By Olaf Behnke, Kevin Kroninger, Gregory Schott, Thomas Schorner-Sadenius
This useful consultant covers the fundamental projects in statistical facts research encountered in excessive power physics and gives entire suggestion for general questions and difficulties. the fundamental tools for inferring effects from info are awarded in addition to instruments for complicated initiatives akin to enhancing the signal-to-background ratio, correcting detector results, settling on systematics and so forth. Concrete functions are mentioned in research walkthroughs. each one bankruptcy is supplemented through a variety of examples and workouts and by means of a listing of literature and suitable hyperlinks. The e-book objectives a extensive readership in any respect profession degrees - from scholars to senior researchers. An accompanying web site offers extra algorithms in addition to updated info and links.
* unfastened strategies guide on hand for academics at www.wiley-vch.de/supplements/
Chapter 1 basic options (pages 1–26): Roger Barlow
Chapter 2 Parameter Estimation (pages 27–73): Dr. Olaf Behnke and Lorenzo Moneta
Chapter three speculation trying out (pages 75–105): Dr. Gregory Schott
Chapter four period Estimation (pages 107–151): Luc Demortier
Chapter five type (pages 153–186): Helge Voss
Chapter 6 Unfolding (pages 187–225): Volker Blobel
Chapter 7 limited matches (pages 227–262): Benno List
Chapter eight how one can take care of Systematic Uncertainties (pages 263–296): Rainer Wanke
Chapter nine conception Uncertainties (pages 297–328): Markus Diehl
Chapter 10 Statistical equipment typical in excessive strength Physics (pages 329–356): Carsten Hensel and Dr. Kevin Kroninger
Chapter eleven research Walk?Throughs (pages 357–379): Aart Heijboer and Ivo van Vulpen
Chapter 12 functions in Astronomy (pages 381–407): Harrison B. Prosper
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Additional info for Data Analysis in High Energy Physics, A Practical Guide to Statistical Methods
2 below) the minimum of the negative log-likelihood function of m parameters cannot be found analytically as a function of the data x and one has to use a numerical procedure. 2. In practice numerical minimisation is quite involved, and the reader is advised to use standard tools. In high energy physics it is very popular to use the minuit program  for parameter estimation, which comes with several built-in minimisation algorithms. A general discussion of numerical minimisation is beyond the scope of this book and the reader is referred to the expert literature such as .
30) leading to the result τO D N 1 X ti . 31) In this particular case the maximum-likelihood estimator coincides with the sample mean. It can also be shown that τO is an unbiased estimator of τ. 23)), is σO τO D q D VO ( τO ) D Â N 2 X ti τO 3 iD1 ˇ Ã 1/2 @2 ln L ˇˇ @τ 2 ˇτDOτ ! 1/2 N τO D p . 32) The following table lists the uncertainty values σO τO for exemplary cases with two and eight observed decays for a hypothetical value τO D 1. 47 Also listed are the negative and positive uncertainties ∆ τO and ∆ τO C , determined from the two points where ln L drops by 1/2 from its maximum.
5. These tests are based on ensembles of simulated events and allow uncertainties to be estimated for almost every experimental situation. In the case that the proba- 39 40 2 Parameter Estimation bility density is known, ensemble tests can be used to determine also how far (if at all) the MLE is from reaching the MVB, for any number of events N. 4 The Method of Least Squares A very popular method is that of least squares. Since its introduction by Gauss in 1795 it has been the most widely used tool to ﬁt model parameters to experimental observations.
Data Analysis in High Energy Physics, A Practical Guide to Statistical Methods by Olaf Behnke, Kevin Kroninger, Gregory Schott, Thomas Schorner-Sadenius