Statistical analysis of multivariate computer output

Many scientific investigations rely on computer models for simulating plausible real situations. In trying to describe the complexities of reality, some computer models are themselves very complex and are therefore expensive to run. In response to some of these issues, a recent approach proposes to use statistical models as less computationally demanding surrogates of such complex computer models. The statistical surrogates do not exactly match the computer model output in a new situation, but these have the capability to describe the associated uncertainty. Ideally, the completed statistical model would not require as many computational resources as the original computer model.;Chapter 1 surveys briefly the literature related to the statistical analysis of computer experiments. While most applications implementing the above statistical methodology deal with scalar output, this dissertation suggests methodologies for analyzing multivariate computer output. In particular, Chapter 2 implements a method for the statistical analysis of time series produced by finite difference solvers of differential equations. This statistical model makes use of the underlying code information and, as a result, is second-order non-stationary. The Lotka-Volterra competing species differential system is used as an example to illustrate the methods. It is shown that the statistical model proposed here is more accurate than a statistical model that extends directly the existing scalar methodology to the multivariate case. However, the method is useful only in cases where the output can be easily saved and manipulated numerically. Chapter 3 suggests a two-stage method for the analysis of multivariate computer output in cases when at least one dimension is large, in particular when the number of temporal points is large. A double-gyre ocean system of partial differential equations is used to illustrate this method. Chapter 4 outlines preliminary work on two additional methodologies concerning the statistical analysis of multivariate computer output

Parameter estimation for computationally intensive nonlinear regression with an application to climate modeling

Nonlinear regression is a useful statistical tool, relating observed data and a nonlinear function of unknown parameters. When the parameter-dependent nonlinear function is computationally intensive, a straightforward regression analysis by maximum likelihood is not feasible. The method presented in this paper proposes to construct a faster running surrogate for such a computationally intensive nonlinear function, and to use it in a related nonlinear statistical model that accounts for the uncertainty associated with this surrogate. A pivotal quantity in the Earth's climate system is the climate sensitivity: the change in global temperature due to doubling of atmospheric $\mathrm{CO}_2$ concentrations. This, along with other climate parameters, are estimated by applying the statistical method developed in this paper, where the computationally intensive nonlinear function is the MIT 2D climate model.Comment: Published in at http://dx.doi.org/10.1214/08-AOAS210 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

Statistical analysis of multivariate computer output

Many scientific investigations rely on computer models for simulating plausible real situations. In trying to describe the complexities of reality, some computer models are themselves very complex and are therefore expensive to run. In response to some of these issues, a recent approach proposes to use statistical models as less computationally demanding surrogates of such complex computer models. The statistical surrogates do not exactly match the computer model output in a new situation, but these have the capability to describe the associated uncertainty. Ideally, the completed statistical model would not require as many computational resources as the original computer model.;Chapter 1 surveys briefly the literature related to the statistical analysis of computer experiments. While most applications implementing the above statistical methodology deal with scalar output, this dissertation suggests methodologies for analyzing multivariate computer output. In particular, Chapter 2 implements a method for the statistical analysis of time series produced by finite difference solvers of differential equations. This statistical model makes use of the underlying code information and, as a result, is second-order non-stationary. The Lotka-Volterra competing species differential system is used as an example to illustrate the methods. It is shown that the statistical model proposed here is more accurate than a statistical model that extends directly the existing scalar methodology to the multivariate case. However, the method is useful only in cases where the output can be easily saved and manipulated numerically. Chapter 3 suggests a two-stage method for the analysis of multivariate computer output in cases when at least one dimension is large, in particular when the number of temporal points is large. A double-gyre ocean system of partial differential equations is used to illustrate this method. Chapter 4 outlines preliminary work on two additional methodologies concerning the statistical analysis of multivariate computer output.</p

Trends of Summer Air Temperatures in the Romanian Carpathians Detected by Using a Serially Correlated Errors Model

This paper investigates summer temperature trends in the Romanian Carpathian Mountains, for three types of topographies: summit, slope and depression. We used a change-point regression model with serially correlated errors and compared it with a mainstream change-point model with independent errors. Statistical theory ensures that the former model gives a more accurate trend analysis than the latter model. For both models we identified strongly decreasing trends before the change-point and strongly increasing trends afterwards for most summer temperature series. The change-points are more consistent with each other, in the early 80’s, when using the former model. These general results occur for all topography types. A separate multiple regression model reveals that the temperature dynamics in the Romanian Carpathians can be explained by a linear effect of several major atmospheric circulation pattern

A Variable-Size Local Domain Approach to Computer Model Validation in Design Optimization

A common approach to the validation of simulation models focuses on validation throughout the entire design space. A more recent methodology validates designs as they are generated during a simulation-based optimization process. The latter method relies on validating the simulation model in a sequence of local domains. To improve its computational efficiency, this paper proposes an iterative process, where the size and shape of local domains at the current step are determined from a parametric bootstrap methodology involving maximum likelihood estimators of unknown model parameters from the previous step. Validation is carried out in the local domain at each step. The iterative process continues until the local domain does not change from iteration to iteration during the optimization process ensuring that a converged design optimum has been obtained. The proposed methodology is illustrated using a thermal, one-dimensional, linear heat conduction problem in a solid slab with heat flux boundary conditionsUpprättat;2011;20110822 (andbra); Konferensartikel i tidskrift;Bibliografisk uppgift: Paper Presented At: SAE 2011 World Congress &amp; Exhibition ,2011-04-12 ,Detroit, Michigan, United States.</p