A simple Bayesian procedure for forecasting the outcomes of the UEFA Champions League matches

This article presents a Bayesian implementation of a cumulative probit model to forecast the outcomes of the UEFA Champions League matches. The argument of the normal CDF involves a cut-off point, a home vs away playing effect and the difference in strength of the two competing teams. Team strength is assumed to follow a Gaussian distribution the expectation of which is expressed as a linear regression on an external rating of the team from eg the UEFA Club Ranking (UEFACR) or the Football Club World Ranking (FCWR). Priors on these parameters are updated at the beginning of each season from their posterior distributions obtained at the end of the previous one. This allows making predictions of match results for each phase of the competition: group stage and knock-out. An application is presented for the 2013-2014 season. Adjustment based on the FCWR performs better than on UEFACR.Comment: 14 pages, 7 table

Another look at multiplicative models in quantitative genetics

This paper reviews basic theory and features of the multiplicative model of gene action. A formal decomposition of the mean and of the genotypic variance is presented. Connections between the statistical parameters of this model and those of the factorial decomposition into additive, dominance and epistatic effects are also emphasized. General formulae for the genotypic covariance among inbred relatives are given in the case of linkage equilibrium. It is shown that neglecting the epistatic components of variation makes the multiplicative model a pseudo-additive one, since this approximation does not break the strong dependency between mean and variance effects. Similarities and differences between the classical polygenic ’additive-dominance’ and the multiplicative gene action approaches are outlined and discussed. Numerical examples for the biallelic case are produced to illustrate that comparison.Cet article présente la théorie et les principales caractéristiques du modèle multiplicatif d’action des gènes. Une décomposition formelle de la moyenne et de la variance génotypique permet d’établir les relations entre les paramètres statistiques de ce modèle et ceux issus de la décomposition factorielle de l’effet des gènes en effets additifs, de dominance et d’épistasie. Une formule générale de la covariance entre apparentés dans une population consanguine en équilibre de liaison est proposée. On montre que les composantes épistatiques de la variabilité génétique peuvent être négligées ; le modèle multiplicatif devient alors un modèle pseudo-additif, l’approximation ne supprimant pas la forte liaison entre moyenne et variance. Les similitudes et les différences entre le modèle polygénique « additif-dominance » classique et le modèle multiplicatif d’action des gènes sont discutées et illustrées par des exemples dans le cas biallélique

An overview of the Weitzman approach to diversity

The diversity of a set of breeds or species is defined in the Weitzman approach by a recursion formula using the pairwise genetic distances between the elements of the set. The algorithm for computing the diversity function of Weitzman is described. It also provides a taxonomy of the set which is interpreted as the maximum likelihood phylogeny. The theory is illustrated by an application to 19 European cattle breeds. The possible uses of the method for defining optimal conservation strategies are briefly discussed.Un aperçu sur l’approche de la diversité selon Weitzman. La diversité d’un ensemble d’espèces, ou de races, est définie par Weitzman de façon récursive ; les données de départ sont les distances génétiques entre les éléments de l’ensemble pris deux à deux. L’algorithme de calcul de la diversité fournit, comme résultat intermédiaire, un arbre de classement des espèces en présence, qui est interprété comme une phylogénie du maximum de vraisemblance. La théorie est illustrée par un exemple d’application à 19 races bovines européennes, et les utilisations possibles de la méthode pour définir des stratégies optimales de conservation sont discutées brièvement

A completion simulator for the two-sided truncated normal distribution

This paper presents simulation formulae of two-sided truncated normal random variables using a completion distribution and its two corresponding conditionals generated via a Gibbs sampler. This procedure extends formulae given by Robert and Casella for the one-sided case

On the precision of estimation of genetic distance

This article gives a formal proof of a formula for the precision of estimated genetic distances proposed by Barker et al. which can be used in designing experimental sampling programmes. The derivation is given in the general multiallelic case using the Sanghvi distance. Two sources of sampling are considered, i.e. i) among individuals (or gametes) within locus and ii) among loci within populations. Distribution assumptions about gene frequencies are discussed, especially the normal used in Barker et al. versus the Dirichlet via simulation

The PX-EM algorithm for fast stable fitting of Henderson's mixed model

This paper presents procedures for implementing the PX-EM algorithm of Liu, Rubin and Wu to compute REML estimates of variance covariance components in Henderson's linear mixed models. The class of models considered encompasses several correlated random factors having the same vector length e.g., as in random regression models for longitudinal data analysis and in sire-maternal grandsire models for genetic evaluation. Numerical examples are presented to illustrate the procedures. Much better results in terms of convergence characteristics (number of iterations and time required for convergence) are obtained for PX-EM relative to the basic EM algorithm in the random regression

EM-REML estimation of covariance parameters in Gaussian mixed models for longitudinal data analysis

This paper presents procedures for implementing the EM algorithm to compute REML estimates of variance covariance components in Gaussian mixed models for longitudinal data analysis. The class of models considered includes random coefficient factors, stationary time processes and measurement errors. The EM algorithm allows separation of the computations pertaining to parameters involved in the random coefficient factors from those pertaining to the time processes and errors. The procedures are illustrated with Pothoff and Roy's data example on growth measurements taken on 11 girls and 16 boys at four ages. Several variants and extensions are discussed