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