REFERENCES (Under Construction)
1. 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
2. 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
3. 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.” PDF
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.” PDF
4. 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