Improving PSF modelling for weak gravitational lensing using new methods in model selection

A simple theoretical framework for the description and interpretation of spatially correlated modelling residuals is presented, and the resulting tools are found to provide a useful aid to model selection in the context of weak gravitational lensing. The description is focused upon the specific problem of modelling the spatial variation of a telescope point spread function (PSF) across the instrument field of view, a crucial stage in lensing data analysis, but the technique may be used to rank competing models wherever data are described empirically. As such it may, with further development, provide useful extra information when used in combination with existing model selection techniques such as the Akaike and Bayesian Information Criteria, or the Bayesian evidence. Two independent diagnostic correlation functions are described and the interpretation of these functions demonstrated using a simulated PSF anisotropy field. The efficacy of these diagnostic functions as an aid to the correct choice of empirical model is then demonstrated by analyzing results for a suite of Monte Carlo simulations of random PSF fields with varying degrees of spatial structure, and it is shown how the diagnostic functions can be related to requirements for precision cosmic shear measurement. The limitations of the technique, and opportunities for improvements and applications to fields other than weak gravitational lensing, are discussed.Comment: 18 pages, 12 figures. Modified to match version accepted for publication in MNRA

Practice makes the model: a critical review of stormwater green infrastructure modelling practice

Green infrastructures (GIs) have in recent decades emerged as sustainable technologies for urban stormwater management, and numerous studies have been conducted to develop and improve hydrological models for GIs. This review aims to assess current practice in GI hydrological modelling, encompassing the selection of model structure, equations, model parametrization and testing, uncertainty analysis, sensitivity analysis, the selection of objective functions for model calibration, and the interpretation of modelling results. During a quantitative and qualitative analysis, based on a paper analysis methodology applied across a sample of 270 published studies, we found that the authors of GI modelling studies generally fail to justify their modelling choices and their alignments between modelling objectives and methods. Some practices, such as uncertainty analysis, were also found to be limited, despite their necessity being widely acknowledged by the scientific community and their application in other fields. In order to improve current GI modelling practice, the authors suggest the following: i) a framework, called STAMP, designed to promote the standardisation of the documentation of GI modelling studies, and ii) improvements in modelling tools for facilitating good practices, iii) the sharing of data for better model testing, iv) the evaluation of the suitability of hydrological equations for GI application, v) the publication of clear statements regarding model limitations and negative results.publishedVersio

A Model Selection Procedure for Stream Re-Aeration Coefficient Modelling

Model selection is finding wide applications in a lot of modelling and environmental problems. However, applications of model selection to re-aeration coefficient studies are still limited. The current study explores the use of model selection in re-aeration coefficient studies by combining several suggestions from numerous authors on the interpretation of data regarding re-aeration coefficient modelling. The model selection procedure applied in this research made use of Akaike information criteria, measures of agreement such as percent bias (PBIAS), Nash-Sutcliffe Efficiency (NSE) and root mean square error (RMSE) observation Standard deviation Ratio (RSR) and gragh analysis in selecting the best performing model. An algorithm prescribing a generic model selection procedure was also provided. Out of ten candidates models used in this study, the O’Connor and Dobbins (1958) model emerged as the top performing model in its application to data collected from River Atuwara in Nigeria. The suggested process could save software and model developers lots of time and resources, which would otherwise be spent in investigating and developing new models. The procedure is also ideal in selecting a model in situations where there is no overwhelming support for any particular model by observed data

Modelling Lorenz Curves:robust and semi-parametric issues

Modelling Lorenz curves (LC) for stochastic dominance comparisons is central to the analysis of income distribution. It is conventional to use non-parametric statistics based on empirical income cumulants which are in the construction of LC and other related second-order dominance criteria. However, although attractive because of its simplicity and its apparent flexibility, this approach suffers from important drawbacks. While no assumptions need to be made regarding the data-generating process (income distribution model), the empirical LC can be very sensitive to data particularities, especially in the upper tail of the distribution. This robustness problem can lead in practice to 'wrong' interpretation of dominance orders. A possible remedy for this problem is the use of parametric or semi-parametric models for the datagenerating process and robust estimators to obtain parameter estimates. In this paper, we focus on the robust estimation of semi parametric LC and investigate issues such as sensitivity of LC estimators to data contamination (Cowell and Victoria-Feser 2002), trimmed LC (Cowell and Victoria-Feser 2006) and inference for trimmed LC (Cowell and Victoria-Feser 2003), robust semi-parametric estimation for LC (Cowell and Victoria-Feser 2007) selection of optimal thresholds for (robust) semi parametric modelling (Dupuis and Victoria-Feser 2006) and use both simulations and real data to illustrate these points.

Robust optimisation and its application to portfolio planning

This thesis was submitted for the degree of Doctor of Philosophy and awarded by Brunel University.Decision making under uncertainty presents major challenges from both modelling and solution methods perspectives. The need for stochastic optimisation methods is widely recognised; however, compromises typically have to be made in order to develop computationally tractable models. Robust optimisation is a practical alternative to stochastic optimisation approaches, particularly suited for problems in which parameter values are unknown and variable. In this thesis, we review robust optimisation, in which parameter uncertainty is defined by budgeted polyhedral uncertainty sets as opposed to ellipsoidal sets, and consider its application to portfolio selection. The modelling of parameter uncertainty within a robust optimisation framework, in terms of structure and scale, and the use of uncertainty sets is examined in detail. We investigate the effect of different definitions of the bounds on the uncertainty sets. An interpretation of the robust counterpart from a min-max perspective, as applied to portfolio selection, is given. We propose an extension of the robust portfolio selection model, which includes a buy-in threshold and an upper limit on cardinality. We investigate the application of robust optimisation to portfolio selection through an extensive empirical investigation of cost, robustness and performance with respect to risk-adjusted return measures and worst case portfolio returns. We present new insights into modelling uncertainty and the properties of robust optimal decisions and model parameters. Our experimental results, in the application of portfolio selection, show that robust solutions come at a cost, but in exchange for a guaranteed probability of optimality on the objective function value, significantly greater achieved robustness, and generally better realisations under worst case scenarios

The stellar evolution of Luminous Red Galaxies, and its dependence on colour, redshift, luminosity and modelling

We present a series of colour evolution models for Luminous Red Galaxies (LRGs) in the 7th spectroscopic data release of the Sloan Digital Sky Survey (SDSS), computed using the full-spectrum fitting code VESPA on high signal-to-noise stacked spectra. The colour-evolution models are computed as a function of colour, luminosity and redshift, and we do not a-priori assume that LRGs constitute a uniform population of galaxies in terms of stellar evolution. By computing star-formation histories from the fossil record, the measured stellar evolution of the galaxies is decoupled from the survey's selection function, which also evolves with redshift. We present these evolutionary models computed using three different sets of Stellar Population Synthesis (SPS) codes. We show that the traditional fiducial model of purely passive stellar evolution of LRGs is broadly correct, but it is not sufficient to explain the full spectral signature. We also find that higher-order corrections to this model are dependent on the SPS used, particularly when calculating the amount of recent star formation. The amount of young stars can be non-negligible in some cases, and has important implications for the interpretation of the number density of LRGs within the selection box as a function of redshift. Dust extinction, however, is more robust to the SPS modelling: extinction increases with decreasing luminosity, increasing redshift, and increasing r-i colour. We are making the colour evolution tracks publicly available at http://www.icg.port.ac.uk/~tojeiror/lrg_evolution/.Comment: 29 pages, 34 figures, re-submitted to MNRAS after addressing the referee's repor

A ‘How to’ Guide for Interpreting Parameters in Habitat-Selection Analyses

Habitat-selection analyses allow researchers to link animals to their environment via habitat-selection or step-selection functions, and are commonly used to address questions related to wildlife management and conservation efforts. Habitat-selection analyses that incorporate movement characteristics, referred to as integrated step-selection analyses, are particularly appealing because they allow modelling of both movement and habitat-selection processes. Despite their popularity, many users struggle with interpreting parameters in habitat-selection and step-selection functions. Integrated step-selection analyses also require several additional steps to translate model parameters into a full-fledged movement model, and the mathematics supporting this approach can be challenging for many to understand. Using simple examples, we demonstrate how weighted distribution theory and the inhomogeneous Poisson point process can facilitate parameter interpretation in habitat-selection analyses. Furthermore, we provide a ‘how to’ guide illustrating the steps required to implement integrated step-selection analyses using the AMT package By providing clear examples with open-source code, we hope to make habitat-selection analyses more understandable and accessible to end users

Population thinking and natural selection in dual-inheritance theory

A deflationary perspective on theories of cultural evolution, in particular dual-inheritance theory, has recently been proposed by Lewens. On this ‘pop-culture’ analysis, dual-inheritance theorists apply population thinking to cultural phenomena, without claiming that cultural items evolve by natural selection. This paper argues against this pop-culture analysis of dual-inheritance theory. First, it focuses on recent dual-inheritance models of specific patterns of cultural change. These models exemplify population thinking without a commitment to natural selection of cultural items. There are grounds, however, for doubting the added explanatory value of the models in their disciplinary context—and thus grounds for engaging in other potentially explanatory projects based on dual-inheritance theory. One such project is suggested by advocates of the theory. Some of the motivational narratives that they offer can be interpreted as setting up an adaptationist project with regard to cumulative change in cultural items. We develop this interpretation here. On it, dual-inheritance theory features two interrelated selection processes, one on the level of genetically inherited learning mechanisms, another on the level of the cultural items transmitted through these mechanisms. This interpretation identifies a need for further modelling efforts, but also offers scope for enhancing the explanatory power of dual-inheritance theory

Effect of Methodological and Ecological Approaches on Heterogeneity of Nest-Site Selection of a Long-Lived Vulture

The application of scientific-based conservation measures requires that sampling methodologies in studies modelling similar ecological aspects produce comparable results making easier their interpretation. We aimed to show how the choice of different methodological and ecological approaches can affect conclusions in nest-site selection studies along different Palearctic meta-populations of an indicator species. First, a multivariate analysis of the variables affecting nest-site selection in a breeding colony of cinereous vulture (Aegypius monachus) in central Spain was performed. Then, a meta-analysis was applied to establish how methodological and habitat-type factors determine differences and similarities in the results obtained by previous studies that have modelled the forest breeding habitat of the species. Our results revealed patterns in nesting-habitat modelling by the cinereous vulture throughout its whole range: steep and south-facing slopes, great cover of large trees and distance to human activities were generally selected. The ratio and situation of the studied plots (nests/random), the use of plots vs. polygons as sampling units and the number of years of data set determined the variability explained by the model. Moreover, a greater size of the breeding colony implied that ecological and geomorphological variables at landscape level were more influential. Additionally, human activities affected in greater proportion to colonies situated in Mediterranean forests. For the first time, a meta-analysis regarding the factors determining nest-site selection heterogeneity for a single species at broad scale was achieved. It is essential to homogenize and coordinate experimental design in modelling the selection of species' ecological requirements in order to avoid that differences in results among studies would be due to methodological heterogeneity. This would optimize best conservation and management practices for habitats and species in a global context