Updated A.Y. 2018-2019
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; condence intervals and notes on nonparametric inference.
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.
- Methods of Finding Estimators: Methods of Moments, Maximum Likelihood Estimators
- Evaluation of estimators: Unbiasedness, Consistency, Fisher Information and the Cramer-Rao theorem.
- Confidence Intervals
- 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