This work defines a new correction for the likelihood ratio test for a two-sample problem within the multivariate normal context. This correction applies to decomposable graphical models, where testing equality of distributions can be decomposed into lower dimensional problems.

A biodegradable hybrid polymer patch was invented at the University of Cincinnati to cover gaps on the skin over the spinal column of a growing fetus, characterized by the medical condition spina bifida. The inserted patch faces amniotic fluid (AF) on one side and cerebrospinal fluid on the other side. The goal is to provide a profile of the roughness of a patch over time at 0, 4, 8, 12, and 16 weeks with a 95% confidence band. The patch is soaked in a test tube filled with either amniotic fluid (AF) or phosphate-buffered saline (PBS) in the lab. If roughness is measured at any time point for a patch, the patch is destroyed. Thus, it is impossible to measure roughness at all weeks of interest for any patch. It is important to assess the roughness of a patch because the rougher the patch is, the faster the skin grows under the patch. We use a model-based approach with Monte Carlo simulations to estimate the profile over time with a 95% confidence band. The roughness profiles are similar with both liquids. The profile can be used as a template for future experiments on the composition of patches.

There is a limited understanding of the survival responses of Campylobacter jejuni during thermal processing, which must be investigated for appropriate risk assessment and processing. Therefore, we aimed to elucidate the survival response of C. jejuni and develop a predictive model considering strain variability and uncertainty, which are important for quantitative microbial risk assessment (QMRA) or risk-based processing control measures. We employed the most probable curve (MPC) method to consider the uncertainty in cell concentrations. Further, the multivariate normal (MVN) distribution served as a model for strain variability in bacterial survival behavior. The prediction curves from the MVN successfully captured the parameter variability of the most probable curves of each strain. More than ten reference strains effectively described the strain variability in parameters using the MVN distribution. The findings indicated that, with sufficient strain data, the MVN could estimate the strain variability, including unknown strains. The multi-level model for strain variability can potentially become a specialized tool for QMRA and risk-based processing controls. The combined approach of MPC and MVN provides valuable insights into strain variability, emphasizing the importance of accounting for variability and uncertainty in predictive models for QMRA and risk-based processing control measures.

In this paper, the problem of estimating the mean vector under non-negative constraints on location vector of the multivariate normal distribution is investigated. The value of the wavelet threshold based on Stein\'s unbiased risk estimators is calculated for the shrinkage estimator in restricted parameter space. We suppose that covariance matrix is unknown and we find the dominant class of shrinkage estimators under Balance loss function. The performance evaluation of the proposed class of estimators is checked through a simulation study by using risk and average mean square error values.

In genome-wide quantitative trait locus (QTL) mapping studies, multiple quantitative traits are often measured along with the marker genotypes. Multi-trait QTL (MtQTL) analysis, which includes multiple quantitative traits together in a single model, is an efficient technique to increase the power of QTL identification. The two most widely used classical approaches for MtQTL mapping are Gaussian Mixture Model-based MtQTL (GMM-MtQTL) and Linear Regression Model-based MtQTL (LRM-MtQTL) analyses. There are two types of LRM-MtQTL approach known as least squares-based LRM-MtQTL (LS-LRM-MtQTL) and maximum likelihood-based LRM-MtQTL (ML-LRM-MtQTL). These three classical approaches are equivalent alternatives for QTL detection, but ML-LRM-MtQTL is computationally faster than GMM-MtQTL and LS-LRM-MtQTL. However, one major limitation common to all the above classical approaches is that they are very sensitive to outliers, which leads to misleading results. Therefore, in this study, we developed an LRM-based robust MtQTL approach, called LRM-RobMtQTL, for the backcross population based on the robust estimation of regression parameters by maximizing the β-likelihood function induced from the β-divergence with multivariate normal distribution. When β = 0, the proposed LRM-RobMtQTL method reduces to the classical ML-LRM-MtQTL approach. Simulation studies showed that both ML-LRM-MtQTL and LRM-RobMtQTL methods identified the same QTL positions in the absence of outliers. However, in the presence of outliers, only the proposed method was able to identify all the true QTL positions. Real data analysis results revealed that in the presence of outliers only our LRM-RobMtQTL approach can identify all the QTL positions as those identified in the absence of outliers by both methods. We conclude that our proposed LRM-RobMtQTL analysis approach outperforms the classical MtQTL analysis methods.

Multivariate simple interval mapping (SIM) is one of the most popular approaches for multiple quantitative trait locus (QTL) analysis. Both maximum likelihood (ML) and least squares (LS) multivariate regression (MVR) are widely used methods for multi-trait SIM. ML-based MVR (MVR-ML) is an expectation maximization (EM) algorithm based iterative and complex time-consuming approach. Although the LS-based MVR (MVR-LS) approach is not an iterative process, the calculation of likelihood ratio (LR) statistic in MVR-LS is also a time-consuming complex process. We have introduced a new approach (called FastMtQTL) for multi-trait QTL analysis based on the assumption of multivariate normal distribution of phenotypic observations. Our proposed method can identify almost the same QTL positions as those identified by the existing methods. Moreover, the proposed method takes comparatively less computation time because of the simplicity in the calculation of LR statistic by this method. In the proposed method, LR statistic is calculated only using the sample variance-covariance matrix of phenotypes and the conditional probability of QTL genotype given the marker genotypes. This improvement in computation time is advantageous when the numbers of phenotypes and individuals are larger, and the markers are very dense resulting in a QTL mapping with a bigger dataset.

Multiple testing problems are often seen in clinical trials. An appropriate testing procedure should be specified to deal with the potential inflation of type I error rate due to multiplicity. In this article, we propose a stepwise progressive parametric multiple (SPPM) testing procedure, which constructs the testing using the products of all the combinations of local [Formula: see text]-values and the critical values are determined by numerical integrations progressively using the closure principle. We have compared the performance of SPPM to several other procedures, and demonstrate the advantage of SPPM procedure, in terms of power, for the certain situations of multiple testing.

We present a computational model that allows for rapid prediction of correlations among a set of residue pairs when the fluctuations of another set of residues are perturbed. The simple theory presented here is based on the knowledge of the fluctuation covariance matrix only. In this sense, the theory is model independent and therefore universal. Perturbation of any set of fluctuations and the resulting response of the remaining set are calculated using conditional probabilities of a multivariate normal distribution. The model is expected to rapidly and accurately map the consequences of mutations in proteins, as well as allosteric activity and ligand binding. Knowledge of triple correlations of fluctuations of residues i, j, and k, 〈 Δ R i Δ R j Δ R k 〉 emerges as the necessary source of information for controlling residue pairs by perturbing a distant residue. Triple correlations have not received wide attention in literature. Perturbation-response-function relations for ubiquitin (UBQ) are discussed as an example. Covariance matrix for UBQ obtained from the Gaussian Network Model combined with the present computational algorithm is able to reflect the millisecond molecular dynamics correlations and observed NMR results. © 2018 Wiley Periodicals, Inc.

Multivariate regression methods generally assume a constant covariance matrix for the observations. In case a heteroscedastic model is needed, the parametric and nonparametric covariance regression approaches can be restrictive in the literature. We propose a multilevel regression model for the mean and covariance structure, including random intercepts in both components and allowing for correlation between them. The implied conditional covariance function can be different across clusters as a result of the random effect in the variance structure. In addition, allowing for correlation between the random intercepts in the mean and covariance makes the model convenient for skewedly distributed responses. Furthermore, it permits us to analyse directly the relation between the mean response level and the variability in each cluster. Parameter estimation is carried out via Gibbs sampling. We compare the performance of our model to other covariance modelling approaches in a simulation study. Finally, the proposed model is applied to the RN4CAST dataset to identify the variables that impact burnout of nurses in Belgium.

Randomisation schemes are rules that assign patients to treatments in a clinical trial. Many of these schemes have the common aim of maintaining balance in the numbers of patients across treatment groups. The properties of imbalance that have been investigated in the literature are based on two treatment groups. In this paper, their properties for K > 2 treatments are studied for two randomisation schemes: centre-stratified permuted-block and complete randomisation. For both randomisation schemes, analytical approaches are investigated assuming that the patient recruitment process follows a Poisson-gamma model. When the number of centres involved in a trial is large, the imbalance for both schemes is approximated by a multivariate normal distribution. The accuracy of the approximations is assessed by simulation. A test for treatment differences is also considered for normal responses, and numerical values for its power are presented for centre-stratified permuted-block randomisation. To speed up the calculations, a combined analytical/approximate approach is used. Copyright © 2016 John Wiley & Sons, Ltd.