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Bayes Theorem, Bayesian networks, Bayesian sampling methods, Bayesian inference, machine learning and much more Bayesian Statistics is a fascinating field and today the centerpiece of many statistical applications in data science and machine learning. In this course, we will cover the main concepts of Bayesian Statistics including among others Bayes Theorem, Bayesian networks, Enumeration & Elimination for inference in such networks, sampling methods such as Gibbs sampling and the Metropolis-Hastings algorithm, Bayesian inference and the relation to machine learning. This course is designed around examples and exercises that provide plenty of opportunities to build intuition and apply your gathered knowledge. Many examples come from real-world applications in science, business or engineering or are taken from data science job interviews. While this is not a programming course, I have included multiple references to programming resources relevant to Bayesian statistics. The course is specifically designed for students without many years of formal mathematical education. The only prerequisite is high-school level mathematics, ideally a first-year university mathematics course and a basic understanding of probability. What you’ll learn- Bayes Theorem
- Conditional & Absolute independence
- Bayesian networks & d separation
- Enumeration & Elimination
- Sampling methods (rejection sampling, Gibbs sampling, Metropolis Hastings)
- Bayesian inference
- Continuous Bayesian statistics
- Bayesian statistics & machine learning

**+ Table of Contents**

**Introduction**

1 Primer on probability 1

2 Primer on probability 2

3 Primer on probability 3

4 Primer on probability – Exercise 1

5 Primer on probability – Exercise 2

6 Overarching problem 1

7 Overarching problem 2

8 Course outline

9 Outro

**Bayes Theorem**

10 Intro

11 Bayes Theorem – Contingency table

12 Bayes Theorem – Contingency table exercise

13 Bayes Theorem – Formula

14 Bayes Theorem – Formula exercise

15 Bayes Theorem

16 Overarching problem exercise

17 Monty Hall problem

18 Outro

**Absolute & Conditional Independence**

19 Intro

20 Some more probability 1

21 Some more probability 2

22 even more probability

23 Absolute & Conditional Independence

24 Conditional — Absolute Independence 1

25 Conditional — Absolute Independence 2 exercise

26 Conditional — Absolute Independence 3

27 Absolute — Conditional Independence 1

28 Absolute — Conditional Independence 2

29 Absolute — Conditional Independence 3

30 Absolute — Conditional Independence 4 exercise

31 Summary

32 Outro

**Bayesian networks & d separation**

33 Intro

34 Intro to Bayesian networks

35 Bayesian networks – Overarching problem

36 Bayesian networks – Independence 1 exercise

37 Bayesian networks – Independence 2 exercise

38 Bayesian networks – Independence 3

39 D separation 1

40 D separation 2

41 D separation 3

42 D separation 4 exercise

43 D separation 5 exercise

44 D separation 6 exercise

45 Outro

**Enumeration & Elimination**

46 Intro

47 Recap on probability

48 Calculating posteriors in Bayesian networks

49 Approach 1 Enumeration

50 Approach 1 Enumeration continued

51 Approach 2 Elimination

52 Enumeration vs Elimination

53 Approach 1 Enumeration exercise

54 Approach 2 Elimination exercise

55 Outro

**Miniproject – overarching problem**

56 Intro

57 Overarching problem

58 Miniproject – Exercise 1

59 Miniproject – Exercise 2

60 Miniproject – Exercise 3

61 Miniproject – Exercise 4

62 Outro

**Sampling methods**

63 Intro

64 Overarching problem

65 Rejection sampling 1

66 Rejection sampling 2

67 Rejection sampling 3

68 Gibbs sampling 1

69 Gibbs sampling 2

70 Gibbs sampling 3

71 Metropolis-Hastings algorithm 1

72 Metropolis-Hastings algorithm 2

73 Metropolis-Hastings algorithm 3

74 Outro

**Bayesian inference**

75 Intro

76 Frequentist vs Bayesian

77 Intro hypothesis testing

78 Frequentist hypothesis testing

79 Bayesian hypothesis testing 1

80 Bayesian hypothesis testing 2

81 Inference

82 Frequentist hypothesis testing – Exercise

83 Bayesian hypothesis testing – Exercise

84 Loss function 1 exercise

85 Loss function 2

86 Loss function 3

87 Confidence interval

88 Credible interval

89 Outro

**Continuous Bayesian Statistics**

90 Intro

91 Primer on distributions 1

92 Primer on distributions 2

93 Conjugacy 1

94 Conjugacy 2 exercise

95 Conjugacy 3

96 Distributions & conjugate priors

97 Continuous hypothesis testing

98 Rejection sampling

99 Metropolis-Hastings algorithm 1

100 Metropolis-Hastings algorithm 2

101 Comparison of sampling methods

102 Sampling methods – Exercise

103 Outro

**Bayesian statistics & machine learning**

104 Intro

105 Primer on machine learning

106 Overarching problem

107 Naive Bayes – Training

108 Naive Bayes – Training exercise

109 Naive Bayes – Testing exercise

110 Tree Augmented Naive Bayes

111 Linear Discriminant Analysis 1

112 Linear Discriminant Analysis 2

113 k-means

114 Gaussian mixture models

115 Outro

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