Data, Uncertainty and Inference (2^nd 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 ----------

• ...In the Final Analysis

---------- Appendices ----------

A Random-number Code

B Gibbs-sampling Code

C Model Syntax for Selected Software

Details

Title: Data, Uncertainty and Inference (2^nd 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.