Embark on a comprehensive journey through Bayesian statistics with this 6-hour course. Gain a solid foundation in probability distributions, marginal and conditional probability, and the Bayesian formula. Compare Bayesian and Frequentist approaches, explore likelihood concepts, and learn to specify priors. Delve into conjugate priors, credible intervals, and Objective Bayesian analysis. Discover forecasting techniques, Markov Chain Monte Carlo methods, and hypothesis testing. Explore hierarchical models and linear regression. Through practical examples and intuitive explanations, master key concepts with minimal mathematical complexity, making this course accessible to learners with limited prior knowledge.
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
