Introduction to Bayesian Statistics

Explore the contrast between bayesian and frequentist views of probability, presenting objective frequencies versus subjective degrees of belief through dice, horse races, and baby gender examples.

Explore conditional probability through a simple example of 12 characters, highlighting how to compute dog and glasses probabilities and dog given glasses, leading toward Bayes' theorem.

Apply conditional probability to a Venn diagram, using Bayes' theorem to compute P(Mira late | Jane late) as 0.6 (3/5) from the given probabilities.

Use a tree diagram to apply Bayes theorem to update the probability of it being sunny given that Tanya played tennis, yielding a 77 percent posterior.

Apply Bayesian updating with a tree diagram to find the posterior probability of a recession given Tom lost his job, using a 10 percent prior and conditional losses.

Apply Bayes’ theorem to update the probability that a runner completes 100 meters in under 13.5 seconds after knowing she qualifies for the team, under a normal distribution model.

Explore how conditional probability and Bayes' theorem reveal counterintuitive effects of small mean shifts and increased spread on genius probabilities in a normal IQ model.

Apply Bayes' theorem to update the probability of disease X from a 10 percent prior to a 31 percent posterior after an 80 percent reliable test.

Explore how Bayes' theorem updates beliefs using a librarian vs farmer example, identifying prior, likelihood, posterior, and the evidence to compute probabilities.

Explore Thomas Bayes' puzzle of Alice and Bob, contrasting frequentist and Bayesian approaches, and derive the probability of Bob winning via binomial reasoning.

Apply Bayes' theorem to update Bob's win probability given a five-to-three score, deriving 1/11, and contrast with a simple three-eighths cubed calculation.

Simulate thousands of games in excel to compare frequentist five percent and Bayesian nine percent estimates, using binomial probability and the law of large numbers.

Celebrate the beauty, elegance, and power of Bayes Theorem and apply Bayesian thinking to understand the world a little better.