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.

### Syllabus

### Taught by

Ox educ