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Exercises

Basics of Bayesian statistics

• Checking the sum and product rules, and their consequences
• Radioactive lighthouse problem
• Exploring PDFs
• Bayesian Statistics for Physicists: Interactive Bayesian updating (coin flipping)
• Standard medical example by applying Bayesian rules of probability
• Error propagation using Bayesian methods

Bayesian parameter estimation

• Revisiting parameter estimation in the bayesTALENT_intro notebook
• Parameter estimation example: fitting a straight line
• Linear algebra games including SVD for PCA
• Amplitude of a signal in the presence of background

MCMC sampling

• Random walk
• Write your own Metropolis-Hastings MCMC sampler

Assigning probabilities

• Maximum Entropy for reconstructing a function from its moments
• Maximum entropy for deriving probability distributions

Gaussian processes

• Gaussian Process models with GPy

Model checking

• Correlated Truncation Errors in Effective Field Theory: The code behind the manuscript

Special topic: Bayesian methods and machine learning

• Bayesian optimization
• Bayesian neural networks