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StatisticsStatistics is the science and practice of developing human knowledge through the use of empirical data. It is based soundly on statistical theory which is a branch of applied mathematics. Within statistical theory, randomness and uncertainty are modelled by probability theory. Statistical practice includes the planning, summarizing, and interpreting of uncertain observations. Because the aim of statistics is to produce the "best" information from available data, some authors make statistics a branch of decision theory.
Origin
The word statistics comes from the modern Latin phrase statisticum collegium (lecture about state affairs), from which came the Italian word statista, which means "statesman" or "politician" (compare to status) and the German Statistik, originally designating the analysis of data about the state. It acquired the meaning of the collection and classification of data generally in the early nineteenth century. The collection of data about states and localities continues, largely through national and international statistical services; in particular, censuses provide regular information about the population.
Statistical methods
We describe our knowledge (and ignorance) mathematically and attempt to learn more from whatever we can observe. This requires us to
- plan our observations to control their variability (experiment design),
- summarize a collection of observations to feature their commonality by suppressing details (descriptive statistics), and
- reach consensus about what the observations tell us about the world we observe (statistical inference).
In some forms of descriptive statistics, notably data mining, the second and third of these steps become so prominent that the first step (planning) appears to become less important. In these disciplines, data often are collected outside the control of the person doing the analysis, and the result of the analysis may be more an operational model than a consensus report about the world.
Probability
The probability of an event is often defined as a number between one and zero. In reality however there is virtually nothing that has a probability of 1 or 0. You could say that the sun will certainly rise in the morning, but what if an extremely unlikely event destroys the sun? What if there is a nuclear war and the sky is covered in ash and smoke?
We often round the probability of such things up or down because they are so likely or unlikely to occur, that it's easier to recognise them as a probability of one or zero.
However, this can often lead to misunderstandings and dangerous behaviour, because people are unable to distinguish between, e.g., a probability of 10-4 and a probability of 10-9, despite the very practical difference between them. If you expect to cross the road about 105 or 106 times in your life, then reducing your risk of being run over per road crossing to 10-9 will make you safe for your whole life, while a risk per road crossing of 10-4 will make it very likely that you will have an accident, despite the intuitive feeling that 0.01% is a very small risk.
Use of prior probabilities of 0 (or 1) causes problems in Bayesian statistics, since the posterior distribution is then forced to be 0 (or 1) as well. In other words, the data is not taken into account at all! As Lindley puts it, if a coherent Bayesian attaches a prior probability of zero to the hypothesis that the Moon is made of green cheese, then even whole armies of astronauts coming back bearing green cheese cannot convince him. Lindley advocates never using prior probabilities of 0 or 1. He calls it Cromwell's Rule, from a letter Oliver Cromwell wrote to the synod of the Church of Scotland on August 5th, 1650 in which he said "I beseech you, in the bowels of Christ, consider it possible that you are mistaken."
Specialized disciplines
Some sciences use applied statistics so extensively that they have specialized terminology. These disciplines include:
Statistics form a key basis tool in business and manufacturing as well. It is used to understand measurement systems variability, control processes (as in statistical process control or SPC), for summarizing data, and to make data-driven decisions. In these roles it is a key tool, and perhaps the only reliable tool.
See also
Lindley, D. Making Decisions. John Wiley. Second Edition 1985.
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(Ireland) National University of Ireland, Galway
Department of Mathematics, including Chair of Statistics.
http://tedser.ucg.ie/
(Belgium) University of Antwerp
Statistics Group.
http://win-www.uia.ac.be/u/statis/index.html
(Belgium) University of Brussels
Home page of SMG (Service de Mathématiques de la Gestion), Operations research, multicriteria decision aid, ...
http://smg.ulb.ac.be/
(Spain) Technical University of Catalonia (UPC)
Department of Statistics and Operational Research.
http://www-eio.upc.es/
University of Vaasa
Department of Mathematics and Statistics.
http://www.uwasa.fi/~mathdept/ind_eng.html
(Bulgaria) University of Sofia
Department of Probability, Operational Research and Statistics.
http://www.fmi.uni-sofia.bg/fmi/statist/
Bulgarian Academy of Sciences, Sofia
Department of Probability and Statistics.
http://www.math.bas.bg/~statlab/
(Czech Republic) University of West Bohemia, Plzen
Department of Statistics and Operational Research.
http://juno.fek.zcu.cz/eng/katedry/kso/kso.htm
(France) École des Mines de Paris
Centre de Géostatistique. General information, research, teaching, geostatistics application domains and software development.
http://cg.ensmp.fr/index.html.en
(Norway) University of Oslo
Department of Mathematics, Statistics Division
http://www.math.uio.no/avdc/statistics.html
(Norway) The Norwegian University of Science and Technology
Department of Mathematical Sciences, Statistics Group
http://www.math.ntnu.no/stat/indexe.html
(Spain) University of Valladolid
Department of Statistics and Operations Research
http://www.est.cie.uva.es/
(France) IMAG Grenoble
Équipe Statistique et Modélisation Stochastique. English site.
http://www-lmc.imag.fr/SMS/sms.html
(France) INRIA Rhône-Alpes
IS2: statistical modelling project. Site in English and French.
http://www.inrialpes.fr/is2/pub
(Greece) Athens University of Economics and Business
Department of Statistics
http://stat-athens.aueb.gr/
(Austria) Vienna University of Technology
Department of Statistics, Probability Theory and Actuarial Mathematics.
http://www.statistik.tuwien.ac.at/
(Greece) University of Crete
Department of Mathematics, including research in Statistics.
http://www.math.uoc.gr/
(Ireland) University College, Cork
Department of Statistics.
http://www.ucc.ie/acad/stats/
(Greece) University of Ioannina
Department of Mathematics: Section(C) Probability, Statistics and Operational Research.
http://www.uoi.gr/schools/scmath/math/secc.htm
(Ukraine) Taras Shevchenko University of Kiev
Applied Statistics Department.
http://applstat.univ.kiev.ua/
(Malta) University of Malta
Department of Statistics and Operations Research (STATOR).
http://www.stator.um.edu.mt/
(Ireland) University of Dublin Trinity College
Department of Statistics
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(Belgium) Universite Catholique de Louvain
Institute of Statistics
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(Austria) University of Vienna
Department of Statistics and Decision Support Systems
http://www.univie.ac.at/statistics/
Statistics Departments in UK and Irish Universities
Statistics Departments in UK and Irish Universities
http://www.ma.hw.ac.uk/stat/depts.html
(Greece) University of Piraeus
Department of Statistics and Insurance Science.
http://www.unipi.gr/eng_site/akad_tmhm/stat_asfal/stat_asfal_index_eng.html
Committee of Professors of Statistics
The organisation of academic groups in statistics in the universities of the UK and Ireland. It aims to speak for these groups on matters of public interest, and to support their work through publicity and coordination.
http://www.copstat.ac.uk/
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