Kullback–Leibler life time testing

Model averaging has long been used as a powerful approach to reduce the risk of model misspecification. However, there is little work on model averaging methods under generalized semiparametric models. In this article, we study model averaging in generalized partially linear varying‐coefficient models and propose a semiparametric model averaging estimation (SMAE) method for the canonical parameters. Specifically, we take the partially linear varying‐coefficient model as candidate models in which there is only one varying‐coefficient component. The different covariates could enjoy the benefit of matching the optimal degrees of freedom and each candidate model can take into account the confounding effects among predictors as well. Moreover, the weight choice criterion based on the Kullback–Leibler divergence is adopted to determine the weights. We prove that the corresponding model averaging estimator is asymptotically optimal under certain regularity conditions. Finally, some simulation studies and a real data analysis are conducted to compare with existing methods, and the results show that the proposed method has better out‐of‐sample performance.

Outlier detection is imperative in biomedical data analysis to achieve reliable knowledge discovery. In this paper, a new outlier detection method based on Kullback-Leibler (KL) divergence is presented. The original concept of KL divergence was designed as a measure of distance between two distributions. Stemming from that, we extend it to biological sample outlier detection by forming sample sets composed of nearest neighbors. To handle the non-linearity during the KL divergence calculation and to tackle with the singularity problem due to small sample size, we map the original data into a higher feature space and apply kernel functions without resorting to a mapping function. A sample possessing the largest KL divergence is detected as an outlier. The proposed method is tested with one synthetic data, two public gene expression data sets, and our own mass spectrometry data generated for prostate cancer study.

BackgroundWe propose a novel Markov Blanket-based repeated-fishing strategy (MBRFS) in attempt to increase the power of existing Markov Blanket method (DASSO-MB) and maintain its advantages in omic data analysis.ResultsBoth simulation and real data analysis were conducted to assess its performances by comparing with other methods including χ2 test with Bonferroni and B-H adjustment, least absolute shrinkage and selection operator (LASSO) and DASSO-MB. A serious of simulation studies showed that the true discovery rate (TDR) of proposed MBRFS was always close to zero under null hypothesis (odds ratio = 1 for each SNPs) with excellent stability in all three scenarios of independent phenotype-related SNPs without linkage disequilibrium (LD) around them, correlated phenotype-related SNPs without LD around them, and phenotype-related SNPs with strong LD around them. As expected, under different odds ratio and minor allel frequency (MAFs), MBRFS always had the best performances in capturing the true phenotype-related biomarkers with higher matthews correlation coefficience (MCC) for all three scenarios above. More importantly, since proposed MBRFS using the repeated fishing strategy, it still captures more phenotype-related SNPs with minor effects when non-significant phenotype-related SNPs emerged under χ2 test after Bonferroni multiple correction. The various real omics data analysis, including GWAS data, DNA methylation data, gene expression data and metabolites data, indicated that the proposed MBRFS always detected relatively reasonable biomarkers.ConclusionsOur proposed MBRFS can exactly capture the true phenotype-related biomarkers with the reduction of false negative rate when the phenotype-related biomarkers are independent or correlated, as well as the circumstance that phenotype-related biomarkers are associated with non-phenotype-related ones.Electronic supplementary materialThe online version of this article (doi:10.1186/s12863-016-0358-5) contains supplementary material, which is available to authorized users.

Detection of biomarker genes and their regulatory doses of chemical compounds (DCCs) is one of the most important tasks in toxicogenomic studies as well as in drug design and development. There is an online computational platform “Toxygates” to identify biomarker genes and their regulatory DCCs by co-clustering approach. Nevertheless, the algorithm of that platform based on hierarchical clustering (HC) does not share gene-DCC two-way information simultaneously during co-clustering between genes and DCCs. Also it is sensitive to outlying observations. Thus, this platform may produce misleading results in some cases. The probabilistic hidden variable model (PHVM) is a more effective co-clustering approach that share two-way information simultaneously, but it is also sensitive to outlying observations. Therefore, in this paper we have proposed logistic probabilistic hidden variable model (LPHVM) for robust co-clustering between genes and DCCs, since gene expression data are often contaminated by outlying observations. We have investigated the performance of the proposed LPHVM co-clustering approach in a comparison with the conventional PHVM and Toxygates co-clustering approaches using simulated and real life TGP gene expression datasets, respectively. Simulation results show that the proposed method improved the performance over the conventional PHVM in presence of outliers; otherwise, it keeps equal performance. In the case of real life TGP data analysis, three DCCs (glibenclamide-low, perhexilline-low, and hexachlorobenzene-medium) for glutathione metabolism pathway dataset as well as two DCCs (acetaminophen-medium and methapyrilene-low) for PPAR signaling pathway dataset were incorrectly co-clustered by the Toxygates online platform, while only one DCC (hexachlorobenzene-low) for glutathione metabolism pathway was incorrectly co-clustered by the proposed LPHVM approach. Our findings from the real data analysis are also supported by the other findings in the literature.

Facial Expressions play major role in interpersonal communication and imparting intelligence to computer for identifying facial expressions is a crucial task. In this paper we present an efficient preprocessing algorithm combined with feature extraction using Local Binary Patterns (LBP) followed by classification using Kullback Leibler (KL) divergence. Firstly Viola Jones algorithm is used to detect pair of eyes using which effective part of face is obtained which is further processed to eliminate illumination effect. LBP operator is then applied on the preprocessed image to extract local features represented by histogram. Template histograms for seven basic expressions using training images are formed which are compared with the test histogram distribution using an efficient KL divergence for dissimilarity measure. This algorithm is implemented on JAFFE database resulting in a high classification accuracy of 95.24%.

We consider ordinary differential equations (ODEs) with a known Lyapunov function V. To ensure that a numerical integrator reflects the correct dynamical behaviour of the system, the numerical integrator should have V as a discrete Lyapunov function. Only second-order geometric integrators of this type are known for arbitrary Lyapunov functions. In this paper we describe projection-based methods of arbitrary order that preserve any given Lyapunov function.

Geometric integration methods that unconditionally contract volume

Structural health monitoring is crucial to maintain the structural performance safely. Moreover, the Kullback-Leibler divergence (KLD) is applied usually to asset the similarity between different probability density functions in the pattern recognition. In this study, the KLD is employed to detect the damage. However the asymmetry of the KLD is a shortcoming for the damage detection, to overcoming this shortcoming, two other divergences and one statistic distribution are proposed. Then the damage identification by the KLD and its three descriptions from the symmetric point of view is investigated. In order to improve the reliability and accuracy of the four divergences, the gapped smoothing method (GSM) is adopted. On the basis of the damage index approach, the new damage index (DI) for detect damage more accurately based on the four divergences is developed. In the last, the grey relational coefficient and hypothesis test (GRCHT) is utilized to obtain the more precise damage identification results. Finally, a clear remarkable improvement can be observed. To demonstrate the feasibility and accuracy of the proposed method, examples of an isotropic beam with different damage scenarios are employed so as to check the present approaches numerically. The final results show that the developed approach successfully located the damaged region in all cases effect and accurately.

The generalized power Weibull (GPW) distribution has recently attracted attention as a flexible model for lifetime data, but existing work has focused mainly on unconditional inference under progressive Type~II censoring, comparing maximum likelihood, maximum product spacing and Bayesian estimation in the two-parameter case without covariates. In practical reliability and survival studies, however, lifetimes are typically influenced by explanatory variables and censoring is often implemented through progressive schemes. In this paper we develop a regression framework based on a scale-extended GPW distribution under right censoring, with particular emphasis on progressive Type~II designs: the individual-specific scale parameter is linked to covariates via a log-linear model, while the shape parameters are common across units. We derive the likelihood under non-informative censoring, obtain maximum likelihood estimators and their asymptotic covariance matrix, propose maximum product spacing estimators based on transformed uniform variables, and develop a Bayesian version with gamma priors on the shape parameters and a multivariate normal prior on the regression coefficients, estimated via a Metropolis–Hastings-within-Gibbs sampler. A Monte Carlo study examines finite-sample performance across sample sizes, censoring levels and covariate configurations, and a real data analysis with covariates shows that the GPW regression model can outperform classical Weibull and log-normal regression, extending the scope of the GPW family from unconditional modelling to a flexible regression tool for censored lifetime data.

Outliers often occur during data collection, which could impact the result seriously and lead to a large inference error; therefore, it is important to detect outliers before data analysis. Gamma distribution is a popular distribution in statistics; this paper proposes a method for detecting multiple upper outliers from gamma (m,θ). For computing the critical value of the test statistic in our method, we derive the density function for the case of a single outlier and design two algorithms based on the Monte Carlo and the kernel density estimation for the case of multiple upper outliers. A simulation study shows that the test statistic proposed in this paper outperforms some common test statistics. Finally, we propose an improved testing method to reduce the impact of the swamping effect, which is demonstrated by real data analyses.

We consider the geometric numerical integration of Hamiltonian systems subject to both equality and ``hard” inequality constraints. As in the standard geometric integration setting, we target long-term structure preservation. Additionally, however, we also consider invariant preservation over persistent, simultaneous, and/or frequent boundary interactions. Appropriately formulating geometric methods for these cases has long remained challenging due the inherent nonsmoothness and one-sided conditions that they impose. To resolve these issues we thus focus both on symplectic-momentum preserving behavior and the preservation of additional structures, unique to the inequality constrained setting. Toward these goals we introduce, for the first time, a fully nonsmooth, discrete Hamilton's principle and obtain an associated framework for composing geometric numerical integration methods for inequality-equality--constrained systems. Applying this framework, we formulate a new family of geometric numerical integra...

In this paper, Bayes estimators of the unknown shape and scale parameters of the Exponentiated Inverse Rayleigh Distribution (EIRD) have been derived using both the frequentist and bayesian methods. The Bayes theorem was adopted to obtain the posterior distribution of the shape and scale parameters of an Exponentiated Inverse Rayleigh Distribution (EIRD) using both conjugate and non-conjugate prior distribution under different loss functions (such as Entropy Loss Function, Linex Loss Function and Scale Invariant Squared Error Loss Function). The posterior distribution derived for both shape and scale parameters are intractable and a Lindley approximation was adopted to obtain the parameters of interest. The loss function were employed to obtain the estimates for both scale and shape parameters with an assumption that the both scale and shape parameters are unknown and independent. Also the Bayes estimate for the simulated datasets and real life datasets were obtained. The Bayes estimates obtained under dierent loss functions are close to the true parameter value of the shape and scale parameters. The estimators are then compared in terms of their Mean Square Error (MSE) using R programming language. We deduce that the MSE reduces as the sample size (n) increases.

A square law for the analysis of real time ellipsometric nucleation and growth data

This paper introduces a novel approach by implementing Type II censoring on both stages of the stage life testing (SLT) experiment. First, we have assumed that the lifetime of the experimental units follows a combination of Weibull distribution on initial stage and an exponential distribution on the accelerated stage. Furthermore, we have also considered a case where the lifetime of the experimental units on both stages follows Weibull distribution with same shape parameter and different scale parameters. The distributions under the two stress levels are connected through the cumulative exposure model. We derive maximum likelihood estimation (MLE) in the SLT model under different lifetime distributions. As an alternative to MLE, we also derive the maximum product of spacings (MPS) estimation method and compare the performance of the MPS and MLE methods through a simulation study. Additionally, we derive asymptotic confidence intervals (CIs) based on the asymptotic normality of MLE, and we also employ bootstrap methods to obtain the boot‐ and boot‐ CIs. Further, we proposed an optimal design for the SLT experiment based on two optimality criteria. Finally, an extensive simulation study and a real data analysis have been carried out to demonstrate the effectiveness of our approach.

SummaryIn this article, we study the inference for the exponentiated Weibull stress‐strength reliability. Based on the assumption that stress and strength variables follow the three‐parameter exponentiated Weibull distributions with unequal scale and shape parameters, the maximum likelihood estimation and bootstrap‐p confidence interval for the reliability are derived. Additionally, based on the proposed modified generalized pivotal quantity, we obtain two point estimators and a modified generalized confidence interval for the reliability. Monte Carlo simulations are adopted to compare the performances of the proposed methodology. Finally, a real data analysis is provided for the illustrative purpose.