Noel Cressie and Christopher WikleHardcover: 624 pagesYear: 2011Publisher: John WileyISBN-13: 978-0471692744Here is the new reference book about spatial and spatio-temporal statistical modeling! No...

Statistics for Spatio-Temporal Data

Statistics for spatial data: by Noel Cressie, 1991, John Wiley & Sons, New York, 900 p., ISBN 0-471-84336-9, US $89.95

Advances in surrogate based modeling, feasibility analysis, and optimization: A review

(2003). Statistical Process Adjustment for Quality Control. Technometrics: Vol. 45, No. 1, pp. 102-103.

Statistical Process Adjustment for Quality Control

MOBOpt — multi-objective Bayesian optimization

Finding the global optimum(s) of a non-convex function is of great importance in numerous applications in science and engineering where the function takes the form of an expensive computer code and its inputs are the independent variables. For this type of problem, Jones et al. [12] proposed the idea of expected improvement (EI) and embedded it in an algorithm called ecient global optimization, or EGO. Neither EI nor EGO consider the uncertainty in the parameter estimates. One way to account for these uncertainties is to use Bootstrapping. In this paper, instead, we formulate the expected improvement method from a fully Bayesian perspective which results in a corresponding Bayesian EGO method. The performance of the proposed Bayesian EGO is illustrated and compared with the standard EGO method of Jones et al. and the bootstrapped EGO of Kleijnen et al. [13]. Furthermore, we apply the Bayesian EGO algorithm for the optimization of a stochastic inventory simulation model.

/pdf/a-fully-bayesian-approach-to-the-efficient-global-4ta61ztojc.pdf

A Fully Bayesian Approach to the Efficient Global Optimization Algorithm

We present a new method for estimating multivariate, second-order stationary Gaussian Random Field (GRF) models based on the Sparse Precision matrix Selection (SPS) algorithm, proposed by Davanloo et al. (2015) for estimating scalar GRF models. Theoretical convergence rates for the estimated between-response covariance matrix and for the estimated parameters of the underlying spatial correlation function are established. Numerical tests using simulated and real datasets validate our theoretical findings. Data segmentation is used to handle large data sets.

Generalized Sparse Precision Matrix Selection for Fitting Multivariate Gaussian Random Fields to Large Data Sets

Iterative methods for fitting a Gaussian Random Field (GRF) model via maximum likelihood (ML) estimation requires solving a nonconvex optimization problem. The problem is aggravated for anisotropic GRFs where the number of covariance function parameters increases with the dimension. Even evaluation of the likelihood function requires $O(n^3)$ floating point operations, where $n$ denotes the number of data locations. In this paper, we propose a new two-stage procedure to estimate the parameters of second-order stationary GRFs. First, a convex likelihood problem regularized with a weighted $\ell_1$-norm, utilizing the available distance information between observation locations, is solved to fit a sparse precision (inverse covariance) matrix to the observed data. Second, the parameters of the covariance function are estimated by solving a least squares problem. Theoretical error bounds for the solutions of stage I and II problems are provided, and their tightness are investigated.

On the Theoretical Guarantees for Parameter Estimation of Gaussian Random Field Models: A Sparse Precision Matrix Approach

/pdf/generalized-sparse-precision-matrix-selection-for-fitting-4nx4cj1wjb.pdf

Generalized sparse precision matrix selection for fitting multivariate Gaussian random fields to large data sets

We propose a stochastic variance-reduced cubic regularized Newton algorithm for the finite-sum problem over Riemannian manifolds. The proposed algorithm requires full gradient and Hessian updates at the beginning of each epoch while it performs stochastic variance-reduced updates in the iterations within each epoch. The iteration complexity of the algorithm to attain an $(\epsilon,\delta)$-second order stationary point is shown to be $O(\max\{\epsilon^{-3/2},\delta^{-3}\})$. Furthermore, the paper proposes a computationally more appealing version of the algorithm which only requires inexact solution of the cubic regularized Newton subproblem with the same rate of convergence. Numerical results verify our theoretical findings. Furthermore, the performance of the proposed method is compared with other second-order optimization algorithms for Riemannian manifolds.

Riemannian Stochastic Variance-Reduced Cubic Regularized Newton Method

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