James L. Beck
George W. Housner Professor of Engineering and Applied Science
Department of Computing and Mathematical Sciences
Department of Mechanical and Civil Engineering

Summer Lectures at Caltech on Stochastic System Analysis and Bayesian Updating (2005)

References:

Probability Logic and Information

Cox, R.T. (1961). "The algebra of probable inference." On reserve at SFL

Cox, R.T. (1946). "Probability, frequency and reasonable expectation." (pdf)

Jaynes, E.T. (1983). "Papers on probability statistics and statistical physics." (Rosenkrantz, R.D. (Ed.))

Jeffreys, H. (1961). "Theory of probability, 3rd Edn." On reserve at SFL

Jaynes, E.T. (2003). "Probability theory: The logic of science." On reserve at SFL

Jaynes, E.T. (1957). "Information theory and statistical mechanics." (pdf)

Cover, T.M, and Thomas, J.A. (1991). "Elements of information theory." On reserve at SFL

Sivia, D.S. (1996). "Data analysis: a Bayesian tutorial." On reserve at SFL

Robust Predictive Analysis and Bayesian Updating

Beck, J.L., and Yuen, K.V. (2004). "Model selection using response measurements: Bayesian probabilistic approach" (pdf)

Beck, J.L., and Katafygiotis, L.S. (1998). "Updating models and their uncertainties. I: Bayesian statistical framework." (pdf)

Papadimitriou, C., Beck, J.L., and Katafygiotis, L.S. (1997). "Asymptotic expansions for reliability and moments of uncertain systems." (pdf)

Yuen, K.V., and Beck, J.L. (2003). "Updating properties of nonlinear dynamical systems with uncertain input." (pdf)

Papadimitriou, C., Beck, J.L., and Katafygiotis, L.S. (2001). "Updating robust reliability using structural test data." (pdf)

Au, S.K, Papadimitriou, C., and Beck, J.L. (1999). "Reliability of uncertain dynamical systems with multiple design points." (pdf)

Katafygiotis, L., and Lam, H.F (2002). "Tangential-projection algorithm for manifold representation in unidentifiable model updating problems." (pdf)
 

Stochastic Simulation

Rubinstein, R. V. (1981). "Simulation and the Monte Carlo Method." Wiley Series in Probability and Mathematical Statistics, John Wiley & Sons.

Robert, C. P., and Casella, G. (1999). "Monte Carlo Statistical Methods." Springer Texts in Statistics, Springer.

Mackay, J.D.C. "Introduction to Monte Carlo methods." (pdf)

Au, S.K, and Beck, J.L. (2001). "First excursion probabilities for linear systems by very efficient importance sampling." (pdf)

Au, S.K, and Beck, J.L. (2001). "Estimation of small failure probabilities in high dimensions by subset simulation." (pdf)

Au, S. K., and Beck, J.L. (2003). "Subset simulation and its applications to seismic risk based on dynamic analysis."

Beirlant, J., Dudewicz, E.J., Gyorfi, L., and van der Meulen, E.C. (2001). "Nonparametric entropy estimation: an overview." (pdf)

Gelfand, A.E, Hills, S.E, Racine-Poon, A., and Smith, A.F.M. (1990). "Illustration of Bayesian inference in normal data models using Gibbs sampler."
 

Bayesian Sequential Estimation

Doucet, A., Godsill, J.S., and Andrieu, C. "On sequential Monte Carlo sampling methods for Bayesian filtering." (pdf)

Godsill, J.S., Doucet, A., and West, M. (2002). "Monte Carlo smoothing for non-linear time series." (pdf)

Julier, S.J, and Uhlmann, J.K. "A new extension of the Kalman filter to nonlinear systems." (pdf)

Ching, J., Beck, J.L, and Porter, K.A. (2005). "Bayesian state and parameter estimation of uncertain dynamical systems. (pdf)