# 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)
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 ----------
• Looking back and forward

### 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