A Likelihood-Based Multiple Change Point Algorithm for Count Data with Allowance for Over-Dispersion

Count data is almost always over-dispersed where the variance exceeds the mean. Several count data models have been proposed by researchers but the problem of over-dispersion still remains unresolved, more so in the context of change point analysis. This study develops a likelihood-based algorithm that detects and estimates multiple change points in a set of count data assumed to follow the Negative Binomial distribution. Discrete change point procedures discussed in literature work well for equi-dispersed data. The new algorithm produces reliable estimates of change points in cases of both equi-dispersed and over-dispersed count data;hence its advantage over other count data change point techniques. The Negative Binomial Multiple Change Point Algorithm was tested using simulated data for different sample sizes and varying positions of change. Changes in the distribution parameters were detected and estimated by conducting a likelihood ratio test on several partitions of data obtained through step-wise recursive binary segmentation. Critical values for the likelihood ratio test were developed and used to check for significance of the maximum likelihood estimates of the change points. The change point algorithm was found to work best for large datasets, though it also works well for small and medium-sized datasets with little to no error in the location of change points. The algorithm correctly detects changes when present and fails to detect changes when change is absent in actual sense. Power analysis of the likelihood ratio test for change was performed through Monte-Carlo simulation in the single change point setting. Sensitivity analysis of the test power showed that likelihood ratio test is the most powerful when the simulated change points are located mid-way through the sample data as opposed to when changes were located in the periphery. Further, the test is more powerful when the change was located three-quarter-way through the sample data compared to when the change point is closer (quarter-way) to the first observation.

子空间干扰加高斯杂波背景下基于GLRT的斜对称方向检测器设计

文章研究了背景为子空间干扰加高斯杂波的距离扩展目标方向检测问题。杂波是均值为零协方差矩阵未知但具有斜对称特性的高斯杂波,目标与干扰分别通过具备斜对称特性的目标子空间和干扰子空间描述。针对方向检测问题,利用上述斜对称性,根据广义似然比检验(Generalized Likeli-hood Ratio Test,GLRT)准则的一步与两步设计方法,设计了基于GLRT的一步法与两步法的距离扩展目标方向检测器。通过理论推导证明了这2种检测器相对于未知杂波协方差矩阵都具有恒虚警率。对比相同背景下已有检测器,特别是在辅助数据有限的场景下,文章提出的2个检测器表现出了优越的检测性能。

ASYMPTOTIC DISTRIBUTION OF LIKELIHOOD RATIO STATISTIC FOR TESTING SPHERICTY IN GROWTH CURVE MODELS

In this paper, asymptotic expansions of the distribution of the likelihood ratio statistic for testing sphericity in a crowth curve model have been derived in the null and nonnull cases when the alternatives are dose to the null hypothesis. These expansions are given in series form of beta distributions.

NONNULL DISTRIBUTION OF THE LIKELIHOOD RATIO CRITERION FOR TESTING THE EQUALITY OF DIAGONAL BLOCKS WITH BLOCKWISE INDEPENDENCE

In this paper, the nonnull moments and the distributions of the likelihood ratio criterion for testing the equality of diagonal blocks with blockwise independence under certain alternatives have derived.

Voice activity detection based on deep belief networks using likelihood ratio

A novel technique is proposed to improve the performance of voice activity detection(VAD) by using deep belief networks(DBN) with a likelihood ratio(LR). The likelihood ratio is derived from the speech and noise spectral components that are assumed to follow the Gaussian probability density function(PDF). The proposed algorithm employs DBN learning in order to classify voice activity by using the input signal to calculate the likelihood ratio. Experiments show that the proposed algorithm yields improved results in various noise environments, compared to the conventional VAD algorithms. Furthermore, the DBN based algorithm decreases the detection probability of error with [0.7, 2.6] compared to the support vector machine based algorithm.

THE ASYMPTOTIC DISTRIBUTIONS OF EMPIRICAL LIKELIHOOD RATIO STATISTICS IN THE PRESENCE OF MEASUREMENT ERROR

Suppose that several different imperfect instruments and one perfect instrument are independently used to measure some characteristics of a population. Thus, measurements of two or more sets of samples with varying accuracies are obtained. Statistical inference should be based on the pooled samples. In this article, the authors also assumes that all the imperfect instruments are unbiased. They consider the problem of combining this information to make statistical tests for parameters more relevant. They define the empirical likelihood ratio functions and obtain their asymptotic distributions in the presence of measurement error.

Modified likelihood ratio test for homogeneity in normal mixtures with two samples

This paper investigates the modified likelihood ratio test（LRT） for homogeneity in normal mixtures of two samples with mixing proportions unknown. It is proved that the limit distribution of the modified likelihood ratio test is X^2（1）.

A Note on Approximation of Likelihood Ratio Statistic in Exploratory Factor Analysis

In normal theory exploratory factor analysis, likelihood ratio (LR) statistic plays an important role in evaluating the goodness-of-fit of the model. In this paper, we derive an approximation of the LR statistic. The approximation is then used to show explicitly that the expectation of the LR statistic agrees with the degrees of freedom of the asymptotic chi-square distribution.

Likelihood Ratio and Strong Limit Theorems for the Discrete Random Variable

This in virtue of the notion of likelihood ratio and the tool of moment generating function, the limit properties of the sequences of random discrete random variables are studied, and a class of strong deviation theorems which represented by inequalities between random variables and their expectation are obtained. As a result, we obtain some strong deviation theorems for Poisson distribution and binomial distribution.

Profile Likelihood Tests for Common Risk Ratios in Meta-Analysis Studies

It is well-known that the power of Cochran’s Q test to assess the presence of heterogeneity among treatment effects in a clinical meta-analysis is low due to the small number of studies combined. Two modified tests (PL1, PL2) were proposed by replacing the profile maximum likelihood estimator (PMLE) into the variance formula of logarithm of risk ratio in the standard chi-square test statistic for testing the null common risk ratios across all k studies (i = 1, L, k). The simply naive test (SIM) as another comparative candidate has considerably arisen. The performance of tests in terms of type I error rate under the null hypothesis and power of test under the random effects hypothesis was done via a simulation plan with various combinations of significance levels, numbers of studies, sample sizes in treatment and control arms, and true risk ratios as effect sizes of interest. The results indicated that for moderate to large study sizes (k?≥ 16)?in combination with moderate to large sample sizes?(?≥ 50), three tests (PL1, PL2, and Q) could control type I error rates in almost all situations. Two proposed tests (PL1, PL2) performed best with the highest power when?k?≥ 16?and moderate sample sizes (= 50,100);this finding was very useful to make a recommendation to use them in practical situations. Meanwhile, the standard Q test performed best when?k?≥ 16 and large sample sizes (≥ 500). Moreover, no tests were reasonable for small sample sizes (≤ 10), regardless of study size k. The simply naive test (SIM) is recommended to be adopted with high performance when k = 4 in combination with (≥ 500).

Generalized Likelihood Ratio Tests for Varying-Coefficient Models with Censored Data

In this paper, we extend the generalized likelihood ratio test to the varying-coefficient models with censored data. We investigate the asymptotic behavior of the proposed test and demonstrate that its limiting null distribution follows a distribution, with the scale constant and the number of degree of freedom being independent of nuisance parameters or functions, which is called the wilks phenomenon. Both simulated and real data examples are given to illustrate the performance of the testing approach.

Maximum likelihood channel estimation algorithm combines logarithm likelihood ratio decoding in the coal mine application

The environment of the wireless communication system in the coal mine has unique characteristics： great noise, strong multiple path interference, and the wireless communication of orthogonal frequency division multiplexing （OFDM） in underground coal mine is sensitive to the frequency selection of multiple path fading channel, whose decoding is separated from the traditional channel estimation algorithm. In order to increase its accuracy and reliability, a new iterating channel estimation algorithm combining the logarithm likelihood ratio （LLR） decode iterate based on the maximum likelihood estimation （ML） is proposed in this paper, which estimates iteration channel in combination with LLR decode. Without estimating the channel noise power, it exchanges the information between the ML channel estimation and the LLR decode using the feedback information of LLR decode. The decoding speed is very quick, and the satisfied result will be obtained by iterating in some time. The simulation results of the shortwave broadband channel in the coal mine show that the error rate of the system is basically convergent after the iteration in two times.

Log Likelihood Ratio-Based Relaying for Distributed Turbo Codes

A distributed turbo codes（ DTC） scheme with log likelihood ratio（ LLR）-based threshold at the relay for a two-hop relay networks is proposed. Different from traditional DTC schemes,the retransmission scheme at the relay,where imperfect decoding occurs,is considered in the proposed scheme. By employing a LLR-based threshold at the relay in the proposed scheme,the reliability of decoder-LLRs can be measured. As a result,only reliable symbols will be forwarded to the destination and a maximum ratio combiner（ MRC） is used to combine signals received from both the source and the relay. In order to obtain the optimal threshold at the relay,an equivalent model of decoderLLRs is investigated,so as to derive the expression of the bit error probability（ BEP） of the proposed scheme under binary phase shift keying（ BPSK） modulation. Simulation results demonstrate that the proposed scheme can effectively mitigate error propagation at the relay and also outperforms other existing methods.

Local Empirical Likelihood Diagnosis of Varying Coefficient Density-Ratio Models Based on Case-Control Data

In this paper, a varying-coefficient density-ratio model for case-control studies is developed. We investigate the local empirical likelihood diagnosis of varying coefficient density-ratio model for case-control data. The local empirical log-likelihood ratios for the nonparametric coefficient functions are introduced. First, the estimation equations based on empirical likelihood method are established. Then, a few of diagnostic statistics are proposed. At last, we also examine the performance of proposed method for finite sample sizes through simulation studies.

基于极化SAR梯度和复Wishart分类器的舰船检测

舰船检测是极化SAR系统的重要应用之一。现有的舰船检测方法容易受到旁瓣泄露的干扰,使得舰船目标的形态难以提取,导致检测结果不符合真实情况。此外,在舰船过于密集、尺度不一致的情况下,相邻舰船由于旁瓣的影响有时会被认为是单个目标,从而造成漏检。针对这些问题,该文提出一种基于极化SAR梯度和复Wishart分类器的舰船检测方法。首先,将似然比检验(LRT)梯度引入对数比值梯度框架,使其适用于极化SAR数据;基于LRT梯度图进行恒虚警(CFAR)检测,提取舰船的边缘信息,消除伪影的同时抑制强旁瓣对舰船精细轮廓提取的影响。其次,利用复Wishart迭代分类器对舰船强散射部分进行检测,可排除大部分的杂波干扰且保持舰船形态细节。最后,将二者信息融合,从而可以保持舰船形态细节的同时克服旁瓣和伪信号的虚警。该文在3幅来自ALOS-2卫星的极化SAR图像上进行了对比实验,实验表明与其他方法相比,该文所提算法具有更少的虚警和漏检,且能够有效克服旁瓣泄露,保持舰船形态细节。

基于自适应ZUPT与航向角误差修正的INS约束算法

为提高行人惯性导航系统(INS)的定位精度,提出了一种基于自适应零速修正算法(ZUPT)与航向角误差修正的INS约束算法。首先,利用基于广义似然比的零速检测阈值与检验统计量的特征值建立关系式,实现对零速检测阈值的自适应调整。然后,对INS解算位置建立线性回归模型,结合主航向与解算航向的航向差,根据行人运动类型构建观测向量和观测矩阵,对INS误差进行修正。最后,经实验验证,当行人在复杂路线变速运动时,相较于固定阈值的零速检测算法和主航向修正算法,所提算法的解算轨迹更接近真实轨迹,平均闭环误差从3.31%D减小至1.45%D,有效提高了INS定位精度,具有较好的工程应用价值。

基于全体数据分布规律的指纹证据似然比评价方法研究

为解决千万人级数据库中指纹自动识别系统比对得分全体数据难以获取的问题,构建科学有效的指纹证据似然比模型,需要对全体数据的分布规律进行探索。以指纹查询比对得分为数据基础,通过R语言采用矩估计和极大似然估计等数理统计方法,对Beta、Norm、Weibull和Gamma 4种参数估计分布函数进行数据拟合和误差计算,以确定最佳的参数估计方法。根据最佳拟合参数方法模拟全体数据,构建似然比模型并计算同源和异源似然比对数值以直方图评估其性能。实验结果表明,Beta分布在单枚和多枚指纹的不同细节特征数量分布规律中误差值最小,拟合效果最好。分段和整体考虑二者细节特征数量所构建的模型相似,随特征数量从5至16个的增加,同源和异源得分数据的概率密度函数曲线分离程度变大,模型性能变强,尤其当细节特征数量超过12个后,同源和异源曲线几乎完全分离,直至16个细节特征时都表现出极好的区分识别能力。针对单枚指纹所分的三段模型与指纹鉴定实际工作相符,但考虑所有特征数量时,会因综合数据较多而使模型性能下降。Beta分布可较好地展现异源条件下全体指纹数据的分布规律,以此构建的似然比模型的区分识别能力较强,具有很好的实用前景,有助于推动指纹证据评价从经验走向科学。

微囊藻毒素-LR完全抗原的设计及制备

从偶联位点、偶联剂、载体蛋白和偶联步骤等分析出发,设计了微囊藻毒素-LR (Microcystin- LR ,MC- LR)完全抗原的制备方法.在半抗原分子第7位氨基酸分子上引进1个自由的氨基;再用戊二醛2步法将此中间产物(H2 N etMC- LR)分别与BSA和OVA偶联.中间产物和偶联产物分别经固相萃取和透析纯化后,经SDS凝胶电泳、紫外扫描及生物质谱技术鉴定,结果表明MC- LR与BSA的平均偶联比能达到5以上,满足了进一步免疫的要求.

距离像先验引导的扩展目标检测方法

扩展目标检测通常采用距离像能量积累检测的方法,由于距离像信息掌握不完备,陷落损失会降低检测性能。本文提出一种距离像先验引导的扩展目标检测方法,通过利用距离像包络模先验,对信号进行积累以提升检测性能。该方法考虑了复距离像与复高斯白噪声的相干叠加与相位预测不准的因素,采用将观测数据取模的检测模型,基于似然比检测(Likelihood Ratio Test,LRT)理论推导了低信噪比下的特征平方匹配检测器。该检测器将目标复距离像的包络模与观测数据的包络模进行平方匹配,并通过门限判决来判断目标是否存在。包络模先验的获取是通过从ISAR图像提取二维散射中心,向对应姿态角下的雷达视线方向进行投影,来获得目标近似的一维散射中心模型,再由该模型进一步生成目标距离像的包络模先验。同时,本文从理论与实验两方面分析了能量检测器和特征平方匹配检测器之间的关系,通过散射中心模型重构与暗室测量的方法获取数据进行了实验验证。实验结果表明:在低信噪比下,距离像先验引导的特征平方匹配检测器能有效提升目标的检测性能,并且对先验模型失配的情况具有良好的适应性。

局部均匀背景中距离扩展目标的GLRT检测器及性能分析

在复合高斯杂波满足局部均匀的背景下,对均匀杂波分组模型进行推广,建立了广义杂波分组模型.进一步,利用广义似然比检验(GLRT)原理,提出了距离扩展目标的基于广义杂波分组的GLRT检测器(GCC-GLRT),并推导了检测器虚警概率与检测门限关系的表达式.GCC-GLRT有效地解决了基于均匀杂波分组的GLRT检测器(CCGLRT)在非均匀杂波分组背景下不具备CFAR特性的问题.仿真结果还表明,对于稀疏散射点目标,在合适的杂波分组情况下,GCC-GLRT能有效克服采用NSDD-GLRT检测器出现的"坍塌损失",改善检测器的检测性能.