Uncertainty Quantification in Engineering Science

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Unit 1
Bayesian Inference
Lecture 01 - Introduction to models and their uncertainty. Use of probability to quantify uncertainty with probability distributions. Important theorems from Probability Theory.
Creator: Costas Papadimitriou		 2014-10-09 
Lecture 02 - Measures of uncertainty in output quantities of interest. Bayes Theorem using observations, and example. Uncertainty propagation for the simple linear model case. Gaussian distribution.
Creator: Costas Papadimitriou		 2014-11-10 
Lecture 03 - Multivariate Gaussian distribution and its properties. Linear transformation of Gaussian vectors. Quadratic forms. Nonlinear model uncertainty propagation.
Creator: Costas Papadimitriou		 2014-11-14 
Lecture 04 - Uncertainty propagation for nonlinear models using Taylor series. Posterior system analysis. Likelihood function estimation.
Creator: Costas Papadimitriou		 2014-11-20 
Lecture 05 - Likelihood function construction. Bayesian Parameter Estimation for one-dimensional models. Taylor series approximation of the posterior pdf. Bayesian Central Limit Theorem.
Creator: Costas Papadimitriou		 2014-11-25 
Lecture 06 - Multi-dimensional Bayesian Parameter Estimation & Bayesian Central Limit Theorem. Taylor series expansions for many variables. Eigenvalue and eigenvector Hessian matrix analysis.
Creator: Costas Papadimitriou		 2014-12-11 
Lecture 07 - Application of multidimensional bayesian parameter estimation in curve fitting.
Creator: Costas Papadimitriou		 2014-12-12 
Lecture 08 - Example in uncertainty propagation using Gaussian approximations. Robust Posterior Predictions. Laplace asymptotic approximations of integrals.
Creator: Costas Papadimitriou		 2014-12-18 
Unit 2
Optimal Experimental Design
Lecture 09 - Shannon Information Entropy. Principle of Maximum Information Entropy for assigning probabilities.
Creator: Costas Papadimitriou		 2014-12-20 
Lecture 10 - Bayesian optimal experimental design for estimation of model parameters.
Creator: Costas Papadimitriou		 2015-01-07 
Lecture 11 - Optimal sensor placement for structural dynamics applications.
Creator: Costas Papadimitriou		 2015-01-07 
Unit 3
Sampling Techniques
Lecture 12 - Stochastic Simulation Algorithms for Bayesian Computations. Drawing samples from a pdf. Monte Carlo integration of important Bayesian integrals.
Creator: Costas Papadimitriou		 2015-01-08 
Lecture 13 - Markov Chain Monte Carlo algorithms. Metropolis-Hasting algorithm for probability distribution sampling. Uncertainty propagation using posterior samples.
Creator: Costas Papadimitriou		 2015-01-10