High-precision measurements of the co-polar correlation coefficient: non-Gaussian errors and retrieval of the dispersion parameter µ in rainfall

The co-polar correlation coefficient (ρhv) has many applications, including hydrometeor classification, ground clutter and melting layer identification, interpretation of ice microphysics and the retrieval of rain drop size distributions (DSDs). However, we currently lack the quantitative error estimates that are necessary if these applications are to be fully exploited. Previous error estimates of ρhv rely on knowledge of the unknown "true" ρhv and implicitly assume a Gaussian probability distribution function of ρhv samples. We show that frequency distributions of ρhv estimates are in fact highly negatively skewed. A new variable: L = -log10(1 - ρhv) is defined, which does have Gaussian error statistics, and a standard deviation depending only on the number of independent radar pulses. This is verified using observations of spherical drizzle drops, allowing, for the first time, the construction of rigorous confidence intervals in estimates of ρhv. In addition, we demonstrate how the imperfect co-location of the horizontal and vertical polarisation sample volumes may be accounted for. The possibility of using L to estimate the dispersion parameter (µ) in the gamma drop size distribution is investigated. We find that including drop oscillations is essential for this application, otherwise there could be biases in retrieved µ of up to ~8. Preliminary results in rainfall are presented. In a convective rain case study, our estimates show µ to be substantially larger than 0 (an exponential DSD). In this particular rain event, rain rate would be overestimated by up to 50% if a simple exponential DSD is assumed.

On the nature of over-dispersion in motor vehicle crash prediction models

Statistical modeling of traffic crashes has been of interest to researchers for decades. Over the most recent decade many crash models have accounted for extra-variation in crash counts—variation over and above that accounted for by the Poisson density. The extra-variation – or dispersion – is theorized to capture unaccounted for variation in crashes across sites. The majority of studies have assumed fixed dispersion parameters in over-dispersed crash models—tantamount to assuming that unaccounted for variation is proportional to the expected crash count. Miaou and Lord [Miaou, S.P., Lord, D., 2003. Modeling traffic crash-flow relationships for intersections: dispersion parameter, functional form, and Bayes versus empirical Bayes methods. Transport. Res. Rec. 1840, 31–40] challenged the fixed dispersion parameter assumption, and examined various dispersion parameter relationships when modeling urban signalized intersection accidents in Toronto. They suggested that further work is needed to determine the appropriateness of the findings for rural as well as other intersection types, to corroborate their findings, and to explore alternative dispersion functions. This study builds upon the work of Miaou and Lord, with exploration of additional dispersion functions, the use of an independent data set, and presents an opportunity to corroborate their findings. Data from Georgia are used in this study. A Bayesian modeling approach with non-informative priors is adopted, using sampling-based estimation via Markov Chain Monte Carlo (MCMC) and the Gibbs sampler. A total of eight model specifications were developed; four of them employed traffic flows as explanatory factors in mean structure while the remainder of them included geometric factors in addition to major and minor road traffic flows. The models were compared and contrasted using the significance of coefficients, standard deviance, chi-square goodness-of-fit, and deviance information criteria (DIC) statistics. The findings indicate that the modeling of the dispersion parameter, which essentially explains the extra-variance structure, depends greatly on how the mean structure is modeled. In the presence of a well-defined mean function, the extra-variance structure generally becomes insignificant, i.e. the variance structure is a simple function of the mean. It appears that extra-variation is a function of covariates when the mean structure (expected crash count) is poorly specified and suffers from omitted variables. In contrast, when sufficient explanatory variables are used to model the mean (expected crash count), extra-Poisson variation is not significantly related to these variables. If these results are generalizable, they suggest that model specification may be improved by testing extra-variation functions for significance. They also suggest that known influences of expected crash counts are likely to be different than factors that might help to explain unaccounted for variation in crashes across sites

Parameter-transformation relations for traveling-wave solutions of kdv-burgers equation

 Burgers suggested that the main properties of free-turbulence in the boundless area without basic flow might be understood with the aid of the following equation, which was much simpler than those of fluid dynamics, 更多还原

Bias-corrected estimators for dispersion models with dispersion covariates

In this paper we discuss bias-corrected estimators for the regression and the dispersion parameters in an extended class of dispersion models (Jorgensen, 1997b). This class extends the regular dispersion models by letting the dispersion parameter vary throughout the observations, and contains the dispersion models as particular case. General formulae for the O(n(-1)) bias are obtained explicitly in dispersion models with dispersion covariates, which generalize previous results obtained by Botter and Cordeiro (1998), Cordeiro and McCullagh (1991), Cordeiro and Vasconcellos (1999), and Paula (1992). The practical use of the formulae is that we can derive closed-form expressions for the O(n(-1)) biases of the maximum likelihood estimators of the regression and dispersion parameters when the information matrix has a closed-form. Various expressions for the O(n(-1)) biases are given for special models. The formulae have advantages for numerical purposes because they require only a supplementary weighted linear regression. We also compare these bias-corrected estimators with two different estimators which are also bias-free to order O(n(-1)) that are based on bootstrap methods. These estimators are compared by simulation. (C) 2011 Elsevier B.V. All rights reserved.

Dispersion engineering of highly nonlinear chalcogenide suspended-core fibers

Chalcogenide optical fibers are currently undergoing intensive investigation with the aim of exploiting the excellent glass transmission and nonlinear characteristics in the near- and mid-infrared for several applications. Further enhancement of these properties can be obtained, for a particular application, with optical fibers specifically designed that are capable of providing low effective area together with a properly tailored dispersion, matching the characteristics of the laser sources used to excite nonlinear effects. Suspended-core photonic crystal fibers are ideal candidates for nonlinear applications, providing small-core waveguides with large index contrast and tunable dispersion. In this paper, the dispersion properties of As2S3 suspended-core fibers are numerically analyzed, taking into account, for the first time, all the structural parameters, including the size and the number of the glass bridges. The results show that a proper design of the cladding struts can be exploited to significantly change the fiber properties, altering the maximum value of the dispersion parameter and shifting the zero-dispersion wavelengths over a range of 400 nm.

Aplicação da equação de Poisson-Boltzmann modificada em sistemas biológicos: análise da partição iônica em um eritrócito

Neste trabalho, a partição iônica e o potencial de membrana em um eritrócito são analisados via equação de Poisson-Boltzmann modificada, considerando as interações não eletrostáticas presentes entre os íons e macromoléculas, assim como, o potencial β. Este potencial é atribuído à diferença de potencial químico de referência entre os meios intracelular e extracelular e ao transporte ativo de íons. O potencial de Gibbs-Donnan via equação de Poisson-Boltzmann na presença de carga fixa em um sistema contendo uma membrana semipermeável também é estudado. O método de aproximação paraboloide em elementos finitos em um sistema estacionário e unidimensionalé aplicado para resolver a equação de Poisson-Boltzmann em coordenadas cartesianas e esféricas. O parâmetro de dispersão relativo às interações não eletrostáticas écalculado via teoria de Lifshitz. Os resultados em relação ao potencial de Gibbs-Donnan mostram-se adequados, podendo ser calculado pela equação de Poisson-Boltzmann. No sistema contendo um eritrócito, quando o potencial β é considerado igual a zero, não se verifica a diferença iônica observada experimentalmente entre os meios intracelular e extracelular. Dessa forma, os potenciais não eletrostáticos calculados via teoria de Lifshitz têm apenas uma pequena influência no que se refere à alta concentração de íon K+ no meio intracelular em relação ao íon Na+

Optical properties of aluminum-, gallium-, and indium-doped Bi4Ti3O12 thin films

Undoped and Al-, Ga-, and In-doped Bi4Ti3O12 thin films were prepared on fused quartz substrates by chemical solution deposition. Their microstructures and optical properties were investigated by x-ray diffraction and UV-visible-NIR spectrophotometer, respectively. The optical band-gap energies, Urbach energies, and linear refractive indices of all the films are derived from the transmittance spectrum. Following the single oscillator model, the dispersion parameters such as the average oscillator energy (E-0) and dispersion energy (E-d) are achieved. The energy band gap and refractive indices are found to decrease with introducing the dopants of Al, Ga, and In, which is useful for the band-gap engineering and optical waveguide devices. The refractive index dispersion parameter (E-0/S-0) increases and the chemical bonding quantity (beta) decreases in all the films compared with those of bulk. It is supposed to be caused by the nanosize grains in films. (c) 2009 American Institute of Physics. [DOI 10.1063/1.3138813]

Effect of incorporating nonlanthanoidal indium on optical properties of ferroelectric Bi4Ti3O12 thin films

Bi4Ti3O12 (BTO) and Bi3.25In0.75Ti3O12 (BTO:In) thin films were prepared on fused quartz and LaNiO3/Si (LNO) substrates by chemical solution deposition (CSD). Their microstructures, ferroelectric and optical properties were investigated by X-ray diffraction, scanning electron microscope, ferroelectric tester and UV-visible-NIR spectrophotometer, respectively. The optical band-gaps of the films were found to be 3.64 and 3.45 eV for the BTO and BTO:In films, respectively. Optical constants (refractive indexes and extinction coefficients) were determined from the optical transmittance spectra using the envelope method. Following the single electronic oscillator model, the single oscillator energy E-0, the dispersion energy E-d, the average interband oscillator wavelength lambda(0), the average oscillator strength S-0, the refractive index dispersion parameter (E-0/S-0), the chemical bonding quantity beta, and the long wavelength refractive index n(infinity) were obtained and analyzed. Both the refractive index and extinction coefficient of the BTO:In films are smaller than those of the BTO films. Furthermore, the refractive index dispersion parameter (E-0/S-0) increases and the chemical bonding quantity beta decreases in the BTO and BTO:In films compared with those of bulk. (C) 2007 Published by Elsevier B.V.

Lognormal and gamma mixed negative binomial regression

In regression analysis of counts, a lack of simple and efficient algorithms for posterior computation has made Bayesian approaches appear unattractive and thus underdeveloped. We propose a lognormal and gamma mixed negative binomial (NB) regression model for counts, and present efficient closed-form Bayesian inference; unlike conventional Poisson models, the proposed approach has two free parameters to include two different kinds of random effects, and allows the incorporation of prior information, such as sparsity in the regression coefficients. By placing a gamma distribution prior on the NB dispersion parameter r, and connecting a log-normal distribution prior with the logit of the NB probability parameter p, efficient Gibbs sampling and variational Bayes inference are both developed. The closed-form updates are obtained by exploiting conditional conjugacy via both a compound Poisson representation and a Polya-Gamma distribution based data augmentation approach. The proposed Bayesian inference can be implemented routinely, while being easily generalizable to more complex settings involving multivariate dependence structures. The algorithms are illustrated using real examples. Copyright 2012 by the author(s)/owner(s).

Estimating drizzle drop size and precipitation rate using two-colour lidar measurements

A method to estimate the size and liquid water content of drizzle drops using lidar measurements at two wavelengths is described. The method exploits the differential absorption of infrared light by liquid water at 905 nm and 1.5 μm, which leads to a different backscatter cross section for water drops larger than ≈50 μm. The ratio of backscatter measured from drizzle samples below cloud base at these two wavelengths (the colour ratio) provides a measure of the median volume drop diameter D0. This is a strong effect: for D0=200 μm, a colour ratio of ≈6 dB is predicted. Once D0 is known, the measured backscatter at 905 nm can be used to calculate the liquid water content (LWC) and other moments of the drizzle drop distribution. The method is applied to observations of drizzle falling from stratocumulus and stratus clouds. High resolution (32 s, 36 m) profiles of D0, LWC and precipitation rate R are derived. The main sources of error in the technique are the need to assume a value for the dispersion parameter μ in the drop size spectrum (leading to at most a 35% error in R) and the influence of aerosol returns on the retrieval (≈10% error in R for the cases considered here). Radar reflectivities are also computed from the lidar data, and compared to independent measurements from a colocated cloud radar, offering independent validation of the derived drop size distributions.

A flexible model for survival data with a cure rate: a Bayesian approach

In this paper we deal with a Bayesian analysis for right-censored survival data suitable for populations with a cure rate. We consider a cure rate model based on the negative binomial distribution, encompassing as a special case the promotion time cure model. Bayesian analysis is based on Markov chain Monte Carlo (MCMC) methods. We also present some discussion on model selection and an illustration with a real dataset.

A hands-on approach for fitting long-term survival models under the GAMLSS framework

In many data sets from clinical studies there are patients insusceptible to the occurrence of the event of interest. Survival models which ignore this fact are generally inadequate. The main goal of this paper is to describe an application of the generalized additive models for location, scale, and shape (GAMLSS) framework to the fitting of long-term survival models. in this work the number of competing causes of the event of interest follows the negative binomial distribution. In this way, some well known models found in the literature are characterized as particular cases of our proposal. The model is conveniently parameterized in terms of the cured fraction, which is then linked to covariates. We explore the use of the gamlss package in R as a powerful tool for inference in long-term survival models. The procedure is illustrated with a numerical example. (C) 2009 Elsevier Ireland Ltd. All rights reserved.

Transformed generalized linear models

The estimation of data transformation is very useful to yield response variables satisfying closely a normal linear model, Generalized linear models enable the fitting of models to a wide range of data types. These models are based on exponential dispersion models. We propose a new class of transformed generalized linear models to extend the Box and Cox models and the generalized linear models. We use the generalized linear model framework to fit these models and discuss maximum likelihood estimation and inference. We give a simple formula to estimate the parameter that index the transformation of the response variable for a subclass of models. We also give a simple formula to estimate the rth moment of the original dependent variable. We explore the possibility of using these models to time series data to extend the generalized autoregressive moving average models discussed by Benjamin er al. [Generalized autoregressive moving average models. J. Amer. Statist. Assoc. 98, 214-223]. The usefulness of these models is illustrated in a Simulation study and in applications to three real data sets. (C) 2009 Elsevier B.V. All rights reserved.

Transformed symmetric models

For the first time, we introduce a class of transformed symmetric models to extend the Box and Cox models to more general symmetric models. The new class of models includes all symmetric continuous distributions with a possible non-linear structure for the mean and enables the fitting of a wide range of models to several data types. The proposed methods offer more flexible alternatives to Box-Cox or other existing procedures. We derive a very simple iterative process for fitting these models by maximum likelihood, whereas a direct unconditional maximization would be more difficult. We give simple formulae to estimate the parameter that indexes the transformation of the response variable and the moments of the original dependent variable which generalize previous published results. We discuss inference on the model parameters. The usefulness of the new class of models is illustrated in one application to a real dataset.

A Bayesian Long-term Survival Model Parametrized in the Cured Fraction

The main goal of this paper is to investigate a cure rate model that comprehends some well-known proposals found in the literature. In our work the number of competing causes of the event of interest follows the negative binomial distribution. The model is conveniently reparametrized through the cured fraction, which is then linked to covariates by means of the logistic link. We explore the use of Markov chain Monte Carlo methods to develop a Bayesian analysis in the proposed model. The procedure is illustrated with a numerical example.