882 resultados para Bayesian model selection


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Tämän tutkielman tavoitteena oli määrittää uuden markkinan valinnan perusteita teolliselle tuotteelle. Tutkielma keskittyi jo tunnettuihin kansainvälisen markkinavalinnan lähestymistapoihin ja pyrki soveltamaan yhtä menetelmää käytäntöön tutkielman empiria osassa case-tutkimuksen avulla. Tutkimusote oli tutkiva, eksploratiivinen ja perustui sekundääri analyysiin. Käytetyt tiedon lähteet olivat suureksi osin sekundäärisiä tuottaen kvalitatiivista tietoa. Kuitenkin haastatteluita suoritettiin myös. Kattava kirjallisuus katsaus tunnetuista teoreettisista lähestymistavoista kansainväliseen markkinavalintaan oli osa tutkielmaa. Kolme tärkeintä lähestymistapaa esiteltiin tarkemmin. Yksi lähestymistavoista, ei-järjestelmällinen, muodosti viitekehyksen tutkielman empiria-osalle. Empiria pyrki soveltamaan yhtä ei-järjestelmällisen lähestymistavan malleista kansainvälisessä paperiteollisuudessa. Tarkoituksena oli tunnistaa kaikkein houkuttelevimmat maat mahdollisille markkinointitoimenpiteille tuotteen yhdellä loppukäyttöalueella. Tutkielmassa päädyttiin käyttämään ilmastollisia olosuhteita, siipikarjan päälukua sekä siipikarjan kasvuprosenttia suodattimina pyrittäessä vähentämään mahdollisten maiden lukumäärää. Tutkielman empiria-osa kärsi selkeästi relevantin tiedon puutteesta. Siten myös tutkielman reliabiliteetti ja validiteetti voidaan jossain määrin kyseenalaistaa.

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This thesis is composed of three main parts. The first consists of a state of the art of the different notions that are significant to understand the elements surrounding art authentication in general, and of signatures in particular, and that the author deemed them necessary to fully grasp the microcosm that makes up this particular market. Individuals with a solid knowledge of the art and expertise area, and that are particularly interested in the present study are advised to advance directly to the fourth Chapter. The expertise of the signature, it's reliability, and the factors impacting the expert's conclusions are brought forward. The final aim of the state of the art is to offer a general list of recommendations based on an exhaustive review of the current literature and given in light of all of the exposed issues. These guidelines are specifically formulated for the expertise of signatures on paintings, but can also be applied to wider themes in the area of signature examination. The second part of this thesis covers the experimental stages of the research. It consists of the method developed to authenticate painted signatures on works of art. This method is articulated around several main objectives: defining measurable features on painted signatures and defining their relevance in order to establish the separation capacities between groups of authentic and simulated signatures. For the first time, numerical analyses of painted signatures have been obtained and are used to attribute their authorship to given artists. An in-depth discussion of the developed method constitutes the third and final part of this study. It evaluates the opportunities and constraints when applied by signature and handwriting experts in forensic science. A brief summary covering each chapter allows a rapid overview of the study and summarizes the aims and main themes of each chapter. These outlines presented below summarize the aims and main themes addressed in each chapter. Part I - Theory Chapter 1 exposes legal aspects surrounding the authentication of works of art by art experts. The definition of what is legally authentic, the quality and types of the experts that can express an opinion concerning the authorship of a specific painting, and standard deontological rules are addressed. The practices applied in Switzerland will be specifically dealt with. Chapter 2 presents an overview of the different scientific analyses that can be carried out on paintings (from the canvas to the top coat). Scientific examinations of works of art have become more common, as more and more museums equip themselves with laboratories, thus an understanding of their role in the art authentication process is vital. The added value that a signature expertise can have in comparison to other scientific techniques is also addressed. Chapter 3 provides a historical overview of the signature on paintings throughout the ages, in order to offer the reader an understanding of the origin of the signature on works of art and its evolution through time. An explanation is given on the transitions that the signature went through from the 15th century on and how it progressively took on its widely known modern form. Both this chapter and chapter 2 are presented to show the reader the rich sources of information that can be provided to describe a painting, and how the signature is one of these sources. Chapter 4 focuses on the different hypotheses the FHE must keep in mind when examining a painted signature, since a number of scenarios can be encountered when dealing with signatures on works of art. The different forms of signatures, as well as the variables that may have an influence on the painted signatures, are also presented. Finally, the current state of knowledge of the examination procedure of signatures in forensic science in general, and in particular for painted signatures, is exposed. The state of the art of the assessment of the authorship of signatures on paintings is established and discussed in light of the theoretical facets mentioned previously. Chapter 5 considers key elements that can have an impact on the FHE during his or her2 examinations. This includes a discussion on elements such as the skill, confidence and competence of an expert, as well as the potential bias effects he might encounter. A better understanding of elements surrounding handwriting examinations, to, in turn, better communicate results and conclusions to an audience, is also undertaken. Chapter 6 reviews the judicial acceptance of signature analysis in Courts and closes the state of the art section of this thesis. This chapter brings forward the current issues pertaining to the appreciation of this expertise by the non- forensic community, and will discuss the increasing number of claims of the unscientific nature of signature authentication. The necessity to aim for more scientific, comprehensive and transparent authentication methods will be discussed. The theoretical part of this thesis is concluded by a series of general recommendations for forensic handwriting examiners in forensic science, specifically for the expertise of signatures on paintings. These recommendations stem from the exhaustive review of the literature and the issues exposed from this review and can also be applied to the traditional examination of signatures (on paper). Part II - Experimental part Chapter 7 describes and defines the sampling, extraction and analysis phases of the research. The sampling stage of artists' signatures and their respective simulations are presented, followed by the steps that were undertaken to extract and determine sets of characteristics, specific to each artist, that describe their signatures. The method is based on a study of five artists and a group of individuals acting as forgers for the sake of this study. Finally, the analysis procedure of these characteristics to assess of the strength of evidence, and based on a Bayesian reasoning process, is presented. Chapter 8 outlines the results concerning both the artist and simulation corpuses after their optical observation, followed by the results of the analysis phase of the research. The feature selection process and the likelihood ratio evaluation are the main themes that are addressed. The discrimination power between both corpuses is illustrated through multivariate analysis. Part III - Discussion Chapter 9 discusses the materials, the methods, and the obtained results of the research. The opportunities, but also constraints and limits, of the developed method are exposed. Future works that can be carried out subsequent to the results of the study are also presented. Chapter 10, the last chapter of this thesis, proposes a strategy to incorporate the model developed in the last chapters into the traditional signature expertise procedures. Thus, the strength of this expertise is discussed in conjunction with the traditional conclusions reached by forensic handwriting examiners in forensic science. Finally, this chapter summarizes and advocates a list of formal recommendations for good practices for handwriting examiners. In conclusion, the research highlights the interdisciplinary aspect of signature examination of signatures on paintings. The current state of knowledge of the judicial quality of art experts, along with the scientific and historical analysis of paintings and signatures, are overviewed to give the reader a feel of the different factors that have an impact on this particular subject. The temperamental acceptance of forensic signature analysis in court, also presented in the state of the art, explicitly demonstrates the necessity of a better recognition of signature expertise by courts of law. This general acceptance, however, can only be achieved by producing high quality results through a well-defined examination process. This research offers an original approach to attribute a painted signature to a certain artist: for the first time, a probabilistic model used to measure the discriminative potential between authentic and simulated painted signatures is studied. The opportunities and limits that lie within this method of scientifically establishing the authorship of signatures on works of art are thus presented. In addition, the second key contribution of this work proposes a procedure to combine the developed method into that used traditionally signature experts in forensic science. Such an implementation into the holistic traditional signature examination casework is a large step providing the forensic, judicial and art communities with a solid-based reasoning framework for the examination of signatures on paintings. The framework and preliminary results associated with this research have been published (Montani, 2009a) and presented at international forensic science conferences (Montani, 2009b; Montani, 2012).

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Many species are able to learn to associate behaviours with rewards as this gives fitness advantages in changing environments. Social interactions between population members may, however, require more cognitive abilities than simple trial-and-error learning, in particular the capacity to make accurate hypotheses about the material payoff consequences of alternative action combinations. It is unclear in this context whether natural selection necessarily favours individuals to use information about payoffs associated with nontried actions (hypothetical payoffs), as opposed to simple reinforcement of realized payoff. Here, we develop an evolutionary model in which individuals are genetically determined to use either trial-and-error learning or learning based on hypothetical reinforcements, and ask what is the evolutionarily stable learning rule under pairwise symmetric two-action stochastic repeated games played over the individual's lifetime. We analyse through stochastic approximation theory and simulations the learning dynamics on the behavioural timescale, and derive conditions where trial-and-error learning outcompetes hypothetical reinforcement learning on the evolutionary timescale. This occurs in particular under repeated cooperative interactions with the same partner. By contrast, we find that hypothetical reinforcement learners tend to be favoured under random interactions, but stable polymorphisms can also obtain where trial-and-error learners are maintained at a low frequency. We conclude that specific game structures can select for trial-and-error learning even in the absence of costs of cognition, which illustrates that cost-free increased cognition can be counterselected under social interactions.

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Within Data Envelopment Analysis, several alternative models allow for an environmental adjustment. The majority of them deliver divergent results. Decision makers face the difficult task of selecting the most suitable model. This study is performed to overcome this difficulty. By doing so, it fills a research gap. First, a two-step web-based survey is conducted. It aims (1) to identify the selection criteria, (2) to prioritize and weight the selection criteria with respect to the goal of selecting the most suitable model and (3) to collect the preferences about which model is preferable to fulfil each selection criterion. Second, Analytic Hierarchy Process is used to quantify the preferences expressed in the survey. Results show that the understandability, the applicability and the acceptability of the alternative models are valid selection criteria. The selection of the most suitable model depends on the preferences of the decision makers with regards to these criteria.

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Probabilistic inversion methods based on Markov chain Monte Carlo (MCMC) simulation are well suited to quantify parameter and model uncertainty of nonlinear inverse problems. Yet, application of such methods to CPU-intensive forward models can be a daunting task, particularly if the parameter space is high dimensional. Here, we present a 2-D pixel-based MCMC inversion of plane-wave electromagnetic (EM) data. Using synthetic data, we investigate how model parameter uncertainty depends on model structure constraints using different norms of the likelihood function and the model constraints, and study the added benefits of joint inversion of EM and electrical resistivity tomography (ERT) data. Our results demonstrate that model structure constraints are necessary to stabilize the MCMC inversion results of a highly discretized model. These constraints decrease model parameter uncertainty and facilitate model interpretation. A drawback is that these constraints may lead to posterior distributions that do not fully include the true underlying model, because some of its features exhibit a low sensitivity to the EM data, and hence are difficult to resolve. This problem can be partly mitigated if the plane-wave EM data is augmented with ERT observations. The hierarchical Bayesian inverse formulation introduced and used herein is able to successfully recover the probabilistic properties of the measurement data errors and a model regularization weight. Application of the proposed inversion methodology to field data from an aquifer demonstrates that the posterior mean model realization is very similar to that derived from a deterministic inversion with similar model constraints.

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La spectroscopie infrarouge (FTIR) est une technique de choix dans l'analyse des peintures en spray (traces ou bonbonnes de référence), grâce à son fort pouvoir discriminant, sa sensibilité, et ses nombreuses possibilités d'échantillonnage. La comparaison des spectres obtenus est aujourd'hui principalement faite visuellement, mais cette procédure présente des limitations telles que la subjectivité de la prise de décision car celle-ci dépend de l'expérience et de la formation suivie par l'expert. De ce fait, de faibles différences d'intensités relatives entre deux pics peuvent être perçues différemment par des experts, même au sein d'un même laboratoire. Lorsqu'il s'agit de justifier ces différences, certains les expliqueront par la méthode analytique utilisée, alors que d'autres estimeront plutôt qu'il s'agit d'une variabilité intrinsèque à la peinture et/ou à son vécu (par exemple homogénéité, sprayage, ou dégradation). Ce travail propose d'étudier statistiquement les différentes sources de variabilité observables dans les spectres infrarouges, de les identifier, de les comprendre et tenter de les minimiser. Le deuxième objectif principal est de proposer une procédure de comparaison des spectres qui soit davantage transparente et permette d'obtenir des réponses reproductibles indépendamment des experts interrogés. La première partie du travail traite de l'optimisation de la mesure infrarouge et des principaux paramètres analytiques. Les conditions nécessaires afin d'obtenir des spectres reproductibles et minimisant la variation au sein d'un même échantillon (intra-variabilité) sont présentées. Par la suite une procédure de correction des spectres est proposée au moyen de prétraitements et de sélections de variables, afin de minimiser les erreurs systématiques et aléatoires restantes, et de maximiser l'information chimique pertinente. La seconde partie présente une étude de marché effectuée sur 74 bonbonnes de peintures en spray représentatives du marché suisse. Les capacités de discrimination de la méthode FTIR au niveau de la marque et du modèle sont évaluées au moyen d'une procédure visuelle, et comparées à diverses procédures statistiques. Les limites inférieures de discrimination sont testées sur des peintures de marques et modèles identiques mais provenant de différents lots de production. Les résultats ont montré que la composition en pigments était particulièrement discriminante, à cause des étapes de corrections et d'ajustement de la couleur subies lors de la production. Les particularités associées aux peintures en spray présentes sous forme de traces (graffitis, gouttelettes) ont également été testées. Trois éléments sont mis en évidence et leur influence sur le spectre infrarouge résultant testée : 1) le temps minimum de secouage nécessaire afin d'obtenir une homogénéité suffisante de la peinture et, en conséquence, de la surface peinte, 2) la dégradation initiée par le rayonnement ultra- violet en extérieur, et 3) la contamination provenant du support lors du prélèvement. Finalement une étude de population a été réalisée sur 35 graffitis de la région lausannoise et les résultats comparés à l'étude de marché des bonbonnes en spray. La dernière partie de ce travail s'est concentrée sur l'étape de prise de décision lors de la comparaison de spectres deux-à-deux, en essayant premièrement de comprendre la pratique actuelle au sein des laboratoires au moyen d'un questionnaire, puis de proposer une méthode statistique de comparaison permettant d'améliorer l'objectivité et la transparence lors de la prise de décision. Une méthode de comparaison basée sur la corrélation entre les spectres est proposée, et ensuite combinée à une évaluation Bayesienne de l'élément de preuve au niveau de la source et au niveau de l'activité. Finalement des exemples pratiques sont présentés et la méthodologie est discutée afin de définir le rôle précis de l'expert et des statistiques dans la procédure globale d'analyse des peintures. -- Infrared spectroscopy (FTIR) is a technique of choice for analyzing spray paint speciments (i.e. traces) and reference samples (i.e. cans seized from suspects) due to its high discriminating power, sensitivity and sampling possibilities. The comparison of the spectra is currently carried out visually, but this procedure has limitations such as the subjectivity in the decision due to its dependency on the experience and training of the expert. This implies that small differences in the relative intensity of two peaks can be perceived differently by experts, even between analysts working in the same laboratory. When it comes to justifying these differences, some will explain them by the analytical technique, while others will estimate that the observed differences are mostly due to an intrinsic variability from the paint sample and/or its acquired characteristics (for example homogeneity, spraying, or degradation). This work proposes to statistically study the different sources of variability observed in infrared spectra, to identify them, understand them and try to minimize them. The second goal is to propose a procedure for spectra comparison that is more transparent, and allows obtaining reproducible answers being independent from the expert. The first part of the manuscript focuses on the optimization of infrared measurement and on the main analytical parameters. The necessary conditions to obtain reproducible spectra with a minimized variation within a sample (intra-variability) are presented. Following that a procedure of spectral correction is then proposed using pretreatments and variable selection methods, in order to minimize systematic and random errors, and increase simultaneously relevant chemical information. The second part presents a market study of 74 spray paints representative of the Swiss market. The discrimination capabilities of FTIR at the brand and model level are evaluated by means of visual and statistical procedures. The inferior limits of discrimination are tested on paints coming from the same brand and model, but from different production batches. The results showed that the pigment composition was particularly discriminatory, because of the corrections and adjustments made to the paint color during its manufacturing process. The features associated with spray paint traces (graffitis, droplets) were also tested. Three elements were identified and their influence on the resulting infrared spectra were tested: 1) the minimum shaking time necessary to obtain a sufficient homogeneity of the paint and subsequently of the painted surface, 2) the degradation initiated by ultraviolet radiation in an exterior environment, and 3) the contamination from the support when paint is recovered. Finally a population study was performed on 35 graffitis coming from the city of Lausanne and surroundings areas, and the results were compared to the previous market study of spray cans. The last part concentrated on the decision process during the pairwise comparison of spectra. First, an understanding of the actual practice among laboratories was initiated by submitting a questionnaire. Then, a proposition for a statistical method of comparison was advanced to improve the objectivity and transparency during the decision process. A method of comparison based on the correlation between spectra is proposed, followed by the integration into a Bayesian framework at both source and activity levels. Finally, some case examples are presented and the recommended methodology is discussed in order to define the role of the expert as well as the contribution of the tested statistical approach within a global analytical sequence for paint examinations.

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Complete sex chromosome dosage compensation has more often been observed in XY than ZW species. In this study, using a population genetic model and the chicken transcriptome, we assess whether sexual conflict can account for this difference. Sexual conflict over expression is inevitable when mutation effects are correlated across the sexes, as compensatory mutations in the heterogametic sex lead to hyperexpression in the homogametic sex. Coupled with stronger selection and greater reproductive variance in males, this results in slower and less complete evolution of Z compared with X dosage compensation. Using expression variance as a measure of selection strength, we find that, as predicted by the model, dosage compensation in the chicken is most pronounced in genes that are under strong selection biased towards females. Our study explains the pattern of weak dosage compensation in ZW systems, and suggests that sexual selection plays a major role in shaping sex chromosome dosage compensation.

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The interplay between selection and aspects of the genetic architecture of traits (such as linkage, dominance, and epistasis) can either drive or constrain speciation [1-3]. Despite accumulating evidence that speciation can progress to "intermediate" stages-with populations evolving only partial reproductive isolation-studies describing selective mechanisms that impose constraints on speciation are more rare than those describing drivers. The stick insect Timema cristinae provides an example of a system in which partial reproductive isolation has evolved between populations adapted to different host plant environments, in part due to divergent selection acting on a pattern polymorphism [4, 5]. Here, we demonstrate how selection on a green/melanistic color polymorphism counteracts speciation in this system. Specifically, divergent selection between hosts does not occur on color phenotypes because melanistic T. cristinae are cryptic on the stems of both host species, are resistant to a fungal pathogen, and have a mating advantage. Using genetic crosses and genome-wide association mapping, we quantify the genetic architecture of both the pattern and color polymorphism, illustrating their simple genetic control. We use these empirical results to develop an individual-based model that shows how the melanistic phenotype acts as a "genetic bridge" that increases gene flow between populations living on different hosts. Our results demonstrate how variation in the nature of selection acting on traits, and aspects of trait genetic architecture, can impose constraints on both local adaptation and speciation.

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Gene filtering is a useful preprocessing technique often applied to microarray datasets. However, it is no common practice because clear guidelines are lacking and it bears the risk of excluding some potentially relevant genes. In this work, we propose to model microarray data as a mixture of two Gaussian distributions that will allow us to obtain an optimal filter threshold in terms of the gene expression level.

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BACKGROUND: The bacterial flagellum is the most important organelle of motility in bacteria and plays a key role in many bacterial lifestyles, including virulence. The flagellum also provides a paradigm of how hierarchical gene regulation, intricate protein-protein interactions and controlled protein secretion can result in the assembly of a complex multi-protein structure tightly orchestrated in time and space. As if to stress its importance, plants and animals produce receptors specifically dedicated to the recognition of flagella. Aside from motility, the flagellum also moonlights as an adhesion and has been adapted by humans as a tool for peptide display. Flagellar sequence variation constitutes a marker with widespread potential uses for studies of population genetics and phylogeny of bacterial species. RESULTS: We sequenced the complete flagellin gene (flaA) in 18 different species and subspecies of Aeromonas. Sequences ranged in size from 870 (A. allosaccharophila) to 921 nucleotides (A. popoffii). The multiple alignment displayed 924 sites, 66 of which presented alignment gaps. The phylogenetic tree revealed the existence of two groups of species exhibiting different FlaA flagellins (FlaA1 and FlaA2). Maximum likelihood models of codon substitution were used to analyze flaA sequences. Likelihood ratio tests suggested a low variation in selective pressure among lineages, with an omega ratio of less than 1 indicating the presence of purifying selection in almost all cases. Only one site under potential diversifying selection was identified (isoleucine in position 179). However, 17 amino acid positions were inferred as sites that are likely to be under positive selection using the branch-site model. Ancestral reconstruction revealed that these 17 amino acids were among the amino acid changes detected in the ancestral sequence. CONCLUSION: The models applied to our set of sequences allowed us to determine the possible evolutionary pathway followed by the flaA gene in Aeromonas, suggesting that this gene have probably been evolving independently in the two groups of Aeromonas species since the divergence of a distant common ancestor after one or several episodes of positive selection. REVIEWERS: This article was reviewed by Alexey Kondrashov, John Logsdon and Olivier Tenaillon (nominated by Laurence D Hurst).

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Over the past few decades, age estimation of living persons has represented a challenging task for many forensic services worldwide. In general, the process for age estimation includes the observation of the degree of maturity reached by some physical attributes, such as dentition or several ossification centers. The estimated chronological age or the probability that an individual belongs to a meaningful class of ages is then obtained from the observed degree of maturity by means of various statistical methods. Among these methods, those developed in a Bayesian framework offer to users the possibility of coherently dealing with the uncertainty associated with age estimation and of assessing in a transparent and logical way the probability that an examined individual is younger or older than a given age threshold. Recently, a Bayesian network for age estimation has been presented in scientific literature; this kind of probabilistic graphical tool may facilitate the use of the probabilistic approach. Probabilities of interest in the network are assigned by means of transition analysis, a statistical parametric model, which links the chronological age and the degree of maturity by means of specific regression models, such as logit or probit models. Since different regression models can be employed in transition analysis, the aim of this paper is to study the influence of the model in the classification of individuals. The analysis was performed using a dataset related to the ossifications status of the medial clavicular epiphysis and results support that the classification of individuals is not dependent on the choice of the regression model.

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Building on the instrumental model of group conflict (IMGC), the present experiment investigates the support for discriminatory and meritocratic method of selections at university in a sample of local and immigrant students. Results showed that local students were supporting in a larger proportion selection method that favors them over immigrants in comparison to method that consists in selecting the best applicants without considering his/her origin. Supporting the assumption of the IMGC, this effect was stronger for locals who perceived immigrants as competing for resources. Immigrant students supported more strongly the meritocratic selection method than the one that discriminated them. However, contrasting with the assumption of the IMGC, this effect was only present in students who perceived immigrants as weakly competing for locals' resources. Results demonstrate that selection methods used at university can be perceived differently depending on students' origin. Further, they suggest that the mechanisms underlying the perception of discriminatory and meritocratic selection methods differ between local and immigrant students. Hence, the present experiment makes a theoretical contribution to the IMGC by delimiting its assumptions to the ingroup facing a competitive situation with a relevant outgroup. Practical implication for universities recruitment policies are discussed.

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The fact that individuals learn can change the relationship between genotype and phenotype in the population, and thus affect the evolutionary response to selection. Here we ask how male ability to learn from female response affects the evolution of a novel male behavioral courtship trait under pre-existing female preference (sensory drive). We assume a courtship trait which has both a genetic and a learned component, and a two-level female response to males. With individual-based simulations we show that, under this scenario, learning generally increases the strength of selection on the genetic component of the courtship trait, at least when the population genetic mean is still low. As a consequence, learning not only accelerates the evolution of the courtship trait, but also enables it when the trait is costly, which in the absence of learning results in an adaptive valley. Furthermore, learning can enable the evolution of the novel trait in the face of gene flow mediated by immigration of males that show superior attractiveness to females based on another, non-heritable trait. However, rather than increasing monotonically with the speed of learning, the effect of learning on evolution is maximized at intermediate learning rates. This model shows that, at least under some scenarios, the ability to learn can drive the evolution of mating behaviors through a process equivalent to Waddington's genetic assimilation.

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Peer-reviewed

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In mathematical modeling the estimation of the model parameters is one of the most common problems. The goal is to seek parameters that fit to the measurements as well as possible. There is always error in the measurements which implies uncertainty to the model estimates. In Bayesian statistics all the unknown quantities are presented as probability distributions. If there is knowledge about parameters beforehand, it can be formulated as a prior distribution. The Bays’ rule combines the prior and the measurements to posterior distribution. Mathematical models are typically nonlinear, to produce statistics for them requires efficient sampling algorithms. In this thesis both Metropolis-Hastings (MH), Adaptive Metropolis (AM) algorithms and Gibbs sampling are introduced. In the thesis different ways to present prior distributions are introduced. The main issue is in the measurement error estimation and how to obtain prior knowledge for variance or covariance. Variance and covariance sampling is combined with the algorithms above. The examples of the hyperprior models are applied to estimation of model parameters and error in an outlier case.