Markov basis and Groebner basis of Segre-Veronese configuration for testing independence in group-wise selections

We consider testing independence in group-wise selections with some restrictions on combinations of choices. We present models for frequency data of selections for which it is easy to perform conditional tests by Markov chain Monte Carlo (MCMC) methods. When the restrictions on the combinations can be described in terms of a Segre-Veronese configuration, an explicit form of a Gr\"obner basis consisting of moves of degree two is readily available for performing a Markov chain. We illustrate our setting with the National Center Test for university entrance examinations in Japan. We also apply our method to testing independence hypotheses involving genotypes at more than one locus or haplotypes of alleles on the same chromosome.Comment: 25 pages, 5 figure

Large-scale discovery of novel genetic causes of developmental disorders

Despite three decades of successful, predominantly phenotype-driven discovery of the genetic causes of monogenic disorders1, up to half of children with severe developmental disorders of probable genetic origin remain without a genetic diagnosis. Particularly challenging are those disorders rare enough to have eluded recognition as a discrete clinical entity, those with highly variable clinical manifestations, and those that are difficult to distinguish from other, very similar, disorders. Here we demonstrate the power of using an unbiased genotype-driven approach2 to identify subsets of patients with similar disorders. By studying 1,133 children with severe, undiagnosed developmental disorders, and their parents, using a combination of exome sequencing3,4,5,6,7,8,9,10,11 and array-based detection of chromosomal rearrangements, we discovered 12 novel genes associated with developmental disorders. These newly implicated genes increase by 10% (from 28% to 31%) the proportion of children that could be diagnosed. Clustering of missense mutations in six of these newly implicated genes suggests that normal development is being perturbed by an activating or dominant-negative mechanism. Our findings demonstrate the value of adopting a comprehensive strategy, both genome-wide and nationwide, to elucidate the underlying causes of rare genetic disorders

Inference on the ratio of two coefficients of variation of two lognormal distributions

The coefficient of variation (CV) can be used as an index of reliability of measurement. The lognormal distribution has been applied to fit data in many fields. We developed approximate interval estimation of the ratio of two coefficients of variation (CsV) for lognormal distributions by using the Wald-type, Fieller-type, log methods, and method of variance estimates recovery (MOVER). The simulation studies show that empirical coverage rates of the methods are satisfactorily close to a nominal coverage rate for medium sample sizes