Computational Statistics

Aim

After completion of the course the student should be able to: - account for how computer arithmetics affects statistical computations, - develop computer implementations of standard methods for simulating from complex statistical distributions

• develop computer implementations of commonly used deterministic and stochastic optimization methods in statistics and machine learning
• select a suitable computer intensive uncertainty estimation methods for a given problem, and develop an implementation of the algorithm in a programming language
• interpret the results obtained by various simulation and estimation methods

Content

The course comprises a set of computational models and mathematical tools that enables performing computationally intensive statistical inference for complex challenging problems in statistics, machine learning and engineering.

The following topics are included in the course: - effect of computer arithmetics on statistical computations, - basic methods for random number generation, including inverse CDF method and acceptance/rejection method, - Monte Carlo methods for simulation and inference, including bootstrap and jackknife, - Markov Chain Monte Carlo (MCMC) simulation, including Metropolis-Hastings and Gibbs samplers, - introduction to unconstrained optimization and stochastic optimization.