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1 Probability  

EQuS Bayesian Inference 2016

In this workshop, we'll introduce and examine the consequences of probability theory in various areas of physics. From the meaning of probabilities, to how to reason with incomplete information, model comparison, parameter estimation, and modelling with Bayesian networks. The approach will view probabilities as an extension of logic (i.e. following Laplace, Bernoulli, Cox, Jaynes, etc)

3 Probability  

Comparing Models

Model comparison is one of the principal tasks on inference. Given some data, how does the plausibility of different models change? Does the data select out a particular model as being better?

3 Probability  

Probability and Frequency

Given that we are interpreting probability as a measure of plausibility, just what is the relationship of probabilities to frequencies?

3 Probability  

Bayes' rule

Some consequences of the product rule are explored including the famous Bayes' rule.

3 Probability  

Maximum entropy with average constraints

Find the probability distribution that maximises the entropy subject to requiring some averages to be fixed.

4 Probability  

Bayesian Inference Workshop 2016

In this workshop we'll introduce and examine the consequences of probability theory in various areas of physics. From the meaning of probabilities, to how to reason with incomplete information, model comparison, parameter estimation, and modelling with Bayesian networks. The approach will view probabilities as an extension of logic (i.e. following Laplace, Bernoulli, Cox, Jaynes, etc)

2 Probability  

Marginalization

Variables are introduced and then some consequences of the sum-rule are explored.

2 Rotation Dynamics  

Gyroscopic Motion

Equations of motion for a gyroscope are derived by considering the torques.

2 Rotation Dynamics  

Rotating coordinate system

In a rotating coordinate system, a free particle moves in a way that appears to be affected by three forces: the centrifugal force, the Coriolis force and the Euler force. These forces arise only from the rotation of the coordinate system.

1 Rotation Dynamics  

2D Rotational Dynamics

The description of 2D rotational motion is further developed in analogue to linear dynamics by introducing the rotational equivalents of force, momentum and mass.