One of the strengths of this book is the author's ability to motivate the use of Bayesian methods through simple yet effective examples. - Katie St. Clair MAA Reviews Intro -- Contents -- PART I: THE ESSENTIALS -- 1. The basics -- 1.1 Introduction:...
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One of the strengths of this book is the author's ability to motivate the use of Bayesian methods through simple yet effective examples. - Katie St. Clair MAA Reviews Intro -- Contents -- PART I: THE ESSENTIALS -- 1. The basics -- 1.1 Introduction: deductive logic versus plausible reasoning -- 1.2 Probability: Cox and the rules for consistent reasoning -- 1.3 Corollaries: Bayes' theorem and marginalization -- 1.4 Some history: Bayes, Laplace and orthodox statistics -- 1.5 Outline of book -- 2. Parameter estimation I -- 2.1 Example 1: is this a fair coin? -- 2.2 Reliabilities: best estimates, error-bars and confidence intervals -- 2.3 Example 2: Gaussian noise and averages -- 2.4 Example 3: the lighthouse problem -- 3. Parameter estimation II -- 3.1 Example 4: amplitude of a signal in the presence of background -- 3.2 Reliabilities: best estimates, correlations and error-bars -- 3.3 Example 5: Gaussian noise revisited -- 3.4 Algorithms: a numerical interlude -- 3.5 Approximations: maximum likelihood and least-squares -- 3.6 Error-propagation: changing variables -- 4. Model selection -- 4.1 Introduction: the story of Mr A and Mr B -- 4.2 Example 6: how many lines are there? -- 4.3 Other examples: means, variance, dating and so on -- 5. Assigning probabilities -- 5.1 Ignorance: indifference and transformation groups -- 5.2 Testable information: the principle of maximum entropy -- 5.3 MaxEnt examples: some common pdfs -- 5.4 Approximations: interconnections and simplifications -- 5.5 Hangups: priors versus likelihoods -- PART II: ADVANCED TOPICS -- 6. Non-parametric estimation -- 6.1 Introduction: free-form solutions -- 6.2 MaxEnt: images, monkeys and a non-uniform prior -- 6.3 Smoothness: fuzzy pixels and spatial correlations -- 6.4 Generalizations: some extensions and comments -- 7. Experimental design -- 7.1 Introduction: general issues -- 7.2 Example 7: optimizing resolution functions -- 7.3 Calibration, model selection and binning -- 7.4 Information gain: quantifying the worth of an experiment.
