A characterization of multivariate normality through univariate projections

This paper introduces a new characterization of multivariate normality of a random vector based on univariate normality of linear combinations of its components.

Robust regression based genome-wide multi-trait QTL analysis

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.

Modeling strain variability in Campylobacter jejuni thermal inactivation by quantifying the number of strains required

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.

A Bartlett-type correction for likelihood ratio tests with application to testing equality of Gaussian graphical models

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.

Relations among Three Parametric Multiple Testing Methods for Correlated Tests

Multiple endpoints in clinical trials are usually correlated. To control the family-wise type I error rate, both Huque and Alosh's flexible fixed-sequence (FFS) testing method and Li and Mehrotra's adaptive alpha allocation approach (4A) have taken into account correlations among endpoints. I suggested a weighted multiple testing correction (WMTC) for correlated tests and compared it with FFS. However, the relationship between the 4A method and the FFS method or the relationship between the 4A method and the WMTC method has not been studied. In this paper, simulations are conducted to investigate these relationships. Tentative guidelines to help choosing an appropriate method are provided.