This comprehensive course on Bayesian statistics aims to introduce learners to key concepts with minimal math. By covering topics such as probability distributions, Bayesian vs. Frequentist statistics, Likelihood, conjugate priors, Markov Chain Monte Carlo, hypothesis testing, and hierarchical models, the course equips students with the skills to specify priors, analyze data, and make informed forecasts using Bayesian methods. The teaching method includes explanations, examples, proofs, and introductions to various probability distributions commonly used in Bayesian data analysis. This course is designed for individuals interested in expanding their statistical knowledge and understanding Bayesian approaches to data analysis.
Overview
Syllabus
Bayesian statistics syllabus.
Bayesian vs frequentist statistics.
Bayesian vs frequentist statistics probability - part 1.
Bayesian vs frequentist statistics probability - part 2.
What is a probability distribution?.
What is a marginal probability?.
What is a conditional probability?.
Conditional probability : example breast cancer mammogram part 1.
Conditional probability : example breast cancer mammogram part 2.
Conditional probability - Monty Hall problem.
1 - Marginal probability for continuous variables.
2 Conditional probability continuous rvs.
A derivation of Bayes' rule.
4 - Bayes' rule - an intuitive explanation.
5 - Bayes' rule in statistics.
6 - Bayes' rule in inference - likelihood.
7 Bayes' rule in inference the prior and denominator.
8 - Bayes' rule in inference - example: the posterior distribution.
9 - Bayes' rule in inference - example: forgetting the denominator.
10 - Bayes' rule in inference - example: graphical intuition.
11 The definition of exchangeability.
12 exchangeability and iid.
13 exchangeability what is its significance?.
14 - Bayes' rule denominator: discrete and continuous.
15 Bayes' rule: why likelihood is not a probability.
15a - Maximum likelihood estimator - short introduction.
16 Sequential Bayes: Data order invariance.
17 - Conjugate priors - an introduction.
18 - Bernoulli and Binomial distributions - an introduction.
19 - Beta distribution - an introduction.
20 - Beta conjugate prior to Binomial and Bernoulli likelihoods.
21 - Beta conjugate to Binomial and Bernoulli likelihoods - full proof.
22 - Beta conjugate to Binomial and Bernoulli likelihoods - full proof 2.
23 - Beta conjugate to Binomial and Bernoulli likelihoods - full proof 3.
24 - Bayesian inference in practice - posterior distribution: example Disease prevalence.
25 - Bayesian inference in practice - Disease prevalence.
26 - Prior and posterior predictive distributions - an introduction.
27 - Prior predictive distribution: example Disease - 1.
27 - Prior predictive distribution: example Disease - 2.
29 - Posterior predictive distribution: example Disease.
30 - Normal prior and likelihood - known variance.
31 - Normal prior conjugate to normal likelihood - proof 1.
32 - Normal prior conjugate to normal likelihood - proof 2.
33 - Normal prior conjugate to normal likelihood - intuition.
34 - Normal prior and likelihood - prior predictive distribution.
35 - Normal prior and likelihood - posterior predictive distribution.
36 - Population mean test score - normal prior and likelihood.
37 - The Poisson distribution - an introduction - 1.
38 - The Poisson distribution - an introduction - 2.
39 - The gamma distribution - an introduction.
40 - Poisson model: crime count example introduction.
41 - Proof: Gamma prior is conjugate to Poisson likelihood.
42 - Prior predictive distribution for Gamma prior to Poisson likelihood.
43 - Prior predictive distribution (a negative binomial) for gamma prior to poisson likelihood 2.
44 - Posterior predictive distribution a negative binomial for gamma prior to poisson likelihood.
Taught by
Ox educ
