Advanced Topics in Statistics (1 º Sem 2020/2021)
Program
- Probability: Axiomatics, independence, random variable, expected values and parameters, forms of stochastic convergence, central limit theorem, laws of large numbers, delta method;
- Statistics: Classical statistical model, statistics, sufficiency, ancilarity and completeness, information measures, exponential family and location-scale family. Bayesian statistical model, Bayes theorem as an inferential tool, non-informative and conjugate families of prior distributions. Controversies surrounding the foundations of Statistical Inference;
- Statistical Decision: Structure of a decision problem, inference and decision, classical and Bayesian decision, point and interval estimation, hypotheses testing, prediction;
- Computational and approximate methods: Optimization techniques and analytical approximations. Simulation: Monte Carlo, importance sampling, resampling methods, Markov chain Monte Carlo.
- Statistics: Classical statistical model, statistics, sufficiency, ancilarity and completeness, information measures, exponential family and location-scale family. Bayesian statistical model, Bayes theorem as an inferential tool, non-informative and conjugate families of prior distributions. Controversies surrounding the foundations of Statistical Inference;
- Statistical Decision: Structure of a decision problem, inference and decision, classical and Bayesian decision, point and interval estimation, hypotheses testing, prediction;
- Computational and approximate methods: Optimization techniques and analytical approximations. Simulation: Monte Carlo, importance sampling, resampling methods, Markov chain Monte Carlo.