Probabilistic Inference and Forecasting in the Sciences -- Syllabus

  - Uncertainty in measurements: a critical introduction.
    Some metrological premises, following the ISO's GUM recommendations.
  - Concept and evaluation of probability: basic rules; uncertain
    numbers and vectors (aka 'random variables'), discrete and continuous:
    remarkable distributions and relations among them.
    Main theorems of probability theory.
  - Distribution of functions of uncertain numbers ('propagation of uncertainties'):
    exact and approximated methods. Introduction to Monte Carlo methods.
  - Short introduction to the R language (students might use Python
    or possibly Julia, or whatever they like). 
  - From probability of effects to probability of causes: meaning and
    use of the so called 'Bayes rule'. Parametric inference and forecasting
    in the case of Gaussian, binomial and Poisson 'likelihoods'.
  - Probabilistic ('Bayesian') networks: general ideal and practical approach
    using HUGIN (and Netica).
  - Probabilistic forecasting and decision making.   
  - Combinations of results. Treatment of uncertainties due to systematic errors.  
  - Critical cases in frontier type measurements: upper/lower bounds.
  - Fits (just parametric inference): general approach and details in simple cases. 
    Recovering approximated methods (e.g. maximum likelihood and least squares)
    under well understood assumptions.
  - Other applications, including unfolding experimental distributions
    distorted because of instrumental and/or physical effects.
  - Computational issues: Gaussian approximation; conjugate priors;
    Monte Carlo methods and, in particular, Markov Chain Monte Carlo (MCMC).
    Use of JAGS (Just Another Gibbs Sampler) for inference and forecasting.
  . Role of the probabilistic treatment of uncertainty in Artificial Intelligence.