Everything You Wanted to Know About Data Analysis and Fitting but Were Afraid to Ask [Elektronisk resurs] / by Peter Young.

• 1 Introduction -- 2 Averages and Error Bars -- 2.1 Basic Analysis -- 2.2 Advanced Analysis -- 2.2.1 Traditional Method -- 2.2.2 Jackknife -- 2.2.3 Bootstrap -- 2.2.4 Jackknife or Bootstrap? -- 3 Fitting Data to a Model -- 3.1 Fitting to a Straight Line -- 3.2 Fitting to a Polynomial -- 3.3 Error Bars -- 3.4 Interpolating -- 3.5 Fitting to a Non-linear Model -- 3.6 Confidence Limits -- 3.7 Confidence Limits by Resampling the Data -- 3.8 A Tale of Two Probabilities. When Can One Rule Out a Fit? -- 3.9 Model Selection (i.e. How to Avoid Over-Fitting): Maximum Likelihood Versus Bayes -- 3.9.1 Maximum Likelihood -- 3.9.2 A Bayesian Approach -- 3.9.3 Conclusions for Model Selection -- Appendix A: Central Limit Theorem -- Appendix B: The Number of Degrees of Freedom -- Appendix C: The Chi-squared Distribution and the Goodness of Fit Parameter Q -- Appendix D: Asymptotic Standard Error and How to Get Correct Error Bars from Gnuplot -- Appendix E: The Distribution of Fitted Parameters Determined from Simulated Datasets -- Appendix F: The Distribution of Fitted Parameters from Repeated Sets of Measurements -- Appendix G: Fitting Correlated Data -- Appendix H: Scripts for Some Data Analysis and Fitting Tasks. 

• These notes describe how to average and fit numerical data that have been obtained either by simulation or measurement. Following an introduction on how to estimate various average values, they discuss how to determine error bars on those estimates, and how to proceed for combinations of measured values. Techniques for fitting data to a given set of models will be described in the second part of these notes. This primer equips readers to properly derive the results covered, presenting the content in a style suitable for a physics audience. It also includes scripts in python, perl and gnuplot for performing a number of tasks in data analysis and fitting, thereby providing readers with a useful reference guide. 

Ämnesord

Mathematical physics  (LCSH)

Maximal subgroups  (LCSH)

Numerical analysis  (LCSH)

Physics  (LCSH)

Physics 

Measurement Science and Instrumentation 

Statistics for Engineering, Physics, Computer Science, Chemistry and Earth Sciences 

Numerical and Computational Physics 

Klassifikation

T50 (LCC)

PDDM (ämneskategori)

SCI068000 (ämneskategori)

530.8 (DDC)

Tf (kssb/8 (machine generated))