Abstract
In many ways a course on the phasing of macromolecules from diffraction data can be seen as a study of applied statistics: statistical theory pervades the whole subject, so it is important that the basics of the subject are described and understood at the outset. Statistics can be divided into three related disciplines:
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(a)
Probability theory: the fundamentals of the subject and its associated mathematics
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(b)
Data analysis: the collection, display and summary of the raw experimental data.
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(c)
Statistical Inference: drawing statistical conclusions from data using the rules of probability theory.
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References
Gonick, L., and Smith, W. (1993) The Cartoon Guide to Statistics HarperPerennial Publishers, New York.
Shmueli, U., and Weiss, G.H. (1995) Introduction to Crystallographic Statistics International Union of Crystallography an Oxford University Press, Oxford.
Lee, P.M. (1989) Bayesian Statistics Oxford University Press, Oxford.
Fischer, N.I. (1993) Statistical Analysis of Circular Data Cambridge University Press, Cambridge.
von Mises, R (1918) Über die “Grazzahligkeit” der Atomgewichte und Verwandte Fragen Physikal Z. 19, 490–500.
O’Hagen, A. (1988) Probability: Methods and Measurement Chapman and Hall, London.
Edwards, A.W.F. (1972) Likelihood Cambridge University Press, Cambridge.
French, S. (1978) A Bayesian three stage model in crystallography Acta Cryst. A34, 728–738.
Bricogne, G. (1984) Maximum entropy and the foundations of direct methods, Acta Cryst. A40, 410–445.
Bricogne, G. (1988) A Bayesian statistical theory of the phase problem. I. A multichannel maximum entropy formalism for constructing generalized joint probability distributions of structure factors Acta Cryst. A44 (1988). 517–545.
Gilmore, C.J. (1996) Maximum entropy and Bayesian statistics in crystallography: a review of practical applications Acta Cryst. A52 (1996). 561–589.
Shannon, C.E. & Weaver, W. (1949). The Mathematical Theory of Communication. University of Illinois Press, Urbana, USA.
Jaynes, E.T. (1986). Where do we stand on maximum entropy? in J.H. Justice (ed.), Maximum Entropy and Bayesian Methods in AppliedStatistics, Cambridge University Press, Cambridge, pp 26–58.
Wilson, A.J.C. (1949) The probability distribution of X-ray intensities Acta Cryst. 2 318–321.
Hauptman, H. and Karle, J. (1953) The Solution of the Phase Problem. I. The Centrosymmetric Crystal ACA Monograph no. 3. Polycrystal Book Service, New York.
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Gilmore, C.J. (1998). An Introduction to Probability Theory. In: Fortier, S. (eds) Direct Methods for Solving Macromolecular Structures. NATO ASI Series, vol 507. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-9093-8_5
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DOI: https://doi.org/10.1007/978-94-015-9093-8_5
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