Chapter 10
Statistics
Samples, splits, estimators, bias and variance, likelihood, uncertainty, and validation.
What this chapter does
Statistics connects data to claims. This chapter teaches how samples, estimators, splits, likelihood, uncertainty, and validation help you decide what a result actually supports.
Lessons
Read these in order.
Start with the chapter introduction, then move through the topic lessons. The order is chosen so each page can reuse ideas from the pages before it.
- 01Introduction
Why statistics gives machine learning its caution.
- 02Datasets and Samples
Observed data, sampled evidence, and the population we care about.
- 03Train, Validation, and Test Splits
Separating fitting, choosing, and final reporting.
- 04Estimators
Rules that use data to estimate unknown quantities.
- 05Bias and Variance
Systematic error and sensitivity to the sample.
- 06Likelihood
How plausible the observed data is under a parameter choice.
- 07Maximum Likelihood
Choosing parameters that make the observed data most plausible.
- 08Bayesian Updating
Combining prior belief with evidence.
- 09Confidence Intervals
Ranges that express sampling uncertainty.
- 10Hypothesis Tests
Evidence against a baseline assumption.
- 11Cross-Validation
Repeated held-out evaluation across folds.
- 12Resampling
Repeated samples used to study estimate variability.
Review and practice
Close the chapter deliberately.
Use the conclusion and revision notes before the chapter exercises. Hints and solutions are collected here, while lesson-level exercises reveal their own help inline.
What Chapter 10 accomplished and how it prepares information theory.
Summary and Revision NotesA compact review of estimates, uncertainty, and validation.
ExercisesChapter-level practice for statistics.
HintsLow-spoiler nudges for the Chapter 10 exercises.
SolutionsExplained solutions for the Chapter 10 exercises.
Before moving on
- Reason about data splits, model estimates, and sampling uncertainty.
- Understand why likelihood and maximum likelihood appear in training.
- Separate development evidence from final evaluation evidence.
- Read validation results with caution and context.
Where this leads
- Evaluation
- Probabilistic Models