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Statistical data analysis for the physical sciences /
A modern introduction to statistics for undergraduates in physics, with worked examples and case studies to illustrate techniques presented.
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Cambridge, UK ; New York :
Cambridge University Press,
2013.
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| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- Preface; 1 Introduction; 1.1 Measuring g, the coefficient of acceleration due to gravity; 1.2 Verification of Ohm's law; 1.3 Measuring the half-life of an isotope; 1.4 Summary; 2 Sets; 2.1 Relationships between sets; 2.1.1 Equivalence; 2.1.2 Subset; 2.1.3 Superset; 2.1.4 Intersection; 2.1.5 Set difference; 2.1.6 Union; 2.1.7 Complement; 2.2 Summary; Exercises; 3 Probability; 3.1 Elementary rules; 3.2 Bayesian probability; 3.2.1 Priors; 3.3 Classic approach; 3.4 Frequentist probability; 3.4.1 Which approach should I use?; 3.5 Probability density functions; 3.6 Likelihood.
- 3.7 Case studies; 3.7.1 Tossing a coin (classical); 3.7.2 The national lottery (classical); 3.7.3 Blackjack (classical); 3.7.4 Will it rain tomorrow? (Bayesian); 3.7.5 The three cups problem (Bayesian); 3.8 Summary; Exercises; 4 Visualising and quantifying the properties of data; 4.1 Visual representation of data; 4.1.1 Histograms; 4.1.2 Graphs; 4.1.3 Continuous distributions; 4.2 Mode, median, mean; 4.3 Quantifying the spread of data; 4.3.1 Variance; 4.3.2 Standard deviation; 4.4 Presenting a measurement; 4.4.1 Full width at half maximum; 4.5 Skew; 4.6 Measurements of more than one observable.
- 6.1 The nature of errors; 6.1.1 Central limit theorem; 6.1.2 The Gaussian nature of statistical uncertainty; 6.1.3 Repeating measurements with a more precise experiment; 6.2 Combination of errors; 6.2.1 Functions of one variable; 6.2.2 Functions of two variables; 6.2.3 Functions involving powers of x; 6.2.4 Correlations revisited; 6.2.5 Correlated and uncorrelated uncertainties; 6.3 Binomial error; 6.4 Averaging results; 6.4.1 Weighted average of a set of measurements for a single observable; 6.4.2 Weighted average of a set of measurements for a set of observables.
- 6.5 Systematic errors and systematic bias; 6.6 Blind analysis technique; 6.7 Case studies; 6.7.1 Total uncertainty on a measurement; 6.7.2 Tracking uncertainty; 6.7.3 Weighted average of measurements of correlated observables; 6.8 Summary; Exercises; 7 Confidence intervals; 7.1 Two-sided intervals; 7.2 Upper and lower limit calculations; 7.3 Limits for a Gaussian distribution; 7.4 Limits for a Poisson distribution; 7.5 Limits for a binomial distribution; 7.6 Unified approach to analysis of small signals; 7.7 Monte Carlo method; 7.8 Case studies; 7.8.1 Multivariate normal distribution.