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principles
aperiodic crystals
biological macromolecules
crystal growth and characterization of materials
crystallographic computing
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crystallography in art and cultural heritage
crystallography of materials
electron crystallography
high pressure
inorganic and mineral structures
international tables
journals
magnetic structures
mathematical and theoretical crystallography
neutron scattering
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quantum crystallography
small-angle scattering
structural chemistry
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congress
2020 iucr xxv
2017 iucr xxiv
2014 iucr xxiii
2011 iucr xxii
2008 iucr xxi
2005 iucr xx
2002 iucr xix
1999 iucr xviii
1996 iucr xvii
1993 iucr xvi
1990 iucr xv
1987 iucr xiv
1984 iucr xiii
1981 iucr xii
1978 iucr xi
1975 iucr x
1972 iucr ix
1969 iucr viii
1966 iucr vii
1963 iucr vi
1960 iucr v
1957 iucr iv
1954 iucr iii
1951 iucr ii
1948 iucr i

people
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agre
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curl
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klug
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pauling
perutz
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sumner
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walker
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watson
wilkins
yonath

resources
commissions
aperiodic crystals
biological macromolecules
crystal growth and characterization of materials
crystallographic computing
crystallographic nomenclature
crystallographic teaching
crystallography in art and cultural heritage
crystallography of materials
electron crystallography
high pressure
inorganic and mineral structures
international tables
journals
magnetic structures
mathematical and theoretical crystallography
neutron scattering
NMR crystallography
powder diffraction
quantum crystallography
small-angle scattering
structural chemistry
synchrotron radiation
xafs

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Problems arising from the interface between the mathematical theory of probability and statistics and the practising experimentalist are not confined to procedural issues. One cannot tackle such problems without realizing their important philosophical component originating from the need to justify the lack of rigour and the unavoidable approximations in the treatment of experimental data. For this reason, the attention of the non-specialist is drawn to the two main interpretations of probability used by statisticians.

In the **frequentist** point of view, the probability of an event is taken to be equal to the limit of the relative frequency of the chosen event with respect to all possible events as the number of trials goes to infinity. The appeal of the frequentist approach for physical scientists lies in the apparent objectivity of its treatment of data. Almost all textbooks of statistics written for physical scientists follow this approach (*e.g.* Hamilton, 1964).

On the other hand, the **Bayesian** approach extends the interpretation of probability to include degrees of belief or knowledge in propositions. We pass from the probability of events (frequentist) to the probability of propositions (Bayesian). Nevertheless the axioms used to define the mathematical properties of probability remain unchanged. Consequently many of the statistical procedures of the two approaches are identical, apart from some changes of emphasis. The Bayesian approach is very scantily mentioned in textbooks for physical scientists (see however, French, 1978; Box & Tiao, 1973).

The frequentist school reproaches the Bayesians for their apparent lack of objectivity. The Bayesians consider that objectivity in statistics is illusory, noting that everything is interpreted through the use of preconceived models. Most physical scientists argue in terms of frequentist concepts but implicitly use a more subjective or Bayesian touch in dealing with their experimental data. Often encountered-expressions like 'the probable value of a parameter' are meaningful only in the Bayesian framework (French & Oatley, 1982).

* Copies of NIST Technical Note 1297 may be obtained from the NIST Calibration Program or from Dr. B.N. Taylor or Dr. C.E. Kuyatt, National Institute of Standards and Technology, Gaithersburg, MD 20899, USA.

© 1989, 1995 International Union of Crystallography

Updated 18th Sept. 1996

The International Union of Crystallography is a non-profit scientific union serving the world-wide interests of crystallographers and other scientists employing crystallographic methods.

© International Union of Crystallography