Stochastic processes for graphs, extreme values and their causality: inference, asymptotic theory and applications

This thesis provides some theoretical and practical statistical inference tools for multivariate stochastic processes to better understand the behaviours and properties present in the data. In particular, we focus on the modelling of graphs, that is a family of nodes linked together by a collection of edges, and extreme values, that are values above a high threshold to have their own dynamics compared to the typical behaviour of the process. We develop an ensemble of statistical models, statistical inference methods and their asymptotic study to ensure the good behaviour of estimation schemes in a wide variety of settings. We also devote a chapter to the formulation of a methodology based on pre-existing theory to unveil the causal dependency structure behind high-impact events.Open Acces

High-frequency Estimation of the L\'evy-driven Graph Ornstein-Uhlenbeck process

We consider the Graph Ornstein-Uhlenbeck (GrOU) process observed on a non-uniform discrete time grid and introduce discretised maximum likelihood estimators with parameters specific to the whole graph or specific to each component, or node. Under a high-frequency sampling scheme, we study the asymptotic behaviour of those estimators as the mesh size of the observation grid goes to zero. We prove two stable central limit theorems to the same distribution as in the continuously-observed case under both finite and infinite jump activity for the L\'evy driving noise. When a graph structure is not explicitly available, the stable convergence allows to consider purpose-specific sparse inference procedures, i.e. pruning, on the edges themselves in parallel to the GrOU inference and preserve its asymptotic properties. We apply the new estimators to wind capacity factor measurements, i.e. the ratio between the wind power produced locally compared to its rated peak power, across fifty locations in Northern Spain and Portugal. We show the superiority of those estimators compared to the standard least squares estimator through a simulation study extending known univariate results across graph configurations, noise types and amplitudes

Advancing social simulation: lessons from demography

Previous work has proposed that computational modelling of social systems is composed of two primary streams of re-search: systems sociology, which is focused on the genera-tion of social theory; and social simulation, which focuses on the study of real-world social systems. Here we argue that the social simulation stream stands to benefit from recent methodological and theoretical advances in demography. De-mography has long been an empirically focused discipline fo-cused primarily on mathematical modelling; however, agent-based simulation have proven influential of late as demogra-phers seek to link individual-level behaviours to macro-level patterns. Here we characterise this shift as a move toward system-based modelling, a paradigm in which the scientific object of interest is neither the individual nor the population, but rather the interactions between them. We first describe the four successive paradigms of demography: the period, co-hort, event-history and multilevel perspectives. Then we ex-amine how system-based modelling can assist demographers with several major challenges: overcoming complexity in so-cial research; reducing uncertainty; and enhancing theoretical foundations. We propose that this new paradigm can enhance the broader study of populations via social simulation

Multilevel synthesis. From the group to the individual

The purpose of this book is to present a historical panorama of the evolution of demographic thought from its seventeenth-century origins up to the present day, use it to demonstrate how the multilevel approach can resolve some of the contradictions that have become apparent and achieve a synthesis of the different approaches employed. Part one guides the reader from period analysis to multilevel analysis, examining longitudinal and event history analysis on the way. Part two is a detailed account of multilevel analysis, its methods, and the relevant mathematical models notably as regards the type of variables being used. Numerous examples, examined across successive sections, make the book clear and easy to follow. The theoretical and epistemological treatment of these problems, during which the foundations of sociology and demography are revisited, and the logical development that leads to the most recent approaches, are handled sufficiently rigorously to satisfy social science specialists while remaining accessible for readers new to the field. The whole adds up to a comprehensive account of progress in sociological and demographic savoir-faire, as well as being both a textbook and an assessment of the multilevel analysis that tackles one of the major problems of empirical sociology: that of integrating analysis at the individual and group levels

Probability and social science : methodologial relationships between the two approaches ?

This work examines in depth the methodological relationships that probability and statistics have maintained with the social sciences. It covers both the history of thought and current methods. First, it examines in detail the history of the different paradigms and axioms for probability, from their emergence in the seventeenth century up to the most recent developments of the three major concepts: objective, subjective and logicist probability. It shows the statistical inference they permit, different applications to social sciences and the main problems they encounter. In the other side, from social sciences—particularly population sciences— to probability, it shows the different uses they made of probabilistic concepts during their history, from the seventeenth century, according to their paradigms: cross-sectional, longitudinal, event-history, hierarchical, contextual and multilevel approaches. While the ties may have seemed loose at times, they have more often been very close: some advances in probability were driven by the search for answers to questions raised by the social sciences; conversely, the latter have made progress thanks to advances in probability. This dual approach sheds new light on the historical development of the social sciences, probability and statistics, and on the enduring relevance of their links. It permits also to solve a number of methodological problems encountered all along their history

Estimation indirecte de l'âge en paléodémographie : approche bayésienne

International audienceEn vue d'estimer la structure par âge des populations du passé en ne disposant que d'indicateurs biologiques, les paléodémographes ont développé un certain nombre de méthodes statistiques, utilisant une population de référence pour apprécier les probabilités conditionnelles de l'âge connaissant l'indicateur. Compte tenu du faible nombre de données disponibles et du caractère instable du problème, ces méthodes sont en général décevantes. Nous montrons comment les améliorer en introduisant une méthode bayésienne simple intégrant un maximum d'informations non réductibles aux données proprement dites

Inférence statistique, échangeabilité et approche mutiniveau

Cet article examine les problèmes posés par une inférence statistique en sciences sociales. Pour pouvoir passer d’une population à un nouvel individu sur qui on veut effectuer l’inférence, il est utile d’utiliser le concept d’échangeabilité, mis en évidence par de Finetti. Cela est montré pour un modèle logit simple avec deux groupes et pour un modèle multiniveau où l’on observe un plus grand nombre de groupes. Dans ces deux cas le paradoxe de Simpson vient jouer et peut fournir des résultats inverses selon que l’on travaille sur les données agrégées ou décomposées par groupe. Le concept d’échangeabilité permet, en utilisant les probabilités appropriées, de résoudre un certain nombre de problèmes posé par cette inférence. Mais il est nécessaire d’utiliser à la fois les données sur la population et des informations obtenues par d’autres moyens sur le sujet étudié, pour pouvoir réaliser cette inférence.This paper is concerned with the problems of statistical inference in social sciences. In order to pass from a population to a new individual by inference, de Finetti’s idea of exchangeability is useful. This is shown in a simple logit model and in a multilevel model, with a larger number of observed groups, where the Simpson’s paradox arises depending on whether you work on aggregate data or on group data. The concept of exchangeability permits, by using the appropriate probabilities, to solve a number of problems arising in statistical inference. But it is necessary to use not only the data but also information inferred by other means in order to make the final inference

Évolution ou révolutions dans la pensée démographique ?

This paper displays the way demography overrun different pathbreaking issues encountered during its history, draws the main paradigms followed and shows their strengths and weaknesses. From a cross-sectional to a cohort approach demography, from its origins, was a holism. However, these methods were followed by an event history approach, which introduced methodological individualism. Finally, a multilevel approach released demography from the opposition between holism and individualism: it introduces different aggregation levels, to be simultaneously considered, and permits a synthesis of the previous approaches, while going beyond their initial purpose.Cet article montre comment la démographie a pu dépasser les différents clivages apparus tout au long de son histoire et dégage les principaux paradigmes qui se sont succédé, en montrant leurs forces et leurs faiblesses. D'une approche transversale à une approche longitudinale, elle est au départ un holisme. L'approche biographique, qui les suit, va au contraire développer un individualisme méthodologique. L'approche multiniveau libère enfin la démographie de l'opposition entre holisme et individualisme : elle introduit des niveaux d'agrégation multiples à considérer simultanément et permet une synthèse des approches précédentes, tout en les dépassant