A singular vector perspective of 4D-Var: Filtering and interpolation

Four-dimensional variational data assimilation (4D-Var) combines the information from a time sequence of observations with the model dynamics and a background state to produce an analysis. In this paper, a new mathematical insight into the behaviour of 4D-Var is gained from an extension of concepts that are used to assess the qualitative information content of observations in satellite retrievals. It is shown that the 4D-Var analysis increments can be written as a linear combination of the singular vectors of a matrix which is a function of both the observational and the forecast model systems. This formulation is used to consider the filtering and interpolating aspects of 4D-Var using idealized case-studies based on a simple model of baroclinic instability. The results of the 4D-Var case-studies exhibit the reconstruction of the state in unobserved regions as a consequence of the interpolation of observations through time. The results also exhibit the filtering of components with small spatial scales that correspond to noise, and the filtering of structures in unobserved regions. The singular vector perspective gives a very clear view of this filtering and interpolating by the 4D-Var algorithm and shows that the appropriate specification of the a priori statistics is vital to extract the largest possible amount of useful information from the observations. Copyright © 2005 Royal Meteorological Society

Input usage, output mix and industry deregulation: an analysis of the Australian dairy manufacturing industry

In this paper we estimate a Translog output distance function for a balanced panel of state level data for the Australian dairy processing sector. We estimate a fixed effects specification employing Bayesian methods, with and without the imposition of monotonicity and curvature restrictions. Our results indicate that Tasmania and Victoria are the most technically efficient states with New South Wales being the least efficient. The imposition of theoretical restrictions marginally affects the results especially with respect to estimates of technical change and industry deregulation. Importantly, our bias estimates show changes in both input use and output mix that result from deregulation. Specifically, we find that deregulation has positively biased the production of butter, cheese and powders.

Consumer willingness to pay for in-flight service and comfort levels: A choice experiment

In the competitive aviation market as a result of the emergence of low cost carriers, charter airlines have had to reconsider their approach to service provision. Specifically, the reduction in service and comfort levels offered by the low cost airlines provides charter carriers with an opportunity to differentiate their product based on the quality of the offering. To consider this strategic option we employ an on-line choice experiment to examine consumer choices with respect to the bundle of services on offer when deciding to purchase a flight, With these data we use the Bayesian methods to estimate a mixed logit specification. Our results reveal that in principle passengers are willing to pay a relatively large amount for enhanced service quality. (C) 2008 Elsevier Ltd. All rights reserved.

Time patterns in UK demand for alcohol and tobacco: an application of the EM algorithm

Capturing the pattern of structural change is a relevant task in applied demand analysis, as consumer preferences may vary significantly over time. Filtering and smoothing techniques have recently played an increasingly relevant role. A dynamic Almost Ideal Demand System with random walk parameters is estimated in order to detect modifications in consumer habits and preferences, as well as changes in the behavioural response to prices and income. Systemwise estimation, consistent with the underlying constraints from economic theory, is achieved through the EM algorithm. The proposed model is applied to UK aggregate consumption of alcohol and tobacco, using quarterly data from 1963 to 2003. Increased alcohol consumption is explained by a preference shift, addictive behaviour and a lower price elasticity. The dynamic and time-varying specification is consistent with the theoretical requirements imposed at each sample point. (c) 2005 Elsevier B.V. All rights reserved.

Influence of vegetation on the local climate and hydrology in the tropics: sensitivity to soil parameters

Land use change with accompanying major modifications to the vegetation cover is widespread in the tropics, due to increasing demands for agricultural land, and may have significant impacts on the climate. This study investigates (1) the influence of vegetation on the local climate in the tropics; (2) how that influence varies from region to region; and (3) how the sensitivity of the local climate to vegetation, and hence land use change, depends on the hydraulic characteristics of the soil. A series of idealised experiments with the Hadley Centre atmospheric model, HadAM3, are described in which the influence of vegetation in the tropics is assessed by comparing the results of integrations with and without tropical vegetation. The sensitivity of the results to the soil characteristics is then explored by repeating the experiments with a differing, but equally valid, description of soil hydraulic parameters. The results have shown that vegetation has a significant moderating effect on the climate throughout the tropics by cooling the surface through enhanced latent heat fluxes. The influence of vegetation is, however, seasonally dependent, with much greater impacts during the dry season when the availability of surface moisture is limited. Furthermore, there are significant regional variations both in terms of the magnitude of the cooling and in the response of the precipitation. Not all regions show a feedback of vegetation on the local precipitation; this result has been related both to vegetation type and to the prevailing meteorological conditions. An important finding has been the sensitivity of the results to the specification of the soil hydraulic parameters. The introduction of more freely draining soils has changed the soil-moisture contents of the control, vegetated system and has reduced, significantly, the climate sensitivity to vegetation and by implication, land use change. Changes to the soil parameters have also had an impact on the soil hydrology and its interaction with vegetation, by altering the partitioning between fast and slow runoff processes. These results raise important questions about the representation of highly heterogeneous soil characteristics in climate models, as well as the potential influence of land use change on the soil characteristics themselves.

Mixed Logit Model Performance and Distributional Assumptions: Preferences and GM foods

Using mixed logit models to analyse choice data is common but requires ex ante specification of the functional forms of preference distributions. We make the case for greater use of bounded functional forms and propose the use of the Marginal Likelihood, calculated using Bayesian techniques, as a single measure of model performance across non nested mixed logit specifications. Using this measure leads to very different rankings of model specifications compared to alternative rule of thumb measures. The approach is illustrated using data from a choice experiment regarding GM food types which provides insights regarding the recent WTO dispute between the EU and the US, Canada and Argentina and whether labelling and trade regimes should be based on the production process or product composition.

An adaptive approach to implementing bivariate group sequential clinical trial designs

In clinical trials, situations often arise where more than one response from each patient is of interest; and it is required that any decision to stop the study be based upon some or all of these measures simultaneously. Theory for the design of sequential experiments with simultaneous bivariate responses is described by Jennison and Turnbull (Jennison, C., Turnbull, B. W. (1993). Group sequential tests for bivariate response: interim analyses of clinical trials with both efficacy and safety endpoints. Biometrics 49:741-752) and Cook and Farewell (Cook, R. J., Farewell, V. T. (1994). Guidelines for monitoring efficacy and toxicity responses in clinical trials. Biometrics 50:1146-1152) in the context of one efficacy and one safety response. These expositions are in terms of normally distributed data with known covariance. The methods proposed require specification of the correlation, ρ between test statistics monitored as part of the sequential test. It can be difficult to quantify ρ and previous authors have suggested simply taking the lowest plausible value, as this will guarantee power. This paper begins with an illustration of the effect that inappropriate specification of ρ can have on the preservation of trial error rates. It is shown that both the type I error and the power can be adversely affected. As a possible solution to this problem, formulas are provided for the calculation of correlation from data collected as part of the trial. An adaptive approach is proposed and evaluated that makes use of these formulas and an example is provided to illustrate the method. Attention is restricted to the bivariate case for ease of computation, although the formulas derived are applicable in the general multivariate case.

Statistical design and analysis of pharmacogenetic trials

Pharmacogenetic trials investigate the effect of genotype on treatment response. When there are two or more treatment groups and two or more genetic groups, investigation of gene-treatment interactions is of key interest. However, calculation of the power to detect such interactions is complicated because this depends not only on the treatment effect size within each genetic group, but also on the number of genetic groups, the size of each genetic group, and the type of genetic effect that is both present and tested for. The scale chosen to measure the magnitude of an interaction can also be problematic, especially for the binary case. Elston et al. proposed a test for detecting the presence of gene-treatment interactions for binary responses, and gave appropriate power calculations. This paper shows how the same approach can also be used for normally distributed responses. We also propose a method for analysing and performing sample size calculations based on a generalized linear model (GLM) approach. The power of the Elston et al. and GLM approaches are compared for the binary and normal case using several illustrative examples. While more sensitive to errors in model specification than the Elston et al. approach, the GLM approach is much more flexible and in many cases more powerful. Copyright © 2005 John Wiley & Sons, Ltd.

Wnt6 controls amniote neural crest induction through the non-canonical signaling pathway

The neural crest is a multipotent embryonic cell population that arises from neural ectoderm and forms derivatives essential for vertebrate function. Neural crest induction requires an ectodermal signal, thought to be a Writ ligand, but the identity of the Wnt that performs this function in amniotes is unknown. Here, we demonstrate that Wnt6, derived from the ectoderm, is necessary for chick neural crest induction. Crucially, we also show that Wnt6 acts through the non-canonical pathway and not the beta-catenin-dependant pathway. Surprisingly, we found that canonical Wnt signaling inhibited neural crest production in the chick embryo. In light of studies in anamniotes demonstrating that canonical Wnt signaling induces neural crest, these results indicate a significant and novel change in the mechanism of neural crest induction during vertebrate evolution. These data also highlight a key role for noncanonical Wnt signaling in cell type specification from a stem population during development.

Restricted expression of NADPH oxidase/peroxidase gene (Duox) in zone VII of the ascidian endostyle

The ascidian Ciona intestinalis, a marine invertebrate chordate, is an emerging model system for developmental and evolutionary studies. The endostyle, one of the characteristic organs of ascidians, is a pharyngeal structure with iodine-concentrating and peroxidase activities and is therefore considered to be homologous to the follicular thyroid of higher vertebrates. We have previously reported that a limited part of the endostyle (zone VII) is marked by the expression of orthologs of the thyroid peroxidase (TPO) and thyroid transcription factor-2 (TTF-2/FoxE) genes. In this study, we have identified the Ciona homolog of NADPH oxidase/peroxidase (Duox), which provides hydrogen peroxide (H2O2) for iodine metabolism by TPO in the vertebrate thyroid. Expression patterns assessed by in situ hybridization have revealed that Ciona Duox (Ci-Duox) is predominantly expressed in the dorsal part of zone VII of the endostyle. Furthermore, two-color fluorescent in situ hybridization with Ci-Duox and Ciona TPO (CiTPO) has revealed that the ventral boundary of the Ci-Duox domain of expression is more dorsal than that of CiTPO. We have also characterized several genes, such as Ci-Fgf8/17/18, 5HT7, and Ci-NK4, which are predominantly expressed in the ventral part of zone VII, in a region complementary to the Ci-Duox expression domain. These observations suggest that, at the molecular level, zone VII has a complex organization that might have some impact on the specification of cell types and functions in this thyroid-equivalent element of the ascidian endostyle.

Graphical tracking systems revisited: a practical approach to computer scheduling in horticulture

Graphical tracking is a technique for crop scheduling where the actual plant state is plotted against an ideal target curve which encapsulates all crop and environmental characteristics. Management decisions are made on the basis of the position of the actual crop against the ideal position. Due to the simplicity of the approach it is possible for graphical tracks to be developed on site without the requirement for controlled experimentation. Growth models and graphical tracks are discussed, and an implementation of the Richards curve for graphical tracking described. In many cases, the more intuitively desirable growth models perform sub-optimally due to problems with the specification of starting conditions, environmental factors outside the scope of the original model and the introduction of new cultivars. Accurate specification for a biological model requires detailed and usually costly study, and as such is not adaptable to a changing cultivar range and changing cultivation techniques. Fitting of a new graphical track for a new cultivar can be conducted on site and improved over subsequent seasons. Graphical tracking emphasises the current position relative to the objective, and as such does not require the time consuming or system specific input of an environmental history, although it does require detailed crop measurement. The approach is flexible and could be applied to a variety of specification metrics, with digital imaging providing a route for added value. For decision making regarding crop manipulation from the observed current state, there is a role for simple predictive modelling over the short term to indicate the short term consequences of crop manipulation.

Modelling fatigue damage distribution to inform slip and cut policy for riser tensioner ropes

The paper describes a method whereby the distribution of fatigue damage along riser tensioner ropes is calculated, taking account of heave motion, set tension, system geometry, tidal range and rope specification. From these data the distribution of damage along the rope is calculated for a given time period using a Miner’s summation method. This information can then be used to help the operator decide on the length of rope to ‘slip and cut’ whereby a length from the end of the rope is removed and the rope moved through the system from a storage drum such that sections of rope that have already suffered significant fatigue damage are not moved to positions where there is another peak in the distribution. There are two main advantages to be gained by using the fatigue damage model. The first is that it shows the amount of fatigue damage accumulating at different points along the rope, enabling the most highly damaged section to be removed well before failure. The second is that it makes for greater efficiency, as damage can be spread more evenly along the rope over time, avoiding the need to scrap long sections of undamaged rope.

Enabling older people to stay at home: The costs of substituting and supplementing care with assistive technology

A wide-ranging multiprofessional research project explored issues relating to the introduction of assistive technology into the existing homes of older people in order to provide them with the opportunity to remain at home. The financial relationship between assistive technology and packages of formal care was also explored. The costs of residential care and those of a number of packages containing differing quantities of assistive technology, formal care and informal care were compared. The analyses provide a strong financial case for substituting and/or supplementing formal care with assistive technology, even for individuals with quite disabling conditions. Although needs and hence the cost of provision rise with an increasing level of disability, the savings in care costs accrue quickly. The consideration of a variety of users with different needs and informal care provision, and occupying a very wide range of housing, leads to the conclusion that in comparison with traditional care packages, at worst, incorporating significant amounts of assistive technology into care packages is cost neutral, but that with careful specification of assistive technology major savings are feasible.