The representation of conditional expectations of non-Gaussian noise

For Wiener spaces conditional expectations and $L^{2}$-martingales w.r.t. the natural filtration have a natural representation in terms of chaos expansion. In this note an extension to larger classes of processes is discussed. In particular, it is pointed out that orthogonality of the chaos expansion is not required.

Climate entropy budget of the HadCM3 atmosphere-ocean general circulation model and of FAMOUS, its low resolution version

The entropy budget is calculated of the coupled atmosphere–ocean general circulation model HadCM3. Estimates of the different entropy sources and sinks of the climate system are obtained directly from the diabatic heating terms, and an approximate estimate of the planetary entropy production is also provided. The rate of material entropy production of the climate system is found to be ∼50 mW m−2 K−1, a value intermediate in the range 30–70 mW m−2 K−1 previously reported from different models. The largest part of this is due to sensible and latent heat transport (∼38 mW m−2 K−1). Another 13 mW m−2 K−1 is due to dissipation of kinetic energy in the atmosphere by friction and Reynolds stresses. Numerical entropy production in the atmosphere dynamical core is found to be about 0.7 mW m−2 K−1. The material entropy production within the ocean due to turbulent mixing is ∼1 mW m−2 K−1, a very small contribution to the material entropy production of the climate system. The rate of change of entropy of the model climate system is about 1 mW m−2 K−1 or less, which is comparable with the typical size of the fluctuations of the entropy sources due to interannual variability, and a more accurate closure of the budget than achieved by previous analyses. Results are similar for FAMOUS, which has a lower spatial resolution but similar formulation to HadCM3, while more substantial differences are found with respect to other models, suggesting that the formulation of the model has an important influence on the climate entropy budget. Since this is the first diagnosis of the entropy budget in a climate model of the type and complexity used for projection of twenty-first century climate change, it would be valuable if similar analyses were carried out for other such models.

An entropy-based financial decision support system (e-FDSS) for project analysis in construction SMEs

Uncertainty contributes a major part in the accuracy of a decision-making process while its inconsistency is always difficult to be solved by existing decision-making tools. Entropy has been proved to be useful to evaluate the inconsistency of uncertainty among different respondents. The study demonstrates an entropy-based financial decision support system called e-FDSS. This integrated system provides decision support to evaluate attributes (funding options and multiple risks) available in projects. Fuzzy logic theory is included in the system to deal with the qualitative aspect of these options and risks. An adaptive genetic algorithm (AGA) is also employed to solve the decision algorithm in the system in order to provide optimal and consistent rates to these attributes. Seven simplified and parallel projects from a Hong Kong construction small and medium enterprise (SME) were assessed to evaluate the system. The result shows that the system calculates risk adjusted discount rates (RADR) of projects in an objective way. These rates discount project cash flow impartially. Inconsistency of uncertainty is also successfully evaluated by the use of the entropy method. Finally, the system identifies the favourable funding options that are managed by a scheme called SME Loan Guarantee Scheme (SGS). Based on these results, resource allocation could then be optimized and the best time to start a new project could also be identified throughout the overall project life cycle.

Training conditional and cumulative risk judgements: the role of frequencies, problem-structure and Einstellung

Two experiments implement and evaluate a training scheme for learning to apply frequency formats to probability judgements couched in terms of percentages. Results indicate that both conditional and cumulative probability judgements can be improved in this manner, however the scheme is insufficient to promote any deeper understanding of the problem structure. In both experiments, training on one problem type only (either conditional or cumulative risk judgements) resulted in an inappropriate transfer of a learned method at test. The obstacles facing a frequency-based training programme for teaching appropriate use of probability data are discussed. Copyright (c) 2006 John Wiley & Sons, Ltd.

Thermodynamic analysis of snowball Earth hysteresis experiment: Efficiency, entropy production and irreversibility

We present an extensive thermodynamic analysis of a hysteresis experiment performed on a simplified yet Earth-like climate model. We slowly vary the solar constant by 20% around the present value and detect that for a large range of values of the solar constant the realization of snowball or of regular climate conditions depends on the history of the system. Using recent results on the global climate thermodynamics, we show that the two regimes feature radically different properties. The efficiency of the climate machine monotonically increases with decreasing solar constant in present climate conditions, whereas the opposite takes place in snowball conditions. Instead, entropy production is monotonically increasing with the solar constant in both branches of climate conditions, and its value is about four times larger in the warm branch than in the corresponding cold state. Finally, the degree of irreversibility of the system, measured as the fraction of excess entropy production due to irreversible heat transport processes, is much higher in the warm climate conditions, with an explosive growth in the upper range of the considered values of solar constants. Whereas in the cold climate regime a dominating role is played by changes in the meridional albedo contrast, in the warm climate regime changes in the intensity of latent heat fluxes are crucial for determining the observed properties. This substantiates the importance of addressing correctly the variations of the hydrological cycle in a changing climate. An interpretation of the climate transitions at the tipping points based upon macro-scale thermodynamic properties is also proposed. Our results support the adoption of a new generation of diagnostic tools based on the second law of thermodynamics for auditing climate models and outline a set of parametrizations to be used in conceptual and intermediate-complexity models or for the reconstruction of the past climate conditions. Copyright © 2010 Royal Meteorological Society

Entropy versus APE production: on the buoyancy power input in the oceans energy cycle

This letter argues that the current controversy about whether Wbuoyancy, the power input due to the surface buoyancy fluxes, is large or small in the oceans stems from two distinct and incompatible views on how Wbuoyancy relates to the volume-integrated work of expansion/contraction B. The current prevailing view is that Wbuoyancy should be identified with the net value of B, which current theories estimate to be small. The alternative view, defended here, is that only the positive part of B, i.e., the one converting internal energy into mechanical energy, should enter the definition of Wbuoyancy, since the negative part of B is associated with the non-viscous dissipation of mechanical energy. Two indirect methods suggest that by contrast, the positive part of B is potentially large.

Entropy application to improve construction finance decisions

In financial decision-making processes, the adopted weights of the objective functions have significant impacts on the final decision outcome. However, conventional rating and weighting methods exhibit difficulty in deriving appropriate weights for complex decision-making problems with imprecise information. Entropy is a quantitative measure of uncertainty and has been useful in exploring weights of attributes in decision making. A fuzzy and entropy-based mathematical approach is employed to solve the weighting problem of the objective functions in an overall cash-flow model. The multiproject being undertaken by a medium-size construction firm in Hong Kong was used as a real case study to demonstrate the application of entropy. Its application in multiproject cash flow situations is demonstrated. The results indicate that the overall before-tax profit was HK$ 0.11 millions lower after the introduction of appropriate weights. In addition, the best time to invest in new projects arising from positive cash flow was identified to be two working months earlier than the nonweight system.

Application of the entropy technique and genetic algorithms to construction site layout planning of medium-size projects

Genetic algorithms (GAs) have been introduced into site layout planning as reported in a number of studies. In these studies, the objective functions were defined so as to employ the GAs in searching for the optimal site layout. However, few studies have been carried out to investigate the actual closeness of relationships between site facilities; it is these relationships that ultimately govern the site layout. This study has determined that the underlying factors of site layout planning for medium-size projects include work flow, personnel flow, safety and environment, and personal preferences. By finding the weightings on these factors and the corresponding closeness indices between each facility, a closeness relationship has been deduced. Two contemporary mathematical approaches - fuzzy logic theory and an entropy measure - were adopted in finding these results in order to minimize the uncertainty and vagueness of the collected data and improve the quality of the information. GAs were then applied to searching for the optimal site layout in a medium-size government project using the GeneHunter software. The objective function involved minimizing the total travel distance. An optimal layout was obtained within a short time. This reveals that the application of GA to site layout planning is highly promising and efficient.

Autoregressive conditional kurtosis

This article proposes a new model for autoregressive conditional heteroscedasticity and kurtosis. Via a time-varying degrees of freedom parameter, the conditional variance and conditional kurtosis are permitted to evolve separately. The model uses only the standard Student’s t-density and consequently can be estimated simply using maximum likelihood. The method is applied to a set of four daily financial asset return series comprising U.S. and U.K. stocks and bonds, and significant evidence in favor of the presence of autoregressive conditional kurtosis is observed. Various extensions to the basic model are proposed, and we show that the response of kurtosis to good and bad news is not significantly asymmetric.

Conditional symmetric instability in sting-jet storms

Sting jets are transient mesoscale jets of air that descend from the tip of the cloud head towards the top of the boundary layer in severe extratropical cyclones and can lead to damaging surface wind gusts. This recently identified jet is distinct from the well-documented jets associated with the cold and warm conveyor belts. One mechanism proposed for their development is the release of conditional symmetric instability (CSI). Here the spatial distribution and temporal evolution of several CSI diagnostics in four severe storms are analysed. A sting jet has been identified in three of these storms; for comparison, we also analysed one storm that did not have a sting jet, even though it hadmany of the apparent features of sting-jet storms. The sting-jet storms are distinct from the non-sting-jet storms by having much greater andmore extensive conditional instability (CI) and CSI. CSI is released by ascending air parcels in the cloud head in two of the sting-jet storms and by descending air parcels in the other sting-jet storm. By contrast, only weak CI to ascending air parcels is present at the cloud-head tip in the non-sting-jet storm. CSI released by descending air parcels, as diagnosed by decaying downdraught slantwise convective available potential energy (DSCAPE), is collocated with the sting jets in all three sting-jet storms and has a localisedmaximum in two of them. Consistent evolutions of saturated moist potential vorticity are found.We conclude that CSI release has a role in the generation of the sting jet, that the sting jet may be driven by the release of instability to both ascending and descending parcels, and that DSCAPE could be used as a discriminating diagnostic for the sting jet based on these four case-studies.

Selecting from amongst non–nested conditional variance models: information criteria and portfolio determination

We consider the finite sample properties of model selection by information criteria in conditionally heteroscedastic models. Recent theoretical results show that certain popular criteria are consistent in that they will select the true model asymptotically with probability 1. To examine the empirical relevance of this property, Monte Carlo simulations are conducted for a set of non–nested data generating processes (DGPs) with the set of candidate models consisting of all types of model used as DGPs. In addition, not only is the best model considered but also those with similar values of the information criterion, called close competitors, thus forming a portfolio of eligible models. To supplement the simulations, the criteria are applied to a set of economic and financial series. In the simulations, the criteria are largely ineffective at identifying the correct model, either as best or a close competitor, the parsimonious GARCH(1, 1) model being preferred for most DGPs. In contrast, asymmetric models are generally selected to represent actual data. This leads to the conjecture that the properties of parameterizations of processes commonly used to model heteroscedastic data are more similar than may be imagined and that more attention needs to be paid to the behaviour of the standardized disturbances of such models, both in simulation exercises and in empirical modelling.