Conditional simulation of random fields by successive residuals

This paper presents a new approach to the LU decomposition method for the simulation of stationary and ergodic random fields. The approach overcomes the size limitations of LU and is suitable for any size simulation. The proposed approach can facilitate fast updating of generated realizations with new data, when appropriate, without repeating the full simulation process. Based on a novel column partitioning of the L matrix, expressed in terms of successive conditional covariance matrices, the approach presented here demonstrates that LU simulation is equivalent to the successive solution of kriging residual estimates plus random terms. Consequently, it can be used for the LU decomposition of matrices of any size. The simulation approach is termed conditional simulation by successive residuals as at each step, a small set (group) of random variables is simulated with a LU decomposition of a matrix of updated conditional covariance of residuals. The simulated group is then used to estimate residuals without the need to solve large systems of equations.

Modelling High-Dimensional Data by Mixtures of Factor Analyzers

We focus on mixtures of factor analyzers from the perspective of a method for model-based density estimation from high-dimensional data, and hence for the clustering of such data. This approach enables a normal mixture model to be fitted to a sample of n data points of dimension p, where p is large relative to n. The number of free parameters is controlled through the dimension of the latent factor space. By working in this reduced space, it allows a model for each component-covariance matrix with complexity lying between that of the isotropic and full covariance structure models. We shall illustrate the use of mixtures of factor analyzers in a practical example that considers the clustering of cell lines on the basis of gene expressions from microarray experiments. (C) 2002 Elsevier Science B.V. All rights reserved.

Sex differences in heritability of BMI: A comparative study of results from twin studies in eight countries

Body mass index (BMI), a simple anthropometric measure, is the most frequently used measure of adiposity and has been instrumental in documenting the worldwide increase in the prevalence of obesity witnessed during the last decades. Although this increase in overweight and obesity is thought to be mainly due to environmental changes, i.e., sedentary lifestyles and high caloric diets, consistent evidence from twin studies demonstrates high heritability and the importance of genetic differences for normal variation in BMI. We analysed self-reported data on BMI from approximately 37,000 complete twin pairs (including opposite sex pairs) aged 20-29 and 30-39 from eight different twin registries participating in the GenomEUtwin project. Quantitative genetic analyses were conducted and sex differences were explored. Variation in BMI was greater for women than for men, and in both sexes was primarily explained by additive genetic variance in all countries. Sex differences in the variance components were consistently significant. Results from analyses of opposite sex pairs also showed evidence of sex-specific genetic effects suggesting there may be some differences between men and women in the genetic factors that influence variation in BMI. These results encourage the continued search for genes of importance to the body composition and the development of obesity. Furthermore, they suggest that strategies to identify predisposing genes may benefit from taking into account potential sex specific effects.

The risk-return trade-off in Europe: A temporal and cross-sectional analysis

This paper analyzes the risk-return trade-off in European equities considering both temporal and cross-sectional dimensions. In our analysis, we introduce not only the market portfolio but also 15 industry portfolios comprising the entire market. Several bivariate GARCH models are estimated to obtain the covariance matrix between excess market returns and the industrial portfolios and the existence of a risk-return trade-off is analyzed through a cross-sectional approach using the information in all portfolios. It is obtained evidence for a positive and significant risk-return trade-off in the European market. This conclusion is robust for different GARCH specifications and is even more evident after controlling for the main financial crisis during the sample period.

A influência dos parâmetros nas estimativas VAR: caso prático

Dissertação de Mestrado em Finanças Empresariais

Estimativa de parâmetros genéticos, correlações fenotípicas e ambientais no girassol do cerrado do Distrito Federal.

RESUMO: O propósito deste trabalho foi avaliar a estima - tiva de parâmetros genéticos, correlações fe - notipicas e ambientais no girassol do Cerrado do Distrito Federal. Os caracteres analisados foram: rendimento de grãos, tamanho do ca - pítulo, peso de mil aquênios, altura de plantas e dias para floração inicial. Foram constatadas diferenças altamente significativas entre os ge - nótipos para todas as características morfoa - gronômicas avaliadas. Para o coeficiente CVr a maioria dos valores foram superior a 1 nos dois anos considerados, indicando que para a maioria dos caracteres aferidos há a possibi - lidade de êxito na seleção fenotípica uma vez que a variância genética superou a ambiental. Na herdabilidade, a maior estimativa verifica - da foi para o caráter PMA (98,76%) em 2013 e para DFI (99,68%) em 2014. Foram cons - tatadas diferenças altamente significativas en - tre os genótipos para todas as características morfoagronômicas avaliadas. O alto coeficiente de variação genético destaca a possibilidade de obter ganhos genéticos para todas as caracte - rísticas analisadas salvo em tamanho de capi - tulo. Materiais genéticos com potencial para as características agronômicas pesquisadas foram identificados no trabalho, podem ser indicadas ao sistema de produção irrigado no Cerrado. abstract: The purpose of this study was to estimate ge - netic parameters, phenotypic and environmen - tal correlations in sunflower of Brazilian savan - nah. The characters analyzed were: grain yield, chapter length, weight of a thousand achenes, plant height and days to start flowering. Hi - ghly significant differences were observed among genotypes for all morphoagronomic cha - racteristics evaluated. For the most CVr coe - fficient values were higher than 1 in the two years under consideration, indicating that for the majority of measured characters there is the possibility of successful phenotypic selection once the genetic variance exceeded the envi - ronmental. The heritability estimate was the hi - ghest for the PMA character (98,76%) in 2013 and DFI (99,68%) in 2014. Highly significant differences were observed among genotypes for all morphoagronomic characteristics evalu - ated. The high coefficient of genetic variation show the possibility of obtaining genetic gain for all examined characteristics except in chap - ter length. Genetic material with potential for the researched agronomic characteristics were identified in the work, can be indicated to the irrigated production system in the Brazilian sa - vannah.

Untersuchungen zur Diskriminanzanalyse mit hochdimensionalen Daten

Discriminant analysis, classification error, ridge technique, singular covariance matrix

Male dominance linked to size and age, but not to 'good genes' in brown trout (Salmo trutta).

BACKGROUND: Males that are successful in intra-sexual competition are often assumed to be of superior quality. In the mating system of most salmonid species, intensive dominance fights are common and the winners monopolise most mates and sire most offspring. We drew a random sample of mature male brown trout (Salmo trutta) from two wild populations and determined their dominance hierarchy or traits linked to dominance. The fish were then stripped and their sperm was used for in vitro fertilisations in two full-factorial breeding designs. We recorded embryo viability until hatching in both experiments, and juvenile survival during 20 months after release into a natural streamlet in the second experiment. Since offspring of brown trout get only genes from their fathers, we used offspring survival as a quality measure to test (i) whether males differ in their genetic quality, and if so, (ii) whether dominance or traits linked to dominance reveal 'good genes'. RESULTS: We found significant additive genetic variance on embryo survival, i.e. males differed in their genetic quality. Older, heavier and larger males were more successful in intra-sexual selection. However, neither dominance nor dominance indicators like body length, weight or age were significantly linked to genetic quality measured as embryo or juvenile survival. CONCLUSION: We found no evidence that females can improve their offspring's genetic viability by mating with large and dominant males. If there still were advantages of mating with dominant males, they may be linked to non-genetic benefits or to genetic advantages that are context dependent and therefore possibly not revealed under our experimental conditions - even if we found significant additive genetic variation for embryo viability under such conditions.

Effects of different mating scenarios on embryo viability in brown trout.

Mating with attractive or dominant males is often predicted to offer indirect genetic benefits to females, but it is still largely unclear how important such non-random mating can be with regard to embryo viability. We sampled a natural population of adult migratory brown trout (Salmo trutta), bred them in vitro in a half-sib breeding design to separate genetic from maternal environmental effects, raised 2098 embryos singly until hatching, and exposed them experimentally to different levels of pathogen stress at a late embryonic stage. We found that the embryos' tolerance to the induced pathogen stress was linked to the major histocompatibility complex (MHC) of their parents, i.e. certain MHC genotypes appeared to provide better protection against infection than others. We also found significant additive genetic variance for stress tolerance. Melanin-based dark skin patterns revealed males with 'good genes', i.e. embryos fathered by dark coloured males had a high tolerance to infection. Mating with large and dominant males would, however, not improve embryo viability when compared to random mating. We used simulations to provide estimates of how mate choice based on MHC or melanin-based skin patterns would influence embryos' tolerance to the experimentally induced pathogen stress.

Multivariate contemporaneous-threshold autoregressive models

This paper proposes a contemporaneous-threshold multivariate smooth transition autoregressive (C-MSTAR) model in which the regime weights depend on the ex ante probabilities that latent regime-specific variables exceed certain threshold values. A key feature of the model is that the transition function depends on all the parameters of the model as well as on the data. Since the mixing weights are also a function of the regime-specific innovation covariance matrix, the model can account for contemporaneous regime-specific co-movements of the variables. The stability and distributional properties of the proposed model are discussed, as well as issues of estimation, testing and forecasting. The practical usefulness of the C-MSTAR model is illustrated by examining the relationship between US stock prices and interest rates.

Evolution of life history traits in a natural population of the shrew Crocidura russula

Abstract Life history traits encompass all the decisions concerning fitness an individual is faced with during his life. The study of these traits is crucial to understand the factors shaping the biology of living organisms. Up until now, most of the information on the evolution of life history traits comes from laboratory studies. While these studies are interesting to test the effect of specific parameters, their conclusions are difficult to extrapolate to natural populations. Investigating the evolution of life history traits in natural populations is of great interest. This may be tricky because it requires information on reproduction, survival and morphology of individuals. Mark-recapture methods allow most of this information to be obtained. However, when direct observations of a species are not possible due to its ecology, indirect methods must be used to infer lifetime reproductive success. In this case, molecular markers are particularly helpful in assessing the genetic relationships between individuals and allow the construction of a pedigree. This thesis focuses on a natural population of a small insectivorous mammal, the greater white-toothed shrew, Crocidura russula. Because of its hidden lifestyle, the two complementary techniques mentioned above were combined to gather information on this population. The data were used to explore diverse aspects of evolutionary biology. We demonstrated that the high genetic variance displayed by the species was not maintained by its mating system because this shrew was less monogamous than previously thought. The large genetic diversity was most likely promoted by gene flow from the neighborhood. Dispersal was thus a central topic in this thesis. We showed that dispersal was not driven by inbreeding avoidance. In addition, we did not find any inbreeding depression in the population. Dispersal was promoted by a high number of vacant territories in the population for both sexes, meaning that territory acquisition played an important role in driving dispersal. Moreover, dispersal propensity was shown to have a genetic basis and, once achieved, to have no effect on individual fitness. Body mass was found to be a life history trait strongly influenced by sexual and viability selection in both sexes. Larger individuals had higher access to reproduction through territory acquisition and defense than lighter ones. By contrast, intermediate size individuals were favored by viability selection presumably because of ecological constraints and metabolic costs. Finally, we demonstrated that the majority of the life history traits in our shrew population has the potential to evolve because they maintained substantial amounts of additive genetic variance. Nonetheless, life history traits had no significant heritability due to their high level of nonadditive or environmental variance. Résumé Les traits d'histoire de vie comprennent toutes les décisions auxquelles un individu est confronté au cours de sa vie et qui concernent sa valeur adaptative. L'étude de ces traits est cruciale pour comprendre les facteurs qui façonnent la biologie des êtres vivants. Jusqu'à ce jour, la majorité des informations sur l'évolution des traits d'histoire de vie provient d'études réalisées en laboratoire. Alors que ces études sont intéressantes pour tester l'effet de paramètres spécifiques, leurs conclusions sont difficilement extrapolables aux populations naturelles. Il est particulièrement intéressant d'étudier l'évolution des traits d'histoire de vie dans des populations naturelles. Toutefois, ces études peuvent se révéler difficiles parce qu'elles requièrent des informations sur la reproduction, la survie et la morphologie des individus. Des méthodes de marquage-recapture permettent d'obtenir ces informations. Cependant, lorsque l'écologie de l'espèce rend les obervations directes impossibles, des méthodes indirectes doivent être utilisées pour obtenir le succès reproducteur des individus. Dans ce cas, les marqueurs moléculaires sont particulièrement utiles pour évaluer les relations génétiques entre individus et permettre la construction d'un pedigree. Cette thèse porte sur une population naturelle d'un petit mammifère insectivore, la musaraigne musette, Crocidura russula. Parce que cette espèce présente un mode de vie souterrain, les deux techniques complémentaires mentionnées ci-dessus ont été combinées pour acquérir les informations nécessaires. Les données ont été utilisées pour explorer divers aspects de biologie evolutive. Nous avons montré que la grande quantité de variance génétique trouvée chez cette espèce n'est pas maintenue par son système d'appariement. Celle-ci s'est en effet avérée être moins monogame que ce qui était admis jusqu'ici. Sa grande diversité génétique est plutôt entretenue par le flux de gènes provenant du voisinage. La dispersion a donc été un sujet phare dans cette thèse. Nous avons montré qu'elle n'est pas provoquée par un évitement de la consanguinité et nous n'avons pas trouvé de dépression de consanguité dans notre population. L'acquisition d'un territoire joue par contre un rôle important dans la dispersion. En outre, la dispersion possède une base génétique chez cette espèce. De plus, une fois qu'ils ont dispersé, les individus n'ont pas une valeur adaptative differente d'individus philopatriques. Le poids s'est avéré être un trait d'histoire de vie fortement influencé par la sélection sexuelle et de viabilité chez les deux sexes. Les gros individus ont accès à la reproduction parce qu'ils acquièrent et défendent un territoire plus facilement que les plus légers. Au contraire, les individus de taille intermédiaire sont favorisés par la sélection de viabilité, certainement à cause de contraintes écologiques et de coûts métaboliques. Finalement, nous avons montré que la majorité des traits d'histoire de vie dans notre population a le potentiel d'évoluer parce qu'elle maintient des quantités considérables de variance génétique additive. Néanmoins, l'héritabilité de ces traits d'histoire de vie n'est pas significative à cause de la grande quantité de variance non-additive ou environmentale associée à ces traits.

Robust Factor Analysis for Compositional Data

Factor analysis as frequent technique for multivariate data inspection is widely used also for compositional data analysis. The usual way is to use a centered logratio (clr)transformation to obtain the random vector y of dimension D. The factor model istheny = Λf + e (1)with the factors f of dimension k & D, the error term e, and the loadings matrix Λ.Using the usual model assumptions (see, e.g., Basilevsky, 1994), the factor analysismodel (1) can be written asCov(y) = ΛΛT + ψ (2)where ψ = Cov(e) has a diagonal form. The diagonal elements of ψ as well as theloadings matrix Λ are estimated from an estimation of Cov(y).Given observed clr transformed data Y as realizations of the random vectory. Outliers or deviations from the idealized model assumptions of factor analysiscan severely effect the parameter estimation. As a way out, robust estimation ofthe covariance matrix of Y will lead to robust estimates of Λ and ψ in (2), seePison et al. (2003). Well known robust covariance estimators with good statisticalproperties, like the MCD or the S-estimators (see, e.g. Maronna et al., 2006), relyon a full-rank data matrix Y which is not the case for clr transformed data (see,e.g., Aitchison, 1986).The isometric logratio (ilr) transformation (Egozcue et al., 2003) solves thissingularity problem. The data matrix Y is transformed to a matrix Z by usingan orthonormal basis of lower dimension. Using the ilr transformed data, a robustcovariance matrix C(Z) can be estimated. The result can be back-transformed tothe clr space byC(Y ) = V C(Z)V Twhere the matrix V with orthonormal columns comes from the relation betweenthe clr and the ilr transformation. Now the parameters in the model (2) can beestimated (Basilevsky, 1994) and the results have a direct interpretation since thelinks to the original variables are still preserved.The above procedure will be applied to data from geochemistry. Our specialinterest is on comparing the results with those of Reimann et al. (2002) for the Kolaproject data

Analyzing shapes as compositions of distances

We propose to analyze shapes as “compositions” of distances in Aitchison geometry asan alternate and complementary tool to classical shape analysis, especially when sizeis non-informative.Shapes are typically described by the location of user-chosen landmarks. Howeverthe shape – considered as invariant under scaling, translation, mirroring and rotation– does not uniquely define the location of landmarks. A simple approach is to usedistances of landmarks instead of the locations of landmarks them self. Distances arepositive numbers defined up to joint scaling, a mathematical structure quite similar tocompositions. The shape fixes only ratios of distances. Perturbations correspond torelative changes of the size of subshapes and of aspect ratios. The power transformincreases the expression of the shape by increasing distance ratios. In analogy to thesubcompositional consistency, results should not depend too much on the choice ofdistances, because different subsets of the pairwise distances of landmarks uniquelydefine the shape.Various compositional analysis tools can be applied to sets of distances directly or afterminor modifications concerning the singularity of the covariance matrix and yield resultswith direct interpretations in terms of shape changes. The remaining problem isthat not all sets of distances correspond to a valid shape. Nevertheless interpolated orpredicted shapes can be backtransformated by multidimensional scaling (when all pairwisedistances are used) or free geodetic adjustment (when sufficiently many distancesare used)

New insights on river water chemistry by using non-centred simplicial principal component analysis: a case study

The use of perturbation and power transformation operations permits the investigation of linear processes in the simplex as in a vectorial space. When the investigated geochemical processes can be constrained by the use of well-known starting point, the eigenvectors of the covariance matrix of a non-centred principalcomponent analysis allow to model compositional changes compared with a reference point.The results obtained for the chemistry of water collected in River Arno (central-northern Italy) have open new perspectives for considering relative changes of the analysed variables and to hypothesise the relative effect of different acting physical-chemical processes, thus posing the basis for a quantitative modelling

Individual reproductive success and effective population size in the greater white-toothed shrew Crocidura russula.

In order to investigate the determinants of effective population size in the socially monogamous Crocidura russula, the reproductive output of 44 individuals was estimated through genetic assignment methods. The individual variance in breeding success turned out to be surprisingly high, mostly because the males were markedly less monogamous than expected from previous behavioural data. Males paired simultaneously with up to four females and polygynous males had significantly more offspring than monogamous ones. The variance in female reproductive success also exceeded that of a Poisson distribution (though to a lesser extent), partly because females paired with multiply mated males weaned significantly more offspring. Polyandry also occurred occasionally, but only sequentially (i.e. without multiple paternity of litters). Estimates of the effective to census size ratio were ca. 0.60, which excluded the mating system as a potential explanation for the high genetic variance found in this shrew's populations. Our data suggest that gene flow from the neighbourhood (up to one-third of the total recruitment) is the most likely cause of the high levels of genetic diversity observed in this shrew's subpopulations.