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Recommendations
International Tables for Crystallography (2006). Vol. C, Section 8.1.4.5, p. 685 [ doi:10.1107/97809553602060000609 ]
Recommendations 8.1.4.5. Recommendations One situation in which the Gauss-Newton algorithm behaves particularly poorly is in the vicinity of a saddle point in parameter space, where the true Hessian matrix is not positive definite. This occurs in structure refinement where a symmetric model is refined to convergence and then is replaced ...
[more results from section 8.1.4 in volume C]
Conditioning
International Tables for Crystallography (2006). Vol. C, Section 8.1.3.3, p. 682 [ doi:10.1107/97809553602060000609 ]
... selected to make that combination of parameters determinate. References Anderson, E., Bai, Z., Bischof, C., Demmel, J., Dongarra, J., Du Croz ...
[more results from section 8.1.3 in volume C]
Principles of least squares
International Tables for Crystallography (2006). Vol. C, Section 8.1.2, pp. 680-681 [ doi:10.1107/97809553602060000609 ]
... the estimated standard deviation or standard uncertainty (Schwarzenbach, Abrahams, Flack, Prince & Wilson, 1995) of . This criterion states that the curvature ... likelihood principle. Hayward, CA: Institute of Mathematical Statistics. Box, G. E. P. & Tiao, G. C. (1973). Bayesian inference in statistical ... . Theory of optimal experiments, translated by W. J. Studden & E. M. Klimko. New York: Academic Press. Schwarzenbach, D., Abrahams, ...
Statistics
International Tables for Crystallography (2006). Vol. C, Section 8.1.1.2, pp. 679-680 [ doi:10.1107/97809553602060000609 ]
Statistics 8.1.1.2. Statistics A probability density function, which will be abbreviated p.d.f., is a function, [Phi](x), such that the probability of finding the random variable x in the interval is given by A p.d.f. has the properties and A cumulative distribution function, which will be abbreviated c.d.f., is defined by ...
[more results from section 8.1.1 in volume C]
Plausibility of results
International Tables for Crystallography (2006). Vol. C, Section 8.5.4, p. 709 [ doi:10.1107/97809553602060000613 ]
Plausibility of results 8.5.4. Plausibility of results A study of residuals to detect a pattern of discrepancies will reveal the presence of systematic error, or model inadequacy, only if different subsets of the data are affected differently. Some sources of bias, however, have noticeable effects throughout the data set, and missing ...
International Tables for Crystallography (2006). Vol. C, Section 8.1.4.5, p. 685 [ doi:10.1107/97809553602060000609 ]
Recommendations 8.1.4.5. Recommendations One situation in which the Gauss-Newton algorithm behaves particularly poorly is in the vicinity of a saddle point in parameter space, where the true Hessian matrix is not positive definite. This occurs in structure refinement where a symmetric model is refined to convergence and then is replaced ...
[more results from section 8.1.4 in volume C]
Conditioning
International Tables for Crystallography (2006). Vol. C, Section 8.1.3.3, p. 682 [ doi:10.1107/97809553602060000609 ]
... selected to make that combination of parameters determinate. References Anderson, E., Bai, Z., Bischof, C., Demmel, J., Dongarra, J., Du Croz ...
[more results from section 8.1.3 in volume C]
Principles of least squares
International Tables for Crystallography (2006). Vol. C, Section 8.1.2, pp. 680-681 [ doi:10.1107/97809553602060000609 ]
... the estimated standard deviation or standard uncertainty (Schwarzenbach, Abrahams, Flack, Prince & Wilson, 1995) of . This criterion states that the curvature ... likelihood principle. Hayward, CA: Institute of Mathematical Statistics. Box, G. E. P. & Tiao, G. C. (1973). Bayesian inference in statistical ... . Theory of optimal experiments, translated by W. J. Studden & E. M. Klimko. New York: Academic Press. Schwarzenbach, D., Abrahams, ...
Statistics
International Tables for Crystallography (2006). Vol. C, Section 8.1.1.2, pp. 679-680 [ doi:10.1107/97809553602060000609 ]
Statistics 8.1.1.2. Statistics A probability density function, which will be abbreviated p.d.f., is a function, [Phi](x), such that the probability of finding the random variable x in the interval is given by A p.d.f. has the properties and A cumulative distribution function, which will be abbreviated c.d.f., is defined by ...
[more results from section 8.1.1 in volume C]
Plausibility of results
International Tables for Crystallography (2006). Vol. C, Section 8.5.4, p. 709 [ doi:10.1107/97809553602060000613 ]
Plausibility of results 8.5.4. Plausibility of results A study of residuals to detect a pattern of discrepancies will reveal the presence of systematic error, or model inadequacy, only if different subsets of the data are affected differently. Some sources of bias, however, have noticeable effects throughout the data set, and missing ...
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