Statistical analysis and optimization of data
We plan to cover the following topics:
- Basic concepts, expectation values, variance, covariance, correlation functions and errors;
- Simpler models, binomial distribution, the Poisson distribution, simple and multivariate normal distributions;
- Central elements of Bayesian statistics and modeling;
- Gradient methods for data optimization;
- Monte Carlo methods, Markov chains, Gibbs sampling and Metropolis-Hastings sampling (tentative);
- Estimation of errors and resampling techniques such as the cross-validation, blocking, bootstrapping and jackknife methods;
- Principal Component Analysis (PCA) and its mathematical foundation;