Karl Pearson’s Theoretical Errors and the Advances They Inspired

Stigler, Stephen M.

doi:10.1214/08-sts256

Cited by 31 publications

(20 citation statements)

References 34 publications

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“…Interaction energies (IE) were calculated from the single point energy differences between each ligand-residue complex and its constituent monomers, and expressed in kcal/mol. The counterpoise correction was considered and applied in order to correct for basis set superposition error (BSSE) effect [47]. These calculations were performed using the Gaussian09 program package [45] with M062X [23] and X3LYP [24] DFT functionals and 6-311G (d,p) [48] as basis set.…”

Section: Data Processingmentioning

confidence: 99%

Quantum mechanics study of the hydroxyethylamines–BACE-1 active site interaction energies

Gueto-Tettay

Drosos

Vivas‐Reyes

2011

J Comput Aided Mol Des

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The identification of BACE-1, a key enzyme in the production of Amyloid-β (Aβ) peptides, generated by the proteolytic processing of amyloid precursor protein, was a major advance in the field of Alzheimer's disease as this pathology is characterized by the presence of extracellular senile plaques, mainly comprised of Aβ peptides. Hydroxyethylamines have demonstrated a remarkable potential, like candidate drugs, for this disease using BACE-1 as target. Density Functional Theory calculations were employed to estimate interaction energies for the complexes formed between the hydroxyethylamine derivated inhibitors and 24 residues in the BACE-1 active site. The collected data offered not only a general but a particular quantitative description that gives a deep insight of the interactions in the active site, showing at the same time how ligand structural variations affect them. Polar interactions are the major energetic contributors for complex stabilization and those ones with charged aspartate residues are highlighted, as they contribute over 90% of the total attractive interaction energy. Ligand-ARG296 residue interaction reports the most repulsive value and decreasing of the magnitude of this repulsion can be a key feature for the design of novel and more potent BACE-1 inhibitors. Also it was explained why sultam derivated BACE-1 inhibitors are better ones than lactam based. Hydrophobic interactions concentrated at S1 zone and other relevant repulsions and attractions were also evaluated. The comparison of two different theory levels (X3LYP and M062X) allowed to confirm the relevance of the detected interactions as each theory level has its own strength to depict the forces involved, as is the case of M062X which is better describing the hydrophobic interactions. Those facts were also evaluated and confirmed by comparing the quantitative trend, of selected ligand-residue interactions, with MP2 theory level as reference standard method for electrostatic plus dispersion energies.

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Section: Data Processingmentioning

confidence: 99%

Quantum mechanics study of the hydroxyethylamines–BACE-1 active site interaction energies

Gueto-Tettay

Drosos

Vivas‐Reyes

2011

J Comput Aided Mol Des

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“…The two authors considered a very general setting for the estimation problem-a set of multivariate observations with a distribution depending upon a potentially large array of constants to be determined. They did not refer to the constants as parameters, but it would be hard for a modern reader to view them in any other light, even though a close reading of the memoir shows that it lacked the parametric view Fisher was to introduce more than 20 years later (Stigler, 2007).…”

Section: Karl Pearson and L N G Filonmentioning

confidence: 99%

“…Perhaps Gauss's use of a uniform prior, which rendered his solution susceptible to change by nonlinear transformations of the parameters, would be considered an error. Certainly Pearson and Filon erred in their promiscuous use of a naïve passage to a limit in ways where it gave wrong answers (Stigler, 2007). And certainly Fisher's 1921 assumption that sufficient statistics always exist was an error, and Hotelling's 1930 proof of the consistency and asymptotic normality of the maximum likelihood estimate cannot be counted correct for the generality claimed.…”

Section: Of Errors In Theorymentioning

confidence: 99%

The Epic Story of Maximum Likelihood

Stigler¹

2007

Statist. Sci.

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120

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At a superficial level, the idea of maximum likelihood must be prehistoric: early hunters and gatherers may not have used the words ``method of maximum likelihood'' to describe their choice of where and how to hunt and gather, but it is hard to believe they would have been surprised if their method had been described in those terms. It seems a simple, even unassailable idea: Who would rise to argue in favor of a method of minimum likelihood, or even mediocre likelihood? And yet the mathematical history of the topic shows this ``simple idea'' is really anything but simple. Joseph Louis Lagrange, Daniel Bernoulli, Leonard Euler, Pierre Simon Laplace and Carl Friedrich Gauss are only some of those who explored the topic, not always in ways we would sanction today. In this article, that history is reviewed from back well before Fisher to the time of Lucien Le Cam's dissertation. In the process Fisher's unpublished 1930 characterization of conditions for the consistency and efficiency of maximum likelihood estimates is presented, and the mathematical basis of his three proofs discussed. In particular, Fisher's derivation of the information inequality is seen to be derived from his work on the analysis of variance, and his later approach via estimating functions was derived from Euler's Relation for homogeneous functions. The reaction to Fisher's work is reviewed, and some lessons drawn.Comment: Published in at http://dx.doi.org/10.1214/07-STS249 the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org

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“…The list is a mix of founding fathers and more recent stars, but the statistical advances had to be ones of importance to psychologists. The list is all male-however, the gender imbalance has been found in It is worth noting that the degrees of freedom he advised for χ 2 was in error (nk-1 for an n × k contingency table and the null of no association) and was later corrected by Fisher.Even the paper including this error has had a large impact on the discipline (Stigler, 2008). Walker (1958, p. 22) summarizes Pearson's contributions: "Few men in all the history of science have stimulated so many other people to cultivate and to enlarge the fields they had planted."…”

mentioning

confidence: 99%

“…Even the paper including this error has had a large impact on the discipline (Stigler, 2008). Walker (1958, p. 22) summarizes Pearson's contributions: "Few men in all the history of science have stimulated so many other people to cultivate and to enlarge the fields they had planted."…”

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confidence: 99%

Ten Statisticians and Their Impacts for Psychologists

Wright

2009

Perspect Psychol Sci

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ABSTRACT-Although psychologists frequently use statistical procedures, they are often unaware of the statisticians most associated with these procedures. Learning more about the people will aid understanding of the techniques. In this article, I present a list of 10 prominent statisticians: David Cox, Bradley Efron, Ronald Fisher, Leo Goodman, John Nelder, Jerzy Neyman, Karl Pearson, Donald Rubin, Robert Tibshirani, and John Tukey. I then discuss their key contributions and impact for psychology, as well as some aspects of their nonacademic lives. 3The disciplines of psychology and statistics have grown up as close companions; they are "inextricably bound together" (Stigler, 1992, p. 60). Although each can track their intellectual genealogies back millennia, as academic disciplines they are only about 100 years old. Early on, single individuals like Galton and Spearman could make substantive impacts in the core of both fields, but academic specialization and the development of both disciplines make this more difficult in modern times. Many psychologists like Abelson, Cohen, Cronbach, and Meehl have crossed into statistics, but their efforts have been mainly to bring statistical science into psychology. Others like Cattell, Coombs, Luce, Shepard, Stevens, Swets, Thurstone, and Tversky have focused on measurement and psychometrics. Measurement is fundamental for science (Borsboom, 2006), and psychologists have arguably done more for measurement theory than any other discipline (Hand, 2004). The people listed above would be on a list of psychologists worth knowing.The focus of this article is to compile a list of 10 statisticians who have done important work that psychologists should be aware of. The fact that psychologists take statistics courses throughout undergraduate and graduate training and that every empirical article includes statistics are testament to the importance of statistics within psychology.Unfortunately, statistical techniques are often taught as if they were brought down from some statistical mount only to magically appear in SPSS. This gives a false impression of statistics. Statistics is a rapidly evolving discipline with colorful characters still arguing about some of the core aspects of their discipline.The aim of this article is to present a list of the 10 statisticians whom I think psychologists should know about. By statistician, I am referring to people who would 4 likely be in a statistics department in the 21st century. I am not listing names prior to 1900, though interested readers should consult Stigler (1986). Limiting the list to 10 was difficult, and I based the list in part on personal preferences. The list is a mix of founding fathers and more recent stars, but the statistical advances had to be ones of importance to psychologists. The list is all male-however, the gender imbalance has been found in It is worth noting that the degrees of freedom he advised for χ 2 was in error (nk-1 for an n × k contingency table and the null of no association) and was later corrected by Fisher....

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Karl Pearson’s Theoretical Errors and the Advances They Inspired

Cited by 31 publications

References 34 publications

Quantum mechanics study of the hydroxyethylamines–BACE-1 active site interaction energies

Quantum mechanics study of the hydroxyethylamines–BACE-1 active site interaction energies

The Epic Story of Maximum Likelihood

Ten Statisticians and Their Impacts for Psychologists

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