Front Cover -- Philosophy of Statistics -- Copyright Page -- Dedication -- General Preface -- Preface -- Contributors -- Contents -- Philosophy of Statistics: An Iintroduction -- 1 Philosophy, Statistics, and Philosophy of Statistics -- 2 Four Statistical Paradigms -- 3 The Likelihood Principle -- 4 The Curve-Fitting Problem, Problem of Induction, and Role of Simplicity in Inference -- 5 Recent Advances in Model Selection -- 6 Causal Inference in Observational Studies -- 7 Specific Topics of Interest -- 8 An Application of Statistics to Climate Science -- 9 Historical Topics in Probability and Statistics -- 10 Plans Behind Arranging Major Sections/Chapters -- 11 CODA -- Acknowledgements -- Bibliography -- Part I: Probability & Statistics -- Elementary Probability and Statistics: A Primer -- 1 Introduction -- 3 From Probablity to Statistics and a Road-Map for the Rest of the Chapter -- 4 Data Represented and Described -- 5 Random Variables and Probability Distributions -- 6 Statistical Inference -- 7 Conclusion -- Acknowledgements -- Bibliography -- Part II: Philosophical Controversies about Conditional Probability -- Conditional Probability -- 1 Introduction -- 2 Mathematical Theory -- 3 Philosophical Applications -- 4 Problems with the Ratio Analysis of Conditional Probability -- 5 Kolmorogov's Refinement: Conditional Probability as a Random Variable -- 6 Conditional Probability as Primitive -- 7 Conditional Probabilities and Updating Rules -- 8 Some Paradoxes and Puzzles Involving Conditional Probability and Conditionalization -- 9 Probabilities of Conditionals and Conditional Probabilities -- 10 Conclusion -- Bibliography -- The Varieties of Conditional Probability -- 1 Pluralism About Conditional Probability -- 2 Conditional Probability vs. Probability Given the Background -- Bibliography -- Part III: Four Paradigms of Statistics.

Classical Statistics Paradigm -- Error Statistics -- 1 What is Error Statistics? -- 2 A Philosophy for Error Statistics -- 3 Error Statistics vs. The Likelihood Principle -- 4 Error Statistics is Self-Correcting: Testing Statistical Model Assumptions -- Bibliography -- Significance Testing -- 1 Introduction -- 2 The Development and Logic of Significance Tests -- 3 (Mis)Interpreting Significance Tests -- 4 Objections to Significance Tests -- 5 Conclusion -- Acknowledgements -- Bibliography -- Bayesian Paradigm -- The Bayesian Decision-Theoretic Approach to Statistics -- 1 Bayesianism in Inference and Decision -- 2 Decision Problems -- 3 Degrees of Belief and Desire -- 4 Probability Axioms -- 5 Conditionalization -- 6 Bayesian and Classical Statistics Compared -- 7 Appendix: Savage's Representation Theorem -- Bibliography -- Modern Bayesian Inference: Foundations and Objective Methods -- 1 Introduction -- 2 Foundations -- 3 The Bayesian Paradigm -- 4 Reference Analysis -- 5 Inference Summaries -- 6 Discussion -- Bibliography -- Evidential Probability and Objective Bayesian Epistemology -- 1 Introduction -- 2 Evidential Probability -- 3 Second-Order Evidential Probability -- 4 Objective Bayesian Epistemology -- 5 EP-Calibrated Objective Bayesianism -- 6 Conclusion -- Acknowledgements -- Bibliography -- Confirmation Theory -- Introduction -- 1 The Probabilistic Logic of Confirmation Functions -- 2 Two Conceptions of Confirmational Probability -- 3 The Logical Structure of Evidential Support and the Role of Bayes' Theorem in that Logic -- 4 What is Confirmational Probability Anyway? -- 5 The Likelihood Ratio Convergence Theorem -- 6 When the Likelihoods are Vague AND/OR Diverse -- Acknowledgements -- Bibliography -- Challenges to Bayesian Confirmation Theory -- 1 Introduction -- 2 Competing Accounts of the Nature of Inductive Inference.

3 Challenges to Framework Assumptions -- 4 Additivity -- 5 Bayesian Dynamics -- 6 Further Challenges -- 7 Conclusion -- Acknowledgements -- Bibliography -- Bayesianism as a Pure Logic of Inference -- 1 Introduction -- 2 Bolzano and Partial Entailment -- 3 Symmetry and its Problems -- 4 Carnap's Logical Probability -- 5 From Logical Probability to Probabilistic Logic -- 6 Conditional Probability -- 7 Countable Versus Finite Additivity -- 8 Conclusion -- Acknowledgements -- Bibliography -- Bayesian Inductive Logic, Verisimilitude, and Statistics -- 1 Bayesian Inductive Logic and Bayesian Statistics -- 2 Theory of Inductive Probabilities, Confirmation, and Statistics -- 3 Verisimilitude and Statistics -- Acknowledgements -- Bibliography -- Likelihood Paradigm -- Likelihood and its Evidential Framework -- 1 Introduction -- 2 The Likelihood Paradigm -- 3 Reexamination of Accumulating Data ('multiple Looks') -- 4 Measuring Evidence about Several Endpoints Simultaneously ('multiple Comparisons') -- 5 Comments -- Bibliography -- Evidence, Evidence Functions, and Error Probabilities -- 1 Introduction -- 2 Quantifying Evidence, Likelihood Ratios and Evidence Functions -- 3 The Probability of Misleading Evidence and Inference Reliability -- 4 Global & Local Reliability -- 5 Local Reliability and the Evidential Paradigm -- 6 Evidence and Composite Hypotheses -- 7 Selecting Between Composite Hypotheses -- 8 Evidence and the Challenges of Multiplicities -- 9 Discussion -- Acknowledgements -- Bibliography -- Akaikean Paradigm -- AIC Scores as Evidence: A Bayesian Interpretation -- 1 Introduction -- 2 Estimates as Evidence -- 3 Differences in AIC Scores -- 4 Conclusion -- Appendix -- Acknowledgements -- Bibliography -- Part IV: The Likelihood Principle -- The Likelihood Principle -- 1 Introduction -- 2 Calculation, Justification and Classification.

3 Terminology and Caveats -- 4 The Likelihood Principle: Precise Statement -- 5 A Proof of the Likelihood Principle -- 6 A Proof of the Likelihood Principle: Continuation from the WSP and the WCP -- 7 Other Versions of the Likelihood Principle -- 8 Is the Likelihood Function Well Defined? -- Acknowledgements -- Bibliography -- Part V: Recent Advances in Model Selection -- AIC, BIC and Recent Advances in Model Selection -- Overview -- 1 Examples -- 2 The Akaike Information Criterion (AIC) -- 3 Bayes Factor and BIC -- 4 Comparison of AIC and BIC Through an Example -- 5 Recent Advances in Model Selection -- Summing Up -- Acknowledgements -- Bibliography -- Posterior Model Probabilities -- Introduction -- 1 Marginal Likelihood -- 2 Asymptotics -- 3 Improper Priors -- 4 Subjective Model Weights -- 5 'Fully Objective' Formal Priors -- 6 Problems with the Jeffreys Measure -- 7 Examples -- 8 Conclusion -- Acknowledgements -- Bibliography -- A Appendix: Proof of Theorem 1 -- Part VI: Attempts to Understand Different Aspects of "Randomness" -- Defining Randomness -- Randomness Finally Defined -- Inadequacies and Deficiencies -- Commonalities -- Acknowledgements -- Bibliography -- Mathematical Foundations of Randomness -- 1 Introduction -- 2 Strings, Sequences, Cantor Space, and Lebesgue Measure -- 3 Classical Stochastic Randomness in Infinite Sequences -- 4 Algorithms and Post Machines -- 5 Von Mises' Definition of Random Sequence -- 6 Martin-Löf and Solovay Randomness -- 7 Randomness of Finite Strings: Kolmogorov Complexity -- 8 The Prefix-Free Complexity K -- 9 Kolmogorov-Chaitin Randomness and Schnorr's Theorem -- 10 Relative and Stronger Randomness. Hierarchies -- 11 Randomness via Martingales. Other Frequentist Definitions -- 12 Conclusion. The Martin-Löf-Chaitin Thesis -- Acknowledgements -- Bibliography.

Part VII: Probabilistic and Statistical Paradoxes -- Paradoxes of Probability -- 1 Introduction -- 2 Puzzles and Paradoxes -- 3 Simple Puzzles of Probability -- 4 More Complex Problems of Probability -- 5 Paradoxes of Probability and Decision -- Acknowledgements -- Bibliography -- Statistical Paradoxes: Take it to the Limit -- 1 Introduction -- 2 Frequentist vs. Bayesian -- 3 Lindley's Paradox -- 4 Fieller-Creasy Problem -- 5 Concluding Remark -- Acknowledgements -- Bibliography -- Part VIII: Statistics and Inductive Inference -- Statistics as Inductive Inference -- 1 Statistical Procedures as Inductive Logics -- 2 Observational Data -- 3 Inductive Inference -- 4 Neyman-Pearson Testing -- 5 Fisher's Parameter Estimation -- 6 Carnapian Logics -- 7 Bayesian Statistics -- 8 Bayesian Inductive Logic -- 9 Neyman-Pearson Test as an Inference -- 10 In Conclusion -- Acknowledgements -- Bibliography -- Part IX: Various Issues about Causal Inference -- Common Cause in Causal Inference -- 1 Introduction -- 2 Structural Equation Models -- 3 Conditioning Versus Manipulating -- 4 Estimating Manipulated Means -- 5 Open Problems -- 6 Appendix -- Acknowledgements -- Bibliography -- The Logic and Philosophy of Causal Inference: A Statistical Perspective -- Do we need Philosophy of Causation for a Statistical Theory of Causal Inference? -- Potential Outcomes and Structural Equations -- Causal Systems and Causal Diagrams -- Discussion -- Acknowledgements -- Bibliography -- Part X: Some Philosophical Issues Concerning Statistical Learning Theory -- Statistical Learning Theory as a Framework for the Philosophy of Induction -- Pattern Recognition -- Bayes Error Rate R* -- Using Data to Learn the Statistical Probability Distribution? -- Empirical Risk Minimization -- Data Coverage Balanced Against Something Else -- Philosophical Implications -- Conclusion -- Bibliography.

Testability and Statistical Learning Theory.