Multidimensional dependency measures

The problem of dependency between two random variables has been studied throughly in the literature. Many dependency measures have been proposed according to concepts such as concordance, quadrant dependency, etc. More recently, the development of the Theory of Copulas has had a great impact in the study of dependence of random variables specially in the case of continuous random variables. In the case of the multivariate setting, the study of the strong mixing conditions has lead to interesting results that extend some results like the central limit theorem to the case of dependent random variables.In this paper, we study the behavior of a multidimensional extension of two well-known dependency measures, finding their basic properties as well as several examples. The main difference between these measures and others previously proposed is that these ones are based on the definition of independence among n random elements or variables, therefore they provide a nice way to measure dependency.The main purpose of this paper is to present a sample version of one of these measures, find its properties, and based on this sample version to propose a test of independence of multivariate observations. We include several references of applications in Statistics.     

Bayesian estimation of NIG models via Markov chain Monte Carlo methods

The normal inverse Gaussian (NIG) distribution is a promising alternative for modelling financial data since it is a continuous distribution that allows for skewness and fat tails. There is an increasing number of applications of the NIG distribution to financial problems. Due to the complicated nature of its density, estimation procedures are not simple. In this paper we propose Bayesian estimation for the parameters of the NIG distribution via an MCMC scheme based on the Gibbs sampler. Our approach makes use of the data augmentation provided by the mixture representation of the distribution. We also extend the model to allow for modelling heteroscedastic regression situations. Examples with financial and simulated data are provided. Copyright © 2004 John Wiley & Sons, Ltd.     

Numerical computation of mean passage times and absorption probabilities in Markov and Semi-Markov models

This paper discusses an efficient method to compute mean passage times and absorption probabilities in Markov and Semi-Markov models. It uses the state reduction approach introduced by Winfried Grassmann for the computation of the stationary distribution of a Markov model. The method is numerically stable and has a simple probabilistic interpretation. It is especially stressed, that the natural frame for the state reduction method is rather Semi-Markov theory than Markov theory.

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Zusammenfassung Es wird ein wirkungsvolles Rechenverfahren zur Bestimmung von mittleren Zeiten bis zur Absorption und von Absorptions-Wahrscheinlichkeiten in Markoff- und Semi-Markoff-Modellen dargestellt. Die Methode beruht auf dem Zustands-Reduktions-Ansatz, der von Grassmann für die Berechnung stationärer Verteilungen von Markoff-Ketten eingeführt wurde. Das Verfahren ist numerisch stabil und hat eine einfache wahrscheinlichkeitstheoretische Interpretation. Es wird hervorgehoben, da\ der natürliche Rahmen der Methode eher die Semi-Markoff-Theorie als die Markoff-Theorie ist.

     

Tail behaviour of Gaussian processes with applications to the Brownian pillow

In this paper we investigate the tail behaviour of a random variable S which may be viewed as a functional T of a zero mean Gaussian process X, taking special interest in the situation where X obeys the structure which is typical for limiting processes occurring in nonparametric testing of (multivariate) independency and (multivariate) constancy over time. The tail behaviour of S is described by means of a constant a and a random variable R which is defined on the same probability space as S. The constant a acts as an upper bound, and is relevant for the computation of the efficiency of test statistics converging in distribution to S. The random variable R acts as a lower bound, and is instrumental in deriving approximation for the upper percentage points of S by simulation.     

An invariant manifold approach to nonlinear normal modes of oscillation

Summary A method for determining the amplitude-dependent mode shapes and the corresponding modal dynamics of weakly nonlinear vibratory systems is described. The method is a combination of a Galerkin projection and invariant manifold techniques and is applied to a class of distributed parameter vibratory systems. In this paper the general theory for a class of conservative systems is outlined and applied to determine the nonlinear mode shapes and modal dynamics of a linear Euler-Bernoulli team attached to a nonlinear elastic foundation.     

Quantification of two chromatographic unresolved dichlorophenols using gas chromatography-direct deposition-fourier transform infrared spectrometry and multivariate calibration

A method for the quantification of two chromatographically unresolved dichlorophenol isomers in water is described. Acetylation and concentration on graphitized carbon cartridges are carried out as a preliminary step. Detection is made by gas chromatography (GC) coupled to Fourier transform infrared spectroscopy (FTIR), using a direct deposition interface (DD). Infrared spectra in the maximum of the unresolved peak of 2,5- and 2,4-dichlorophenol for a series of standards with different amounts of these two compounds are used, to elaborate a multivariate calibration model (PLS-1 algorithm). By the method described, concentrations of dichlorophenol isomers in water at ng/ml level can be determined.     

强激光场中NO分子多光子选择激发──含时薛定鄂方程的代数解法

报道了在半经典偶极近似下应用二次型非谐振子李代数模型研究强激光场中NO分子的多光子选择激发，并计算了NO分子的跃迁几率．     

矿化垃圾衍生燃料热解过程HCl与H_2S析出规律

采用热重红外质谱联用法(TG-FTIR-MS)和水平管式热解炉/化学吸收法,对比研究了矿化垃圾(ARDF)和常规垃圾(NRDF)衍生燃料热解过程腐蚀性气体(HCl和H_2S)的析出特性,分析了热解温度及热解类型对析出行为的影响并对热解固相产物腐蚀性元素的赋存特点进行了考察。结果表明,慢速热解过程,两者腐蚀性气体的析出特征温度区间相似,均分为两段,HCl析出区间为200-400和420-500℃,H_2S析出区间为230-370和380-670℃,而ARDF表现为较低的HCl和H_2S析出率;快速热解过程,两者腐蚀性气体的析出受热解温度影响较大,且规律有所差别:随热解温度的升高,HCl析出率呈S型变化(先高后低再高),而H_2S析出率呈正相关,均在850℃达到峰值,其中,HCl析出率分别为48.8%(ARDF)和29.4%(NRDF),H_2S析出率分别为6.8%(ARDF)和44.6%(NRDF)。因腐蚀性气体差异性的析出规律,两类垃圾热解固相产物腐蚀性元素的赋存与热解温度相关,ARDF的Cl和S元素最高赋存率分别可达59.4%(450℃)和84.3%(750℃),而NRDF的Cl和S元素最高赋存率分别仅为36.7%(850℃)和15.2%(650℃)。说明在合适的热解条件下,相比NRDF,ARDF腐蚀性元素不易释放,倾向于固相赋存,此为不同垃圾衍生燃料的热利用提供了一定依据和参考。