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Variance Reduction: Importance Sampling and Control Variates
Random Variables and Probability Distributions
Random Processes. Karhunen-Loève Expansions. Gaussian Processes.
Putting the Tools to Work: A €œReal€  Parameter Estimation Problem
Optimal low-rank approximations of Bayesian linear inverse problems
Monte Carlo Methods: Convergence Properties and Error Analysis. Basic Algorithms.
Markov Chain Monte Carlo Methods
Expectation, Covariance. Convergence of Random Variables. Laws of Large Numbers. Central Limit Theorem. Multivariate Gaussian.
Estimators and Confidence Sets. Least Squares.
Conditional Probability and Expectation, Bayes Theorem.
Bayes Risk, Prior Distributions, Summarizing the Posterior. Bayesian Gaussian Linear Model.
Bayesian Filtering. Sequential Monte Carlo.