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