Advanced Statistics




The course develops the basics of probability distributions theory, their treatment and use as probability models, and an overview of likelihood
based inference.

Course outline:

1. Random variables and their characterization. Distribution functions and expectations. Moment generating and other auxiliary function.
2. Main discrete and continuous distributions.
3. Functions of random variables.
4. Elementary probability modelling. Hazard processes
5. Asymptotics. Central limit theorem, law of large numbers.
6. Sampling. Estimation. Likelihood-base inference. Point estimators. Computing maximum likelihood estimators under various circumstances. Censoring. Properties of point estimators.
7. Confidence intervals. Likelihood based (profile) vs pivotal approaches.
8. Test of hypotheses.
9 Goodness of fit. BIC. Likelihood ratio test
10. A short overview of Bayesian inference.
11. Basic bootstrapping.