Statistics.

History of Statistics

The census in History

Censuses have been taking place for thousands of years all over the world, with the first known census undertaken nearly 6000 years ago by the Babylonians in 3800 BC. There are records to suggest that this census was undertaken every 6 or 7 years and counted the number of people and livestock, as well as quantities of butter, honey, milk, wool and vegetables.

The oldest existing census in the world comes from China during the Han Dynasty. This census was taken in the year 2 A.D. and is considered to be quite accurate. It recorded the population as 59.6 million, the world’s largest population.

The census was a key element of the Roman system of administration and was carried out every five years and provided a register of citizens and their property. The word census originates in fact from ancient Rome, from the Latin word ‘censere’ which means ‘estimate’.

The Bible also relates several census stories – the Book of Numbers is named after the counting of the Israelite population during the Flight from Egypt, there are references to King David performing a census and of King Solomon having all foreigners in Israel, and of course the best known reference is to a Roman census when the birth of Jesus occurred in Bethlehem because Mary and Joseph had travelled there to be enumerated in the census.

The most famous historic census in Europe is the Domesday Book which was undertaken by William the Conqueror in 1086.

In the 15th century, the Inca Empire had a unique way to record census information as they did not have a written language. Census information was recorded on quipus which were strings from llama or alpaca hair or cotton cords with numeric and other values encoded by knots in a base-10 positional system.

1500s: Girolamo Cardano calculates probabilities of different dice rolls.

1600s: Edmund Halley relates death rate to age and develops mortality tables.

1700s: Thomas Jefferson directs the first U.S. Census.

1839: The American Statistical Association is formed.

1894: The term “standard deviation” is introduced by Karl Pearson.

1935: R.A. Fisher publishes Design of Experiments.

For more history, check out this timeline of statistics.

History of statistics From Wikipedia, the free encyclopedia

The history of statistics in the modern sense dates from the mid-17th century, with the term statistics itself coined in 1749 in German, although there have been changes to the interpretation of the word over time. The development of statistics is

intimately connected on the one hand with the development of sovereign states, particularly European states following the Peace

of Westphalia (1648); and the other hand with the development of probability theory, which put statistics on a firm theoretical

basis; see History of probability.

In early times, the meaning was restricted to information about states, particularly demographics such as population. This was

later extended to include all collections of information of all types, and later still it was extended to include the analysis and

interpretation of such data. In modern terms, "statistics" means both sets of collected information, as in national

accounts and temperature records, and analytical work which requires statistical inference. Statistical activities are often

associated with models expressed using probabilities, hence the connection with probability theory. The large requirements of

data processing have made statistics a key application of computing; see history of computing hardware. A number of statistical

concepts have an important impact on a wide range of sciences. These include the design of experiments and approaches to

statistical inference such as Bayesian inference, each of which can be considered to have their own sequence in the development

of the ideas underlying modern statistics.

Contents

 1Introduction

 2Etymology

 3Origins in probability theory

o 3.1Development of modern statistics

 4Design of experiments

 5Bayesian statistics

 6Important contributors to statistics

 7References

 8Bibliography

 9External links

Introduction

By the 18th century, the term "statistics" designated the systematic collection of demographic and economic data by states. For

at least two millennia, these data were mainly tabulations of human and material resources that might be taxed or put to military

use. In the early 19th century, collection intensified, and the meaning of "statistics" broadened to include the discipline

concerned with the collection, summary, and analysis of data. Today, data is collected and statistics are computed and widely

distributed in government, business, most of the sciences and sports, and even for many pastimes. Electronic computers have

expedited more elaborate statistical computation even as they have facilitated the collection and aggregation of data. A single

data analyst may have available a set of data-files with millions of records, each with dozens or hundreds of separate

measurements. These were collected over time from computer activity (for example, a stock exchange) or from computerized

sensors, point-of-sale registers, and so on. Computers then produce simple, accurate summaries, and allow more tedious

analyses, such as those that require inverting a large matrix or perform hundreds of steps of iteration, that would never be

attempted by hand. Faster computing has allowed statisticians to develop "computer-intensive" methods which may look at all

permutations, or use randomization to look at 10,000 permutations of a problem, to estimate answers that are not easy to

quantify by theory alone..

The term "mathematical statistics" designates the mathematical theories of probability and statistical inference, which are used

in statistical practice. The relation between statistics and probability theory developed rather late, however. In the 19th century,

statistics increasingly used probability theory, whose initial results were found in the 17th and 18th centuries, particularly in the

analysis of games of chance (gambling). By 1800, astronomy used probability models and statistical theories, particularly

the method of least squares. Early probability theory and statistics was systematized in the 19th century and statistical reasoning

and probability models were used by social scientists to advance the new sciences of experimental psychology and sociology,

and by physical scientists in thermodynamics and statistical mechanics. The development of statistical reasoning was closely

associated with the development of inductive logic and the scientific method, which are concerns that move statisticians away

from the narrower area of mathematical statistics. Much of the theoretical work was readily available by the time computers

were available to exploit them. By the 1970s, Johnson and Kotz produced a four-volume Compendium on Statistical

Distributions (First Edition 1969-1972), which is still an invaluable resource.

Applied statistics can be regarded as not a field of mathematics but an autonomous mathematical science, like computer

science and operations research. Unlike mathematics, statistics had its origins in public administration. Applications arose early

in demography and economics; large areas of micro- and macro-economics today are "statistics" with an emphasis on time-

series analyses. With its emphasis on learning from data and making best predictions, statistics also has been shaped by areas of

academic research including psychological testing, medicine and epidemiology. The ideas of statistical testing have

considerable overlap with decision science. With its concerns with searching and effectively presenting data, statistics has

overlap with information science and computer science.

Etymologyt

The term statistics is ultimately derived from the New Latin statisticum collegium ("council of state") and

the Italian word statista ("statesman" or "politician"). The German Statistik, first introduced by Gottfried Achenwall (1749),

originally designated the analysis of data about the state, signifying the "science of state" (then called political arithmetic in English). It acquired the meaning of the collection and classification of data generally in the early 19th century. It was

introduced into English in 1791 by Sir John Sinclair when he published the first of 21 volumes titled Statistical Account of

Scotland.[1]

Thus, the original principal purpose of Statistik was data to be used by governmental and (often centralized) administrative

bodies. The collection of data about states and localities continues, largely through national and international statistical services.

In particular, censuses provide frequently updated information about the population.

Sir William Petty, a 17th-century economist who used early statistical methods to analyse

demographic data.

The birth of statistics is often dated to 1662, when John Graunt, along with William Petty, developed early human statistical

and census methods that provided a framework for modern demography. He produced the first life table, giving probabilities of

survival to each age. His book Natural and Political Observations Made upon the Bills of Mortality used analysis of

the mortality rolls to make the first statistically based estimation of the population of London. He knew that there were around

13,000 funerals per year in London and that three people died per eleven families per year. He estimated from the parish records

that the average family size was 8 and calculated that the population of London was about 384,000; this is the first known use of

a ratio estimator. Laplace in 1802 estimated the population of France with a similar method; see Ratio estimator § History for

details.

Although the original scope of statistics was limited to data useful for governance, the approach was extended to many fields of

a scientific or commercial nature during the 19th century. The mathematical foundations for the subject heavily drew on the

new probability theory, pioneered in the 16th century by Gerolamo Cardano, Pierre de Fermat and Blaise Pascal. Christiaan Huygens (1657) gave the earliest known scientific treatment of the subject. Jakob Bernoulli's Ars Conjectandi (posthumous,

1713) and Abraham de Moivre's The Doctrine of Chances (1718) treated the subject as a branch of mathematics. In his book

Bernoulli introduced the idea of representing complete certainty as one and probability as a number between zero and one.

A key early application of statistics in the 18th century was to the human sex ratio at birth.[6] John Arbuthnot studied this

question in 1710.[7][8][9][10] Arbuthnot examined birth records in London for each of the 82 years from 1629 to 1710. In every year,

the number of males born in London exceeded the number of females. Considering more male or more female births as equally

likely, the probability of the observed outcome is 0.5^82, or about 1 in 4,8360,0000,0000,0000,0000,0000; in modern terms,

the p-value. This is vanishingly small, leading Arbuthnot that this was not due to chance, but to divine providence: "From

whence it follows, that it is Art, not Chance, that governs." This is and other work by Arbuthnot is credited as "… the first use

of significance tests …"[11] the first example of reasoning about statistical significance and moral certainty,[12] and "… perhaps

the first published report of a nonparametric test …",[8] specifically the sign test; see details at Sign test § History.

The formal study of theory of errors may be traced back to Roger Cotes' Opera Miscellanea (posthumous, 1722), but a memoir

prepared by Thomas Simpson in 1755 (printed 1756) first applied the theory to the discussion of errors of observation. The

reprint (1757) of this memoir lays down the axioms that positive and negative errors are equally probable, and that there are

certain assignable limits within which all errors may be supposed to fall; continuous errors are discussed and a probability curve

is given. Simpson discussed several possible distributions of error. He first considered the uniform distribution and then the

discrete symmetric triangular distribution followed by the continuous symmetric triangle distribution. Tobias Mayer, in his

study of the libration of the moon (Kosmographische Nachrichten, Nuremberg, 1750), invented the first formal method for estimating the unknown quantities by generalized the averaging of observations under identical circumstances to the averaging

of groups of similar equations.

Ruder Boškovic in 1755 based in his work on the shape of the earth proposed in his book De Litteraria expeditione per

pontificiam ditionem ad dimetiendos duos meridiani gradus a PP. Maire et Boscovicli that the true value of a series of

observations would be that which minimises the sum of absolute errors. In modern terminology this value is the median. The

first example of what later became known as the normal curve was studied by Abraham de Moivre who plotted this curve on

November 12, 1733.[13] de Moivre was studying the number of heads that occurred when a 'fair' coin was tossed.

In 1761 Thomas Bayes proved Bayes' theorem and in 1765 Joseph Priestley invented the first timeline charts.

Johann Heinrich Lambert in his 1765 book Anlage zur Architectonic proposed the semicircle as a distribution of errors:

with -1 < x < 1.

Probability density plots for the Laplace distribution.

Pierre-Simon Laplace (1774) made the first attempt to deduce a rule for the combination of observations from the principles of

the theory of probabilities. He represented the law of probability of errors by a curve and deduced a formula for the mean of

three observations.

Laplace in 1774 noted that the frequency of an error could be expressed as an exponential function of its magnitude once its

sign was disregarded.[14][15] This distribution is now known as the Laplace distribution. Lagrange proposed a parabolic

distribution of errors in 1776.

Laplace in 1778 published his second law of errors wherein he noted that the frequency of an error was proportional to the

exponential of the square of its magnitude. This was subsequently rediscovered by Gauss (possibly in 1795) and is now best

known as the normal distribution which is of central importance in statistics.[16] This distribution was first referred to as

the normal distribution by Pierce in 1873 who was studying measurement errors when an object was dropped onto a wooden

base.[17] He chose the term normal because of its frequent occurrence in naturally occurring variables.

Lagrange also suggested in 1781 two other distributions for errors - a raised cosine distribution and a logarithmic distribution.

Laplace gave (1781) a formula for the law of facility of error (a term due to Joseph Louis Lagrange, 1774), but one which led to

unmanageable equations. Daniel Bernoulli (1778) introduced the principle of the maximum product of the probabilities of a

system of concurrent errors.

In 1786 William Playfair (1759-1823) introduced the idea of graphical representation into statistics. He invented the line

chart, bar chart and histogram and incorporated them into his works on economics, the Commercial and Political Atlas. This

was followed in 1795 by his invention of the pie chart and circle chart which he used to display the evolution of England's

imports and exports. These latter charts came to general attention when he published examples in his Statistical Breviary in 1801.

Laplace, in an investigation of the motions of Saturn and Jupiter in 1787, generalized Mayer's method by using different linear

combinations of a single group of equations.

In 1791 Sir John Sinclair introduced the term 'statistics' into English in his Statistical Accounts of Scotland.

In 1802 Laplace estimated the population of France to be 28,328,612.[18] He calculated this figure using the number of births in

the previous year and census data for three communities. The census data of these communities showed that they had 2,037,615

persons and that the number of births were 71,866. Assuming that these samples were representative of France, Laplace

produced his estimate for the entire population.

Carl Friedrich Gauss, mathematician who developed the method of least squares in 1809.

The method of least squares, which was used to minimize errors in data measurement, was published independently by Adrien-

Marie Legendre (1805), Robert Adrain (1808), and Carl Friedrich Gauss (1809). Gauss had used the method in his famous 1801

prediction of the location of the dwarf planet Ceres. The observations that Gauss based his calculations on were made by the

Italian monk Piazzi.

The term probable error (der wahrscheinliche Fehler) - the median deviation from the mean - was introduced in 1815 by the

German astronomer Frederik Wilhelm Bessel. Antoine Augustin Cournot in 1843 was the first to use the term median(valeur

médiane) for the value that divides a probability distribution into two equal halves.

Other contributors to the theory of errors were Ellis (1844), De Morgan (1864), Glaisher (1872), and Giovanni

Schiaparelli(1875).[citation needed] Peters's (1856) formula for , the "probable error" of a single observation was widely used and

inspired early robust statistics (resistant to outliers: see Peirce's criterion).

In the 19th century authors on statistical theory included Laplace, S. Lacroix (1816), Littrow (1833), Dedekind (1860), Helmert

(1872), Laurent (1873), Liagre, Didion, De Morgan and Boole.

Gustav Theodor Fechner used the median (Centralwerth) in sociological and psychological phenomena.[19] It had earlier been used only in astronomy and related fields. Francis Galton used the English term median for the first time in 1881 having earlier

used the terms middle-most value in 1869 and the medium in 1880.[20]

Adolphe Quetelet (1796–1874), another important founder of statistics, introduced the notion of the "average man" (l'homme

moyen) as a means of understanding complex social phenomena such as crime rates, marriage rates, and suicide rates.[21]

The first tests of the normal distribution were invented by the German statistician Wilhelm Lexis in the 1870s. The only data

sets available to him that he was able to show were normally distributed were birth rates.

Development of modern statistics[edit]

Although the origins of statistical theory lie in the 18th century advances in probability, the modern field of statistics only

emerged in the late 19th and early 20th century in three stages. The first wave, at the turn of the century, was led by the work

of Francis Galton and Karl Pearson, who transformed statistics into a rigorous mathematical discipline used for analysis, not

just in science, but in industry and politics as well. The second wave of the 1910s and 20s was initiated by William Gosset, and

reached its culmination in the insights of Ronald Fisher. This involved the development of better design of experiments models,

hypothesis testing and techniques for use with small data samples. The final wave, which mainly saw the refinement and

expansion of earlier developments, emerged from the collaborative work between Egon Pearson and Jerzy Neyman in the

1930s.[22] Today, statistical methods are applied in all fields that involve decision making, for making accurate inferences from a

collated body of data and for making decisions in the face of uncertainty based on statistical methodology.

The original logo of the Royal Statistical Society, founded in 1834.

The first statistical bodies were established in the early 19th century. The Royal Statistical Society was founded in 1834

and Florence Nightingale, its first female member, pioneered the application of statistical analysis to health problems for the

furtherance of epidemiological understanding and public health practice. However, the methods then used would not be

considered as modern statistics today.

The Oxford scholar Francis Ysidro Edgeworth's book, Metretike: or The Method of Measuring Probability and Utility (1887)

dealt with probability as the basis of inductive reasoning, and his later works focused on the 'philosophy of chance'.[23] His first

paper on statistics (1883) explored the law of error (normal distribution), and his Methods of Statistics (1885) introduced an

early version of the t distribution, the Edgeworth expansion, the Edgeworth series, the method of variate transformation and the

asymptotic theory of maximum likelihood estimates.

The Norwegian Anders Nicolai Kiær introduced the concept of stratified sampling in 1895.[24] Arthur Lyon Bowley introduced

new methods of data sampling in 1906 when working on social statistics. Although statistical surveys of social conditions had

started with Charles Booth's "Life and Labour of the People in London" (1889-1903) and Seebohm Rowntree's "Poverty, A

Study of Town Life" (1901), Bowley's, key innovation consisted of the use of random sampling techniques. His efforts

culminated in his New Survey of London Life and Labour.[25]

Francis Galton is credited as one of the principal founders of statistical theory. His contributions to the field included

introducing the concepts of standard deviation, correlation, regression and the application of these methods to the study of the

variety of human characteristics - height, weight, eyelash length among others. He found that many of these could be fitted to a

normal curve distribution.[26]

Galton submitted a paper to Nature in 1907 on the usefulness of the median.[27] He examined the accuracy of 787 guesses of the weight of an ox at a country fair. The actual weight was 1208 pounds: the median guess was 1198. The guesses were markedly

non-normally distributed.

Karl Pearson, the founder of mathematical statistics.

Galton's publication of Natural Inheritance in 1889 sparked the interest of a brilliant mathematician, Karl Pearson,[28] then

working at University College London, and he went on to found the discipline of mathematical statistics.[29] He emphasised the

statistical foundation of scientific laws and promoted its study and his laboratory attracted students from around the world

attracted by his new methods of analysis, including Udny Yule. His work grew to encompass the fields

of biology, epidemiology, anthropometry, medicine and social history. In 1901, with Walter Weldon, founder of biometry, and

Galton, he founded the journal Biometrika as the first journal of mathematical statistics and biometry.

His work, and that of Galton's, underpins many of the 'classical' statistical methods which are in common use today, including

the Correlation coefficient, defined as a product-moment;[30] the method of moments for the fitting of distributions to

samples; Pearson's system of continuous curves that forms the basis of the now conventional continuous probability

distributions; Chi distance a precursor and special case of the Mahalanobis distance[31] and P-value, defined as the probability

measure of the complement of the ball with the hypothesized value as center point and chi distance as radius.[31] He also

introduced the term 'standard deviation'.

He also founded the statistical hypothesis testing theory,[31] Pearson's chi-squared test and principal component analysis.[32][33] In

1911 he founded the world's first university statistics department at University College London.

Ronald Fisher, "A genius who almost single-handedly created the foundations for modern statistical science",[34]

The second wave of mathematical statistics was pioneered by Ronald Fisher who wrote two textbooks, Statistical Methods for

Research Workers, published in 1925 and The Design of Experiments in 1935, that were to define the academic discipline in

universities around the world. He also systematized previous results, putting them on a firm mathematical footing. In his 1918

seminal paper The Correlation between Relatives on the Supposition of Mendelian Inheritance, the first use to use the statistical

term, variance. In 1919, at Rothamsted Experimental Station he started a major study of the extensive collections of data

recorded over many years. This resulted in a series of reports under the general title Studies in Crop Variation. In 1930 he

published The Genetical Theory of Natural Selection where he applied statistics to evolution.

Over the next seven years, he pioneered the principles of the design of experiments (see below) and elaborated his studies of

analysis of variance. He furthered his studies of the statistics of small samples. Perhaps even more important, he began his

systematic approach of the analysis of real data as the springboard for the development of new statistical methods. He

developed computational algorithms for analyzing data from his balanced experimental designs. In 1925, this work resulted in

the publication of his first book, Statistical Methods for Research Workers.[35] This book went through many editions and

translations in later years, and it became the standard reference work for scientists in many disciplines. In 1935, this book was

followed by The Design of Experiments, which was also widely used.

In addition to analysis of variance, Fisher named and promoted the method of maximum likelihood estimation. Fisher also

originated the concepts of sufficiency, ancillary statistics, Fisher's linear discriminator and Fisher information. His article On a distribution yielding the error functions of several well known statistics (1924) presented Pearson's chi-squared test and William

Gosset's t in the same framework as the Gaussian distribution, and his own parameter in the analysis of variance Fisher's z-

distribution (more commonly used decades later in the form of the F distribution).[36] The 5% level of significance appears to

have been introduced by Fisher in 1925.[37] Fisher stated that deviations exceeding twice the standard deviation are regarded as

significant. Before this deviations exceeding three times the probable error were considered significant. For a symmetrical

distribution the probable error is half the interquartile range. For a normal distribution the probable error is approximately 2/3

the standard deviation. It appears that Fisher's 5% criterion was rooted in previous practice.

Other important contributions at this time included Charles Spearman's rank correlation coefficient that was a useful extension

of the Pearson correlation coefficient. William Sealy Gosset, the English statistician better known under his pseudonym

of Student, introduced Student's t-distribution, a continuous probability distribution useful in situations where the sample size is

small and population standard deviation is unknown.

Egon Pearson (Karl's son) and Jerzy Neyman introduced the concepts of "Type II" error, power of a test and confidence

intervals. Jerzy Neyman in 1934 showed that stratified random sampling was in general a better method of estimation than

purposive (quota) sampling.[38]

Design of experimentst

James Lind carried out the first ever clinical trial in 1747, in an effort to find a treatment for scurvy.

In 1747, while serving as surgeon on HM Bark Salisbury, James Lind carried out a controlled experiment to develop a cure for scurvy.[39] In this study his subjects' cases "were as similar as I could have them", that is he provided strict entry requirements

to reduce extraneous variation. The men were paired, which provided blocking. From a modern perspective, the main thing that

is missing is randomized allocation of subjects to treatments.

Lind is today often described as a one-factor-at-a-time experimenter.[40] Similar one-factor-at-a-time (OFAT) experimentation

was performed at the Rothamsted Research Station in the 1840s by Sir John Lawes to determine the optimal inorganic fertilizer

for use on wheat.[40]

A theory of statistical inference was developed by Charles S. Peirce in "Illustrations of the Logic of Science" (1877–1878) and

"A Theory of Probable Inference" (1883), two publications that emphasized the importance of randomization-based inference in

statistics. In another study, Peirce randomly assigned volunteers to a blinded, repeated-measures design to evaluate their ability

to discriminate weights.[41][42][43][44]

Peirce's experiment inspired other researchers in psychology and education, which developed a research tradition of randomized

experiments in laboratories and specialized textbooks in the 1800s.[41][42][43][44] Peirce also contributed the first English-language

publication on an optimal design for regression-models in 1876.[45] A pioneering optimal design for polynomial regression was

suggested by Gergonne in 1815.[citation needed] In 1918 Kirstine Smith published optimal designs for polynomials of degree six (and

less).[46]

The use of a sequence of experiments, where the design of each may depend on the results of previous experiments, including

the possible decision to stop experimenting, was pioneered[47] by Abraham Wald in the context of sequential tests of statistical

hypotheses.[48] Surveys are available of optimal sequential designs,[49] and of adaptive designs.[50] One specific type of sequential

design is the "two-armed bandit", generalized to the multi-armed bandit, on which early work was done by Herbert Robbins in

1952.[51]

The term "design of experiments" (DOE) derives from early statistical work performed by Sir Ronald Fisher. He was described

by Anders Hald as "a genius who almost single-handedly created the foundations for modern statistical science."[52] Fisher

initiated the principles of design of experiments and elaborated on his studies of "analysis of variance". Perhaps even more

important, Fisher began his systematic approach to the analysis of real data as the springboard for the development of new

statistical methods. He began to pay particular attention to the labour involved in the necessary computations performed by

hand, and developed methods that were as practical as they were founded in rigour. In 1925, this work culminated in the

publication of his first book, Statistical Methods for Research Workers.[53] This went into many editions and translations in later

years, and became a standard reference work for scientists in many disciplines.[54]

A methodology for designing experiments was proposed by Ronald A. Fisher, in his innovative book The Design of

Experiments (1935) which also became a standard.[55][56][57][58] As an example, he described how to test the hypothesis that a certain lady could distinguish by flavour alone whether the milk or the tea was first placed in the cup. While this sounds like a

frivolous application, it allowed him to illustrate the most important ideas of experimental design: see Lady tasting tea.

Agricultural science advances served to meet the combination of larger city populations and fewer farms. But for crop scientists

to take due account of widely differing geographical growing climates and needs, it was important to differentiate local growing

conditions. To extrapolate experiments on local crops to a national scale, they had to extend crop sample testing economically

to overall populations. As statistical methods advanced (primarily the efficacy of designed experiments instead of one-factor-at-

a-time experimentation), representative factorial design of experiments began to enable the meaningful extension, by inference,

of experimental sampling results to the population as a whole.[citation needed] But it was hard to decide how representative was the

crop sample chosen.[citation needed]Factorial design methodology showed how to estimate and correct for any random variation within

the sample and also in the data collection procedures.

Bayesian statistics[edit]

Pierre-Simon, marquis de Laplace, one of the main early developers of Bayesian statistics.

The term Bayesian refers to Thomas Bayes (1702–1761), who proved a special case of what is now called Bayes' theorem.

However it was Pierre-Simon Laplace (1749–1827) who introduced a general version of the theorem and applied it to celestial

mechanics, medical statistics, reliability, and jurisprudence.[59] When insufficient knowledge was available to specify an

informed prior, Laplace used uniform priors, according to his "principle of insufficient reason".[59][60] Laplace assumed uniform

priors for mathematical simplicity rather than for philosophical reasons.[59] Laplace also introduced[citation needed] primitive versions

of conjugate priors and the theorem of von Mises and Bernstein, according to which the posteriors corresponding to initially

differing priors ultimately agree, as the number of observations increases.[61]This early Bayesian inference, which used uniform

priors following Laplace's principle of insufficient reason, was called "inverse probability" (because it infers backwards from

observations to parameters, or from effects to causes[62]).

After the 1920s, inverse probability was largely supplanted[citation needed] by a collection of methods that were developed by Ronald

A. Fisher, Jerzy Neyman and Egon Pearson. Their methods came to be called frequentist statistics.[62] Fisher rejected the

Bayesian view, writing that "the theory of inverse probability is founded upon an error, and must be wholly rejected".[63] At the end of his life, however, Fisher expressed greater respect for the essay of Bayes, which Fisher believed to have anticipated his

own, fiducial approach to probability; Fisher still maintained that Laplace's views on probability were "fallacious

rubbish".[63] Neyman started out as a "quasi-Bayesian", but subsequently developed confidence intervals (a key method in

frequentist statistics) because "the whole theory would look nicer if it were built from the start without reference to Bayesianism

and priors".[64] The word Bayesian appeared around 1950, and by the 1960s it became the term preferred by those dissatisfied

with the limitations of frequentist statistics.[62][65]

In the 20th century, the ideas of Laplace were further developed in two different directions, giving rise

to objective and subjective currents in Bayesian practice. In the objectivist stream, the statistical analysis depends on only the model assumed and the data analysed.[66] No subjective decisions need to be involved. In contrast, "subjectivist" statisticians

deny the possibility of fully objective analysis for the general case.

In the further development of Laplace's ideas, subjective ideas predate objectivist positions. The idea that 'probability' should be

interpreted as 'subjective degree of belief in a proposition' was proposed, for example, by John Maynard Keynes in the early

1920s.[citation needed] This idea was taken further by Bruno de Finetti in Italy (Fondamenti Logici del Ragionamento Probabilistico,

1930) and Frank Ramsey in Cambridge (The Foundations of Mathematics, 1931).[67] The approach was devised to solve problems with the frequentist definition of probability but also with the earlier, objectivist approach of Laplace.[66] The

subjective Bayesian methods were further developed and popularized in the 1950s by L.J. Savage.[citation needed]

Objective Bayesian inference was further developed by Harold Jeffreys at the University of Cambridge. His seminal book

"Theory of probability" first appeared in 1939 and played an important role in the revival of the Bayesian view of

probability.[68][69] In 1957, Edwin Jaynes promoted the concept of maximum entropy for constructing priors, which is an

important principle in the formulation of objective methods, mainly for discrete problems. In 1965, Dennis Lindley's 2-volume

work "Introduction to Probability and Statistics from a Bayesian Viewpoint" brought Bayesian methods to a wide audience. In

1979, José-Miguel Bernardo introduced reference analysis,[66] which offers a general applicable framework for objective

analysis.[70] Other well-known proponents of Bayesian probability theory include I.J. Good, B.O. Koopman, Howard

Raiffa, Robert Schlaifer and Alan Turing.

In the 1980s, there was a dramatic growth in research and applications of Bayesian methods, mostly attributed to the discovery

of Markov chain Monte Carlomethods, which removed many of the computational problems, and an increasing interest in

nonstandard, complex applications.[71] Despite growth of Bayesian research, most undergraduate teaching is still based on

frequentist statistics.[72] Nonetheless, Bayesian methods are widely accepted and used, such as for example in the field

of machine learning.[73]

Important contributors to statistics[edit] See also: List of statisticians and Founders of statistics

 Carl Friedrich Gauss

 William Sealey Gosset ("Student")

 Andrey Kolmogorov

 Pierre-Simon Laplace

 Erich L. Lehmann

 Aleksandr Lyapunov

 Anil Kumar Gain

 Prasanta Chandra Mahalanobis

 Abraham De Moivre

 Jerzy Neyman

 Florence Nightingale

References[edit]

1. Jump up^ Ball, Philip (2004). Critical Mass. Farrar, Straus

and Giroux. p. 53. ISBN 0-374-53041-6.

2. Jump up^ Thucydides (1985). History of the Peloponnesian War. New York: Penguin Books, Ltd. p. 204.

3. ^ Jump up to:a b Singh, Simon (2000). The code book : the science of secrecy from ancient Egypt to quantum cryptography (1st Anchor Books ed.). New York: Anchor Books. ISBN 0-385-49532-3.

4. ^ Jump up to:a b Ibrahim A. Al-Kadi "The origins of cryptology: The Arab contributions", Cryptologia, 16(2) (April 1992) pp. 97–126.

5. Jump up^ Villani, Giovanni. Encyclopædia

 Blaise Pascal

 Karl Pearson

 Charles S. Peirce

 Adolphe Quetelet

 C. R. Rao

 Walter A. Shewhart

 Charles Spearman

 Charles Stein

 Thorvald N. Thiele

 John Tukey

 Abraham Wald

Britannica. Encyclopædia Britannica 2006 Ultimate Reference Suite DVD. Retrieved on 2008-03-04.

6. Jump up^ Brian, Éric; Jaisson, Marie (2007). "Physico- Theology and Mathematics (1710–1794)". The Descent of Human Sex Ratio at Birth. Springer Science & Business Media. pp. 1–25. ISBN 978-1-4020-6036-6.

7. Jump up^ John Arbuthnot (1710). "An argument for Divine Providence, taken from the constant regularity observed in the births of both sexes" (PDF). Philosophical Transactions of the Royal Society of London. 27 (325–336): 186– 190. doi:10.1098/rstl.1710.0011.

8. ^ Jump up to:a b Conover, W.J. (1999), "Chapter 3.4: The Sign Test", Practical Nonparametric Statistics (Third ed.), Wiley, pp. 157–176, ISBN 0-471-16068-7

9. Jump up^ Sprent, P. (1989), Applied Nonparametric

Statistical Methods (Second ed.), Chapman & Hall, ISBN 0- 412-44980-3

10. Jump up^ Stigler, Stephen M. (1986). The History of Statistics: The Measurement of Uncertainty Before 1900. Harvard University Press. pp. 225–226. ISBN 0-67440341- X.

11. Jump up^ Bellhouse, P. (2001), "John Arbuthnot", in Statisticians of the Centuries by C.C. Heyde and E. Seneta, Springer, pp. 39–42, ISBN 0-387-95329-9

12. Jump up^ Hald, Anders (1998), "Chapter 4. Chance or Design: Tests of Significance", A History of Mathematical Statistics from 1750 to 1930, Wiley, p. 65

13. Jump up^ de Moivre, A. (1738) The doctrine of chances. Woodfall

14. Jump up^ Laplace, P-S. (1774). "Mémoire sur la probabilité des causes par les évènements". Mémoires de l'Académie Royale des Sciences Présentés par Divers Savants, 6, 621–656

15. Jump up^ Wilson, Edwin Bidwell (1923) "First and second laws of error", Journal of the American Statistical Association, 18 (143), 841-851 JSTOR 2965467

16. Jump up^ Havil J (2003) Gamma: Exploring Euler's Constant. Princeton, NJ: Princeton University Press, p. 157

17. Jump up^ Peirce CS (1873) Theory of errors of observations. Report of the Superintendent US Coast Survey, Washington, Government Printing Office. Appendix no. 21: 200-224

18. Jump up^ Cochran W.G. (1978) "Laplace's ratio estimators". pp 3-10. In David H.A., (ed). Contributions to Survey Sampling and Applied Statistics: papers in honor of H. O. Hartley. Academic Press, New York ISBN 978- 1483237930

19. Jump up^ Keynes, JM (1921) A treatise on probability. Pt II Ch XVII §5 (p 201)

20. Jump up^ Galton F (1881) Report of the Anthropometric Committee pp 245-260. Report of the 51st Meeting of the British Association for the Advancement of Science

21. Jump up^ Stigler (1986, Chapter 5: Quetelet's Two Attempts)

22. Jump up^ Helen Mary Walker (1975). Studies in the history of statistical method. Arno Press.

23. Jump up^ (Stigler 1986, Chapter 9: The Next Generation: Edgeworth)

24. Jump up^ Bellhouse DR (1988) A brief history of random sampling methods. Handbook of statistics. Vol 6 pp 1-14 Elsevier

25. Jump up^ Bowley AL (1906) Address to the Economic Science and Statistics Section of the British Association for

the Advancement of Science. J Roy Stat Soc 69: 548-557

26. Jump up^ Galton F (1877) Typical laws of heredity. Nature 15: 492-553

27. Jump up^ Galton F (1907) One Vote, One Value. Nature 75: 414

28. Jump up^ Stigler (1986, Chapter 10: Pearson and Yule)

29. Jump up^ "The development of modern statistics". JSTOR 27956805.

30. Jump up^ Stigler, S. M. (1989). "Francis Galton's Account of the Invention of Correlation". Statistical Science. 4 (2): 73–79. doi:10.1214/ss/1177012580.

31. ^ Jump up to:a b c Pearson, K. (1900). "On the Criterion that a given System of Deviations from the Probable in the Case of a Correlated System of Variables is such that it can be reasonably supposed to have arisen from Random Sampling". Philosophical Magazine. Series 5. 50 (302): 157–175. doi:10.1080/14786440009463897.

32. Jump up^ Pearson, K. (1901). "On Lines and Planes of Closest Fit to Systems of Points is Space". Philosophical Magazine. Series 6. 2 (11): 559– 572. doi:10.1080/14786440109462720.

33. Jump up^ Jolliffe, I. T. (2002). Principal Component Analysis, 2nd ed. New York: Springer-Verlag.

34. Jump up^ Hald, Anders (1998). A History of Mathematical Statistics. New York: Wiley. ISBN 0-471-17912-4.

35. Jump up^ Box, R. A. Fisher, pp 93–166

36. Jump up^ Agresti, Alan; David B. Hichcock (2005). "Bayesian Inference for Categorical Data Analysis" (PDF). Statistical Methods & Applications. 14 (14): 298. doi:10.1007/s10260-005-0121-y.

37. Jump up^ Fisher RA (1925) Statistical methods for research workers, Edinburgh: Oliver & Boyd

38. Jump up^ Neyman, J (1934) On the two different aspects of the representative method: The method of stratified sampling and the method of purposive selection. Journal of the Royal Statistical Society 97 (4) 557- 625 JSTOR 2342192

39. Jump up^ Dunn, Peter (January 1997). "James Lind (1716-94) of Edinburgh and the treatment of scurvy". Archives of Disease in Childhood: Fetal and Neonatal Edition. United Kingdom: British Medical Journal Publishing Group. 76 (1): 64–

65. doi:10.1136/fn.76.1.F64. PMC 1720613  . PMID 9059193. Retrieved 2009-01-17.

40. ^ Jump up to:a b Klaus Hinkelmann (2012). Design and Analysis of Experiments, Special Designs and Applications. John Wiley & Sons. p. xvii.

41. ^ Jump up to:a b Charles Sanders Peirce and Joseph Jastrow (1885). "On Small Differences in Sensation". Memoirs of the National Academy of Sciences. 3: 73–83.

42. ^ Jump up to:a b Hacking, Ian (September 1988). "Telepathy: Origins of Randomization in Experimental Design". Isis. 79 (A Special Issue on Artifact and Experiment, number 3): 427– 451. doi:10.1086/354775. JSTOR 234674. MR 1013489.

43. ^ Jump up to:a b Stephen M. Stigler (November 1992). "A Historical View of Statistical Concepts in Psychology and Educational Research". American Journal of Education. 101 (1): 60–70. doi:10.1086/444032.

44. ^ Jump up to:a b Trudy Dehue (December 1997). "Deception, Efficiency, and Random Groups: Psychology and the Gradual Origination of the Random Group

Design". Isis. 88(4): 653– 673. doi:10.1086/383850. PMID 9519574.

45. Jump up^ Peirce, C. S. (1876). "Note on the Theory of the Economy of Research". Coast Survey Report: 197–201., actually published 1879, NOAA PDF Eprint. Reprinted in Collected Papers 7, paragraphs 139–157, also in Writings 4, pp. 72–78, and in Peirce, C.S. (July–August 1967). "Note on the Theory of the Economy of Research". Operations Research. 15 (4): 643– 648. doi:10.1287/opre.15.4.643. JSTOR 168276.

46. Jump up^ Smith, Kirstine (1918). "On the Standard Deviations of Adjusted and Interpolated Values of an Observed Polynomial Function and its Constants and the Guidance they give Towards a Proper Choice of the Distribution of Observations". Biometrika. 12 (1/2): 1–

85. doi:10.2307/2331929.

47. Jump up^ Johnson, N.L. (1961). "Sequential analysis: a survey." Journal of the Royal Statistical Society, Series A. Vol. 124 (3), 372–411. (pages 375–376)

48. Jump up^ Wald, A. (1945) "Sequential Tests of Statistical Hypotheses", Annals of Mathematical Statistics, 16 (2), 117–186.

49. Jump up^ Chernoff, H. (1972) Sequential Analysis and Optimal Design, SIAM Monograph. ISBN 978-0898710069

50. Jump up^ Zacks, S. (1996) "Adaptive Designs for Parametric Models". In: Ghosh, S. and Rao, C. R., (Eds) (1996). "Design and Analysis of Experiments," Handbook of Statistics, Volume 13. North-Holland. ISBN 0-444-82061-2. (pages 151–180)

51. Jump up^ Robbins, H. (1952). "Some Aspects of the Sequential Design of Experiments". Bulletin of the American Mathematical Society. 58 (5): 527– 535. doi:10.1090/S0002-9904-1952-09620-8.

52. Jump up^ Hald, Anders (1998) A History of Mathematical Statistics. New York: Wiley.[page needed]

53. Jump up^ Box, Joan Fisher (1978) R. A. Fisher: The Life of a Scientist, Wiley. ISBN 0-471-09300-9 (pp 93–166)

54. Jump up^ Edwards, A.W.F. (2005). "R. A. Fisher, Statistical Methods for Research Workers, 1925". In Grattan-Guinness, Ivor. Landmark writings in Western mathematics 1640-1940. Amsterdam Boston: Elsevier. ISBN 9780444508713.

55. Jump up^ Stanley, J. C. (1966). "The Influence of Fisher's "The Design of Experiments" on Educational Research Thirty Years Later". American Educational Research Journal. 3 (3): 223. doi:10.3102/00028312003003223.

56. Jump up^ Box, JF (February 1980). "R. A. Fisher and the Design of Experiments, 1922-1926". The American Statistician. 34 (1): 1– 7. doi:10.2307/2682986. JSTOR 2682986.

57. Jump up^ Yates, Frank (June 1964). "Sir Ronald Fisher and the Design of Experiments". Biometrics. 20 (2): 307– 321. doi:10.2307/2528399. JSTOR 2528399.

58. Jump up^ Stanley, Julian C. (1966). "The Influence of Fisher's "The Design of Experiments" on Educational Research Thirty Years Later". American Educational Research Journal. 3 (3): 223– 229. doi:10.3102/00028312003003223. JSTOR 1161806.

59. ^ Jump up to:a b c Stigler (1986, Chapter 3: Inverse Probability)

60. Jump up^ Hald (1998)[page needed]

61. Jump up^ Lucien Le Cam (1986) Asymptotic Methods in Statistical Decision Theory: Pages 336 and 618–621 (von

Mises and Bernstein).

62. ^ Jump up to:a b c Stephen. E. Fienberg, (2006) When did Bayesian Inference become "Bayesian"? Archived 2014- 09-10 at the Wayback Machine. Bayesian Analysis, 1 (1), 1–40. See page 5.

63. ^ Jump up to:a b Aldrich, A. (2008) "R. A. Fisher on Bayes and Bayes' Theorem"Archived 2014-09-06 at the Wayback Machine., Bayesian analysis, 3 (1),161–170

64. Jump up^ Neyman, J. (1977). "Frequentist probability and frequentist statistics". Synthese. 36 (1): 97– 131. doi:10.1007/BF00485695.

65. Jump up^ Jeff Miller, "Earliest Known Uses of Some of the Words of Mathematics (B)""The term Bayesian entered circulation around 1950. R. A. Fisher used it in the notes he wrote to accompany the papers in his Contributions to Mathematical Statistics (1950). Fisher thought Bayes's argument was all but extinct for the only recent work to take it seriously was Harold Jeffreys's Theory of Probability (1939). In 1951 L. J. Savage, reviewing Wald's Statistical Decisions Functions, referred to "modern, or unBayesian, statistical theory" ("The Theory of Statistical Decision," Journal of the American Statistical Association, 46, p. 58.). Soon after, however, Savage changed from being an unBayesian to being a Bayesian."

66. ^ Jump up to:a b c Bernardo J (2005). "Reference analysis". Handbook of statistics. Handbook of Statistics. 25: 17–90. doi:10.1016/S0169-7161(05)25002- 2. ISBN 9780444515391.

67. Jump up^ Gillies, D. (2000), Philosophical Theories of Probability. Routledge. ISBN 0-415-18276-X pp 50–1

68. Jump up^ E. T. Jaynes. Probability Theory: The Logic of Science Cambridge University Press, (2003). ISBN 0-521- 59271-2

69. Jump up^ O'Connor, John J.; Robertson, Edmund F., "History of statistics", MacTutor History of Mathematics archive, University of St Andrews.

70. Jump up^ Bernardo, J. M. and Smith, A. F. M. (1994). "Bayesian Theory". Chichester: Wiley.

71. Jump up^ Wolpert, RL. (2004) "A conversation with James O. Berger", Statistical Science, 9, 205– 218 doi:10.1214/088342304000000053 MR2082155

72. Jump up^ Bernardo, J. M. (2006). "A Bayesian Mathematical Statistics Primer" (PDF). Proceedings of the Seventh International Conference on Teaching Statistics [CDROM]. Salvador (Bahia), Brazil: International Association for Statistical Education.

73. Jump up^ Bishop, C.M. (2007) Pattern Recognition and Machine Learning. Springer ISBN 978-0387310732

Bibliography[edit]

 Freedman, D. (1999). "From association to causation: Some remarks on the history of statistics". Statistical Science. 14 (3): 243– 258. doi:10.1214/ss/1009212409. (Revised version, 2002)

 Hald, Anders (2003). A History of Probability and Statistics and Their Applications before 1750. Hoboken, NJ: Wiley. ISBN 0-471-47129-1.

 Hald, Anders (1998). A History of Mathematical Statistics from 1750 to 1930. New York: Wiley. ISBN 0-471-17912- 4.

 Kotz, S., Johnson, N.L. (1992,1992,1997). Breakthroughs in Statistics, Vols I, II, III. Springer ISBN 0-387-94037- 5, ISBN 0-387-94039-1, ISBN 0-387-94989-5

 Pearson, Egon (1978). The History of Statistics in the 17th and 18th Centuries against the changing background of intellectual, scientific and religious thought (Lectures by Karl Pearson given at University College London during the academic sessions 1921-1933). New York: MacMillan Publishing Co., Inc. p. 744. ISBN 0-02-850120-9.

 Salsburg, David (2001). The Lady Tasting Tea: How Statistics Revolutionized Science in the Twentieth Century. ISBN 0-7167-4106-7

 Stigler, Stephen M. (1986). The History of Statistics: The Measurement of Uncertainty before 1900. Belknap Press/Harvard University Press. ISBN 0-674-40341-X.

 Stigler, Stephen M. (1999) Statistics on the Table: The History of Statistical Concepts and Methods. Harvard University Press. ISBN 0-674-83601-4

 David, H. A. (1995). "First (?) Occurrence of Common Terms in Mathematical Statistics". The American Statistician. 49 (2): 121– 133. doi:10.2307/2684625. JSTOR 2684625.

External links