Statistical Data Analysis for Practitioners

Statistical Data Analysis for Practitioners

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We introduce the basics of probability theory, classical statistics, and 
classical error analysis (p-values, confidence intervals), which serves as the starting point to explore modern methods of statistics (Maximum Likelihood, Bayes). We use these methods to extract information from noisy data through (non-) linear parameter estimation (fitting) and model comparison. We show how to analyze data containing dynamical information by time series analysis (correlation functions, error analysis) and Markov-Chain models and kinetic models described by rate equations.

Content

1. Crash course in statistics
     1. Elements of probability theory
     2. Central limit theorem and error of the mean
     3. Classical error analysis and error propagation
     4. Confidence intervals and p-values
     5. Statistical tests
     6. Maximum likelihood estimation
     7. Bayesian inference
 2. Model fitting
     1. Linear models
     2. Non-linear models
     3. Model comparison
 3. Time series analysis
     1. Autocorrelations
     2. Block-averaging
     3. Bootstrapping / Jackknifing
 4. Markov-chains and kinetic models
     1. Master equation
     2. Monte Carlo sampling
     3. Uncertainty quantification using Monte Carlo sampling

Goal of the course

To overarching goal is to equip the students with the necessary statistical tools to extract information from noisy data reliably and with quantified uncertainties. The students should be able to identify the common pitfalls of statistical data analysis in their own work and be able to critically assess the quality of published data and statistical analysis. These goals will be practised in the practical course on real world examples.

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