Kelter, Riko: The evolution of statistical hypothesis testing : Bayesian statistical solutions to the replication crisis in the biomedical sciences. 2021
Inhalt
- Abstract
- Zusammenfassung
- Preface
- Contents
- Introduction
- I The Evolution of Frequentist Significance - and Hypothesis Testing
- The Protagonists
- Fisher's Theory of Significance Testing
- The Neyman-Pearson Theory of Hypothesis Testing
- The Beginning of a new Theory for statistical Hypothesis testing
- The Criterion of Likelihood
- Optimality Results and the Neyman-Pearson Lemma
- The Final Steps
- The modern hybrid Approach
- II The Evolution of Bayesian Hypothesis Testing
- III The Evolution of Markov-Chain-Monte-Carlo and its Impact on Bayesian Hypothesis Testing
- Markov-Chain-Monte-Carlo
- The Evolution of Markov-Chain-Monte-Carlo
- An Overview of the Evolution of Markov-Chain-Monte-Carlo
- The Introduction of the original Metropolis Algorithm
- The Introduction of the Metropolis-Hastings Algorithm
- The Introduction of Simulated Annealing
- The Invention of the Gibbs-sampler
- Markov-Chain-Monte-Carlo as a generalised statistical Simulation Technique
- Hamiltonian Monte Carlo and further Developments
- The Impact of Markov-Chain-Monte-Carlo on Bayesian Hypothesis Testing
- IV On the Axiomatic Foundations of Statistical Inference
- Philosophical Considerations on Bayesian Statistical Inference
- The traditional Problem of Induction
- Popper's Criticism to Inductive Reasoning
- Reconstructing the Critiques to Inductive Reasoning
- Conclusion
- Axiomatic Considerations on the Foundations of Statistical Inference
- V Bayesian Statistical Solutions to the Replication Crisis in the Biomedical Sciences
- Bayesian Alternatives to Null Hypothesis Significance Testing in the biomedical Sciences with JASP
- Bayesian Survival Analysis in Stan via Hamiltonian-Monte-Carlo
- Introduction
- Flexibility and Application
- A detailed Example – Parametric Survival Analysis
- Conclusion
- Analysis of Bayesian Posterior Significance and Effect Size Indices for the two-sample t-test
- A new Bayesian two-sample t-test for the Effect Size based on the Hodges-Lehmann Paradigm
- Revisiting the Replication Crisis
- Appendices
- Appendices
- Proofs and Derivations for Chapter 15
- Derivation of the single-block Gibbs sampler
- Proof of Theorem 15.2 – Derivation of the full conditionals for the single-block Gibbs sampler
- Proof of Corollary 15.3
- Proof of Theorem 15.8
- Proof of Theorem 15.11
- The Relative Likelihood Principle for continuous Probability Spaces
- Measure-theoretic Foundations of Statistical Inference
- Bibliography