Nonlinear models and small sample performance of the generalized method of moments

In this paper I explore the issue of nonlinearity (both in the datageneration process and in the functional form that establishes therelationship between the parameters and the data) regarding the poorperformance of the Generalized Method of Moments (GMM) in small samples.To this purpose I build a sequence of models starting with a simple linearmodel and enlarging it progressively until I approximate a standard (nonlinear)neoclassical growth model. I then use simulation techniques to find the smallsample distribution of the GMM estimators in each of the models.

Genome-Wide Prediction Methods in Highly Diverse and Heterozygous Species: Proof-of-Concept through Simulation in Grapevine.

Nowadays, genome-wide association studies (GWAS) and genomic selection (GS) methods which use genome-wide marker data for phenotype prediction are of much potential interest in plant breeding. However, to our knowledge, no studies have been performed yet on the predictive ability of these methods for structured traits when using training populations with high levels of genetic diversity. Such an example of a highly heterozygous, perennial species is grapevine. The present study compares the accuracy of models based on GWAS or GS alone, or in combination, for predicting simple or complex traits, linked or not with population structure. In order to explore the relevance of these methods in this context, we performed simulations using approx 90,000 SNPs on a population of 3,000 individuals structured into three groups and corresponding to published diversity grapevine data. To estimate the parameters of the prediction models, we defined four training populations of 1,000 individuals, corresponding to these three groups and a core collection. Finally, to estimate the accuracy of the models, we also simulated four breeding populations of 200 individuals. Although prediction accuracy was low when breeding populations were too distant from the training populations, high accuracy levels were obtained using the sole core-collection as training population. The highest prediction accuracy was obtained (up to 0.9) using the combined GWAS-GS model. We thus recommend using the combined prediction model and a core-collection as training population for grapevine breeding or for other important economic crops with the same characteristics.

Subsampling inference in threshold autoregressive models

This paper discusses inference in self exciting threshold autoregressive (SETAR)models. Of main interest is inference for the threshold parameter. It iswell-known that the asymptotics of the corresponding estimator depend uponwhether the SETAR model is continuous or not. In the continuous case, thelimiting distribution is normal and standard inference is possible. Inthe discontinuous case, the limiting distribution is non-normal and cannotbe estimated consistently. We show valid inference can be drawn by theuse of the subsampling method. Moreover, the method can even be extendedto situations where the (dis)continuity of the model is unknown. In thiscase, also the inference for the regression parameters of the modelbecomes difficult and subsampling can be used advantageously there aswell. In addition, we consider an hypothesis test for the continuity ofthe SETAR model. A simulation study examines small sample performance.

Unfolding nature "in silico" : overcoming practical and metodological limitations of species distribution models

Abstract : The existence of a causal relationship between the spatial distribution of living organisms and their environment, in particular climate, has been long recognized and is the central principle of biogeography. In turn, this recognition has led scientists to the idea of using the climatic, topographic, edaphic and biotic characteristics of the environment to predict its potential suitability for a given species or biological community. In this thesis, my objective is to contribute to the development of methodological improvements in the field of species distribution modeling. More precisely, the objectives are to propose solutions to overcome limitations of species distribution models when applied to conservation biology issues, or when .used as an assessment tool of the potential impacts of global change. The first objective of my thesis is to contribute to evidence the potential of species distribution models for conservation-related applications. I present a methodology to generate pseudo-absences in order to overcome the frequent lack of reliable absence data. I also demonstrate, both theoretically (simulation-based) and practically (field-based), how species distribution models can be successfully used to model and sample rare species. Overall, the results of this first part of the thesis demonstrate the strong potential of species distribution models as a tool for practical applications in conservation biology. The second objective this thesis is to contribute to improve .projections of potential climate change impacts on species distributions, and in particular for mountain flora. I develop and a dynamic model, MIGCLIM, that allows the implementation of dispersal limitations into classic species distribution models and present an application of this model to two virtual species. Given that accounting for dispersal limitations requires information on seed dispersal, distances, a general methodology to classify species into broad dispersal types is also developed. Finally, the M~GCLIM model is applied to a large number of species in a study area of the western Swiss Alps. Overall, the results indicate that while dispersal limitations can have an important impact on the outcome of future projections of species distributions under climate change scenarios, estimating species threat levels (e.g. species extinction rates) for a mountainous areas of limited size (i.e. regional scale) can also be successfully achieved when considering dispersal as unlimited (i.e. ignoring dispersal limitations, which is easier from a practical point of view). Finally, I present the largest fine scale assessment of potential climate change impacts on mountain vegetation that has been carried-out to date. This assessment involves vegetation from 12 study areas distributed across all major western and central European mountain ranges. The results highlight that some mountain ranges (the Pyrenees and the Austrian Alps) are expected to be more affected by climate change than others (Norway and the Scottish Highlands). The results I obtain in this study also indicate that the threat levels projected by fine scale models are less severe than those derived from coarse scale models. This result suggests that some species could persist in small refugias that are not detected by coarse scale models. Résumé : L'existence d'une relation causale entre la répartition des espèces animales et végétales et leur environnement, en particulier le climat, a été mis en évidence depuis longtemps et est un des principes centraux en biogéographie. Ce lien a naturellement conduit à l'idée d'utiliser les caractéristiques climatiques, topographiques, édaphiques et biotiques de l'environnement afin d'en prédire la qualité pour une espèce ou une communauté. Dans ce travail de thèse, mon objectif est de contribuer au développement d'améliorations méthodologiques dans le domaine de la modélisation de la distribution d'espèces dans le paysage. Plus précisément, les objectifs sont de proposer des solutions afin de surmonter certaines limitations des modèles de distribution d'espèces dans des applications pratiques de biologie de la conservation ou dans leur utilisation pour évaluer l'impact potentiel des changements climatiques sur l'environnement. Le premier objectif majeur de mon travail est de contribuer à démontrer le potentiel des modèles de distribution d'espèces pour des applications pratiques en biologie de la conservation. Je propose une méthode pour générer des pseudo-absences qui permet de surmonter le problème récurent du manque de données d'absences fiables. Je démontre aussi, de manière théorique (par simulation) et pratique (par échantillonnage de terrain), comment les modèles de distribution d'espèces peuvent être utilisés pour modéliser et améliorer l'échantillonnage des espèces rares. Ces résultats démontrent le potentiel des modèles de distribution d'espèces comme outils pour des applications de biologie de la conservation. Le deuxième objectif majeur de ce travail est de contribuer à améliorer les projections d'impacts potentiels des changements climatiques sur la flore, en particulier dans les zones de montagnes. Je développe un modèle dynamique de distribution appelé MigClim qui permet de tenir compte des limitations de dispersion dans les projections futures de distribution potentielle d'espèces, et teste son application sur deux espèces virtuelles. Vu que le fait de prendre en compte les limitations dues à la dispersion demande des données supplémentaires importantes (p.ex. la distance de dispersion des graines), ce travail propose aussi une méthode de classification simplifiée des espèces végétales dans de grands "types de disperseurs", ce qui permet ainsi de d'obtenir de bonnes approximations de distances de dispersions pour un grand nombre d'espèces. Finalement, j'applique aussi le modèle MIGCLIM à un grand nombre d'espèces de plantes dans une zone d'études des pré-Alpes vaudoises. Les résultats montrent que les limitations de dispersion peuvent avoir un impact considérable sur la distribution potentielle d'espèces prédites sous des scénarios de changements climatiques. Cependant, quand les modèles sont utilisés pour évaluer les taux d'extinction d'espèces dans des zones de montages de taille limitée (évaluation régionale), il est aussi possible d'obtenir de bonnes approximations en considérant la dispersion des espèces comme illimitée, ce qui est nettement plus simple d'un point dé vue pratique. Pour terminer je présente la plus grande évaluation à fine échelle d'impact potentiel des changements climatiques sur la flore des montagnes conduite à ce jour. Cette évaluation englobe 12 zones d'études réparties sur toutes les chaines de montages principales d'Europe occidentale et centrale. Les résultats montrent que certaines chaines de montagnes (les Pyrénées et les Alpes Autrichiennes) sont projetées comme plus sensibles aux changements climatiques que d'autres (les Alpes Scandinaves et les Highlands d'Ecosse). Les résultats obtenus montrent aussi que les modèles à échelle fine projettent des impacts de changement climatiques (p. ex. taux d'extinction d'espèces) moins sévères que les modèles à échelle large. Cela laisse supposer que les modèles a échelle fine sont capables de modéliser des micro-niches climatiques non-détectées par les modèles à échelle large.

Brownian dynamics simulation of DNA condensation.

DNA condensation observed in vitro with the addition of polyvalent counterions is due to intermolecular attractive forces. We introduce a quantitative model of these forces in a Brownian dynamics simulation in addition to a standard mean-field Poisson-Boltzmann repulsion. The comparison of a theoretical value of the effective diameter calculated from the second virial coefficient in cylindrical geometry with some experimental results allows a quantitative evaluation of the one-parameter attractive potential. We show afterward that with a sufficient concentration of divalent salt (typically approximately 20 mM MgCl(2)), supercoiled DNA adopts a collapsed form where opposing segments of interwound regions present zones of lateral contact. However, under the same conditions the same plasmid without torsional stress does not collapse. The condensed molecules present coexisting open and collapsed plectonemic regions. Furthermore, simulations show that circular DNA in 50% methanol solutions with 20 mM MgCl(2) aggregates without the requirement of torsional energy. This confirms known experimental results. Finally, a simulated DNA molecule confined in a box of variable size also presents some local collapsed zones in 20 mM MgCl(2) above a critical concentration of the DNA. Conformational entropy reduction obtained either by supercoiling or by confinement seems thus to play a crucial role in all forms of condensation of DNA.

The effects of physiologically plausible connectivity structure on local and global dynamics in large scale brain models.

Functionally relevant large scale brain dynamics operates within the framework imposed by anatomical connectivity and time delays due to finite transmission speeds. To gain insight on the reliability and comparability of large scale brain network simulations, we investigate the effects of variations in the anatomical connectivity. Two different sets of detailed global connectivity structures are explored, the first extracted from the CoCoMac database and rescaled to the spatial extent of the human brain, the second derived from white-matter tractography applied to diffusion spectrum imaging (DSI) for a human subject. We use the combination of graph theoretical measures of the connection matrices and numerical simulations to explicate the importance of both connectivity strength and delays in shaping dynamic behaviour. Our results demonstrate that the brain dynamics derived from the CoCoMac database are more complex and biologically more realistic than the one based on the DSI database. We propose that the reason for this difference is the absence of directed weights in the DSI connectivity matrix.

Dynamic compact thermal models with multiple power sources: application to an ultrathin chip stacking technology

Whereas numerical modeling using finite-element methods (FEM) can provide transient temperature distribution in the component with enough accuracy, it is of the most importance the development of compact dynamic thermal models that can be used for electrothermal simulation. While in most cases single power sources are considered, here we focus on the simultaneous presence of multiple sources. The thermal model will be in the form of a thermal impedance matrix containing the thermal impedance transfer functions between two arbitrary ports. Eachindividual transfer function element ( ) is obtained from the analysis of the thermal temperature transient at node ¿ ¿ after a power step at node ¿ .¿ Different options for multiexponential transient analysis are detailed and compared. Among the options explored, small thermal models can be obtained by constrained nonlinear least squares (NLSQ) methods if the order is selected properly using validation signals. The methods are applied to the extraction of dynamic compact thermal models for a new ultrathin chip stack technology (UTCS).

Impact of incorrect assumptions on the covariance structure of random effects and/or residuals in nonlinear mixed models for repeated measures data

In this paper we analyse, using Monte Carlo simulation, the possible consequences of incorrect assumptions on the true structure of the random effects covariance matrix and the true correlation pattern of residuals, over the performance of an estimation method for nonlinear mixed models. The procedure under study is the well known linearization method due to Lindstrom and Bates (1990), implemented in the nlme library of S-Plus and R. Its performance is studied in terms of bias, mean square error (MSE), and true coverage of the associated asymptotic confidence intervals. Ignoring other criteria like the convenience of avoiding over parameterised models, it seems worst to erroneously assume some structure than do not assume any structure when this would be adequate.

SIMSAFADIM-CLASTIC: A new approach to mathematical 3D forward simulation modelling for terrigenous and carbonate marine sedimentation

Most sedimentary modelling programs developed in recent years focus on either terrigenous or carbonate marine sedimentation. Nevertheless, only a few programs have attempted to consider mixed terrigenous-carbonate sedimentation, and most of these are two-dimensional, which is a major restriction since geological processes take place in 3D. This paper presents the basic concepts of a new 3D mathematical forward simulation model for clastic sediments, which was developed from SIMSAFADIM, a previous 3D carbonate sedimentation model. The new extended model, SIMSAFADIM-CLASTIC, simulates processes of autochthonous marine carbonate production and accumulation, together with clastic transport and sedimentation in three dimensions of both carbonate and terrigenous sediments. Other models and modelling strategies may also provide realistic and efficient tools for prediction of stratigraphic architecture and facies distribution of sedimentary deposits. However, SIMSAFADIM-CLASTIC becomes an innovative model that attempts to simulate different sediment types using a process-based approach, therefore being a useful tool for 3D prediction of stratigraphic architecture and facies distribution in sedimentary basins. This model is applied to the neogene Vallès-Penedès half-graben (western Mediterranean, NE Spain) to show the capacity of the program when applied to a realistic geologic situation involving interactions between terrigenous clastics and carbonate sediments.

Use of the swat model for hydro-sedimentologic simulation in a small rural watershed

Mathematical models have great potential to support land use planning, with the goal of improving water and land quality. Before using a model, however, the model must demonstrate that it can correctly simulate the hydrological and erosive processes of a given site. The SWAT model (Soil and Water Assessment Tool) was developed in the United States to evaluate the effects of conservation agriculture on hydrological processes and water quality at the watershed scale. This model was initially proposed for use without calibration, which would eliminate the need for measured hydro-sedimentologic data. In this study, the SWAT model was evaluated in a small rural watershed (1.19 km²) located on the basalt slopes of the state of Rio Grande do Sul in southern Brazil, where farmers have been using cover crops associated with minimum tillage to control soil erosion. Values simulated by the model were compared with measured hydro-sedimentological data. Results for surface and total runoff on a daily basis were considered unsatisfactory (Nash-Sutcliffe efficiency coefficient - NSE < 0.5). However simulation results on monthly and annual scales were significantly better. With regard to the erosion process, the simulated sediment yields for all years of the study were unsatisfactory in comparison with the observed values on a daily and monthly basis (NSE values < -6), and overestimated the annual sediment yield by more than 100 %.

Sex differences in urinary levels of several biological indicators of exposure: a simulation study using a compartmental based toxicokinetic model

Toxicokinetic modeling is a useful tool to describe or predict the behavior of a chemical agent in the human or animal organism. A general model based on four compartments was developed in a previous study in order to quantify the effect of human variability on a wide range of biological exposure indicators. The aim of this study was to adapt this existing general toxicokinetic model to three organic solvents, which were methyl ethyl ketone, 1-methoxy-2-propanol and 1,1,1,-trichloroethane, and to take into account sex differences. We assessed in a previous human volunteer study the impact of sex on different biomarkers of exposure corresponding to the three organic solvents mentioned above. Results from that study suggested that not only physiological differences between men and women but also differences due to sex hormones levels could influence the toxicokinetics of the solvents. In fact the use of hormonal contraceptive had an effect on the urinary levels of several biomarkers, suggesting that exogenous sex hormones could influence CYP2E1 enzyme activity. These experimental data were used to calibrate the toxicokinetic models developed in this study. Our results showed that it was possible to use an existing general toxicokinetic model for other compounds. In fact, most of the simulation results showed good agreement with the experimental data obtained for the studied solvents, with a percentage of model predictions that lies within the 95% confidence interval varying from 44.4 to 90%. Results pointed out that for same exposure conditions, men and women can show important differences in urinary levels of biological indicators of exposure. Moreover, when running the models by simulating industrial working conditions, these differences could even be more pronounced. In conclusion, a general and simple toxicokinetic model, adapted for three well known organic solvents, allowed us to show that metabolic parameters can have an important impact on the urinary levels of the corresponding biomarkers. These observations give evidence of an interindividual variablity, an aspect that should have its place in the approaches for setting limits of occupational exposure.

Numerical simulation of gel electrophoresis of DNA knots in weak and strong electric fields.

Gel electrophoresis allows one to separate knotted DNA (nicked circular) of equal length according to the knot type. At low electric fields, complex knots, being more compact, drift faster than simpler knots. Recent experiments have shown that the drift velocity dependence on the knot type is inverted when changing from low to high electric fields. We present a computer simulation on a lattice of a closed, knotted, charged DNA chain drifting in an external electric field in a topologically restricted medium. Using a Monte Carlo algorithm, the dependence of the electrophoretic migration of the DNA molecules on the knot type and on the electric field intensity is investigated. The results are in qualitative and quantitative agreement with electrophoretic experiments done under conditions of low and high electric fields.

On the problematic of reserving and stochastic loss models

Abstract Traditionally, the common reserving methods used by the non-life actuaries are based on the assumption that future claims are going to behave in the same way as they did in the past. There are two main sources of variability in the processus of development of the claims: the variability of the speed with which the claims are settled and the variability between the severity of the claims from different accident years. High changes in these processes will generate distortions in the estimation of the claims reserves. The main objective of this thesis is to provide an indicator which firstly identifies and quantifies these two influences and secondly to determine which model is adequate for a specific situation. Two stochastic models were analysed and the predictive distributions of the future claims were obtained. The main advantage of the stochastic models is that they provide measures of variability of the reserves estimates. The first model (PDM) combines one conjugate family Dirichlet - Multinomial with the Poisson distribution. The second model (NBDM) improves the first one by combining two conjugate families Poisson -Gamma (for distribution of the ultimate amounts) and Dirichlet Multinomial (for distribution of the incremental claims payments). It was found that the second model allows to find the speed variability in the reporting process and development of the claims severity as function of two above mentioned distributions' parameters. These are the shape parameter of the Gamma distribution and the Dirichlet parameter. Depending on the relation between them we can decide on the adequacy of the claims reserve estimation method. The parameters have been estimated by the Methods of Moments and Maximum Likelihood. The results were tested using chosen simulation data and then using real data originating from the three lines of business: Property/Casualty, General Liability, and Accident Insurance. These data include different developments and specificities. The outcome of the thesis shows that when the Dirichlet parameter is greater than the shape parameter of the Gamma, resulting in a model with positive correlation between the past and future claims payments, suggests the Chain-Ladder method as appropriate for the claims reserve estimation. In terms of claims reserves, if the cumulated payments are high the positive correlation will imply high expectations for the future payments resulting in high claims reserves estimates. The negative correlation appears when the Dirichlet parameter is lower than the shape parameter of the Gamma, meaning low expected future payments for the same high observed cumulated payments. This corresponds to the situation when claims are reported rapidly and fewer claims remain expected subsequently. The extreme case appears in the situation when all claims are reported at the same time leading to expectations for the future payments of zero or equal to the aggregated amount of the ultimate paid claims. For this latter case, the Chain-Ladder is not recommended.

Computer simulation study of liquid lithium at 470 and 843 K

Both structural and dynamical properties of 7Li at 470 and 843 K are studied by molecular dynamics simulation and the results are comapred with the available experimental data. Two effective interatomic potentials are used, i.e., a potential derived from the Ashcroft pseudopotential [Phys. Lett. 23, 48 (1966)] and a recently proposed potential deduced from the neutral pseudoatom method [J. Phys.: Condens. Matter 5, 4283 (1993)]. Although the shape of the two potential functions is very different, the majority of the properties calculated from them are very similar. The differences among the results using the two interaction models are carefully discussed.

Self-dynamic structure factor of dense liquids: Theory and simulation

The self-intermediate dynamic structure factor Fs(k,t) of liquid lithium near the melting temperature is calculated by molecular dynamics. The results are compared with the predictions of several theoretical approaches, paying special attention to the Lovesey model and the Wahnstrm and Sjgren mode-coupling theory. To this end the results for the Fs(k,t) second memory function predicted by both models are compared with the ones calculated from the simulations.