Introduction to Probability
This part introduces the probability concepts that support the rest of the handbook. The goal is practical understanding: how uncertainty is defined, how conditional reasoning works, and how these ideas translate into classification and inference workflows.
You can complete this part with the interactive apps only. R and RStudio are optional for users who want script-based replication.
How This Part Is Structured
| Block | Purpose | Main chapters |
|---|---|---|
| Foundations | Define probability, events, and conditional probability | Definitions of Probability, Jeffreys’ axiom system |
| Bayesian reasoning | Apply conditional probability to posterior updating and diagnostic interpretation | Bayes’ Theorem, Sensitivity and Specificity |
| Applied classification | Use probability for text classification and smoothing logic | Naive Bayes Classifier |
| Asymptotic intuition | Understand convergence of sample averages | Law of Large Numbers |
| Integrated practice | Consolidate concepts through exercises | Problems |
How To Use It
If you are new to probability, read the chapters in order.
If your focus is applied diagnostics or classification, start at Bayes’ Theorem and then return to the foundations as needed.
After this part, move to Probability Distributions for distribution-specific models, and use Appendix A — Method Selection Guide (Appendix A) when you need a fast method choice.