Bayesian statistics the fun way: understanding statistics and probability with Star Wars, LEGO, and Rubber Ducks

Part 1. Introduction to probability. Bayesian thinking and everyday reasoning

Measuring uncertainty

The logic of uncertainty

Creating a binomial probability distribution

The beta distribution

Part 2. Bayesian probability and prior probabilities. Conditional probability

Bayes' theorem with LEGO

The prior, likelihood, and posterior of Bayes' theorem

Bayesian priors and working with probability distributions

Part 3. Parameter estimation. Introduction to averaging and parameter estimation

Measuring the spread of our data

The normal distribution

Tools of parameter estimation : the PDF, CDF, and Quantile function

Parameter estimation with prior probabilities

Part 4. Hypothesis testing: the heart of statistics. From parameter estimation to hypothesis testing : building a Bayesian A/B test

Introduction to the Bayes factor and posterior odds : the competition of ideas

Bayesian reasoning in the twilight zone

When data doesn't convince you

From hypothesis testing to parameter estimation

Appendix A: A quick introduction to R

Appendix B: Enough calculus to get by.

Part 1. Introduction to probability

Ch. 1. Bayesian thinking and everyday reasoning

Ch. 2. Measuring uncertainty

Ch. 3. The logic of uncertainty

Ch. 4. Creating a binomial probability distribution

Ch. 5. The beta distribution

Part 2. Bayesian probability and prior probabilities

Ch. 6. Conditional probability

Ch. 7. Bayes' theorem with LEGO

Ch. 8. The prior, likelihood, and posterior of Bayes' theorem

Ch. 9. Bayesian priors and working with probability distributions

Part 3. Parameter estimation

Ch. 10. Introduction to averaging and parameter estimation

Ch. 11. Measuring the spread of our data

Ch. 12. The normal distribution

Ch. 13. Tools of parameter estimation : the PDF, CDF, and Quantile function

Ch. 14. Parameter estimation with prior probabilities

Part 4. Hypothesis testing : the heart of statistics

Ch. 15. From parameter estimation to hypothesis testing : building a Bayesian A/B test

Ch. 16. Introduction to the Bayes factor and posterior odds : the competition of ideas

Ch. 17. Bayesian reasoning in the twilight zone

Ch. 18. When data doesn't convince you

Ch. 19. From hypothesis testing to parameter estimation

Appendix A: A quick introduction to R

Appendix B: Enough calculus to get by.

Intro; Brief Contents; Contents in Detail; Acknowledgments; Introduction; Why Learn Statistics?; What Is "Bayesian" Statistics?; What's in This Book; Part I: Introduction to Probability; Part II: Bayesian Probability and Prior Probabilities; Part III: Parameter Estimation; Part IV: Hypothesis Testing: The Heart of Statistics; Background for Reading the Book; Now Off on Your Adventure!; Part I: Introduction to Probability; Chapter 1: Bayesian Thinking and Everyday Reasoning; Reasoning About Strange Experiences; Observing Data; Holding Prior Beliefs and Conditioning Probabilities

Forming a HypothesisSpotting Hypotheses in Everyday Speech; Gathering More Evidence and Updating Your Beliefs; Comparing Hypotheses; Data Informs Belief; Belief Should Not Inform Data; Wrapping Up; Exercises; Chapter 2: Measuring Uncertainty; What Is a Probability?; Calculating Probabilities by Counting Outcomes of Events; Calculating Probabilities as Ratios of Beliefs; Using Odds to Determine Probability; Solving for the Probabilities; Measuring Beliefs in a Coin Toss; Wrapping Up; Exercises; Chapter 3: The Logic of Uncertainty; Combining Probabilities with AND

Solving a Combination of Two ProbabilitiesApplying the Product Rule of Probability; Example: Calculating the Probability of Being Late; Combining Probabilities with OR; Calculating OR for Mutually Exclusive Events; Using the Sum Rule for Non-Mutually Exclusive Events; Example: Calculating the Probability of Getting a Hefty Fine; Wrapping Up; Exercises; Chapter 4: Creating a Binomial Probability Distribution; Structure of a Binomial Distribution; Understanding and Abstracting Out the Details of Our Problem; Counting Our Outcomes with the Binomial Coefficient

Combinatorics: Advanced Counting with the Binomial CoefficientCalculating the Probability of the Desired Outcome; Example: Gacha Games; Wrapping Up; Exercises; Chapter 5: The Beta Distribution; A Strange Scenario: Getting the Data; Distinguishing Probability, Statistics, and Inference; Collecting Data; Calculating the Probability of Probabilities; The Beta Distribution; Breaking Down the Probability Density Function; Applying the Probability Density Function to Our Problem; Quantifying Continuous Distributions with Integration; Reverse-Engineering the Gacha Game; Wrapping Up; Exercises

Part II: Bayesian Probability and Prior ProbabilitiesChapter 6: Conditional Probability; Introducing Conditional Probability; Why Conditional Probabilities Are Important; Dependence and the Revised Rules of Probability; Conditional Probabilities in Reverse and Bayes' Theorem; Introducing Bayes' Theorem; Wrapping Up; Exercises; Chapter 7: Bayes' Theorem with LEGO; Working Out Conditional Probabilities Visually; Working Through the Math; Wrapping Up; Exercises; Chapter 8: The Prior, Likelihood, and Posterior of Bayes' Theorem; The Three Parts; Investigating the Scene of a Crime