Principles of uncertainty

Data. Summarizing data. Visualizing data. The fundamental problem of data analysis: uncertainty in our understanding of the data generating process.

Probability. The axiomatic, Bayesian and classical (frequentist) views of probability. Joint, marginal and conditional densities. Bayes theorem.

Distributions. Common probability distributions. Distributions as a means for expressing probabilistic opinions. Distributions as data generators.

Fundamental statistical techniques. Monte Carlo integration. Bootstrap. Maximum likelihood estimation. Bayesian inference.

Basic statistical tasks. Hypothesis testing vs Bayesian estimation.

The multivariate normal distribution. As a linear transformation. Linear regression. PCA.