Robust nonlinear model identification methods using forward regression

In this correspondence new robust nonlinear model construction algorithms for a large class of linear-in-the-parameters models are introduced to enhance model robustness via combined parameter regularization and new robust structural selective criteria. In parallel to parameter regularization, we use two classes of robust model selection criteria based on either experimental design criteria that optimizes model adequacy, or the predicted residual sums of squares (PRESS) statistic that optimizes model generalization capability, respectively. Three robust identification algorithms are introduced, i.e., combined A- and D-optimality with regularized orthogonal least squares algorithm, respectively; and combined PRESS statistic with regularized orthogonal least squares algorithm. A common characteristic of these algorithms is that the inherent computation efficiency associated with the orthogonalization scheme in orthogonal least squares or regularized orthogonal least squares has been extended such that the new algorithms are computationally efficient. Numerical examples are included to demonstrate effectiveness of the algorithms.

Automatic nonlinear predictive model-construction algorithm using forward regression and the PRESS statistic

An automatic nonlinear predictive model-construction algorithm is introduced based on forward regression and the predicted-residual-sums-of-squares (PRESS) statistic. The proposed algorithm is based on the fundamental concept of evaluating a model's generalisation capability through crossvalidation. This is achieved by using the PRESS statistic as a cost function to optimise model structure. In particular, the proposed algorithm is developed with the aim of achieving computational efficiency, such that the computational effort, which would usually be extensive in the computation of the PRESS statistic, is reduced or minimised. The computation of PRESS is simplified by avoiding a matrix inversion through the use of the orthogonalisation procedure inherent in forward regression, and is further reduced significantly by the introduction of a forward-recursive formula. Based on the properties of the PRESS statistic, the proposed algorithm can achieve a fully automated procedure without resort to any other validation data set for iterative model evaluation. Numerical examples are used to demonstrate the efficacy of the algorithm.

CAMCR: Computer-Assisted Mixture model analysis for Capture–Recapture count data

Population size estimation with discrete or nonparametric mixture models is considered, and reliable ways of construction of the nonparametric mixture model estimator are reviewed and set into perspective. Construction of the maximum likelihood estimator of the mixing distribution is done for any number of components up to the global nonparametric maximum likelihood bound using the EM algorithm. In addition, the estimators of Chao and Zelterman are considered with some generalisations of Zelterman’s estimator. All computations are done with CAMCR, a special software developed for population size estimation with mixture models. Several examples and data sets are discussed and the estimators illustrated. Problems using the mixture model-based estimators are highlighted.

Perspex machine X: software development

The Perspex Machine arose from the unification of computation with geometry. We now report significant redevelopment of both a partial C compiler that generates perspex programs and of a Graphical User Interface (GUI). The compiler is constructed with standard compiler-generator tools and produces both an explicit parse tree for C and an Abstract Syntax Tree (AST) that is better suited to code generation. The GUI uses a hash table and a simpler software architecture to achieve an order of magnitude speed up in processing and, consequently, an order of magnitude increase in the number of perspexes that can be manipulated in real time (now 6,000). Two perspex-machine simulators are provided, one using trans-floating-point arithmetic and the other using transrational arithmetic. All of the software described here is available on the world wide web. The compiler generates code in the neural model of the perspex. At each branch point it uses a jumper to return control to the main fibre. This has the effect of pruning out an exponentially increasing number of branching fibres, thereby greatly increasing the efficiency of perspex programs as measured by the number of neurons required to implement an algorithm. The jumpers are placed at unit distance from the main fibre and form a geometrical structure analogous to a myelin sheath in a biological neuron. Both the perspex jumper-sheath and the biological myelin-sheath share the computational function of preventing cross-over of signals to neurons that lie close to an axon. This is an example of convergence driven by similar geometrical and computational constraints in perspex and biological neurons.

Head-controlled assistive telerobot with extended physiological proprioception capability

People with disabilities such as quadriplegia can use mouth-sticks and head-sticks as extension devices to perform desired manipulations. These extensions provide extended proprioception which allows users to directly feel forces and other perceptual cues such as texture present at the tip of the mouth-stick. Such devices are effective for two principle reasons: because of their close contact with the user's tactile and proprioceptive sensing abilities; and because they tend to be lightweight and very stiff, and can thus convey tactile and kinesthetic information with high-bandwidth. Unfortunately, traditional mouth-sticks and head-sticks are limited in workspace and in the mechanical power that can be transferred because of user mobility and strength limitations. We describe an alternative implementation of the head-stick device using the idea of a virtual head-stick: a head-controlled bilateral force-reflecting telerobot. In this system the end-effector of the slave robot moves as if it were at the tip of an imaginary extension of the user's head. The design goal is for the system is to have the same intuitive operation and extended proprioception as a regular mouth-stick effector but with augmentation of workspace volume and mechanical power. The input is through a specially modified six DOF master robot (a PerForceTM hand-controller) whose joints can be back-driven to apply forces at the user's head. The manipulation tasks in the environment are performed by a six degree-of-freedom slave robot (the Zebra-ZEROTM) with a built-in force sensor. We describe the prototype hardware/software implementation of the system, control system design, safety/disability issues, and initial evaluation tasks.

Model-based groupware solution for distributed real-time collaborative 4D planning via teamwork

Construction planning plays a fundamental role in construction project management that requires team working among planners from a diverse range of disciplines and in geographically dispersed working situations. Model-based four-dimensional (4D) computer-aided design (CAD) groupware, though considered a possible approach to supporting collaborative planning, is still short of effective collaborative mechanisms for teamwork due to methodological, technological and social challenges. Targeting this problem, this paper proposes a model-based groupware solution to enable a group of multidisciplinary planners to perform real-time collaborative 4D planning across the Internet. In the light of the interactive definition method, and its computer-supported collaborative work (CSCW) design analysis, the paper discusses the realization of interactive collaborative mechanisms from software architecture, application mode, and data exchange protocol. These mechanisms have been integrated into a groupware solution, which was validated by a planning team in a truly geographically dispersed condition. Analysis of the validation results revealed that the proposed solution is feasible for real-time collaborative 4D planning to gain a robust construction plan through collaborative teamwork. The realization of this solution triggers further considerations about its enhancement for wider groupware applications.

A simple column model to explore anticipated problems in variational assimilation of satellite observations

We investigate a simplified form of variational data assimilation in a fully nonlinear framework with the aim of extracting dynamical development information from a sequence of observations over time. Information on the vertical wind profile, w(z ), and profiles of temperature, T (z , t), and total water content, qt (z , t), as functions of height, z , and time, t, are converted to brightness temperatures at a single horizontal location by defining a two-dimensional (vertical and time) variational assimilation testbed. The profiles of T and qt are updated using a vertical advection scheme. A basic cloud scheme is used to obtain the fractional cloud amount and, when combined with the temperature field, this information is converted into a brightness temperature, using a simple radiative transfer scheme. It is shown that our model exhibits realistic behaviour with regard to the prediction of cloud, but the effects of nonlinearity become non-negligible in the variational data assimilation algorithm. A careful analysis of the application of the data assimilation scheme to this nonlinear problem is presented, the salient difficulties are highlighted, and suggestions for further developments are discussed.

Integrating the Climate Science Modelling Language with geospatial software and services

Much consideration is rightly given to the design of metadata models to describe data. At the other end of the data-delivery spectrum much thought has also been given to the design of geospatial delivery interfaces such as the Open Geospatial Consortium standards, Web Coverage Service (WCS), Web Map Server and Web Feature Service (WFS). Our recent experience with the Climate Science Modelling Language shows that an implementation gap exists where many challenges remain unsolved. To bridge this gap requires transposing information and data from one world view of geospatial climate data to another. Some of the issues include: the loss of information in mapping to a common information model, the need to create ‘views’ onto file-based storage, and the need to map onto an appropriate delivery interface (as with the choice between WFS and WCS for feature types with coverage-valued properties). Here we summarise the approaches we have taken in facing up to these problems.

Strategies: Revolution in climate prediction is both necessary and possible: A declaration at the World Modelling Summit for Climate Prediction

The impending threat of global climate change and its regional manifestations is among the most important and urgent problems facing humanity. Society needs accurate and reliable estimates of changes in the probability of regional weather variations to develop science-based adaptation and mitigation strategies. Recent advances in weather prediction and in our understanding and ability to model the climate system suggest that it is both necessary and possible to revolutionize climate prediction to meet these societal needs. However, the scientific workforce and the computational capability required to bring about such a revolution is not available in any single nation. Motivated by the success of internationally funded infrastructure in other areas of science, this paper argues that, because of the complexity of the climate system, and because the regional manifestations of climate change are mainly through changes in the statistics of regional weather variations, the scientific and computational requirements to predict its behavior reliably are so enormous that the nations of the world should create a small number of multinational high-performance computing facilities dedicated to the grand challenges of developing the capabilities to predict climate variability and change on both global and regional scales over the coming decades. Such facilities will play a key role in the development of next-generation climate models, build global capacity in climate research, nurture a highly trained workforce, and engage the global user community, policy-makers, and stakeholders. We recommend the creation of a small number of multinational facilities with computer capability at each facility of about 20 peta-flops in the near term, about 200 petaflops within five years, and 1 exaflop by the end of the next decade. Each facility should have sufficient scientific workforce to develop and maintain the software and data analysis infrastructure. Such facilities will enable questions of what resolution, both horizontal and vertical, in atmospheric and ocean models, is necessary for more confident predictions at the regional and local level. Current limitations in computing power have placed severe limitations on such an investigation, which is now badly needed. These facilities will also provide the world's scientists with the computational laboratories for fundamental research on weather–climate interactions using 1-km resolution models and on atmospheric, terrestrial, cryospheric, and oceanic processes at even finer scales. Each facility should have enabling infrastructure including hardware, software, and data analysis support, and scientific capacity to interact with the national centers and other visitors. This will accelerate our understanding of how the climate system works and how to model it. It will ultimately enable the climate community to provide society with climate predictions, which are based on our best knowledge of science and the most advanced technology.

Toward a new generation of world climate research and computing facilities

The impending threat of global climate change and its regional manifestations is among the most important and urgent problems facing humanity. Society needs accurate and reliable estimates of changes in the probability of regional weather variations to develop science-based adaptation and mitigation strategies. Recent advances in weather prediction and in our understanding and ability to model the climate system suggest that it is both necessary and possible to revolutionize climate prediction to meet these societal needs. However, the scientific workforce and the computational capability required to bring about such a revolution is not available in any single nation. Motivated by the success of internationally funded infrastructure in other areas of science, this paper argues that, because of the complexity of the climate system, and because the regional manifestations of climate change are mainly through changes in the statistics of regional weather variations, the scientific and computational requirements to predict its behavior reliably are so enormous that the nations of the world should create a small number of multinational high-performance computing facilities dedicated to the grand challenges of developing the capabilities to predict climate variability and change on both global and regional scales over the coming decades. Such facilities will play a key role in the development of next-generation climate models, build global capacity in climate research, nurture a highly trained workforce, and engage the global user community, policy-makers, and stakeholders. We recommend the creation of a small number of multinational facilities with computer capability at each facility of about 20 peta-flops in the near term, about 200 petaflops within five years, and 1 exaflop by the end of the next decade. Each facility should have sufficient scientific workforce to develop and maintain the software and data analysis infrastructure. Such facilities will enable questions of what resolution, both horizontal and vertical, in atmospheric and ocean models, is necessary for more confident predictions at the regional and local level. Current limitations in computing power have placed severe limitations on such an investigation, which is now badly needed. These facilities will also provide the world's scientists with the computational laboratories for fundamental research on weather–climate interactions using 1-km resolution models and on atmospheric, terrestrial, cryospheric, and oceanic processes at even finer scales. Each facility should have enabling infrastructure including hardware, software, and data analysis support, and scientific capacity to interact with the national centers and other visitors. This will accelerate our understanding of how the climate system works and how to model it. It will ultimately enable the climate community to provide society with climate predictions, which are based on our best knowledge of science and the most advanced technology.

Real-time multi-model decadal climate predictions

We present the first climate prediction of the coming decade made with multiple models, initialized with prior observations. This prediction accrues from an international activity to exchange decadal predictions in near real-time, in order to assess differences and similarities, provide a consensus view to prevent over-confidence in forecasts from any single model, and establish current collective capability. We stress that the forecast is experimental, since the skill of the multi-model system is as yet unknown. Nevertheless, the forecast systems used here are based on models that have undergone rigorous evaluation and individually have been evaluated for forecast skill. Moreover, it is important to publish forecasts to enable open evaluation, and to provide a focus on climate change in the coming decade. Initialized forecasts of the year 2011 agree well with observations, with a pattern correlation of 0.62 compared to 0.31 for uninitialized projections. In particular, the forecast correctly predicted La Niña in the Pacific, and warm conditions in the north Atlantic and USA. A similar pattern is predicted for 2012 but with a weaker La Niña. Indices of Atlantic multi-decadal variability and Pacific decadal variability show no signal beyond climatology after 2015, while temperature in the Niño3 region is predicted to warm slightly by about 0.5 °C over the coming decade. However, uncertainties are large for individual years and initialization has little impact beyond the first 4 years in most regions. Relative to uninitialized forecasts, initialized forecasts are significantly warmer in the north Atlantic sub-polar gyre and cooler in the north Pacific throughout the decade. They are also significantly cooler in the global average and over most land and ocean regions out to several years ahead. However, in the absence of volcanic eruptions, global temperature is predicted to continue to rise, with each year from 2013 onwards having a 50 % chance of exceeding the current observed record. Verification of these forecasts will provide an important opportunity to test the performance of models and our understanding and knowledge of the drivers of climate change.

Optimising the FAMOUS climate model: inclusion of global carbon cycling

FAMOUS fills an important role in the hierarchy of climate models, both explicitly resolving atmospheric and oceanic dynamics yet being sufficiently computationally efficient that either very long simulations or large ensembles are possible. An improved set of carbon cycle parameters for this model has been found using a perturbed physics ensemble technique. This is an important step towards building the "Earth System" modelling capability of FAMOUS, which is a reduced resolution, and hence faster running, version of the Hadley Centre Climate model, HadCM3. Two separate 100 member perturbed parameter ensembles were performed; one for the land surface and one for the ocean. The land surface scheme was tested against present-day and past representations of vegetation and the ocean ensemble was tested against observations of nitrate. An advantage of using a relatively fast climate model is that a large number of simulations can be run and hence the model parameter space (a large source of climate model uncertainty) can be more thoroughly sampled. This has the associated benefit of being able to assess the sensitivity of model results to changes in each parameter. The climatologies of surface and tropospheric air temperature and precipitation are improved relative to previous versions of FAMOUS. The improved representation of upper atmosphere temperatures is driven by improved ozone concentrations near the tropopause and better upper level winds.

Sparse model construction using coordinate descent optimization

We propose a new sparse model construction method aimed at maximizing a model’s generalisation capability for a large class of linear-in-the-parameters models. The coordinate descent optimization algorithm is employed with a modified l1- penalized least squares cost function in order to estimate a single parameter and its regularization parameter simultaneously based on the leave one out mean square error (LOOMSE). Our original contribution is to derive a closed form of optimal LOOMSE regularization parameter for a single term model, for which we show that the LOOMSE can be analytically computed without actually splitting the data set leading to a very simple parameter estimation method. We then integrate the new results within the coordinate descent optimization algorithm to update model parameters one at the time for linear-in-the-parameters models. Consequently a fully automated procedure is achieved without resort to any other validation data set for iterative model evaluation. Illustrative examples are included to demonstrate the effectiveness of the new approaches.

A self-similar expansion model for use in solar wind transient propogation studies

Since the advent of wide-angle imaging of the inner heliosphere, a plethora of techniques have been developed to investigate the three-dimensional structure and kinematics of solar wind transients, such as coronal mass ejections, from their signatures in single- and multi-spacecraft imaging observations. These techniques, which range from the highly complex and computationally intensive to methods based on simple curve fitting, all have their inherent advantages and limitations. In the analysis of single-spacecraft imaging observations, much use has been made of the fixed φ fitting (FPF) and harmonic mean fitting (HMF) techniques, in which the solar wind transient is considered to be a radially propagating point source (fixed φ, FP, model) and a radially expanding circle anchored at Sun centre (harmonic mean, HM, model), respectively. Initially, we compare the radial speeds and propagation directions derived from application of the FPF and HMF techniques to a large set of STEREO/Heliospheric Imager (HI) observations. As the geometries on which these two techniques are founded constitute extreme descriptions of solar wind transients in terms of their extent along the line of sight, we describe a single-spacecraft fitting technique based on a more generalized model for which the FP and HM geometries form the limiting cases. In addition to providing estimates of a transient’s speed and propagation direction, the self-similar expansion fitting (SSEF) technique provides, in theory, the capability to estimate the transient’s angular extent in the plane orthogonal to the field of view. Using the HI observations, and also by performing a Monte Carlo simulation, we assess the potential of the SSEF technique.

Benchmarks and the accuracy of GARCH model estimation

This paper reviews nine software packages with particular reference to their GARCH model estimation accuracy when judged against a respected benchmark. We consider the numerical consistency of GARCH and EGARCH estimation and forecasting. Our results have a number of implications for published research and future software development. Finally, we argue that the establishment of benchmarks for other standard non-linear models is long overdue.