A rigorous analysis of the power distribution in plastic clad annular core optical fibers

Using Maxwell's field equations, an analytical investigation is presented of the relative power distributions in the different sections of a step-index plastic clad annular core optical fiber (ACF) operating in the infrared region of the electromagnetic (EM) spectrum. It is assumed that the fiber cross-section is made of two concentric circles, and the EM waves propagate through the annular region. The chosen fiber materials are widely used in low cost optical links. The wave equations are solved in the different sections of the fiber, and the general expressions for power in the core and the cladding regions are finally deduced. Plots are shown of the variation of fractional power (or the power confinement factor) in all the fiber sections against the propagation constants of sustained modes. The cases of three lowest azimuthal modal indices (i.e. meridional as well as skew modes) are described. It is observed that the confinement of power in the core section is increased for ACFs of larger cross-sectional dimensions. Also, a fairly uniform distribution of power over the sustained modes remains for large sized fibers, and this uniformity is greatly affected in ACFs of smaller dimensions. It is suggested that, because of strong evanescent fields, ACFs can be of potential use in chemical sensing. Apart from this, it is also presumed that these may be useful in the areas of communications. The improved mechanical strength adds the potentiality of ACFs.     

偏t正态数据下混合线性联合位置与尺度模型的参数估计

偏t正态分布是分析尖峰,厚尾数据的重要统计工具之一.研究提出了偏t正态数据下混合线性联合位置与尺度模型,通过EM算法和Newton-Raphson方法研究了该模型参数的极大似然估计.并通过随机模拟试验验证了所提出方法的有效性.最后,结合实际数据验证了该模型和方法具有实用性和可行性.     

Bayesian and Maximum Likelihood Estimation for Gaussian Processes on an Incomplete Lattice

This article proposes a new approach for Bayesian and maximum likelihood parameter estimation for stationary Gaussian processes observed on a large lattice with missing values. We propose a Markov chain Monte Carlo approach for Bayesian inference, and a Monte Carlo expectation-maximization algorithm for maximum likelihood inference. Our approach uses data augmentation and circulant embedding of the covariance matrix, and provides likelihood-based inference for the parameters and the missing data. Using simulated data and an application to satellite sea surface temperatures in the Pacific Ocean, we show that our method provides accurate inference on lattices of sizes up to 512 × 512, and is competitive with two popular methods: composite likelihood and spectral approximations.     

Regime-switching stochastic volatility model: estimation and calibration to VIX options

We develop and implement a method for maximum likelihood estimation of a regime-switching stochastic volatility model. Our model uses a continuous time stochastic process for the stock dynamics with the instantaneous variance driven by a Cox–Ingersoll–Ross process and each parameter modulated by a hidden Markov chain. We propose an extension of the EM algorithm through the Baum–Welch implementation to estimate our model and filter the hidden state of the Markov chain while using the VIX index to invert the latent volatility state. Using Monte Carlo simulations, we test the convergence of our algorithm and compare it with an approximate likelihood procedure where the volatility state is replaced by the VIX index. We found that our method is more accurate than the approximate procedure. Then, we apply Fourier methods to derive a semi-analytical expression of S&P500 and VIX option prices, which we calibrate to market data. We show that the model is sufficiently rich to encapsulate important features of the joint dynamics of the stock and the volatility and to consistently fit option market prices.     

Mixed effects regression trees for clustered data

This paper presents an extension of the standard regression tree method to clustered data. Previous works extending tree methods to accommodate correlated data are mainly based on the multivariate repeated-measures approach. We propose a “mixed effects regression tree” method where the correlated observations are viewed as nested within clusters rather than as vectors of multivariate repeated responses. The proposed method can handle unbalanced clusters, allows observations within clusters to be split, and can incorporate random effects and observation-level covariates. We implemented the proposed method using a standard tree algorithm within the framework of the expectation-maximization (EM) algorithm. The simulation results show that the proposed regression tree method provides substantial improvements over standard trees when the random effects are non negligible. A real data example is used to illustrate the method.     

Heteroscedastic nonlinear regression models based on scale mixtures of skew-normal distributions

An extension of some standard likelihood based procedures to heteroscedastic nonlinear regression models under scale mixtures of skew-normal (SMSN) distributions is developed. We derive a simple EM-type algorithm for iteratively computing maximum likelihood (ML) estimates and the observed information matrix is derived analytically. Simulation studies demonstrate the robustness of this flexible class against outlying and influential observations, as well as nice asymptotic properties of the proposed EM-type ML estimates. Finally, the methodology is illustrated using an ultrasonic calibration data.     

Determination of engineered nanoparticles on textiles and in textile wastewaters

Textile materials with engineered nanoparticles (ENPs) have excellent properties as they are antibacterial, antimicrobial, water resistant and protective. The textile industry has recognized the importance and the advantages of ENPs, so they comprise one of the fastest developing branches of processing.The most important sources of ENPs released to the environment from textiles are textile-industry wastewaters and waters from large hospital or hotel laundries. In addition, waste textile materials coated with ENPs present a threat to the environment, if such materials are not properly handled and disposed of after use.Currently, the toxicity and the potential harm of ENPs widely applied on textiles are not thoroughly investigated and/or eliminated. Consequently, there is an urgent need to define the most appropriate analytical methods for monitoring ENPs on textiles.This review presents the most important techniques for monitoring ENPs on textile materials and in textile-wastewater samples, from the perspective of protecting the environment and human health.     

Multi-Period Asset Allocation Under Hidden Markovianly Driven Noises

Abstract

Techniques of filtering and parameter reestimation of a general hidden Markov model are developed and applied to a discrete time multi-period asset allocation problem, where a commonly used mean-variance utility is considered and recursive calculation of an explicit optimal portfolio is provided. Our result is a generalization of that by Robert J. Elliott and John van der Hoek.     

Asymptotic Corrections for Multivariate Posterior Moments with Factored Likelihood Functions

Abstract

Asymptotic corrections are used to compute the means and the variance-covariance matrix of multivariate posterior distributions that are formed from a normal prior distribution and a likelihood function that factors into separate functions for each variable in the posterior distribution. The approximations are illustrated using data from the National Assessment of Educational Progress (NAEP). These corrections produce much more accurate approximations than those produced by two different normal approximations. In a second potential application, the computational methods are applied to logistic regression models for severity adjustment of hospital-specific mortality rates.     

Stable Computation of Maximum Likelihood Estimates in Identity Link Poisson Regression

Identity link Poisson regression is useful when the mean of a count variable depends additively on a collection of predictor variables. It is particularly important in epidemiology, for modeling absolute differences in disease incidence rates as a function of covariates. A complication of such models is that standard computational methods for maximum likelihood estimation can be numerically unstable due to the nonnegativity constraints on the Poisson means. Here we present a straightforward and flexible method that provides stable maximization of the likelihood function over the constrained parameter space. This is achieved by conducting a sequence of maximizations within subsets of the parameter space, after which the global maximum is identified from among the subset maxima. The method adapts and extends EM algorithms that are useful in specialized applications involving Poisson deconvolution, but which do not apply in more general regression contexts. As well as allowing categorical and continuous covariates, the method has the flexibility to accommodate covariates with an unspecified isotonic form. Its computational reliability makes it particularly useful in bootstrap analyses, which may require stable convergence for thousands of implementations. Computations are illustrated using epidemiological data on occupational mortality, and biological data on crab population counts. This article has supplementary material online.