Replication or exploration? Sequential design for stochastic simulation experiments

We investigate the merits of replication, and provide methods for optimal design (including replicates), with the goal of obtaining globally accurate emulation of noisy computer simulation experiments. We first show that replication can be beneficial from both design and computational perspectives, in the context of Gaussian process surrogate modeling. We then develop a lookahead based sequential design scheme that can determine if a new run should be at an existing input location (i.e., replicate) or at a new one (explore). When paired with a newly developed heteroskedastic Gaussian process model, our dynamic design scheme facilitates learning of signal and noise relationships which can vary throughout the input space. We show that it does so efficiently, on both computational and statistical grounds. In addition to illustrative synthetic examples, we demonstrate performance on two challenging real-data simulation experiments, from inventory management and epidemiology.Comment: 34 pages, 9 figure

Small-scale health-related indicator acquisition using secondary data spatial interpolation

<p>Abstract</p> <p>Background</p> <p>Due to the lack of small-scale neighbourhood-level health related indicators, the analysis of social and spatial determinants of health often encounter difficulties in assessing the interrelations of neighbourhood and health. Although secondary data sources are now becoming increasingly available, they usually cannot be directly utilized for analysis in other than the designed study due to sampling issues. This paper aims to develop data handling and spatial interpolation procedures to obtain small area level variables using the Canadian Community Health Surveys (CCHS) data so that meaningful small-scale neighbourhood level health-related indicators can be obtained for community health research and health geographical analysis.</p> <p>Results</p> <p>Through the analysis of spatial autocorrelation, cross validation comparison, and modeled effect comparison with census data, kriging is identified as the most appropriate spatial interpolation method for obtaining predicted values of CCHS variables at unknown locations. Based on the spatial structures of CCHS data, kriging parameters are suggested and potential small-area-level health-related indicators are derived. An empirical study is conducted to demonstrate the effective use of derived neighbourhood variables in spatial statistical modeling. Suggestions are also given on the accuracy, reliability and usage of the obtained small area level indicators, as well as further improvements of the interpolation procedures.</p> <p>Conclusions</p> <p>CCHS variables are moderately spatially autocorrelated, making kriging a valid method for predicting values at unsampled locations. The derived variables are reliable but somewhat smoother, with smaller variations than the real values. As potential neighbourhood exposures in spatial statistical modeling, these variables are more suitable to be used for exploring potential associations than for testing the significance of these associations, especially for associations that are barely significant. Given the spatial dependency of current health-related risks, the developed procedures are expected to be useful for other similar health surveys to obtain small area level indicators.</p

Strategies for Handling Spatial Uncertainty due to Discretization

Geographic information systems (GISs) allow users to analyze geographic phenomena within areas of interest that lead to an understanding of their relationships and thus provide a helpful tool in decision-making. Neglecting the inherent uncertainties in spatial representations may result in undesired misinterpretations. There are several sources of uncertainty contributing to the quality of spatial data within a GIS: imperfections (e.g., inaccuracy and imprecision) and effects of discretization. An example for discretization in the thematic domain is the chosen number of classes to represent a spatial phenomenon (e.g., air temperature). In order to improve the utility of a GIS an inclusion of a formal data quality model is essential. A data quality model stores, specifies, and handles the necessary data required to provide uncertainty information for GIS applications. This dissertation develops a data quality model that associates sources of uncertainty with units of information (e.g., measurement and coverage) in a GIS. The data quality model provides a basis to construct metrics dealing with different sources of uncertainty and to support tools for propagation and cross-propagation. Two specific metrics are developed that focus on two sources of uncertainty: inaccuracy and discretization. The first metric identifies a minimal?resolvable object size within a sampled field of a continuous variable. This metric, called detectability, is calculated as a spatially varying variable. The second metric, called reliability, investigates the effects of discretization on reliability. This metric estimates the variation of an underlying random variable and determines the reliability of a representation. It is also calculated as a spatially varying variable. Subsequently, this metric is used to assess the relationship between the influence of the number of sample points versus the influence of the degree of variation on the reliability of a representation. The results of this investigation show that the variation influences the reliability of a representation more than the number of sample points

Multi-Resolution Functional ANOVA for Large-Scale, Many-Input Computer Experiments

The Gaussian process is a standard tool for building emulators for both deterministic and stochastic computer experiments. However, application of Gaussian process models is greatly limited in practice, particularly for large-scale and many-input computer experiments that have become typical. We propose a multi-resolution functional ANOVA model as a computationally feasible emulation alternative. More generally, this model can be used for large-scale and many-input non-linear regression problems. An overlapping group lasso approach is used for estimation, ensuring computational feasibility in a large-scale and many-input setting. New results on consistency and inference for the (potentially overlapping) group lasso in a high-dimensional setting are developed and applied to the proposed multi-resolution functional ANOVA model. Importantly, these results allow us to quantify the uncertainty in our predictions. Numerical examples demonstrate that the proposed model enjoys marked computational advantages. Data capabilities, both in terms of sample size and dimension, meet or exceed best available emulation tools while meeting or exceeding emulation accuracy

Design Decisions Under Risk and Uncertainty

In the contemporary world of engineering, engineers strive towards designing reliable and robust artifacts while considering and attempting to control manufacturing costs. In due course they have to deal with some sort of uncertainty. Many aspects of the design are the result of properties that are defined within some tolerances, of measurements that are appropriate, and of circumstances and environmental conditions that are out of their control. This uncertainty was typically handled by using factors of safety, and resulted in designs that may have been overly conservative. Therefore, understanding and handling the uncertainties is critical in improving the design, controlling costs and optimizing the product. Since the engineers are typically trained to approach problems systematically, a stepwise procedure which handles uncertainties efficiently should be of significant benefit. This thesis revises the literature, defines some terms, then describes such a stepwise procedure, starting from identifying the sources of uncertainty, to classifying them, handling these uncertainties, and finally to decision making under uncertainties and risk. The document elucidates the methodology introduced by Departments of Mathematical Science and Mechanical Engineering, which considers the after effects of violation of a constraint as a criterion along with the reliability percentage of a design. The approach distinguishes between aleatory and epistemic uncertainties, those that can be assumed to have a certain distribution and those that can only be assumed to be within some bounds. It also attempts to deal with the computational cost issue by approximating the risk surface as a function of the epistemic uncertain variables. The validity of this hypothesis, for this particular problem, is tested by approximating risk surfaces using various numbers of scenarios

Optimisation of Mobile Communication Networks - OMCO NET

The mini conference “Optimisation of Mobile Communication Networks” focuses on advanced methods for search and optimisation applied to wireless communication networks. It is sponsored by Research & Enterprise Fund Southampton Solent University. The conference strives to widen knowledge on advanced search methods capable of optimisation of wireless communications networks. The aim is to provide a forum for exchange of recent knowledge, new ideas and trends in this progressive and challenging area. The conference will popularise new successful approaches on resolving hard tasks such as minimisation of transmit power, cooperative and optimal routing