lectures on stochastic system analysis and bayesian updating open to any caltech student. register before friday, june 10 by emailing: sus

Lectures on Stochastic System Analysis and Bayesian Updating
Open to any Caltech student.
Register before Friday, June 10 by emailing: [email protected]
Wednesday June 29, 2005 - Wednesday July 13, 2005
9:00 am – Noon each Caltech work day
206 Thomas Building, Caltech
James L. Beck, Caltech
Jianye Ching, National Taiwan University of Science and Technology
Siu-Kui Au, Nanyang Technological University, Singapore
This is a new course that the lecturers are jointly preparing that
focuses on stochastic system analysis and Bayesian updating. We will
discuss the interpretation of probability as a logic for plausible
reasoning with incomplete information; Bayesian updating of models of
a system to predict its future behavior based on measured response,
including new stochastic simulation techniques; model class selection
with a new information-theoretic interpretation that shows that it
gives a quantitative principle of model parsimony; recently-developed
stochastic simulation techniques for evaluating the response of
stochastic dynamical systems subject to stochastic excitations;
Bayesian sequential estimation of system states and model parameters;
and other topics.
Course Description:
1. Introduction [Beck]
Big picture: knowledge models, information processing, decision
making; general class of stochastic state-space models for dynamical
systems; conversion of continuous-time stochastic DE to one-step ahead
discrete-time predictive PDF; nominal vs robust analysis; basic
problems to be addressed in course.
2. Basic concepts in probability and information [Beck]
Probability as a multi-valued logic for plausible reasoning with
incomplete information; some history of its origins: Bayes, Laplace,
Jeffreys, Cox, Jaynes; Cox’s derivation of probability axioms for
statements; Kolmogorov axioms for the special case of sets;
probability models for discrete and continuous variables;
marginalization and theorem of total probability; irrelevant
information and independence; quantifying missing information using
probability; Kullback-Liebler relative information; mutual
information; information entropy; principle of maximum entropy and
exponential family of PDFs.
3. Stochastic predictive analysis theory for single model class [Beck]
Basic ingredients: model class of predictive PDFs with prior PDFs;
illustrative examples of probability model classes; initial (prior)
predictive analysis; Bayesian model updating: block and sequential
modes; updated (posterior) predictive analysis; asymptotic
approximations for prior and posterior predictive analysis:
identifiability and domain of applicability of parameter estimation
(e.g. maximum likelihood); illustrative examples, including linear and
nonlinear dynamics in time and frequency domains.
4. Stochastic predictive analysis theory for multiple model classes
[Beck]
Prior and posterior predictive analysis with set of model classes
(model averaging); Bayesian updating for model class selection and its
intrinsic principle of parsimony, with an information-theoretic
interpretation; large-sample approximations: Ockham factor and BIC;
choice of prior PDFs, including non-informative priors, Jeffrey
priors, conjugate priors and maximum entropy priors; illustrative
examples of model class selection for dynamical systems.
5. Stochastic system analysis for rare events: approximate analytical
methods [Au]
Reliability theory and first-order and second-order approximate
methods for calculating failure probabilities for static problems;
first-passage probabilities for dynamical systems under stochastic
excitation: approximate calculation using Rice’s out-crossing theory
and application to linear dynamical systems using Liapunov’s equation.
6. Stochastic system analysis for rare events: stochastic simulation
methods [Au]
Basic Monte Carlo simulation, limiting properties of estimators;
simulation of stochastic processes; variance reduction techniques:
importance sampling; ISEE method for first-passage probabilities for
linear dynamical systems; Markov Chain Monte Carlo methods and
Metropolis-Hastings algorithm; Subset Simulation and illustrative
example of structural dynamics under seismic risk with failure
analysis.
7. Stochastic simulation methods for Bayesian updating [Ching]
Gibbs sampler with adaptive rejection sampling; hybrid Monte Carlo;
slice sampling; multi-level Metropolis-Hastings with re-sampling;
Bayesian model class selection; illustrative examples for model
updating of linear dynamical systems.
8. Bayesian updating for sequential state and parameter estimation
[Ching]
Graphical representation of probability models; uncertainty
propagation for general systems using moment-matching and maximum
entropy; Kalman filter and smoother for linear systems; extended
Kalman filter and unscented Kalman filter for nonlinear systems;
stochastic simulation methods: particle filter and smoother.
9. Other Topics
If time is available other topics will be covered, such as Bayesian
linear regression and classification [Ching] and research on
reliability-based robust stochastic control [Beck].

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