson correlation coefficient,and Francis Galton all cite the following book: Bravais, A (1846). "Analyse mathématique sur les ...
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Interpretation of Huygens Expectation

Christiaan Huygens wrote in "Libelus de Ratiociniis in Ludo Alae" (can be found here: https://math.dartmouth.edu/~doyle/docs/huygens/huygens.pdf page 2, Postulat) : "That any one Chance ...
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8 votes
1 answer
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Is there a real example in which a correlation finally leads to the discovery of a non-trivial causal relationship?

More specifically, I am wondering if there is such an example satisfying the following criteria: The example happened after 1888, it would be better to be after 1900—I think few people have the ...
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2 votes
1 answer
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Why was Bayes' Theory not accepted/popular historically until the late 20th century?

I have to write a math history paper. I was going to write it on the rise of Bayes' Theory. I have read around that Bayes' theory was no widely accepted or used until the 20th century. I need to make ...
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2 votes
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Why a false positive is called type I error and a flase negative a type II error? [duplicate]

I am trying to understand what are the historical reasons behind the choice of the term Type I and Type II error. I think is much more intuitive to use false positive and false negative. These two ...
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2 votes
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Explanation on why SD is better than MD [duplicate]

Trying to understand why Standard Deviation (SD) is widely accepted as a measure of dispersion instead of Mean Deviation (MD) $\frac {1}{N}\sum|X-\mu|$. Revisiting a 90-year-old debate: the advantages ...
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10 votes
1 answer
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Is least squares means (lsmeans) statistical nonsense?

I recently came accross this quote from Brian Ripley, who seems to be well-regarded as a statistician. "Some of us feel that type III sum of squares and so-called ls-means are statistical ...
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5 votes
2 answers
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Origin of terms "sensitivity" and "specificity"

Who coined the terms "sensitivity" and "specificity"—meaning the complements of false positives, and false negatives, respectively in tests and measures—and when did they first do ...
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11 votes
1 answer
357 views

Were SVMs developed as a method of efficiently training neural networks?

This answer contains the following statement: SVMs were initially developed as a method of efficiently training the neural networks. Is that correct? Could anyone provide a reference?
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8 votes
2 answers
549 views

Reference request: Storks bring babies

There is a well-known statistical example, claiming that there is correlation between the number of babies in Alsatian/Danish/Dutch/German villages or European countries and the number of storks in ...
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1 answer
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Reference request of softmax function [closed]

What paper should I cite to reference softmax? Thanks in advance.
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3 votes
1 answer
356 views

Who was the first person to prove the straight line cross probability for a Brownian motion?

In the paper "Heuristic approach to the Kolmogorov-Smirnov theorems" by J.L. Doob (1949) it's mencioned this well-known theorem: If $\zeta=\{\zeta_{t}|t\geq 0\}$ is a Brownian motion then $$...
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4 votes
1 answer
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Who first proposed Bayesian optimisation with Gaussian processes?

From what I understand, the 'standard' approach to Bayesian Optimisation uses a Gaussian process for the prior (as opposed to more recent proposals like TPE or Bayesian Optimisation with random ...
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1 vote
0 answers
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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 ...
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2 votes
1 answer
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Did Fisher consider a joint fiducial distribution for the Gaussian model?

Consider the Gaussian model $y_i \sim_{\text{iid}} \mathcal{N}(\mu,\sigma^2)$, $i = 1, \ldots, n$, with unknown mean $\mu$ and unknown standard deviation $\sigma$. The random variable $t = \tfrac{\...
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1 vote
0 answers
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Researcher who reinvented least squares regression? Urban legend?

I can't recall where I read about this. Supposedly, a young researcher (or student?) in the 1970s or 1980s independently rediscovered and published their methodology for ordinary least squares ...
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7 votes
3 answers
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The explosive AR(1) process with $\varphi>1$, where was this first represented as a stationary, but non-causal, time-series?

According to this question and answer Explosive AR(MA) processes are stationary? the AR(1) process (with $e_t$ white noise): $$X_{t}=\varphi X_{t-1}+e_{t} \qquad , e_t \sim WN(0,\sigma)$$ is a ...
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3 votes
1 answer
67 views

What is the origin of the term 'inverse probability'?

Inverse probability relates strongly, or is synonymous to, Bayesian probability. Thomas Bayes applied the idea in 'An Essay towards solving a Problem in the Doctrine of Chances' (published in 1763). ...
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29 votes
4 answers
7k views

What exactly does the term "inverse probability" mean?

I keep seeing the term "inverse probability" mentioned in passing albeit without any explanation. I know it has to do with Bayesian inference, but what exactly do we mean by inverting a ...
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9 votes
1 answer
464 views

Alternatives to the null hypothesis significance testing framework

How did academics support hypotheses before the null hypothesis significance testing (NHST) framework was, in part, introduced and democratized by Fisher/Neyman & Pearson? Suppose NHST was never a ...
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4 votes
0 answers
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Was the original goal of linear regression to model the conditional expectation, or was that discovered later?

Linear regression (specifically, least squares) is usually motivated as a linear approximation of the conditional expectation function (CEF), and can be shown to be the minimum mean square error ...
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2 votes
1 answer
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What drives the assumptions for ANOVA, if we know that it's actually a likelihood ratio test and can be used to work with any GLM model?

ANOVA, as a likelihood ratio test, can take any two nested models and compare them. This assesses the main effects (equivalent to joint test of appropriate regression model coefficients). And one can ...
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6 votes
1 answer
467 views

Why is the chi-square test more popular than the G-test?

Pearson's chi-square test and the G-test are two goodness-of-fit hypothesis tests for categorical data -- i.e., testing whether a sample came from a given distribution on a finite set. The respective ...
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History of the curved exponential family

Does anyone know the first person who introduced the curved exponential family and also which paper it was first presented? I vaguely remember that it might be Fisher who wrote about it in a paper on ...
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4 votes
1 answer
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Who invented the "Histogram"?

While going through Wikipedia's article History of statistics I found In 1786 William Playfair (1759-1823) introduced the idea of graphical representation into statistics. He invented the line chart, ...
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6 votes
1 answer
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When was Auto-Encoder used for anomaly detection for the first time?

I would like to cite Auto-Encoder based solution for anomaly detection, however I can't find the origin. When was Auto-Encoder used for anomaly detection for the first time?
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5 votes
1 answer
133 views

What do the letter and the subscript in the Shewhart's control chart constants ($A_2, A_3, c_4, c_5, \ldots$) mean?

The expected value of the sample standard deviation is $$E(s) = c_4(n)\sigma$$ where $$ c_4(n) = \sqrt{2\over n-1}{\Gamma({n\over2})\over\Gamma({n-1\over2})} $$ The page on Wikipedia led me ...
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8 votes
2 answers
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Historically, did pseudo RNGs have range [0,1] because of the ease of drawing from $f$ using $F^{-1}(p)$, or for some other reason?

A simple, though not necessarily efficient, way to simulate random draws from a probability density function $f$, is to apply the inverse cumulative distribution function to a random variate ...
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12 votes
1 answer
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Why does R have a different definition on convolution?

I found convolution in R works differently from Python. In Python, it will flip the input and run the convolution. In the R documentation, it says Note that the usual definition of convolution of ...
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9 votes
1 answer
620 views

Why is the Beta Distribution Called the Beta Distribution?

In my research, I've been unable to find a historical explanation for why the Beta distribution has the name it does. I'm aware of what Wikipedia says about how it got its name, but so far I haven't ...
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9 votes
4 answers
413 views

Where does the logistic function come from?

I first learned the logistic function in machine learning, where it is just a function that map a real number to 0 to 1. We can use calculus to get the derivative and use it for some optimization ...
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