- You will understand basic principles, assumptions and limitations of statistical data analysis in the physical sciences
- You will be able to apply statistical methods in the analysis and interpretation of experimental results
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The course will cover the following topics:
• Basic properties of probability (density) functions (Moments, Characteristic function, Commonly used functions)
• Describing the outcome of an experiment as a random variable (Central limit theorem, Law of large numbers)
• Parameter estimation (Criteria of quality of parameter estimation, Estimation of expected value and variance from experimental data (direct and indirect measurements))
• Method of moments, Maximum likelihood, Information and the Cramer-Rao minimum variance bound)
• Fits of experimental data (Least squares and linear least squares, Assessing quality of fit and χ2-distribution)
• Confidence intervals (One-sided / two-sided / multi-dimensional, Bayesian reasoning)
• Hypothesis testing (Errors of the first and second kind, Simple and composite hypothesis, p-value, Comparison of two normally distributed samples, Student’s t-distribution)
• Other statistical tests (Run, Kolmogorov-Smirnov)
Instructional Modes
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| Numerical Methods and basic programming skills (MATLAB, C++, or Python) |
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The exam consists of two parts:
- A take-home part, which is intended to test one's ability to solve a practical statistical inference problem numerically.
- An oral part, which is meant to test one's theoretical understanding.
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