# Computer Intensive Methods

## Subject description

Monte Carlo methods:

• Basic characteristics
• Uses of statistical simulations:
• Estimating standard errors
• Hypothesis testing
• Testing statistical methods
• Metropolis-Hastings algorithm and Gibbs sampling

Bootstrap:

• Basic characteristics
• Uses of statistical simulations:
• Estimating standard errors
• Computing confidence intervals
• Hypothesis testing
• Estimating and correcting bias
• Expansions

Permutation tests:

• Basic characteristics
• Assumptions
• Hypothesis testing

Model validation:

• "Jackknife"
• Cross-validation

Missing values:

• Types and mechanisms of missing values
• Methods for dealing with missing values:
• Multiple imputations
• EM algorithm

## Objectives and competences

The aim of the course is to enable the students for learning, adapting and using computer intensive methods in statistics. After the course students should be able to use these methods for solving real statistical problems that cannot be solved analytically.

## Teaching and learning methods

Lectures, tutorials, exercises, seminar papers, consultations.

Part of the pedagogical process will be carried out with the help of ICT technologies and the opportunities they offer.

## Expected study results

Knowledge and understanding:

Students learn selected computer intensive methods and understand basic principles of these methods. They are able to use them on problems disused in the class and to adapt and use them on similar problems.

## Basic sources and literature

1. Efron B., Tibshirani R. (1993): An Introduction to the Bootstrap. NewYork: Chapman&Hall.

2. Good P.I. (2005): Permutation, Parametric, and Bootstrap Tests of Hypotheses (Springer Series in Statistics). New York: Springer.

3. Good P.I. (2006): Resampling Methods: A Practical Guide to Data Analysis. Boston: Birkhäuser.

4. Morris, T. P., White, I. R., & Crowther, M. J. (2019). Using simulation studies to evaluate statistical methods. Statistics in Medicine, 38(11), 2074–2102. doi: 10.1002/sim.8086

5. Asmussen S., Glynn P.W. (2007). Stochastic Simulation: Algorithms and Analysis. New York; London: Springer.

6. Suess E.A., Bruce E.T. (2010) Introduction to Probability Simulation and Gibbs Sampling with R. Springer Science & Business Media.

7. Braun W.J., Murdoch D.J. (2008) A First Course in Statistical Programming with R. 1 edition. Cheltenham: Cambridge University Press.

8. Graham, J. W. (2012) Missing Data: Analysis and Design. Springer.

9. Izbrani članki

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