Statistics 204 Syllabus

• multivariate densities, change-of-variable formula

 
• multivariate normal and related distributions, symmetric positive definite matrices, Karhunen-Loeve expansion

 
• Poisson approximation, Stein-Chen method

 
• transforms (generation functions, Laplace transforms, characteristic functions)

 
• modes of convergence

 
• laws of large numbers, Glivenko-Cantelli theorem

 
• central limit theorem, normal approximation, delta method

 
• large deviations, entropy, information, relative entropy, Sanov's theorem

 
• Markov chains, Markov chain Monte Carlo methods, Metropolis algorithm, Gibbs sampler

 
• discrete-time martingales, martingale transforms, optional sampling, convergence theorems

 
• stationary processes, ergodic theorem, subadditive ergodic theorem, Shannon-McMillan-Breiman theorem

 
• Brownian motion, diffusions