Use of the ratio plot in capture-recapture estimation

Statistical graphics are a fundamental, yet often overlooked, set of components in the repertoire of data analytic tools. Graphs are quick and efficient, yet simple instruments of preliminary exploration of a dataset to understand its structure and to provide insight into influential aspects of inference such as departures from assumptions and latent patterns. In this paper, we present and assess a graphical device for choosing a method for estimating population size in capture-recapture studies of closed populations. The basic concept is derived from a homogeneous Poisson distribution where the ratios of neighboring Poisson probabilities multiplied by the value of the larger neighbor count are constant. This property extends to the zero-truncated Poisson distribution which is of fundamental importance in capture–recapture studies. In practice however, this distributional property is often violated. The graphical device developed here, the ratio plot, can be used for assessing specific departures from a Poisson distribution. For example, simple contaminations of an otherwise homogeneous Poisson model can be easily detected and a robust estimator for the population size can be suggested. Several robust estimators are developed and a simulation study is provided to give some guidance on which should be used in practice. More systematic departures can also easily be detected using the ratio plot. In this paper, the focus is on Gamma mixtures of the Poisson distribution which leads to a linear pattern (called structured heterogeneity) in the ratio plot. More generally, the paper shows that the ratio plot is monotone for arbitrary mixtures of power series densities.

Adjoint methods in data assimilation for estimating model error

Data assimilation aims to incorporate measured observations into a dynamical system model in order to produce accurate estimates of all the current (and future) state variables of the system. The optimal estimates minimize a variational principle and can be found using adjoint methods. The model equations are treated as strong constraints on the problem. In reality, the model does not represent the system behaviour exactly and errors arise due to lack of resolution and inaccuracies in physical parameters, boundary conditions and forcing terms. A technique for estimating systematic and time-correlated errors as part of the variational assimilation procedure is described here. The modified method determines a correction term that compensates for model error and leads to improved predictions of the system states. The technique is illustrated in two test cases. Applications to the 1-D nonlinear shallow water equations demonstrate the effectiveness of the new procedure.

Estimating the volume of tephra deposits: a new simple strategy

Volume determination of tephra deposits is necessary for the assessment of the dynamics and hazards of explosive volcanoes. Several methods have been proposed during the past 40 years that include the analysis of crystal concentration of large pumices, integrations of various thinning relationships, and the inversion of field observations using analytical and computational models. Regardless of their strong dependence on tephra-deposit exposure and distribution of isomass/isopach contours, empirical integrations of deposit thinning trends still represent the most widely adopted strategy due to their practical and fast application. The most recent methods involve the best fitting of thinning data using various exponential seg- ments or a power-law curve on semilog plots of thickness (or mass/area) versus square root of isopach area. The exponential method is mainly sensitive to the number and the choice of straight segments, whereas the power-law method can better reproduce the natural thinning of tephra deposits but is strongly sensitive to the proximal or distal extreme of integration. We analyze a large data set of tephra deposits and propose a new empirical method for the deter- mination of tephra-deposit volumes that is based on the integration of the Weibull function. The new method shows a better agreement with observed data, reconciling the debate on the use of the exponential versus power-law method. In fact, the Weibull best fitting only depends on three free parameters, can well reproduce the gradual thinning of tephra deposits, and does not depend on the choice of arbitrary segments or of arbitrary extremes of integration.

Estimating reliability and resolution of probability forecasts through decomposition of the empirical score

References (20)Cited By (1)Export CitationAboutAbstract Proper scoring rules provide a useful means to evaluate probabilistic forecasts. Independent from scoring rules, it has been argued that reliability and resolution are desirable forecast attributes. The mathematical expectation value of the score allows for a decomposition into reliability and resolution related terms, demonstrating a relationship between scoring rules and reliability/resolution. A similar decomposition holds for the empirical (i.e. sample average) score over an archive of forecast–observation pairs. This empirical decomposition though provides a too optimistic estimate of the potential score (i.e. the optimum score which could be obtained through recalibration), showing that a forecast assessment based solely on the empirical resolution and reliability terms will be misleading. The differences between the theoretical and empirical decomposition are investigated, and specific recommendations are given how to obtain better estimators of reliability and resolution in the case of the Brier and Ignorance scoring rule.

Estimating natural-ventilation potential considering both thermal comfort and IAQ issues

Natural-ventilation potential (NVP) value can provide the designers significant information to properly design and arrange natural ventilation strategy at the preliminary or conceptual stage of ventilation and building design. Based on the previous study by Yang et al. [Investigation potential of natural driving forces for ventilation in four major cities in China. Building and Environment 2005;40:739–46], we developed a revised model to estimate the potential for natural ventilation considering both thermal comfort and IAQ issues for buildings in China. It differs from the previous one by Yang et al. in two predominant aspects: (1) indoor air temperature varies synchronously with the outdoor air temperature rather than staying at a constant value as assumed by Yang et al. This would recover the real characteristic of natural ventilation, (2) thermal comfort evaluation index is integrated into the model and thus the NVP can be more reasonably predicted. By adopting the same input parameters, the NVP values are obtained and compared with the early work of Yang et al. for a single building in four representative cities which are located in different climates, i.e., Urumqi in severe cold regions, Beijing in cold regions, Shanghai in hot summer and cold winter regions and Guangzhou in hot summer and warm winter regions of China. Our outcome shows that Guangzhou has the highest and best yearly natural-ventilation potential, followed by Shanghai, Beijing and Urumqi, which is quite distinct from that of Yang et al. From the analysis, it is clear that our model evaluates the NVP values more consistently with the outdoor climate data and thus reveals the true value of NVP.

A comparison of models for estimating the riverine export of nitrogen from large watersheds

We evaluated the accuracy of six watershed models of nitrogen export in streams (kg km2 yr−1) developed for use in large watersheds and representing various empirical and quasi-empirical approaches described in the literature. These models differ in their methods of calibration and have varying levels of spatial resolution and process complexity, which potentially affect the accuracy (bias and precision) of the model predictions of nitrogen export and source contributions to export. Using stream monitoring data and detailed estimates of the natural and cultural sources of nitrogen for 16 watersheds in the northeastern United States (drainage sizes = 475 to 70,000 km2), we assessed the accuracy of the model predictions of total nitrogen and nitrate-nitrogen export. The model validation included the use of an error modeling technique to identify biases caused by model deficiencies in quantifying nitrogen sources and biogeochemical processes affecting the transport of nitrogen in watersheds. Most models predicted stream nitrogen export to within 50% of the measured export in a majority of the watersheds. Prediction errors were negatively correlated with cultivated land area, indicating that the watershed models tended to over predict export in less agricultural and more forested watersheds and under predict in more agricultural basins. The magnitude of these biases differed appreciably among the models. Those models having more detailed descriptions of nitrogen sources, land and water attenuation of nitrogen, and water flow paths were found to have considerably lower bias and higher precision in their predictions of nitrogen export.

Estimating regional benefits of reducing targeted pollutants: An application to agricultural effects on water quality and the value of recreational fishing

The general focus of this paper is the regional estimation of marginal benefits of targeted water pollution abatement to instream uses. Benefit estimates are derived from actual consumer choices of recreational fishing activities and the implied expenditures for various levels of water quality. The methodology is applied to measuring the benefits accruing to recreational anglers in Indiana from the abatement of pollutants that are by-products of agricultural crop production.

Estimating root–soil contact from 3D X-ray microtomographs

Adequate contact with the soil is essential for water and nutrient adsorption by plant roots, but the determination of root–soil contact is a challenging task because it is difficult to visualize roots in situ and quantify their interactions with the soil at the scale of micrometres. A method to determine root–soil contact using X-ray microtomography was developed. Contact areas were determined from 3D volumetric images using segmentation and iso-surface determination tools. The accuracy of the method was tested with physical model systems of contact between two objects (phantoms). Volumes, surface areas and contact areas calculated from the measured phantoms were compared with those estimated from image analysis. The volume was accurate to within 0.3%, the surface area to within 2–4%, and the contact area to within 2.5%. Maize and lupin roots were grown in soil (<2 mm) and vermiculite at matric potentials of −0.03 and −1.6 MPa and in aggregate fractions of 4–2, 2–1, 1–0.5 and < 0.5 mm at a matric potential of −0.03 MPa. The contact of the roots with their growth medium was determined from 3D volumetric images. Macroporosity (>70 µm) of the soil sieved to different aggregate fractions was calculated from binarized data. Root-soil contact was greater in soil than in vermiculite and increased with decreasing aggregate or particle size. The differences in root–soil contact could not be explained solely by the decrease in porosity with decreasing aggregate size but may also result from changes in particle and aggregate packing around the root.

Estimating interchannel observation-error correlations for IASI radiance data in the Met Office system

The optimal utilisation of hyper-spectral satellite observations in numerical weather prediction is often inhibited by incorrectly assuming independent interchannel observation errors. However, in order to represent these observation-error covariance structures, an accurate knowledge of the true variances and correlations is needed. This structure is likely to vary with observation type and assimilation system. The work in this article presents the initial results for the estimation of IASI interchannel observation-error correlations when the data are processed in the Met Office one-dimensional (1D-Var) and four-dimensional (4D-Var) variational assimilation systems. The method used to calculate the observation errors is a post-analysis diagnostic which utilises the background and analysis departures from the two systems. The results show significant differences in the source and structure of the observation errors when processed in the two different assimilation systems, but also highlight some common features. When the observations are processed in 1D-Var, the diagnosed error variances are approximately half the size of the error variances used in the current operational system and are very close in size to the instrument noise, suggesting that this is the main source of error. The errors contain no consistent correlations, with the exception of a handful of spectrally close channels. When the observations are processed in 4D-Var, we again find that the observation errors are being overestimated operationally, but the overestimation is significantly larger for many channels. In contrast to 1D-Var, the diagnosed error variances are often larger than the instrument noise in 4D-Var. It is postulated that horizontal errors of representation, not seen in 1D-Var, are a significant contributor to the overall error here. Finally, observation errors diagnosed from 4D-Var are found to contain strong, consistent correlation structures for channels sensitive to water vapour and surface properties.