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Updated A.Y. 2021-2022

The course is an introduction to the fundamental principles and tools of statistical inference, i.e. how to draw conclusions from
data subject to random variation. Topics include: random sampling; principles of data reduction; point and interval estimation (likelihood theory); hypothesis testing; con fidence intervals and notes on nonparametric inference.

In Particular:

Brief review of probability

Random samples and asymptotic methods

  • Sampling and sums of random variables
  • Laws of large numbers and central limit theorem

Principles of Data Reduction

The Likelihood Principle: the Likelihood Function.

Point Estimation

  • Methods of Finding Estimators: Methods of Moments, Maximum Likelihood Estimators
  • Evaluation of estimators: Unbiasedness, Consistency, Fisher Information and the Cramer-Rao theorem.
  • Confidence Intervals

Hypothesis Testing

  • Methods of Finding Tests: Neyman Pearson lemma
  • Large sample tests: Likelihood Ratio Tests, Score Test, Wald Test 
  • Methods of Evaluating Tests: the Power Function, Most Powerful Tests.
  • The p-value.

Notes on Bayesian Inference

Non Parametric Inference

  • Kolmogorov-Smirnov Test