Likelihood Ratio Test For Hypothesis Research Articles

Multivariable degradation modeling and life prediction using multivariate fractional Brownian motion

In system prognostics and health management, multivariable degradation models have been widely developed to predict the life of complex systems using degradation data of multiple Performance Characteristics (PCs). Recent studies have detected a Long-Term Memory (LTM) effect among the degradation process of various PCs, implying a strong coupling phenomenon between the future degradation behavior and historical degradation trajectory. Although the LTM has been widely integrated into single-PC-based degradation modeling, it has not been considered in multi-PC-based scenarios. To capture LTM among multiple PCs, this article proposes a novel LTM-integrated Multivariate Degradation Model (MDM) for system life prediction based on multivariate fractional Brownian motion, which simultaneously incorporates the cross-correlation among different PCs. To estimate parameters of the LTM-integrated MDM, a maximum likelihood method is developed. Two likelihood-ratio hypothesis tests are developed to test the existence of the overall and individual LTM effect among multiple PCs. Both simulation studies and physical experiments on the performance degradation of solar energy conversion and storage devices are conducted to validate the proposed model. Results reveal that the proposed LTM-integrated MDM significantly outperforms existing MDMs in life prediction, while the lifetime uncertainty is heavily underestimated by those traditional approaches that neglect the LTM.

Fast kernel methods for data quality monitoring as a goodness-of-fit test

We propose an accurate and efficient machine learning approach for monitoring particle detectors in real-time. The goal is to assess the compatibility of incoming experimental data with a reference dataset, characterising the data behaviour under normal circumstances, via a likelihood-ratio hypothesis test. The model is based on a modern implementation of kernel methods, nonparametric algorithms that can learn any continuous function given enough data. The resulting approach is efficient and agnostic to the type of anomaly that may be present in the data. Our study demonstrates the effectiveness of this strategy on multivariate data from drift tube chamber muon detectors.

Reliability analysis of multicomponent stress–strength reliability from a bathtub-shaped distribution

In this paper, inference for a multicomponent stress–strength model is studied. When latent strength and stress random variables follow a bathtub-shaped distribution and the failure times are Type-II censored, the maximum likelihood estimate of the multicomponent stress–strength reliability (MSR) is established when there are common strength and stress parameters. Approximate confidence interval is also constructed by using the asymptotic distribution theory and delta method. Furthermore, another alternative generalized point and confidence interval estimators for the MSR are constructed based on pivotal quantities. Moreover, the likelihood and the pivotal quantities-based estimates for the MSR are also provided under unequal strength and stress parameter case. To compare the equivalence of the stress and strength parameters, the likelihood ratio test for hypothesis of interest is also provided. Finally, simulation studies and a real data example are given for illustration.

Accelerated Degradation Testing With Long-Term Memory Effects

The accelerated degradation testing (ADT) has been widely applied as an efficient strategy to obtain the reliability (life) information of the assets in a shorter-than-normal period of time by exposing the assets to higher-than-normal stresses. Recently, with advances in the sensor technology, it has been revealed that the degradation of some assets demonstrates a long-term memory effect, which implies that the future degradation process not only depends on the current degradation state but also strongly correlates with the past degradation history across a long period of time, and the degradation increments are correlated for nonoverlapping time intervals. The existing ADT methods do not consider the long-term memories, which could lead to biased life testing results. In this article, we propose a novel ADT model by integrating the long-term degradation memory effect based on a utilization of the fractional Brownian motion. A maximum likelihood approach is developed to estimate the model parameters. A likelihood-ratio hypothesis test is designed to test the existence of long-term memories. Simulation studies are implemented to illustrate the developed methods. Physical experiments on accelerated testing of a atalyst are designed and conducted to demonstrate the proposed model and its advantage over benchmark approaches. The results show that the traditional ADT paradigm, which ignores the long-term memories, significantly underestimates asset lifetime uncertainties.

Reliability inference for a multicomponent stress–strength model based on Kumaraswamy distribution

In this paper, inference for a multicomponent stress–strength (MSS) model is studied under censored data. When both latent strength and stress random variables follow Kumaraswamy distributions with common shape parameters, the maximum likelihood estimate of MSS reliability is established and associated approximate confidence interval is constructed using the asymptotic distribution theory and delta method. Moreover, pivotal quantities based generalized point and confidence interval estimates are presented for the MSS reliability. Furthermore, likelihood and generalized pivotal based estimates are also presented when the strength and stress variables have unequal shape parameters. For complementary and comparison, bootstrap confidence intervals are provided as well under common and unequal parameter cases. In addition, to compare the equivalence between strength and stress shape parameters, the likelihood ratio test for hypothesis of interest is also discussed. Finally, simulation study and a real data example are provided to investigate the performance of proposed procedures.

Learning new physics from a machine

We propose using neural networks to detect data departures from a given reference model, with no prior bias on the nature of the new physics responsible for the discrepancy. The virtues of neural networks as unbiased function approximants make them particularly suited for this task. An algorithm that implements this idea is constructed, as a straightforward application of the likelihood-ratio hypothesis test. The algorithm compares observations with an auxiliary set of reference-distributed events, possibly obtained with a Monte Carlo event generator. It returns a p-value, which measures the compatibility of the reference model with the data. It also identifies the most discrepant phase-space region of the data set, to be selected for further investigation. The most interesting potential applications are model-independent new physics searches, although our approach could also be used to compare the theoretical predictions of different Monte Carlo event generators, or for data validation algorithms. In this work we study the performance of our algorithm on a few simple examples. The results confirm the model-independence of the approach, namely that it displays good sensitivity to a variety of putative signals. Furthermore, we show that the reach does not depend much on whether a favorable signal region is selected based on prior expectations. We identify directions for improvement towards applications to real experimental data sets.

Inference for Constant-Stress Accelerated Life Tests With Dependent Competing Risks From Bivariate Birnbaum–Saunders Distribution Based on Adaptive Progressively Hybrid Censoring

In life testing, the competing risks model is usually discussed under the assumption of independence. In this paper, we consider a dependent competing risks model using bivariate Birnbaum–Saunders distribution in constant-stress accelerated life testing. To observe expected failure times and terminate the life tests around a predetermined time, the adaptive progressively hybrid censoring scheme is adopted. Based on the accelerated competing risks model with the adaptive progressively hybrid censoring scheme, we obtain the maximum-likelihood estimators, approximate confidence intervals, and bootstrap confidence intervals of unknown parameters. To test the independence between the bivariate competing risks and find the relationship of shape and scale parameters, we discuss the likelihood ratio tests for hypotheses of interest. In addition, we compute the maximum-likelihood predictors of unobserved competing risks times in the constant-stress accelerated life tests. Finally, a simulation study and an illustrative example are provided to support the proposed model and methods, and to examine the performance of estimators and testing.

LCA*: an entropy-based measure for taxonomic assignment within assembled metagenomes.

Motivation: A perennial problem in the analysis of environmental sequence information is the assignment of reads or assembled sequences, e.g. contigs or scaffolds, to discrete taxonomic bins. In the absence of reference genomes for most environmental microorganisms, the use of intrinsic nucleotide patterns and phylogenetic anchors can improve assembly-dependent binning needed for more accurate taxonomic and functional annotation in communities of microorganisms, and assist in identifying mobile genetic elements or lateral gene transfer events.Results: Here, we present a statistic called LCA* inspired by Information and Voting theories that uses the NCBI Taxonomic Database hierarchy to assign taxonomy to contigs assembled from environmental sequence information. The LCA* algorithm identifies a sufficiently strong majority on the hierarchy while minimizing entropy changes to the observed taxonomic distribution resulting in improved statistical properties. Moreover, we apply results from the order-statistic literature to formulate a likelihood-ratio hypothesis test and P-value for testing the supremacy of the assigned LCA* taxonomy. Using simulated and real-world datasets, we empirically demonstrate that voting-based methods, majority vote and LCA*, in the presence of known reference annotations, are consistently more accurate in identifying contig taxonomy than the lowest common ancestor algorithm popularized by MEGAN, and that LCA* taxonomy strikes a balance between specificity and confidence to provide an estimate appropriate to the available information in the data.Availability and Implementation: The LCA* has been implemented as a stand-alone Python library compatible with the MetaPathways pipeline; both of which are available on GitHub with installation instructions and use-cases (http://www.github.com/hallamlab/LCAStar/).Contact: shallam@mail.ubc.caSupplementary information: Supplementary data are available at Bioinformatics online.

Testing Against a Linear Regression Model Using Ideas from Shape-Restricted Estimation

Summary A formal likelihood ratio hypothesis test for the validity of a parametric regression function is proposed, using a large dimensional, non-parametric double-cone alternative. For example, the test against a constant function uses the alternative of increasing or decreasing regression functions, and the test against a linear function uses the convex or concave alternative. The test proposed is exact and unbiased and the critical value is easily computed. The power of the test increases to 1 as the sample size increases, under very mild assumptions—even when the alternative is misspecified, i.e. the power of the test converges to 1 for any true regression function that deviates (in a non-degenerate way) from the parametric null hypothesis. We also formulate tests for the linear versus partial linear model and consider the special case of the additive model. Simulations show that our procedure behaves well consistently when compared with other methods. Although the alternative fit is non-parametric, no tuning parameters are involved. Supplementary materials with proofs and technical details are available on line.

“<i>BIVARIATE DISTRIBUTION</i>” FOR INFRASTRUCTURES AMONG OPERATIVE, NATURAL AND NO MENOPAUSES

Menopause is not an illness but rather an important event as it changes the body physiology and mental cognition via hormonal changes. During data analysis of menopauses incidence data, new bivariate distribution is discovered. Their marginal, conditional distribution and statistical properties including the inter and partial correlations are explored and utilized to interpret menopauses data. A likelihood ratio hypothesis testing procedure is constructed to test the statistical significance of the sample estimate of the chance for menopause and estimate of the chance for operative menopause. The menopause data are analyzed and interpreted in the illustration. Research directions for future work are pointed out.

Função de Intensidade Poisson Perturbada pelo Número de Eventos Recorrentes

Neste trabalho modela-se a funcao de intensidade de um processo de Poisson considerando o tempo e o total de recorrencias, condicionados ao momento anterior, em uma unidade amostral. Adotamos um componente para o processo de Poisson e outro para o numero total de eventos ocorridos na unidade. Estudos de simulacao e testes de hipoteses empiricos da significância dos parâmetros no modelo foram reali-zados. A significância dos testes de hipotese Wald e da razao de verossimilhanca foi aproximadamente 10% para mais de 50 ocorrencias. Um conjunto de dados com tempos de recorrencia na aquisicao de cosmeticos foi modelado adequadamente, tendo parâmetros significativos e valores estimados proximos dos valores observados, justificando a utilizacao do modelo proposto para tempos e numeros de recorrencias em uma unidade amostral.

A Model-Agnostic Framework for Fast Spatial Anomaly Detection

Given a spatial dataset placed on an n × n grid, our goal is to find the rectangular regions within which subsets of the dataset exhibit anomalous behavior. We develop algorithms that, given any user-supplied arbitrary likelihood function, conduct a likelihood ratio hypothesis test (LRT) over each rectangular region in the grid, rank all of the rectangles based on the computed LRT statistics, and return the top few most interesting rectangles. To speed this process, we develop methods to prune rectangles without computing their associated LRT statistics.

Statistical power of an information-based test and its application to wave height data

Modeling wave heights is crucial for many maritime applications. An appropriate statistical distribution for describing wave heights is the Rayleigh distribution. Estimating and testing the significance of the parameters of a distribution are important in statistical modeling and allow meaningful predictions about uncertain events. We propose an information-based method to test the significance of parameters of a given one-dimensional distribution. The power of the proposed test is compared to that of the likelihood ratio tests for hypotheses on the parameters of the exponential and Rayleigh distributions. Monte Carlo simulations demonstrate that the proposed method yields a satisfactory power level that is comparable to that of the likelihood ratio test. The method is illustrated using real wave height data.

Construction of classical confidence regions of model parameters in nonlinear regression analyses

Feldman-Cousins' unified approach provides an unique confidence region for parameters under estimation and assures an exact coverage for the constructed confidence region. We present a procedure to implement this approach in least-squares regression analyses. The procedure is based on a series of the most powerful likelihood-ratio tests of hypothesis using a single number as a test statistic. The procedure thereby avoids the complications of the Feldman-Cousins method arising when the number of free parameters is more than one. Applying the procedure to a case of nonlinear regression problems where the estimated parameters are not generally Gaussian distributed, we show that one has to use the procedure when the results of the regression analysis are to be carefully investigated near a boundary of the physical region.

Hierarchical models in ecology: confidence intervals, hypothesis testing, and model selection using data cloning

Hierarchical statistical models are increasingly being used to describe complex ecological processes. The data cloning (DC) method is a new general technique that uses Markov chain Monte Carlo (MCMC) algorithms to compute maximum likelihood (ML) estimates along with their asymptotic variance estimates for hierarchical models. Despite its generality, the method has two inferential limitations. First, it only provides Wald-type confidence intervals, known to be inaccurate in small samples. Second, it only yields ML parameter estimates, but not the maximized likelihood values used for profile likelihood intervals, likelihood ratio hypothesis tests, and information-theoretic model selection. Here we describe how to overcome these inferential limitations with a computationally efficient method for calculating likelihood ratios via data cloning. The ability to calculate likelihood ratios allows one to do hypothesis tests, construct accurate confidence intervals and undertake information-based model selection with hierarchical models in a frequentist context. To demonstrate the use of these tools with complex ecological models, we reanalyze part of Gause's classic Paramecium data with state-space population models containing both environmental noise and sampling error. The analysis results include improved confidence intervals for parameters, a hypothesis test of laboratory replication, and a comparison of the Beverton-Holt and the Ricker growth forms based on a model selection index.

A maximum likelihood method for studying gene–environment interactions under conditional independence of genotype and exposure

Given the biomedical interest in gene-environment interactions along with the difficulties inherent in gathering genetic data from controls, epidemiologists need methodologies that can increase precision of estimating interactions while minimizing the genotyping of controls. To achieve this purpose, many epidemiologists suggested that one can use case-only design. In this paper, we present a maximum likelihood method for making inference about gene-environment interactions using case-only data. The probability of disease development is described by a logistic risk model. Thus the interactions are model parameters measuring the departure of joint effects of exposure and genotype from multiplicative odds ratios. We extend the typical inference method derived under the assumption of independence between genotype and exposure to that under a more general assumption of conditional independence. Our maximum likelihood method can be applied to analyse both categorical and continuous environmental factors, and generalized to make inference about gene-gene-environment interactions. Moreover, the application of this method can be reduced to simply fitting a multinomial logistic model when we have case-only data. As a consequence, the maximum likelihood estimates of interactions and likelihood ratio tests for hypotheses concerning interactions can be easily computed. The methodology is illustrated through an example based on a study about the joint effects of XRCC1 polymorphisms and smoking on bladder cancer. We also give two simulation studies to show that the proposed method is reliable in finite sample situation.

Likelihood ratio tests in curved exponential families with nuisance parameters present only under the alternative

SUMMARY For submodels of an exponential family, we consider likelihood ratio tests for hypotheses that render some parameters nonidentifiable. First, we establish the asymptotic equivalence between the likelihood ratio test and the score test. Secondly, the score-test representation is used to derive the asymptotic distribution of the likelihood ratio test. These results are derived for general submodels of an exponential family without assuming compactness of the parameter space. We then exemplify the results on a class of multivariate normal models, where null hypotheses concerning the covariance structure lead to loss of identifi ability of a parameter. Our motivating problem throughout the paper is to test a random intercepts model against an alternative covariance structure allowing for serial correlation.

PepNovo: De Novo Peptide Sequencing via Probabilistic Network Modeling

We present a novel scoring method for de novo interpretation of peptides from tandem mass spectrometry data. Our scoring method uses a probabilistic network whose structure reflects the chemical and physical rules that govern the peptide fragmentation. We use a likelihood ratio hypothesis test to determine whether the peaks observed in the mass spectrum are more likely to have been produced under our fragmentation model than under a model that treats peaks as random events. We tested our de novo algorithm PepNovo on ion trap data and achieved results that are superior to popular de novo peptide sequencing algorithms. PepNovo can be accessed via the URL http://www-cse.ucsd.edu/groups/bioinformatics/software.html.

Smoothing spline based tests for non-linearity in a partially linear model

This paper deals with testing for non-linearity in a regression model with one possibly non-linear component being estimated non-parametrically using smoothing splines. We propose two new variance–covariance based tests for detecting non-linearity applying a likelihood ratio hypothesis testing approach. The first test is for the inclusion of a possibly non-linear component and the second one is for linearity of a possibly non-linear component. The tests are based on a stochastic model in state space form given by Wahba (J. Roy. Statist. Soc. Ser. B 40 (1978) 364), Wecker and Ansley (J. Amer. Statist. Assoc. 78 (1983) 81) and de Jong and Mazzi (Modeling and smoothing unequally spaced sequence data, University of York and University of British Columbia, Unpublished paper) for which smoothing splines provide an optimal estimate. Pitrun (A smoothing spline approach to non-linear interface for time series, Department of Econometrics and Business Statistics, Monash University, Unpublished Ph.D. thesis) derived the variance–covariance structure of this model, which allows the use of a marginal likelihood approach. This leads naturally to marginal-likelihood based likelihood ratio tests for non-linearity. Small sample properties of the new tests have been investigated via Monte Carlo studies.

Statistical phylogeography: methods of evaluating and minimizing inference errors.

Nested clade phylogeographical analysis (NCPA) has become a common tool in intraspecific phylogeography. To evaluate the validity of its inferences, NCPA was applied to actual data sets with 150 strong a priori expectations, the majority of which had not been analysed previously by NCPA. NCPA did well overall, but it sometimes failed to detect an expected event and less commonly resulted in a false positive. An examination of these errors suggested some alterations in the NCPA inference key, and these modifications reduce the incidence of false positives at the cost of a slight reduction in power. Moreover, NCPA does equally well in inferring events regardless of the presence or absence of other, unrelated events. A reanalysis of some recent computer simulations that are seemingly discordant with these results revealed that NCPA performed appropriately in these simulated samples and was not prone to a high rate of false positives under sampling assumptions that typify real data sets. NCPA makes a posteriori use of an explicit inference key for biological interpretation after statistical hypothesis testing. Alternatives to NCPA that claim that biological inference emerges directly from statistical testing are shown in fact to use an a priori inference key, albeit implicitly. It is argued that the a priori and a posteriori approaches to intraspecific phylogeography are complementary, not contradictory. Finally, cross-validation using multiple DNA regions is shown to be a powerful method of minimizing inference errors. A likelihood ratio hypothesis testing framework has been developed that allows testing of phylogeographical hypotheses, extends NCPA to testing specific hypotheses not within the formal inference key (such as the out-of-Africa replacement hypothesis of recent human evolution) and integrates intra- and interspecific phylogeographical inference.