Mathematical Methods of Modern Statistics and Simulation

Karlstad University

Module 1: Statistical data analysis A. Theory Probability, conditional probability, Bayes' theorem, discrete and continuous random variables, probability function, distribution function, density function, averages, dispersion measures, multidimensional random variables, dependence measures. B. Practice Data processing with programming or statistical software, data reduction, sparsity and compression, principal component analysis, cluster analysis, machine learning. Module 2: Statistical inference A. Theory Random sample, sample distributions (t and F distributions), methods for parameter estimation (least squares method, maximum likelihood method), calculation of point and interval estimates for relevant parameters, variance analysis (ANOVA) and variance reduction. B. Practice Inverse transform sampling, implementation of parameter estimates with controlled variance, comparison of estimates based om maximum likelihood method (or other methods for parameter estimation) and estimates based on machine learning.

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