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Bayesian Inference Q2Q 2018 Alexei Gilchrist
A Nexus mindmap
Introduction
0
Logic
0
Plausibility
1
Desiderata
2
Product rule
3
Sum rule
4
Probability as extended logic
5
Plausibility reasoning
0
Foundations of
probability
3
Probability theory is nothing but
common sense reduced to calculus
Laplace, 1819
1
0
0
Product rule
0
1
Sum rule
0
2
Rules for
probabilities
2
Foundations
1
Variables
0
Some consequences
of the sum rule
2
Adding and removing variables
1
Marginalisation
0
Bayes' rule
0
Chaining
1
Some consequences
of the product rule
2
Bayes' rule
1
Assigning numbers
2
Numbers that
summarise a
distribution
0
mean
1
median
2
mode
3
moments
4
Summarising
3
Basics
2
Exponential process
0
Least squares solution
0
Fitting a line
2
Occam's razor
1
Monty Hall revisited
3
Application
4
(That would be useful or interesting)
5
A great way of modelling
complex relationships
0
Finding independencies between variables
1
Bayesian Networks
0
Why Gaussians are the right thing to use
1
Gibbs ensemble and stat. mech.
2
Another way of assigning probabilities
0
Maximum entropy
1
Efficient numerical methods to
sample the posterior distribution
0
Bypass the final marginalisation
1
Markov Chain Monte
Carlo methods
2
Bayesian decision theory
3
Bayesian experimental design
4
Things not covered
5
0
Parameter estimation
0
0
Model selection
1
Basic tasks
3
Bayesian Inference
Q2Q
2018
Alexei Gilchrist