Data, Uncertainty and Inference (2nd ed.)
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
- Measurement errors
- 4. Continuous Data
- Univariate and multivariate data
- Moments
- Combination of variances
- Pseudo-continuous data
- 5. Errors and Ignorance
- Errors vs. ignorance
- Accuracy vs. precision
- Significant figures
---------- Uncertainty ----------
- 6. Randomness
- Random variates
- Generating random variates
- 7. Probability
- Discussion of odds and probability
- Defining probability
- Describing probability
- Some important theory
- A Monte Carlo simulation
- 8. Rules of Probability
- Symbology
- Sum Rule and Product Rule
- Corollaries of the two rules
- 9. Some Common Distributions
- Continuous
- Discrete
- Mixtures
- Truncated and Censored
- Relationships
---------- Inference ----------
- 10. Data Analysis
- Reducing uncertainty
- Desiderata of valid inference
- 11. Making an Inference
- Bayes’ Rule
- Bayesian inference
- Prior
- Likelihood
- Posterior
- Marginal likelihood
- Comparison to frequentist methodology
- Numerical example
- Bayesian models
- Computing the posterior
- 12. Markov-chain Monte Carlo (MCMC)
- How it works
- Details for the Metropolis algorithm
- Marginals and credible intervals
- Why it works
- Computing the marginal likelihood
- Model comparison
- 13. MCMC Addenda
- How MCMC can go wrong (with suggested solutions)
- Additional MCMC algorithms
- Complete example for the Gibbs algorithm (with C++11 code)
- MCMC software
---------- Modeling ----------
- 14. Basic Procedure
- A real-world Bayesian model (full details)
- Outliers
- 15. Deterministic Models
- 9 Examples
- 16. Stochastic Models
- 10 Examples
- 17. Other Models
- Poisson regression
- ANOVA
- Logistic regression
- 18. Heterogeneous Mixtures
- Discrete components
- Continuous components
- 19. Homogeneous Mixtures
- Relabeling
- Classification assignments
- 20. Goodness-of-fit
- Algorithms
- 2 Examples
---------- Case Studies ----------
- 21. In the Lab
- 22. When Data Don't Exist
---------- Epilogue ----------
---------- Appendices ----------
- A Random-number Code
- B Gibbs-sampling Code
- C Model Syntax for Selected Software
Details
Title: Data, Uncertainty and Inference (2nd ed.)
Author: Michael P. McLaughlin
Published: November, 2024
Contents: xvi+321 pages, 144 figures, 97 tables, 42 models
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This is a free (but copyrighted) ebook in PDF format. It may be downloaded (9.2 Mb) at
Data, Uncertainty and Inference
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This page last updated on 17 November 2024.