Should the advanced measurement approach be replaced with the standardized measurement approach for operational risk?

Recently, Basel Committee for Banking Supervision proposed to replace all approaches, including Advanced Measurement Approach (AMA), for operational risk capital with a simple formula referred to as the Standardised Measurement Approach (SMA). This paper discusses and studies the weaknesses and pitfalls of SMA such as instability, risk insensitivity, super-additivity and the implicit relationship between SMA capital model and systemic risk in the banking sector. We also discuss the issues with closely related operational risk Capital-at-Risk (OpCar) Basel Committee proposed model which is the precursor to the SMA. In conclusion, we advocate to maintain the AMA internal model framework and suggest as an alternative a number of standardization recommendations that could be considered to unify internal modelling of operational risk. The findings and views presented in this paper have been discussed with and supported by many OpRisk practitioners and academics in Australia, Europe, UK and USA, and recently at OpRisk Europe 2016 conference in London

Robust Subspace Learning: Robust PCA, Robust Subspace Tracking, and Robust Subspace Recovery

PCA is one of the most widely used dimension reduction techniques. A related easier problem is "subspace learning" or "subspace estimation". Given relatively clean data, both are easily solved via singular value decomposition (SVD). The problem of subspace learning or PCA in the presence of outliers is called robust subspace learning or robust PCA (RPCA). For long data sequences, if one tries to use a single lower dimensional subspace to represent the data, the required subspace dimension may end up being quite large. For such data, a better model is to assume that it lies in a low-dimensional subspace that can change over time, albeit gradually. The problem of tracking such data (and the subspaces) while being robust to outliers is called robust subspace tracking (RST). This article provides a magazine-style overview of the entire field of robust subspace learning and tracking. In particular solutions for three problems are discussed in detail: RPCA via sparse+low-rank matrix decomposition (S+LR), RST via S+LR, and "robust subspace recovery (RSR)". RSR assumes that an entire data vector is either an outlier or an inlier. The S+LR formulation instead assumes that outliers occur on only a few data vector indices and hence are well modeled as sparse corruptions.Comment: To appear, IEEE Signal Processing Magazine, July 201

GREAT3 results I: systematic errors in shear estimation and the impact of real galaxy morphology

We present first results from the third GRavitational lEnsing Accuracy Testing (GREAT3) challenge, the third in a sequence of challenges for testing methods of inferring weak gravitational lensing shear distortions from simulated galaxy images. GREAT3 was divided into experiments to test three specific questions, and included simulated space- and ground-based data with constant or cosmologically-varying shear fields. The simplest (control) experiment included parametric galaxies with a realistic distribution of signal-to-noise, size, and ellipticity, and a complex point spread function (PSF). The other experiments tested the additional impact of realistic galaxy morphology, multiple exposure imaging, and the uncertainty about a spatially-varying PSF; the last two questions will be explored in Paper II. The 24 participating teams competed to estimate lensing shears to within systematic error tolerances for upcoming Stage-IV dark energy surveys, making 1525 submissions overall. GREAT3 saw considerable variety and innovation in the types of methods applied. Several teams now meet or exceed the targets in many of the tests conducted (to within the statistical errors). We conclude that the presence of realistic galaxy morphology in simulations changes shear calibration biases by $\sim 1$ per cent for a wide range of methods. Other effects such as truncation biases due to finite galaxy postage stamps, and the impact of galaxy type as measured by the S\'{e}rsic index, are quantified for the first time. Our results generalize previous studies regarding sensitivities to galaxy size and signal-to-noise, and to PSF properties such as seeing and defocus. Almost all methods' results support the simple model in which additive shear biases depend linearly on PSF ellipticity.Comment: 32 pages + 15 pages of technical appendices; 28 figures; submitted to MNRAS; latest version has minor updates in presentation of 4 figures, no changes in content or conclusion

Estimating photometric redshifts with artificial neural networks

A new approach to estimating photometric redshifts - using Artificial Neural Networks (ANNs) - is investigated. Unlike the standard template-fitting photometric redshift technique, a large spectroscopically-identified training set is required but, where one is available, ANNs produce photometric redshift accuracies at least as good as and often better than the template-fitting method. The Bayesian priors on the underlying redshift distribution are automatically taken into account. Furthermore, inputs other than galaxy colours - such as morphology, angular size and surface brightness - may be easily incorporated, and their utility assessed. Different ANN architectures are tested on a semi-analytic model galaxy catalogue and the results are compared with the template-fitting method. Finally the method is tested on a sample of ~ 20000 galaxies from the Sloan Digital Sky Survey. The r.m.s. redshift error in the range z < 0.35 is ~ 0.021.Comment: Submitted to MNRAS, 9 pages, 9 figures, substantial improvements to paper structur

Marked decline in forest-dependent small mammals following habitat loss and fragmentation in an Amazonian deforestation frontier

Agricultural frontier expansion into the Amazon over the last four decades has created million hectares of fragmented forests. While many species undergo local extinctions within remaining forest patches, this may be compensated by native species from neighbouring open-habitat areas potentially invading these patches, particularly as forest habitats become increasingly degraded. Here, we examine the effects of habitat loss, fragmentation and degradation on small mammal assemblages in a southern Amazonian deforestation frontier, while accounting for species-specific degree of forest-dependency. We surveyed small mammals at three continuous forest sites and 19 forest patches of different sizes and degrees of isolation. We further sampled matrix habitats adjacent to forest patches, which allowed us to classify each species according to forest-dependency and generate a community-averaged forest-dependency index for each site. Based on 21,568 trap-nights, we recorded 970 small mammals representing 20 species: 12 forest-dependents, 5 matrix-tolerants and 3 open-habitat specialists. Across the gradient of forest patch size, small mammal assemblages failed to show the typical species-area relationship, but this relationship held true when either species abundance or composition was considered. Species composition was further mediated by community-averaged forest-dependency, so that smaller forest patches were occupied by a lower proportion of forest-dependent rodents and marsupials. Both species richness and abundance increased in less isolated fragments surrounded by structurally simplified matrix habitats (e.g. active or abandoned cattle pastures). While shorter distances between forest patches may favour small mammal abundances, forest area and matrix complexity dictated which species could persist within forest fragments according to their degree of forest-dependency. Small mammal local extinctions in small forest patches within Amazonian deforestation frontiers are therefore likely offset by the incursion of open-habitat species. To preclude the dominance of those species, and consequent losses of native species and associated ecosystem functions, management actions should limit or reduce areas dedicated to pasture, additionally maintaining more structurally complex matrix habitats across fragmented landscapes

Cautious NMPC with Gaussian Process Dynamics for Autonomous Miniature Race Cars

This paper presents an adaptive high performance control method for autonomous miniature race cars. Racing dynamics are notoriously hard to model from first principles, which is addressed by means of a cautious nonlinear model predictive control (NMPC) approach that learns to improve its dynamics model from data and safely increases racing performance. The approach makes use of a Gaussian Process (GP) and takes residual model uncertainty into account through a chance constrained formulation. We present a sparse GP approximation with dynamically adjusting inducing inputs, enabling a real-time implementable controller. The formulation is demonstrated in simulations, which show significant improvement with respect to both lap time and constraint satisfaction compared to an NMPC without model learning