Results for STATS310

This is the first of a two course sequence on modern Bayesian statistics. Topics covered include: real world examples of large scale Bayesian analysis; basic tools (models, conjugate priors and their mixtures); Bayesian estimates, tests and credible intervals; foundations (axioms, exchangeability, likelihood principle); Bayesian computations (Gibbs sampler, data augmentation, etc.); prior specification. Prerequisites: statistics and probability at the level of Stats300A, Stats305, and Stats310.

Mathematical tools: sigma algebras, measure theory, connections between coin tossing and Lebesgue measure, basic convergence theorems. Probability: independence, Borel-Cantelli lemmas, almost sure and Lp convergence, weak and strong laws of large numbers. Large deviations. Weak convergence; central limit theorems; Poisson convergence; Stein's method. Prerequisites: 116, MATH 171.

Conditional expectations, discrete time martingales, stopping times, uniform integrability, applications to 0-1 laws, Radon-Nikodym Theorem, ruin problems, etc. Other topics as time allows selected from (i) local limit theorems, (ii) renewal theory, (iii) discrete time Markov chains, (iv) random walk theory,n(v) ergodic theory. Prerequisite: 310A or MATH 230A.

Continuous time stochastic processes: martingales, Brownian motion, stationary independent increments, Markov jump processes and Gaussian processes. Invariance principle, random walks, LIL and functional CLT. Markov and strong Markov property. Infinitely divisible laws. Some ergodic theory. Prerequisite: 310B or MATH 230B. http://statweb.stanford.edu/~adembo/stat-310c/

This is the first of a two course sequence on modern Bayesian statistics. Topics covered include: real world examples of large scale Bayesian analysis; basic tools (models, conjugate priors and their mixtures); Bayesian estimates, tests and credible intervals; foundations (axioms, exchangeability, likelihood principle); Bayesian computations (Gibbs sampler, data augmentation, etc.); prior specification. Prerequisites: statistics and probability at the level of Stats300A, Stats305, and Stats310.