Data Reduction and Error Analysis for the Physical SciencesThe purpose of this book is to provide an introduction to the concepts of statistical analysis of data for students at the undergraduate and graduate level, and to provide tools for data reduction and error analysis commonly required in the physical sciences. The presentation is developed from a practical point of view, including enough derivation to justify the results, but emphasizing methods of handling data more than theory. The text provides a variety of numerical and graphical techniques. Computer programs that support these techniques will be available on an accompanying website in both Fortran and C++. |
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Page 147
... Minimum 60 130 145 160 175 190 205 220 a5 FIGURE 8.3 Plot of x2 versus a single parameter a in the region of a local minimum . The location of the minimum is calculated by fitting a parabola through the three indicated data points . We ...
... Minimum 60 130 145 160 175 190 205 220 a5 FIGURE 8.3 Plot of x2 versus a single parameter a in the region of a local minimum . The location of the minimum is calculated by fitting a parabola through the three indicated data points . We ...
Page 151
... minimum ) and the associated values of x2 to determine the minimum of the parabola , which passes through the three points as illustrated in Figure 8.3 . [ See Equation ( 8.12 ) . ] 5 . Repeat to minimize x2 with respect to each ...
... minimum ) and the associated values of x2 to determine the minimum of the parabola , which passes through the three points as illustrated in Figure 8.3 . [ See Equation ( 8.12 ) . ] 5 . Repeat to minimize x2 with respect to each ...
Page 155
... minimum , a parabolic interpretation of x2 is used to improve the determination of the minimum . A more sophisticated approach would be to use second partial derivatives of x2 to determine changes in the gradient along the search path ...
... minimum , a parabolic interpretation of x2 is used to improve the determination of the minimum . A more sophisticated approach would be to use second partial derivatives of x2 to determine changes in the gradient along the search path ...
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Data Reduction and Error Analysis for the Physical Sciences Philip R. Bevington,D. Keith Robinson No preview available - 2003 |
Common terms and phrases
a₁ a₂ Appendix approximation assume binomial distribution bins CALCCHISQ calculated Chapter CHI2 CHISQR column correlation corresponding counts per minute data of Example data points data sample decay defined degrees of freedom determined digit ENDIF Equation error matrix estimate experiment experimental factor fiducial Figure fitting function function y(x Gaussian distribution Gaussian function Gaussian probability graph histogram independent variable integral interval inverse matrix kaon least-squares fit Legendre polynomials likelihood function linear linear-correlation coefficient mean and standard mean µ minimum nonlinear number of counts number of degrees number of events observations obtain parameters parent distribution parent population particles peak plot Poisson distribution polynomial probability density probability density function probability distribution probability function problem random numbers result RETURN END routines SAN DIEGO square standard deviation starting values statistical Table tion uncertainties v₁ v₂ value of x² variance x₁ y₁ σ² στ