Questions tagged [history]
Questions about the history of statistics.
225
questions
2
votes
1
answer
156
views
When and how was the Bernoulli distribution with real binomial proportion introduced?
I certainly should read Jakob Bernoulli's Ars Conjectandi again but let me share my concerns.
I'm just wondering when and how the Bernoulli distribution $Be(p)$ (and related distributions like the ...
- 39
1
vote
0
answers
20
views
Who first described a statistical estimate as an approximation of a population parameter?
At some point in the history of statistics, there surely was a transition from thinking of statistical measures strictly as imperfect approximations of real quantities, to thinking of them as ...
- 336
5
votes
1
answer
215
views
Who first suggested weak stationarity and strict stationarity?
I wonder who first suggested and defined weak stationarity, and which paper it is. It seems that many paper using it as given, but I'm just curious of how it is defined and proved, and the discussions ...
- 53
0
votes
0
answers
26
views
Why standard deviation is based on squared value? [duplicate]
Why is not "standard deviation" = $\frac{Σ|X-μ|}{N}$, $μ$ being the mean, and is the formula we know today?
This could be considered a philosophical question until you try to connect word &...
- 101
3
votes
1
answer
720
views
When was the Leaky ReLU activation function first used?
An earlier question discovered the first use of the ReLU function. In what paper was the Leaky ReLU activation function first used? By that, I mean the first use of this equation:
$$
f(x, \alpha) = \...
- 131
6
votes
2
answers
1k
views
Why is Neyman-Pearson lemma a lemma or is it a theorem?
A classical result in statistical theory is the Neyman-Pearson lemma, which not only shows the existence of tests with the most power that return a pre-specified level of Type I error, but also a way ...
- 581
9
votes
1
answer
459
views
When was the earliest appearance of Empirical Cumulative Distribution Plots?
I would be surprised if we actually had a date here. I am curious who, if anyone, created the ecdf plot. When did the ecdf make its first appearance? If we do not know when the first ecdf plot was ...
- 1,921
13
votes
2
answers
3k
views
How did the “Hat Matrix” get its name
How did the hat matrix get its name
$\hat{\mathbf{H}} = \mathbf{X} \left( \mathbf{X}^\textsf{T} \mathbf{X} \right)^{-1} \mathbf{X}^\textsf{T}$
I am interested in the etymology of the term. Who gave it ...
- 1,921
12
votes
1
answer
948
views
If Galton did not use least squares then how was he drawing his regression slopes?
I read the following from a document online here.
Galton was full of
ideas but was no
mathematician. He
didn’t even use least
squares, preferring to
avoid unpleasant
computations.
If Galton did not ...
- 1,921
6
votes
2
answers
61
views
Who estimated war casualties from tightly-controlled government news sources?
I've read about this historical case before so I thought it would be very easy to Google, but after a few dozen queries that come up with nothing relevant I'm ready to punt.
The story goes like this. ...
- 313
2
votes
1
answer
91
views
how standard is R model formula notation
I like using R model formula notation such as $Y \sim X_1 + X_2$ when thinking of regression relationships at a high level. The same for lmer notation such as $Y \sim X | group$. I am wondering how ...
- 129
4
votes
1
answer
221
views
History of terms type 1 error and type 2 error?
The terms "type I" (or "alpha) and "type II" (or "beta) error, to denote false positive and false negative, are often used. What is the history of those terms?
- 41
5
votes
1
answer
626
views
Where does the Logistic Distribution get its name?
Having read around on the topic I understand its application as a close approximation of the normal distribution with a nicer mathematical form, but where does its name come from?
Is it associated ...
- 369
3
votes
0
answers
77
views
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 ...
- 68.3k
30
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, ...
- 1,313
2
votes
1
answer
214
views
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$?
- 6,988
5
votes
2
answers
139
views
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 ...
- 53
3
votes
0
answers
39
views
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/...
1
vote
1
answer
460
views
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 ...
- 211
0
votes
0
answers
58
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 ...
13
votes
2
answers
1k
views
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 ...
- 557
0
votes
1
answer
101
views
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 ...
- 1
1
vote
1
answer
63
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 ...
- 23
8
votes
1
answer
1k
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 ...
- 6,988
7
votes
3
answers
328
views
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 ...
- 1,313
9
votes
1
answer
313
views
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 ...
- 68.3k
4
votes
1
answer
166
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, \...
- 455
1
vote
0
answers
14
views
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....
- 281
3
votes
4
answers
350
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. ...
- 6,988
38
votes
1
answer
818
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 ...
- 1,286
8
votes
2
answers
319
views
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 ...
- 2,019
3
votes
0
answers
188
views
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 ...
- 6,988
0
votes
0
answers
54
views
Interpretation of Huygens Expectation
Christiaan Huygens wrote in "Libelus de Ratiociniis in Ludo Alae"
(can be found here - page 2, Postulat) :
That any one Chance or Expectation to win any thing
is worth just such a Sum, as ...
- 1
8
votes
1
answer
99
views
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 ...
- 181
2
votes
1
answer
111
views
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 ...
- 21
2
votes
0
answers
38
views
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 ...
- 291
2
votes
0
answers
573
views
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 ...
- 1,334
11
votes
1
answer
3k
views
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 ...
- 3,514
7
votes
2
answers
239
views
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 ...
- 28.9k
11
votes
1
answer
450
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?
- 63.6k
8
votes
2
answers
770
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 ...
- 183
0
votes
1
answer
614
views
Reference request of softmax function [closed]
What paper should I cite to reference softmax?
Thanks in advance.
- 1
4
votes
1
answer
402
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
$$...
- 41
4
votes
1
answer
431
views
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 ...
- 139
1
vote
0
answers
149
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 ...
- 4,632
2
votes
1
answer
35
views
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{\...
- 18.3k
1
vote
0
answers
46
views
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 ...
- 5,442
8
votes
3
answers
2k
views
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 ...
- 68.3k
4
votes
1
answer
89
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).
...
- 68.3k
30
votes
4
answers
9k
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 ...
- 1,665