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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

Description:

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.

Bayesian Statistics - A Comprehensive Course

Ox educ

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#Mathematics #Statistics & Probability #Bayesian Statistics #Data Science #Data Analysis #Hypothesis Testing #Probability Theory #Probability Distributions #Forecasting #Statistical Methods #Markov Chain Monte Carlo

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