Data Analysis and Machine Learning: Elements of Bayesian theory and Bayesian Neural Networks
Contents
Why Bayesian Statistics?
Inference
Statistical Inference
Some history
The Bayesian recipe
Bayes' theorem
The friends of Bayes' theorem
Inference With Parametric Models
Illustrative examples with python code
Example: Is this a fair coin?
A few words on different priors
Bayesian parameter estimation (single parameter)
Example: Measured flux from a star
Simple Photon Counts: Frequentist Approach
Simple Photon Counts: Bayesian Approach
A note about priors
Simple Photon Counts: Bayesian approach in practice
Best estimates and confidence intervals
Simple Photon Counts: Best estimates and confidence intervals
Bayesian parameter estimation (multiple parameters, covariance)
Bayesian model selection
Illustrative examples with python code
Is this a fair coin? (analytical)
Flux from a star (single parameter, MCMC)
The lighthouse problem (two parameters, MCMC)
Linear fit with outliers (nuisance parameters)
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