| Description |
1 online resource |
| Physical Medium |
polychrome |
| Description |
text file |
| Bibliography |
Includes bibliographical references (pages 313-323) and index. |
| Summary |
A multi-level introduction to Bayesian reasoning (as opposed to "conventional statistics") and its applications to data analysis. The basic ideas of this approach to the quantification of uncertainty are presented using examples from research and everyday life. Applications covered include: parametric inference; combination of results; treatment of uncertainty due to systematic errors and background; comparison of hypotheses; unfolding of experimental distributions; upper/lower bounds in frontier-type measurements. Approximate methods for routine use are derived and are shown often to coincide - under well-defined assumptions - with "standard" methods, which can therefore be seen as special cases of the more general Bayesian methods. In dealing with uncertainty in measurements, modern metrological ideas are utilized, including the ISO classification of uncertainty into type A and type B. These are shown to fit well into the Bayesian framework. |
| Contents |
pt. 1 Critical review and outline of the Bayesian alternative. 1. Uncertainty in physics and the usual methods of handling it. 1.1. Uncertainty in physics. 1.2. True value, error and uncertainty. 1.3. Sources of measurement uncertainty. 1.4. Usual handling of measurement uncertainties. 1.5. Probability of observables versus probability of 'true values'. 1.6. Probability of the causes. 1.7. Unsuitability of frequentistic confidence intervals. 1.8. Misunderstandings caused by the standard paradigm of hypothesis tests. 1.9. Statistical significance versus probability of hypotheses -- 2. A probabilistic theory of measurement uncertainty. 2.1. Where to restart from? 2.2. Concepts of probability. 2.3. Subjective probability. 2.4. Learning from observations: the 'problem of induction'. 2.5. Beyond Popper's falsification scheme. 2.6. From the probability of the effects to the probability of the causes. 2.7. Bayes' theorem for uncertain quantities. 2.8. Afraid of 'prejudices'? Logical necessity versus frequent practical irrelevance of priors. 2.9. Recovering standard methods and short-cuts to Bayesian reasoning. 2.10. Evaluation of measurement uncertainty: general scheme -- pt. 2. A Bayesian primer. 3. Subjective probability and Bayes' theorem. 3.1 What is probability? 3.2. Subjective definition of probability. 3.3. Rules of probability. 3.4. Subjective probability and 'objective' description of the physical world. 3.5. Conditional probability and Bayes' theorem. 3.6. Bayesian statistics: learning by experience. 3.7. Hypothesis 'test' (discrete case). 3.8. Falsificationism and Bayesian statistics. 3.9. Probability versus decision. 3.10. Probability of hypotheses versus probability of observations. 3.11. Choice of the initial probabilities (discrete case). 3.12. Solution to some problems. 3.13. Some further examples showing the crucial role of background knowledge -- 4. Probability distributions (a concise reminder). 4.1. Discrete variables. 4.2. Continuous variables: probability and probability density function. 4.3. Distribution of several random variables. 4.4. Propagation of uncertainty. 4.5. Central limit theorem. 4.6 Laws of large numbers -- 5. Bayesian inference of continuous quantities. 5.1. Measurement error and measurement uncertainty. 5.2. Bayesian inference and maximum likelihood. 5.3. The dog, the hunter and the biased Bayesian estimators. 5.4. Choice of the initial probability density function. |
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6. Gaussian likelihood. 6.1. Normally distributed observables. 6.2. Final distribution, prevision and credibility intervals of the true value. 6.3. Combination of several measurements -- Role of priors. 6.4. Conjugate priors. 6.5. Improper priors -- never take models literally! 6.6. Predictive distribution. 6.7. Measurements close to the edge of the physical region. 6.8. Uncertainty of the instrument scale offset. 6.9. Correction for known systematic errors. 6.10. Measuring two quantities with the same instrument having an uncertainty of the scale offset. 6.11. Indirect calibration. 6.12. The Gauss derivation of the Gaussian -- 7. Counting experiments. 7.1. Binomially distributed observables. 7.2. The Bayes problem. 7.3. Predicting relative frequencies -- Terms and interpretation of Bernoulli's theorem. 7.4. Poisson distributed observables. 7.5. Conjugate prior of the Poisson likelihood. 7.6. Predicting future counts. 7.7. A deeper look to the Poissonian case -- 8. Bypassing Bayes' theorem for routine applications. 8.1. Maximum likelihood and least squares as particular cases of Bayesian inference. 8.2. Linear fit. 8.3. Linear fit with errors on both axes. 8.4. More complex cases. 8.5. Systematic errors and 'integrated likelihood'. 8.6. Linearization of the effects of influence quantities and approximate formulae. 8.7. BIPM and ISO recommendations. 8.8. Evaluation of type B uncertainties. 8.9. Examples of type B uncertainties. 8.10. Comments on the use of type B uncertainties. 8.11. Caveat concerning the blind use of approximate methods. 8.12. Propagation of uncertainty. 8.13. Covariance matrix of experimental results -- more details. 8.14. Use and misuse of the covariance matrix to fit correlated data -- 9. Bayesian unfolding. 9.1. Problem and typical solutions. 9.2. Bayes' theorem stated in terms of causes and effects. 9.3. Unfolding an experimental distribution. |
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pt. 3. Further comments, examples and applications -- 10. Miscellanea on general issues in probability and inference. 10.1. Unifying role of subjective approach. 10.2. Frequentists and combinatorial evaluation of probability. 10.3. Interpretation of conditional probability. 10.4. Are the beliefs in contradiction to the perceived objectivity of physics? 10.5. Frequentists and Bayesian 'sects'. 10.6. Biased Bayesian estimators and Monte Carlo checks of Bayesian procedures. 10.7. Frequentistic coverage. 10.8. Why do frequentistic hypothesis tests 'often work'? 10.9. Comparing 'complex' hypotheses -- automatic Ockham' Razor. 10.10. Bayesian networks -- 11. Combination of experimental results: a closer look. 11.1. Use and misuse of the standard combination rule. 11.2. 'Apparently incompatible' experimental results. 11.3. Sceptical combination of experimental results -- 12. Asymmetric uncertainties and nonlinear propagation. 12.1. Usual combination of 'statistic and systematic errors'. 12.2. Sources of asymmetric uncertainties in standard statistical procedures. 12.3. General solution of the problem. 12.4. Approximate solution -- 13. Which priors for frontier physics? 13.1. Frontier physics measurements at the limit to the detector sensitivity. 13.2. Desiderata for an optimal report of search results. 13.3. Master example: Inferring the intensity of a Poisson process in the presence of background. 13.4. Modelling the inferential process. 13.5. Choice of priors. 13.6. Prior-free presentation of the experimental evidence. 13.7. Some examples of [symbol]-function based on real data. 13.8. Sensitivity bound versus probabilistic bound. 13.9. Open versus closed likelihood -- pt. 4. Conclusion -- 14. Conclusions and bibliography. 14.1. About subjective probability and Bayesian inference. 14.2. Conservative or realistic uncertainty evaluation? 14.3. Assessment of uncertainty is not a mathematical game. 14.4. Bibliographic note. |
| Local Note |
eBooks on EBSCOhost EBSCO eBook Subscription Academic Collection - North America |
| Subject |
Bayesian statistical decision theory.
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Bayesian statistical decision theory. |
| Genre/Form |
Electronic books.
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Libros electronicos.
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Electronic books.
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| Other Form: |
Print version: D'Agostini, Giulio. Bayesian Reasoning in Data Analysis : A Critical Introduction. Singapore : World Scientific Publishing Company, ©2003 9789812383563 |
| ISBN |
9789812775511 (electronic book) |
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981277551X (electronic book) |
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9789812383563 |
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9812383565 |
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981277551X |
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1281928216 |
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9781281928214 |
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