Analysis of incomplete data in presence of competing risks among several groups

In reliability analysis, an investigator is often interested in the assessment of a specific risk in presence of other risk factors. It is well known as the competing risks problem in the statistical literature. In this paper, we consider the analysis of incomplete data in the presence of competing risks among several groups. We mainly consider the latent failure times model formulation, and it is assumed that the lifetime distributions of the different latent failure times of a particular group follow Weibull distributions with different scale parameters, but the same shape parameter. Maximum likelihood estimators of the different parameters are obtained using a simple iterative procedure, and also by EM algorithm. Asymptotic distributions of the maximum likelihood estimators of the different parameters are obtained, and based on the asymptotic distributions, asymptotic confidence intervals are also proposed. Testing equality of the parameters among several groups is performed. One data set has been analysed for illustrative purposes.     

Parametric inference of incomplete data with competing risks among several groups

We develop parametric inferential methods for the competing risks problem where data arise due to multiple causes of failure in several groups with censoring and possibly missing causes. We provide the general likelihood method and the closed-form maximum-likelihood estimators for the exponential model. Parametric tests are given for comparing different causes and groups. An extensive numerical and graphical investigation is presented to substantiate the proposed methods. A real-data example is illustrated.     

Parameter estimation for Markov modulated Poisson processes via the EM algorithm with time discretization

The Markov modulated Poisson process (MMPP) has been proposed as a suitable model for characterizing the input traffic to a statistical multiplexer [6]. This paper describes a novel method of parameter estimation for MMPPs. The idea is to employ time discretization to convert an MMPP from the continuous-time domain into the discrete-time domain and then to use a powerful statistical inference technique, known as the EM algorithm, to obtain maximum-likelihood estimates of the model parameters. Tests conducted through a series of simulation experiments indicate that the new method yields results that are significantly more accurate compared to the method described in [8]. In addition, the new method is more flexible and general in that it is applicable to MMPPs with any number of states while retaining nearly constant simplicity in its implementation. Detailed experimental results on the sensitivity of the estimation accuracy to (1) the initialization of the model, (2) the size of the observation interarrival interval data available for the estimation, and (3) the inherent separability of the MMPP states are presented.     

Parameter estimation of weak space-based ADS-B signals using genetic algorithm

Space-based automatic dependent surveillance-broadcast (ADS-B) is an important emerging augmentation of existing ground-based ADS-B systems. In this paper, the problem of space-based ultra-long-range reception processing of ADS-B signals is described. We first introduce a header detection method for accurately determining the pulse position of a weak ADS-B signal. We designed a signal encoding method, shaping method, and fitness function. We then employed a genetic algorithm to perform high-precision frequency and phase estimations of the detected weak signal. The advantage of this algorithm is that it can simultaneously estimate the frequency and phase, meaning a direct coherent demodulation can be implemented. To address the computational complexity of the genetic algorithm, we improved the ratio algorithm for frequency estimation and raised the accuracy beyond that of the original ratio algorithm with only a slight increase in the computational complexity using relatively few sampling points.     

Adaptive MLSDE using the EM algorithm

The theory of adaptive sequence detection incorporating estimation of channel and related parameters is studied in the context of maximum-likelihood (ML) principles in a general framework based on the expectation and maximization (EM) algorithm. A generalized ML sequence detection and estimation (GMLSDE) criterion is derived based on the EM approach, and it is shown how the per-survivor processing and per-branch processing methods emerge naturally from GMLSDE. GMLSDE is developed into a real time detection/estimation algorithm using the online EM algorithm with coupling between estimation and detection. By utilizing Titterington's (1984) stochastic approximation approach, different adaptive ML sequence detection and estimation (MLSDE) algorithms are formulated in a unified manner for different channel models and for different amounts of channel knowledge available at the receiver. Computer simulation results are presented for differentially encoded quadrature phase-shift keying in frequency flat and selective fading channels, and comparisons are made among the performances of the various adaptive MLSDE algorithms derived earlier     

Bayesian reconstructions from emission tomography data using a modified EM algorithm

A novel method of reconstruction from single-photon emission computerized tomography data is proposed. This method builds on the expectation-maximization (EM) approach to maximum likelihood reconstruction from emission tomography data, but aims instead at maximum posterior probability estimation, which takes account of prior belief about smoothness in the isotope concentration. A novel modification to the EM algorithm yields a practical method. The method is illustrated by an application to data from brain scans.     

Adaptive snakes using the EM algorithm.

Deformable models (e.g., snakes) perform poorly in many image analysis problems. The contour model is attracted by edge points detected in the image. However, many edge points do not belong to the object contour, preventing the active contour from converging toward the object boundary. A new algorithm is proposed in this paper to overcome this difficulty. The algorithm is based on two key ideas. First, edge points are associated in strokes. Second, each stroke is classified as valid (inlier) or invalid (outlier) and a confidence degree is associated to each stroke. The expectation maximization algorithm is used to update the confidence degrees and to estimate the object contour. It is shown that this is equivalent to the use of an adaptive potential function which varies during the optimization process. Valid strokes receive high confidence degrees while confidence degrees of invalid strokes tend to zero during the optimization process. Experimental results are presented to illustrate the performance of the proposed algorithm in the presence of clutter, showing a remarkable robustness.     

Multispectral image segmentation using the rough-set-initialized EM algorithm

The problem of segmentation of multispectral satellite images is addressed. An integration of rough-set-theoretic knowledge extraction, the Expectation Maximization (EM) algorithm, and minimal spanning tree (MST) clustering is described. EM provides the statistical model of the data and handles the associated measurement and representation uncertainties. Rough-set theory helps in faster convergence and in avoiding the local minima problem, thereby enhancing the performance of EM. For rough-set-theoretic rule generation, each band is discretized using fuzzy-correlation-based gray-level thresholding. MST enables determination of nonconvex clusters. Since this is applied on Gaussians, determined by granules, rather than on the original data points, time required is very low. These features are demonstrated on two IRS-1A four-band images. Comparison with related methods is made in terms of computation time and a cluster quality measure.     

改进的高效MIMO-OFDM系统EM信道估计算法

针对MIMO-OFDM系统中期望最大化(EM)信道估计算法在高信噪比(SNR)下带来的误差地板(EF)现象,且OFDM符号的数据传输效率随发射天线数的增加而明显降低,提出一种改进的高效EM信道估计算法。该算法首先引入一种准确的等效信号模型并推导出一种修正的EM算法,改善了EM算法在高SNR下的性能;在多个OFDM间利用相位正交导频序列来提高数据传输效率,同时进行联合信道估计以提高估计性能。仿真实验验证了所提算法具有更高的信道估计性能和更高的数据传输效率。     

Parameter estimation using pseudorandom binary sequences

The instrumental-variable technique for parameter estimation is applied when the input is a pseudorandom binary sequence (p.r.b.s.). The instrumental variables proposed are time-weighted elements of a p.r.b.s., and this is shown to be equivalent to obtaining the mean value of several estimates obtained from noisy measurements. The estimates of the parameters are asymptotically unbiased.     

A generalized EM algorithm for 3-D Bayesian reconstruction from Poisson data using Gibbs priors

A generalized expectation-maximization (GEM) algorithm is developed for Bayesian reconstruction, based on locally correlated Markov random-field priors in the form of Gibbs functions and on the Poisson data model. For the M-step of the algorithm, a form of coordinate gradient ascent is derived. The algorithm reduces to the EM maximum-likelihood algorithm as the Markov random-field prior tends towards a uniform distribution. Three different Gibbs function priors are examined. Reconstructions of 3-D images obtained from the Poisson model of single-photon-emission computed tomography are presented.     

Parameter estimation for autoregressive Gaussian-mixture processes:the EMAX algorithm

The problem of estimating parameters of discrete-time non-Gaussian autoregressive (AR) processes is addressed. The subclass of such processes considered is restricted to those whose driving noise samples are statistically independent and identically distributed according to a Gaussian-mixture probability density function (pdf). Because the likelihood function for this problem is typically unbounded in the vicinity of undesirable, degenerate parameter estimates, the maximum likelihood approach is not fruitful. Hence, an alternative approach is taken whereby a finite local maximum of the likelihood surface is sought. This approach, which is termed the quasimaximum likelihood (QML) approach, is used to obtain estimates of the AR parameters as well as the means, variances, and weighting coefficients that define the Gaussian-mixture pdf. A technique for generating solutions to the QML problem is derived using a generalized version of the expectation-maximization principle. This technique, which is referred to as the EMAX algorithm, is applied in four illustrative examples; its performance is compared directly with that of previously proposed algorithms based on the same data model and that of conventional least-squares techniques     

Application of deterministic annealing EM algorithm to MAP/PH parameter estimation

This paper proposes a variant of EM (expectation-maximization) algorithm for Markovian arrival process (MAP) and phase-type distribution (PH) parameter estimation. Especially, we derive the deterministic annealing EM (DAEM) algorithm for MAP/PH parameter estimation. The DAEM algorithm is one of the methods to overcome a local maxima problem associated with the conventional EM algorithm. This paper derives concrete E- and M-step formulas for MAP parameter estimation from inter-arrival time data and PH parameter estimation from point samples in the framework of DAEM algorithm. Numerical examples demonstrate the DAEM algorithm for Markov-modulated Poisson process (MMPP) and several classes of PH distribution.     

New EM parameter estimation algorithm for a type of micro-motion SFM signal

Aiming at the problem that the existing method has high computational complexity and high SNR,a novel method of multi-component SFM signals parameter estimation based on EM algorithm was proposed as to spinning tar-get's narrow band micro-motion echoes.The echo model of spinning target and its micro-doppler measurements based on time-frequency analysis were given.The iterative parameter estimation steps based on Gaussian mixture model and EM algorithm to measurements were established.The simulation results demonstrate that when SNR is greater than -3 dB and the SFM components are equal or greater than 2,the method can estimate the target’s micro-motion parameters e.g.projection size accurately in narrow band condition.     

OFDM系统中基于EM迭代的时变信道估计与数据检测

针对OFDM系统中难以实时获取时变信道统计信息的问题,提出了一种基于期望最大化(EM, expectation maximization)迭代的多符号联合信道估计和数据检测算法。为了获取合适的迭代初始值,利用梳状导频的信息,设计了基于最小二乘算法的低复杂度的初始化方案。通过分析算法中的信道统计量与信噪比的关系,提出了忽略信道自相关矩阵的简化算法,避免了获取信道统计信息的操作。仿真结果表明,提出的算法对信道的功率延迟分布和多普勒功率谱等统计信息不敏感,在未知信道多普勒功率谱的条件下,仍然具有较低的估计误差和误码率。      

MAP symbol estimation on frequency-flat Rayleigh fading channelsvia a Bayesian EM algorithm

In this paper, an expectation-maximization (EM) technique for maximum a posteriori estimation is employed to devise novel soft-in soft-out algorithms for symbol detection over frequency-flat Rayleigh fading channels. An application of these algorithms to iterative decoding of coded PSK signals is proposed and some performance results are illustrated     

EM框架下实现被动测距的状态估计和参数学习

在红外成像跟踪系统中,通常仅能测量目标的角度信息,不能直接测量目标与观测站间的距离。研究了基于红外成像系统的被动测距技术,首先利用状态空间模型的分析方法建立被动测距的状态估计和参数学习的混合估计模型,然后介绍EM的基本原理和参数的最大似然估计。EM算法的E步利用粒子滤波和粒子平滑器来完成,实现被动测距的状态估计;M步利用梯度搜索的方法来求解参数。被动测距是一个带有未知参数的非线性系统的状态估计,文中利用状态估计与参数学习的状态空间模型来描述,并利用EM法来求解,为被动测距的求解提供了一条新的途径。模拟实验表明,基于粒子滤波和梯度搜索的EM方法能同时完成被动测距的状态估计和参数学习。     

Joint carrier frequency synchronization and channel estimation for OFDM systems via the EM algorithm

A joint carrier frequency synchronization and channel estimation scheme is proposed for orthogonal frequency-division multiplexing (OFDM) system. In the proposed scheme, carrier frequency synchronization and channel estimation are performed iteratively via the expectation-maximization (EM) algorithm using an OFDM preamble symbol. Moreover, we analytically investigate the effect of frequency offset error on the mean square error (MSE) performance of channel estimator. Simulation results present that the proposed scheme achieves almost ideal performance for both channel and frequency offset estimation.     

Multiple frequencies and AR parameters estimation from one bitquantized signal via the EM algorithm

The authors present a novel algorithm which is used to estimate the coefficients of q AR processes from a coarsely quantized signal. The input signal to the quantizer is the superposition of q AR processes and noise. In a related problem a modified version of the above algorithm is used to estimate the frequencies of coarsely quantized data obtained from q sinusoids embedded in noise. The proposed algorithm can accommodate a nonuniform m-level quantizer, as well as the special case of a one bit quantizer. The proposed estimator is based on the maximum likelihood (ML) criterion, and is realized by judiciously combining the expectation-maximization (EM) algorithm of Dempster, Laird and Rubin (1977), and the “Gaussian fit” scheme of Curry (1970). Simulations reveal that they can accurately estimate the coefficients of several AR processes, or the frequencies of several sinusoids, from one bit quantized data at low signal to noise ratios and moderate number of observations     

用于高斯混合模型参数估计的EM算法及其初始化研究

基于有限混合模型的聚类是一种重要的聚类分析方法,而EM算法是混合模型参数估计的重要方法.传统的EM算法对初始聚类中心比较敏感,因此如何选取初始值成为运用EM算法实现高斯混合模型聚类中的一个重要问题.本文提出一种基于网格的聚类算法来初始化EM算法,旨在改善EM算法的初始敏感性,使其达到更佳的聚类效果.此算法根据网格单元密...