1. Review of statistics

• Markov and Cebysef inequalities, and Cebysef theorem

• Bernoulli theorem, law of large numbers

• Central limit theorem

• Theory of parameter estimation

  • definition

  • bias

  • consistency

  • efficiency

  • sufficiency

  • Maximum likelihood estimation

  • properties of ML estimators

• Bayesian approach to inference

  • conditional independence

  • Bayes’ theorem

  • Exchangeability and De Finetti theorem

  • Bayesian networks (no)

  • Definition of a bayesian model

  • Bayesian sufficiency

  • Predictive distributions

  • Prior choice

    • conjugate priors

    • non-informative priors, Jeffrey’s prior

  • Element of decision theory, bayes rules (only for point estimation)

  • Hierarchical models

  • Mixture models

  • Non parametric bayesian statistics

Single topics:

• Sufficiency and Neyman factorization lemma

• Fisher information and Cramer-Rao lower bound

• Hypotesis testing (no)

• Glivenko-Cantelli theorem (fundamental theorem of statistics)

• Delta method