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Bayesian Inference II

External Lecturer: 
Roberto Trotta
Course Type: 
PhD Course
Academic Year: 
January - February
36 h
CFU (LM): 

Each bloc requires 6 hrs; 24 lectures + 4 x 3 hrs labs = 36 hours (5 weeks: 11/01-24/02)

  1. Foundations of Bayesianism: Jaynes’ robot; Cox theorem, objective and subjective Bayes; prior choice (maximum entropy, conjugancy, Jeffreys’ prior, empirical Bayes, hyperpriors, etc); sensitivity analysis.
  2. Lab 1: Sensitivity analysis and volume effects.
  3. Advanced sampling methods: slice sampling, Langevin and Hamiltonian Monte Carlo, collapsed and augmented Gibbs sampling, reversible jump MC.
  4. Lab 2: Writing an MCMC from scratch.
  5. Bayesian model comparison: stopping rule paradox, p-values, Lindley paradox; Bayesian evidence, Bayes factor and interpretation. Savage-Dickey Density Ratio, Laplace approximation, Approximate Bayesian Computation (ABC).
  6. Lab 3: Applications of Bayesian model comparison.
  7. Bayesian model averaging, Bayesian optimization and experiment design.
  8. Lab 4: Bayesian optimization.

Please, notice that this is a course belonging to Data Science Excellence Department programme. MAMA PhD students can plan 33% of their credits (i.e. 50 hrs) from this programme.

Next Lectures: 

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