Probability Distributions.- Linear Models for Regression.- Linear Models for Classification.- Neural Networks.- Kernel Methods.- Sparse Kernel Machines.- Graphical Models.- Mixture Models and EM.- Approximate Inference.- Sampling Methods.- Continuous Latent Variables.- Sequential Data.- Combining Models.

Pattern Recognition and Machine Learning

Statistics for Spatial Data.

Large linear systems of saddle point type arise in a wide variety of applications throughout computational science and engineering. Due to their indefiniteness and often poor spectral properties, such linear systems represent a significant challenge for solver developers. In recent years there has been a surge of interest in saddle point problems, and numerous solution techniques have been proposed for this type of system. The aim of this paper is to present and discuss a large selection of solution methods for linear systems in saddle point form, with an emphasis on iterative methods for large and sparse problems.

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Numerical solution of saddle point problems

Geotechnical variability is a complex attribute that results from many disparate sources of uncertainties. The three primary sources of geotechnical uncertainties are inherent variability, measurem...

Characterization of geotechnical variability

Adaptive sparse polynomial chaos expansion based on least angle regression

To evaluate geotechnical variability on a general basis that will facilitate the use of reliability-based design procedures, it is necessary to assess inherent soil variability, measurement error, ...

Evaluation of geotechnical property variability

Evaluation of Geotechnical Property Variability

Geotechnical variability is a complex attribute that results from many disparate sources of uncertainties. The three primary sources of geotechnical uncertainties are inherent variability, measurement error, and transformation uncertainty. Inherent soil variability is modeled as a random field, which can be described concisely by the coefficient of variation (COV) and scale of fluctuation. Measurement error is extracted from field measurements using a simple additive probabilistic model or is determined directly from comparative laboratory testing programs. Based on an extensive literature review, the COV of inherent variability, scale of fluctuation, and COV of measurement error are evaluated in detail, along with the general soil type and the approximate range of mean value for which the COVs are applicable. Transformation uncertainty and overall property uncertainty are quantified in a companion paper.Key words: inherent soil variability, measurement error, coefficient of variation, scale of fluctuatio...

Characterization of Geotechnical Variability

A random process can be represented as a series expansion involving a complete set of deterministic functions with corresponding random coefficients Karhunen–Loeve (K–L) series expansion is based on the eigen-decomposition of the covariance function Its applicability as a simulation tool for both stationary and non-stationary Gaussian random processes is examined numerically in this paper The study is based on five common covariance models The convergence and accuracy of the K–L expansion are investigated by comparing the second-order statistics of the simulated random process with that of the target process It is shown that the factors affecting convergence are: (a) ratio of the length of the process over correlation parameter, (b) form of the covariance function, and (c) method of solving for the eigen-solutions of the covariance function (namely, analytical or numerical) Comparison with the established and commonly used spectral representation method is made K–L expansion has an edge over the spectral method for highly correlated processes For long stationary processes, the spectral method is generally more efficient as the K–L expansion method requires substantial computational effort to solve the integral equation The main advantage of the K–L expansion method is that it can be easily generalized to simulate non-stationary processes with little additional effort Copyright © 2001 John Wiley & Sons, Ltd

Kok-Kwang Phoon

Papers

Characterization of geotechnical variability

Evaluation of geotechnical property variability

Evaluation of Geotechnical Property Variability

Characterization of Geotechnical Variability

Convergence study of the truncated Karhunen-Loeve expansion for simulation of stochastic processes