Where Does the Alignment Score Distribution Shape Come from?

Alignment algorithms are powerful tools for searching for homologous proteins in databases, providing a score for each sequence present in the database. It has been well known for 20 years that the shape of the score distribution looks like an extreme value distribution. The extremely large number of times biologists face this class of distributions raises the question of the evolutionary origin of this probability law

Variable selection for large p small n regression models with incomplete data: Mapping QTL with epistases

<p>Abstract</p> <p>Background</p> <p>Identifying quantitative trait loci (QTL) for both additive and epistatic effects raises the statistical issue of selecting variables from a large number of candidates using a small number of observations. Missing trait and/or marker values prevent one from directly applying the classical model selection criteria such as Akaike's information criterion (AIC) and Bayesian information criterion (BIC).</p> <p>Results</p> <p>We propose a two-step Bayesian variable selection method which deals with the sparse parameter space and the small sample size issues. The regression coefficient priors are flexible enough to incorporate the characteristic of "large <it>p </it>small <it>n</it>" data. Specifically, sparseness and possible asymmetry of the significant coefficients are dealt with by developing a Gibbs sampling algorithm to stochastically search through low-dimensional subspaces for significant variables. The superior performance of the approach is demonstrated via simulation study. We also applied it to real QTL mapping datasets.</p> <p>Conclusion</p> <p>The two-step procedure coupled with Bayesian classification offers flexibility in modeling "large p small n" data, especially for the sparse and asymmetric parameter space. This approach can be extended to other settings characterized by high dimension and low sample size.</p

Shrinkage Estimators under Spherical Symmetry for the General Linear Model

This paper is primarily concerned with extending the results of Brandwein and Strawderman in the usual canonical setting of a general linear model when sampling from a spherically symmetric distribution. When the location parameter belongs to a proper linear subspace of the sampling space, we give an unbiased estimator of the difference of the risks between the least squares estimator [phi]0 and a general shrinkage estimator [phi] = [phi]0 - [short parallel]X - [phi]0 [short parallel]2 · g o [phi]0. We obtain a general condition of domination for [phi] over [phi]0 which is weaker than that of Brandwein and Strawderman. We do not need any superharmonicity condition on g. Our results are valid for general quadratic loss.

Loss Estimation for Spherically Symmetrical Distributions

In this paper we consider the problem of estimating the quadratic loss of point estimators of a location parameter for a family of spherically symmetric distributions. We compare the unbiased loss estimator of the minimax estimator with a new shrinkage type loss estimator. Conditions on the distributions for the domination of competing estimators are given. It is shown that, in addition to the class of scale mixtures of normal distributions, there exists a more general family for which the domination results hold.

Estimation of a Location Parameter with Restrictions or “vague information” for Spherically Symmetric Distributions

Convex cones, Integration-by-parts, Minimax estimate, Multivariate normal mean, Polyhedral cones, Positively homogeneous set, Quadratic loss, Spherically symmetric distribution, Weakly differentiable function,

Shrinkage Positive Rule Estimators for Spherically Symmetrical Distributions

Tn the normal case it is well known that, although the James-Stein rule is minimax, it is not admissible and the associated positive rule is one way to improve on it. We extend this result to the class of the spherically symmetric distributions and to a large class of shrinkage rules. Moreover we propose a family of generalized positive rules. We compare our results to those of Berger and Bock (Statistical Decision Theory and Related Topics, II, Academic Press, New York. 1976). In particular our conditions on the shrinkage estimator are weaker.