Bayesian Inference Q2Q 2016 A Nexus mindmap 0 Published 4 years posthumously 0 Probability theory: the logic of science Edwin T. Jaynes, ed. G. Larry Bretthorst 0 http://bayes.wustl.edu 1 Unpublished book: Probability Theory, With Applications in Science and Engineering (prepared mid 1970's) + collection of papers and resources 0 0 Bayesian Logical Data Analysis for the Physical Sciences Phil Gregory (2005) 1 0 Probabilistic Graphical Models Principles and Techniques Daphne Koller and Nir Friedman (2009) 0 https://www.coursera.org/course/pgm 1 Also course available on Cousera: Probabilistic Graphical Models (Stanford) 2 3 Probability, frequency, and Reasonable Expectation , Cox, Am. J. Phys 14 , (1946) 4 Bayesian inference in physics Toussaint, Rev. Mod. Phys. 83 , 943 (2011) 0 Principal References 0 Please sign in 0 http://www.entropy.energy/scholar 1 All notes available at 0 It's an introductory workshop, so we'll look at 'simplest in class' problems rather than a deep application 1 But also want to convey why looking at probability leads to interesting conceptual questions within physics 2 Originally this was aimed at MRes students, it's morphed a bit. 0 Well... 3 If you are alergic to mindmaps... 4 Appologies to 388/246 students that will have seen much of this before 0 Instead, I will present what I think is the most remarkable formulation of it. 5 I will not be comparing with other interpretations of probability 6 Warning: probability theory is a rare example of an essentially abtract mathematical problem people get passionate over ... if not down-right angry. 1 General remarks 0 0 0 1 2 3 4 1 0 1 2 0 Explain to your neighbours the solution to the Monty Hall problem 2 To kick off 0 Introduction 0 Logic 1 Plausibility 2 Desiderata 3 Product rule 4 Sum rule 5 Probability as extended logic 0 Plausibility reasoning 1 Foundations of probability 2 Probability theory is nothing but common sense reduced to calculus Laplace, 1819 1 Plausibility 0 Bayes' rule 1 Chaining 2 Some consequences of the product rule 0 Bayes' rule 0 Variables 1 Marginalisation 2 Some consequences of the sum rule 1 Marginalisation 2 Assigning numbers 2 Basics 0 Numbers that summarise a distribution 1 Characteristic function 0 Moments 1 Probability distributions 3 Sampling 0 Comparing models against each other 1 A basic task 0 Model selection 0 Max-likelihood and least squares 1 A basic task 1 Parameter estimation 0 Principle of indifference 1 Flat prior 2 Jeffrey's prior 2 Effect of Priors 4 Bayesian inference 5 Maximum Entropy 0 Probabilities to graphs 1 Information flow 6 Bayesian networks Bayesian Inference Q2Q 2016