Data, Uncertainty and Inference
An Informal Introduction to Data Analysis
Description
This is a book intended for non-experts faced with the task of analyzing some data.
From the Preface—
The purpose of this book is to answer two questions:
What does it mean to analyze data?
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 Mac OS X™ application available
here.
Chapter titles and major topics as follows:
- 1. The Uraniborg Legacy
- General introduction
- Inference in action (three examples)
---------- Data ----------
- 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
---------- Uncertainty ----------
- 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
---------- Inference ----------
- 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
---------- Case Study ----------
- 16. When Data Don't Exist
- A real-world example
---------- Epilogue ----------
Details
Title: Data, Uncertainty and Inference
Author: Michael P. McLaughlin
Published: February, 2019
Contents: xv+265 pages, 118 figures, 75 tables, 31 models
Access
This is a free (but copyrighted) ebook in PDF format. It may be downloaded (7.2 Mb) at
Data, Uncertainty and Inference
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This page last updated on 28 August 2019.