Bayesian Statistics

Bayesian Statistics

English | MP4 | AVC 1280×720 | AAC 44KHz 2ch | 4.6 Hours | 1.36 GB

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