# Advanced Probability and Inference

## Content

- Mathematical background (limits, series, order relations and rates of convergence, continuity, sets)
- Measure theoretic foundations of probability (probability triplets, random variables, independence, expected values, change of variable)
- Stochastic convergence (almost sure convergence, convergence in probability, convergence in distribution, laws of large numbers, central limit theorems, non-iid stochastic variables)
- Conditional probability and expectation
- Statistical tests (size and critical values, power, efficiency, asymptotic tests, asymptotic relative efficiency)
- Estimation (confidence intervals, point estimation, asymptotic efficiency, Fisher Information)
- Nonparametrics (U-statistics, statistical functionals, limit distributions)

## Schedule

Jan 24, 13-16, P258

Jan 25, 9-12, L111

Jan 31, 9-12, G102

Feb 1, 13-16, L111

Feb 21, 9-12, P138

Feb 22, 13-16, P221

March 6, 9-12, P254

March 7, 13-16, P243

March 20, 9-12, P243

March 21, 13-16, L151