From the Preface—

*
The purpose of this book is to answer two questions:
*

How should one go about it?

This is not a textbook, handbook or comprehensive guide to “everything you ever wanted to know” about data analysis. Rather, it is an informal overview intended to provide enough background and practical details for analysts to feel comfortable when reading technical articles that discuss a state-of-the-art analysis. It assumes no previous expertise in analytical methodology and keeps the math to a minimum. It does *not* discuss traditional, frequentist statistics except by way of contrast.

This book is one half of a two-part project. The other half is a free MacOS™ application available here.

**Chapter titles and major topics as follows:**

- 1. The
*Uraniborg*Legacy - General introduction
- Inference in action (three examples)

- 2. Information is Real!
- Physical reality of information (a demonstration)
- 3. Discrete Data
- Types of discrete data
- Summary statistics
- Weighted averages
- Errors
- 4. Continuous Data
- Univariate and multivariate data
- Describing continuous data
- Pseudo-continuous data

- 5. Errors and Ignorance
- Errors vs. ignorance
- Accuracy vs. precision
- Significant figures
- 6. Probability
- Discussion of odds and probability
- Describing probability
- PDF formulas
- Using PDF formulas
- A Monte Carlo simulation
- 7. Rules of Probability
- Symbology
- Sum Rule and Product Rule
- Corollaries of the two rules

- 8. Data Analysis
- Reducing uncertainty
- Desiderata of valid inference
- 9. Making an Inference
- Bayes’ Rule
- Bayesian inference
- Prior
- Likelihood
- Posterior
- Marginal likelihood

- Comparison to frequentist methodology
- Numerical example
- Complete Bayesian models
- Computing the posterior
- 10. Computational Details I
- Analytical computation
- Markov-chain Monte Carlo (MCMC)
- Details for the Metropolis algorithm
- Marginals and credible intervals
- Why MCMC works
- Computing the marginal likelihood
- Model comparison
- 11. Computational Details II
- How MCMC can go wrong (with suggested solutions)
- Additional MCMC algorithms
- Complete example for the Gibbs algorithm (with C++11 code)
- MCMC software
- 12. Modeling
- A real-world Bayesian model (full details)
- Four more non-hierarchical examples
- 13. Goodness-of-fit
- Discrepancy measures
- Posterior-predictive checking
- Example: a continuous mixture
- 14. Hierarchical Models
- Hierarchical models defined
- DAGs
- Full details for 13 examples
- Making predictions
- 15. Discrete Mixtures
- Heterogeneous vs. homogeneneous mixtures
- Relabeling
- Three examples

- 16. When Data Don't Exist
- A real-world example

- Looking back and forward

Author: Michael P. McLaughlin

Published: February, 2019

Contents: xv+265 pages, 118 figures, 75 tables, 31 models

Note: This ebook contains many internal references in adddition to external hyperlinks. For maximum convenience, the PDF reader should have a “back_to_previous_location” button (or menu item) readily available.