Class hour/credit: 40 hours/2
Preparatory courses： theory of probability and statistics, Introduction to astronomy
Purpose of the course: Know how to analyze the observational astronomical data with modern statistical approaches, know how to program in python.
Chapter 1: Introduction to statistics
Chapter 2: The principle concept of probability. Univariate/multivariate probability distributions, Introduction to python and basics about dealing astronomical data in python, basic graphics in python.
Chapter 3: random sampling. Using random sampling to estimate a probability distribution, rejection sampling, Gibbs sampling, Metropolis sampling, Markov chain Monte Carlo sampling.
Chapter 4: Single parameter models. Single parameter Bayesian modeling. Binomial model, Normal model for mean value with known variance, normal model for variance with known mean value.
Chapter 5: Multiple parameters models: multi-parameter Bayesian modeling. Gaussian models with various prior distributions.
Chapter 6: Hierarchical models: Hierarchical normal model, application of hierarchical modeling in astronomy.
Chapter 7: Bayesian modeling. Bayesian regression, Bayesian forward modeling.
Chapter 8: Introduction to machine learning. Supervised machine learning (Bayesian classification, artificial neural networks, support vector machine), unsupervised learning (artificial neural networks).
Chapter 9: Error analysis. Error propagations, bootstrapping, Jack’s knife.
Chapter 10: Summarizing.
Contribution of scores: 50% homework, 50% final exam.