## Agenda

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Bayesian Statistics

Introduction: Quantifying Uncertainty Using Probabilities, Models and Prior Probabilities, Likelihoods and Posterior Probabilities, Bayesian Sequential Analysis - Review of Probability: Events and Sample Spaces, Unions - Intersections, Complements - Marginal and Conditional Probabilities - Bayes’ Rule - Addition and Multiplication Rules

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One-Parameter Models

Bayesian Models - Prior Probability and Prior Distributions - The Posterior Distribution - Conjugate Priors - Inference for a Population Proportion: Frequentist Approach, Bayesian Inference, Bayesian Point Estimates - R for Bayesian Analysis - Inference Using Nonconjugate Priors on Mean and Variance - Noninformative Priors

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Multiparameter Models

Informative Priors for Mean and Variance - Conjugate Joint Prior Density for Mean and Variance

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Model Fit using Markov Chain Monte Carlo (MCMC)

Sampling-Based Methods - Markov Chain Monte Carlo (MCMC) Methods - Bayesian Models - Hierarchical Models: Fitting Bayesian Hierarchical Models, Estimation Based on Hierarchical Models - Software OpenBUGS

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Regression and Hierarchical Regression Models

Review of Linear Regression - Introduction to Bayesian Simple Linear Regression - Generalized Linear Models - Hierarchical Normal Linear Models - Model Comparison, Model Checking, and Hypothesis Testing - Bayes Factors for Model Comparison and Hypothesis Testing - Bayes Factors and Bayesian Hypothesis Testing

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Data Mining and Classification in Bayesian Statistics

Statistics for Machine Learning - Learning as Inference - Principal Components Analysis - Naive Bayes - Nearest Neighbour Classification - Gaussian Processes

## Trainer

Marco Skulschus (born in Germany in 1978) studied economics in Wuppertal (Germany) and Paris (France) and wrote his master´s thesis about semantic data modeling. He started working as a lecturer and consultant in 2002.

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Publications

- Grundlagen empirische Sozialforschung ISBN 978-3-939701-23-1
- System und Systematik von Fragebögen ISBN 978-3-939701-26-2
- Oracle PL/SQL ISBN 978-3-939701-40-8
- MS SQL Server - T-SQL Programmierung und Abfragen ISBN 978-3-939701-69-9

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Projects

- He works as an IT-consultant and project manager. He developed various Business Intelligence systems for industry clients and the public sector. For several years now, he is responsible for a BI-team in India which is mainly involved in BI and OLAP projects, reporting systems as well as statistical analysis and Data Mining.

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Research

He led several research projects and was leading scientist and project manager of a publicly funded project about interactive questionnaires and online surveys.