We adopt a Bayes linear approach to tackle design problems with many variables cross-classified in many ways. We investigate designs where we wish to sample individuals belonging to different groups, exploiting the powerful properties of the adjustment of infinitely second-order exchangeable vectors. The types of information we gain by sampling are identified with the orthogonal canonical directions. We show how we may express these directions in terms of the different factors of the model. This allows us to solve a series of lower dimensional problems, through which we may identify the different aspects of our adjusted beliefs with the different aspects of the choice of design, leading both to qualitative insights and quantitative guidance for the optimal choice of design. These subproblems have an interpretable form in terms of adjustment upon subspaces of the full problem and remain valid when we consider adjusting the underlying population structure and also for predicting future observables from past observation. We then examine the adjustment of finitely second-order exchangeable vectors, and show that the adjustment shares the same powerful properties as the adjustment in the infinite case. We show how if the finite sequence of vectors is extendible, then the differences in the adjustment of the sequence is quantitatively the same for all sequence lengths and it is easy to compare the qualitative differences. Extending to an infinite sequence allows us to draw comparisons between the finite and infinite modelling. Such comparisons may also be made when we consider sampling individuals belonging to different groups, where each group contains only a finite number of individuals.

We investigate the Principle of Predicate Exchangeability in the framework of Pure Inductive Logic. While this principle was known to Rudolf Carnap, who started research in Inductive Logic, the principle has been somewhat neglected in the past. After providing the framework of Pure Inductive Logic, we will show Representation Theorems for probability functions satisfying Predicate Exchangeability, filling the gap in the list of Representation Theorems for functions satisfying certain rational principles. We then introduce a new principle, called the Principle of Strong Predicate Exchangeability, which is weaker than the well-known Principle of Atom Exchangeability, but stronger than Predicate Exchangeability and give examples of functions that satisfy this principle. Finally, we extend the framework of Inductive Logic to Second Order languages, which allows for increasing a rational agent’s expressive strength. We introduce Wilmers’ Principle, a rational principle that rational agents might want to adopt in this extended framework, and give a representation theorem for this principle.

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We show that finite de Finetti-type results may be viewed as results on the approximation of certain continuous functions of a parameter by a sequence of positive operators (Ln) . For distribtions that depend on a finite-dimensional statistic (Tn) only, Ln is the expectation operator of (Tn) under the extremal infinite exchangeable distributions. The rate of approximation of finite exchangeable distributions by mixtures of marginals of infinite exchangeable distributions is the rate of approximation of a single function of the parameter, namely the second indefinite integral of the Fisher information. Our results include a major part of what is known about finite de Finetti theorems. The theory is, however, not only valid for the case when the extremal infinite exchangeable distributions are products of identical distributions. It applies as well to Markov-exchangeable distributions or the linear model. Moreover, the metric is not restricted to the supremum norm. (author's abstract) / Series: Forschungsberichte / Institut für Statistik

We propose and investigate several new principles of rational reasoning within the framework of Pure Inductive Logic, PIL, where probability functions defined on the sentences of a first-order language are used to model an agent's beliefs. The Elephant Principle is concerned with how learning, modelled by conditioning, may be uniquely `remembered'. The Perspective Principle requires that, from a given prior, conditioning on statistically similar experiences should result in similar assignments, and is found to be a necessary condition for Reichenbach's Axiom to hold. The Abductive Inference Principle and some variations are proposed as possible formulations of a restriction of C.S. Peirce's notion of hypothesis in the context of PIL, though characterization results obtained for these principles suggest that they may be too strong. The Finite Values Property holds when a probability function takes only finitely many values when restricted to sentences containing only constant symbols from some fixed finite set. This is shown to entail a certain systematic method of assigning probabilities in terms of possible worlds, and it is considered in this light as a possible principle of inductive reasoning. Classification results are given, stating which members of certain established families of probability functions satisfy each of these new principles. Additionally, we define the theory of a principle P of PIL to be the set of those sentences which are assigned probability 1 by every probability function which satisfies P. We investigate the theory of the established principle of Spectrum Exchangeability by finding separately the theories of heterogeneous and homogeneous functions. The theory of Spectrum Exchangeability is found to be equal to the theory of finite structures. The theory of Johnson's Sufficientness Postulate is also found. Consequently, we find that Spectrum Exchangeability, Johnson's Sufficientness Postulate and the Finite Values Property are all inconsistent with the principle of Super-Regularity: that any consistent sentence should be assigned non-zero probability.

Since the genetic code first was determined, many have claimed that it is organized adaptively, so as to assign similar codons to similar amino acids. This claim has proved difficult to establish due to the absence of relevant comparative data on alternative primordial codes and of objective measures of amino acid exchangeability. Here we use a recently developed measure of exchangeability to evaluate a null hypothesis and two alternative hypotheses about the adaptiveness of the genetic code. The null hypothesis that there is no tendency for exchangeable amino acids to be assigned to similar codons can be excluded here as expected from earlier work. The first alternative hypothesis is that any such correlation between codon distance and amino acid distance is due to incremental mechanisms of code evolution, and not to adaptation to reduce deleterious effects of future mutations. More specifically, new codon assignments that occur by ambiguity reduction or by codon capture will tend to give rise to correlations, whether due to the condition of amino acid ambiguity, or to the condition of similarity between a new tRNA synthetase (or tRNA) and its parent. The second alternative hypothesis, the adaptive hypothesis, then may be defined as an excess relative to what may be expected given the incremental nature of evolution, reflecting true adaptation for robustness rather than an incidental effect. The results reported here indicate that most of the nonrandomness in the amino acids to codon assignments can be explained by incremental code evolution, with a small residue of orderliness that may reflect code adaptation.

Ce projet de thèse vise à étudier les processus géochimiques de l'aluminium dans les sols acides à sulfates. Les résultats obtenus avec le dispositif de dialyse de Donnan montrent que l'aluminium dans la solution du sol est presque exclusivement (> 98%) présent sous forme de complexes de charge négative, vraisemblablement des organo-complexes d'aluminium. Les concentrations d'aluminium isotopiquement échangeables (valeurs-E) et les concentrations obtenues par extractions chimiques révèlent qu'une solution de 1 M KCl sous-estime systématiquement les valeurs E. Une méthode d'extraction séquentielle a révélé qu'une quantité importante de minéraux primaires (initialement présents dans les sols) a déjà été dissoute, comme en témoignent les concentrations élevées d'aluminium présentes en tant que minéraux secondaires d'aluminium. Ces études permettent de mieux comprendre la géochimie de l'aluminium dans les sols CLASS et de pouvoir intégrer ces connaissances dans la gestion des sols. / The aim of this thesis was to further understanding on Al geochemistry in coastal lowland acid sulfate soils (CLASS). It was observed that Al was present almost solely (> 98%) as negatively charged complexes in CLASS pore-waters, presumably with natural organic matter. Isotopically exchangeable concentrations (E-values) of Al and extraction solutions used to estimate the exchangeable pool showed that 1 M KCl always underestimated isotopically exchangeable Al concentrations in these soils and that 0.2 M CuCl2 improved agreement between both methodologies but sometimes overestimated corresponding E values. A sequential extraction procedure showed that substantial amounts of Al have already been dissolved from primary aluminosilicates initially present in the soils and remain in the soils mostly as reactive secondary Al minerals. The outcomes of this thesis significantly further our understanding of Al geochemistry in CLASS environments and how this knowledge can be incorporated into land management practices.

We give an upper bound for the norm distance of (0,1) -valued Markov-exchangeable random variables to mixtures of distributions of Markov processes. A Markov-exchangeable random variable has a distribution that depends only on the starting value and the number of transitions 0-0, 0-1, 1-0 and 1-1. We show that if, for increasing length of variables, the norm distance to mixtures of Markov processes goes to 0, the rate of this convergence may be arbitrarily slow. (author's abstract) / Series: Forschungsberichte / Institut für Statistik

This qualitative interview based essay aims to examine how managers perceive their management role in an organization and more specified to what extent management is shaped by the individual’s personal attributes versus how much is controlled by the organization. The essay’s second central aspect is how scope for action is perceived by managers in their profession, as well as their reasoning concerning their and other managers’ exchangeability. To examine this, we used semi structured interviews with four managers active in different lines of business. Our theoretical framework aimes to enlighten the relationship between organizational and individual. Our results and thereby the conclusion of the essay is that the management role is affected by a correlation between organization and individual. The organization gives the manager space to act/scope for action under the preresquisite that the organization’s goals and demands are achieved. These demands from the organization create a sense of duty in the manager, which results in them tempering their personal values to benefit the organization. The managers’ scope for action also makes it possible for them to put their own stamp on the profession, which in turn leads to them being harder to replace (as a manager). We have found that the personal attributes, in organizations where the manager has been given a lot of scope for action, then have greater significance in shaping the profession. Despite this we found that the organization affects the profession in a greater extent than the individual’s attributes, since the scope for action is given only if the organizations’ goals and demands are achieved.

L'objectif de la thèse est d'étudier le modèle du look-down avec sélection dans le cas d'une population composée seulement de deux types génétiques, l'un deux bénéficiant d'un avantage sélectif. Dans cette thèse, cette sélection est modélisée par un taux de mort pour les individus non avantagés. Tout d'abord, nous nous intéressons dans le cas d'une population de taille infinie. Nous montrons que le modèle est bien défini. Nous montrons aussi que dans la limite d'une population de taille infinie, la proportion d'individu d'un type donné suit la diffusion de Wright-Fisher avec sélection. Ensuite nous étudions ce modèle dans le cas d'une population de taille finie et fixée. Nous proposons deux méthodes de convergence de ce modèle fini vers la diffusion deWright-Fisher avec sélection. Enfin, une autre approche est considérée. Nous étudions le modèle de look-down dans le cas d'une population de taille infinie en remplaçant le modèle de reproduction dual du coalescent de Kingman par le modèle de reproduction dual du Lambda-coalescent. Nous montrons d'abord que le modèle est bien défini. Ensuite nous montrons que la proportion de l'un des types converge en probabilité, quand la taille N de la population tend vers l'infini, vers un processus qui est solution d'une équation différentielle stochastique dirigée par processus ponctuel de Poisson. Pour finir, nous montrons que si Lambda-coalescent descend de l'infini alors l'un des types se fixe en temps fini. / The purpose of the dissertation is to study the look-down model with selection in the case of a population composed only two alleles, one of them has a selective advantage. In this thesis, this selective advantage is modelled by a death rate for the wild-type allele. In the first part, we are interested in the case of a population of infinite size. We show the model is well defined. We show convergence in probability, as the population size tends to infinity, towards the Wright-Fisher diffusion with selection. In the second part we study a variant of the simplest look-down with selection where the size of the population is finite and fixed. We propose two methods of convergence of this finite model towards the Wright-Fisher diffusion with selection. Finally, another approach is considered. We study the look-down model with selection when we replace the usual reproduction model, which is dual to Kingman's coalescent by a population model dual to the Lambda-coalescent in the case of a population of infinite size. We first show this model is well defined. We show that the proportion of one of the two types converges in probability, as the population size N tends to infinity, towards the solution of a stochastic differential equation driven by a Poisson point process. Finally, we show that one of the two types fixate in finite time if and only if the Lambda-coalescent comes down from infinity.