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Unpublished book: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