Bayesian inference: an introduction00:00
Outline00:03
Outline: Motivation and key ideas00:04
Summary: key ideas00:06
Summary: contents03:00
Connections03:15
Machine Learning (As Explained to a Statistician)04:10
Third generation machine intelligence05:41
Statistics and machine learning06:19
Bayesian and frequentist statistics (1)09:28
Bayesian and frequentist statistics (2)10:47
Bayesian inference: some other issues11:50
Outline: Basics13:50
Probability15:12
Bayes theorem (1)16:21
Bayes theorem (2)17:29
Bayes theorem (3)18:25
Bayes theorem (4)19:07
Bayes theorem – prediction20:18
Bayes theorem – decision21:01
Bayes theorem (5)22:13
Consistent use of probability to quantify uncertainty (1)23:11
Epistemological and aleatory (1)24:41
Epistemological and aleatory (2)26:44
Consistent use of probability to quantify uncertainty (2)27:36
Likelihood and prior28:45
Sequential acquisition of data32:03
Utility and loss (1)33:43
Utility and loss (2)34:47
Loss functions and hypothesis testing (1)35:56
Loss functions and hypothesis testing (2)37:00
Loss functions and estimation (1)40:01
Loss functions and estimation (2)41:41
Loss functions and frequentist inference43:17
Conjugacy (1)44:54
Conjugacy (2)46:43
Subjective and Objective Bayes48:47
Uninformative priors50:51
Improper priors54:01
Some principles of Bayesian modelling55:20
Motivation for hierarchical modelling56:01
The ‘surgical’ example (1)56:21
The ‘surgical’ example (2)58:31
The ‘surgical’ example (3)01:00:07
The ‘surgical’ example (4)01:00:53
The ‘surgical’ example (5)01:03:20
The ‘surgical’ example (6)01:03:33
Modelling the excess variation01:03:37
Approximate ‘empirical Bayes’ approach01:04:20
Potential problems with this approach01:05:03
Bayesian hierarchical models01:05:35
Full hierarchical Bayes approach01:06:56
Advantages of this approach01:07:22
Graphical models for surgical example01:08:04
Shrinkage and hierarchical models (1)01:08:54
Shrinkage and hierarchical models (2)01:09:00
Exchangeability and de Finetti’s theorem (1)01:09:05
Exchangeability and de Finetti’s theorem (2)01:11:20
Exchangeability and de Finetti’s theorem (3)01:14:01
What else do hierarchical models address?01:14:57
Summary: why hierarchical?01:15:35
Hidden Markov models and State space models (1)01:16:17
Hidden Markov models and State space models (2)01:17:50
Hidden Markov models01:18:15
State space models (1)01:18:46
State space models (2)01:19:32
Filtering, smoothing and prediction01:19:37
Kalman filtering01:21:23
Kalman filtering and variants01:21:42
Forwards/backwards recursions (1)01:22:18
Forwards/backwards recursions (2)01:22:35
Forwards/backwards recursions (3)01:22:38
Forwards/backwards recursions (4)01:23:03
More general lessons01:23:11
