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Non-Equilibrium Phase Transitions ; Vol. I : Absorbing Phase Transitions
This book describes two main classes of non-equilibrium phase-transitions: (a) static and dynamics of transitions into an absorbing state, and (b) dynamical scaling in far-from-equilibrium relaxation behaviour and ageing. The first volume begins with an introductory chapter which recalls the main concepts of phase-transitions, set for the convenience of the reader in an equilibrium context. The extension to non-equilibrium systems is made by using directed percolation as the main paradigm of absorbing phase transitions and in view of the richness of the known results an entire chapter is devoted to it, including a discussion of recent experimental results. Scaling theories and a large set of both numerical and analytical methods for the study of non-equilibrium phase transitions are thoroughly discussed.
Morphological Models of Random Structures
This book covers methods of Mathematical Morphology to model and simulate random sets and functions (scalar and multivariate). The introduced models concern many physical situations in heterogeneous media, where a probabilistic approach is required, like fracture statistics of materials, scaling up of permeability in porous media, electron microscopy images (including multispectral images), rough surfaces, multi-component composites, biological tissues, textures for image coding and synthesis. The common feature of these random structures is their domain of definition in n dimensions, requiring more general models than standard Stochastic Processes.The main topics of the book cover an introduction to the theory of random sets, random space tessellations, Boolean random sets and functions, space-time random sets and functions (Dead Leaves, Sequential Alternate models, Reaction-Diffusion), prediction of effective properties of random media, and probabilistic fracture theories.
Modélisation et statistique spatiales = Spatial modeling and statistics
Spatial statistics are undergoing significant development due to their use in many fields: earth sciences, environment and climatology, epidemiology, econometrics, image analysis, etc. This book presents the main spatial models used as well as their statistics for the three types of data: geostatistics (observation on a continuous domain), data on a discrete network, point data. The objective is to present in a concise but mathematically complete way the most classical models (second order and variogram; software model and Gibbs-Markov field; point processes) as well as their simulation by MCMC algorithm. Then comes the presentation of statistical tools useful for their study.
Mathématiques de base pour économistes = Basic Mathematics for Economists
This book contains fundamental elements of mathematics and includes the following elements: notion of logic, propositions, theorems, sets, relations and functions; graphical representations of functions, economic applications of lines and functions, sequences, limits and first derivative, differential economic applications of derivatives; integrals: undefined and defined with economic applications; mathematical series; functions of several variables, partial derivatives, Lagrange multiplier with economic applications; linear algebra: matrix calculus, system of linear equations, vectors, differential calculus in matrix form.
Innovations in Derivatives Markets : Fixed Income Modeling, Valuation Adjustments, Risk Management, and Regulation
This book presents 20 peer-reviewed chapters on current aspects of derivatives markets and derivative pricing. The contributions, written by leading researchers in the field as well as experienced authors from the financial industry, present the state of the art in: • Modeling counterparty credit risk: credit valuation adjustment, debit valuation adjustment, funding valuation adjustment, and wrong way risk. • Pricing and hedging in fixed-income markets and multi-curve interest-rate modeling. • Recent developments concerning contingent convertible bonds, the measuring of basis spreads, and the modeling of implied correlations.
Heavy-Tailed Time Series
This book aims to present a comprehensive, self-contained, and concise overview of extreme value theory for time series, incorporating the latest research trends alongside classical methodology.Additionally, the book incorporates complete proofs and exercises with solutions as well as substantive reference lists and appendices, featuring a novel commentary on the theory of vague convergence.
Génetique statistique = Statistical genetics
Presents the main statistical tools useful in genetics: significance tests, analysis methods based on the likelihood function, EM algorithm, modeling, analysis of variance, hierarchical classifications, multiple comparisons, etc. All of them shed light on a number of biological phenomena such as carcinogenesis, population genetics, Hardy-Weinberg equilibrium, natural selection, mutations, heredity, coalescence processes, and even evolution. This book is intended for mathematicians and biologists alike. Written with a great concern for clarity, it is also accessible to non-specialists who will be able, thanks to it, to strengthen their theoretical base and above all to develop their know-how through very concrete applications.
Earthquakes, Tsunamis and Nuclear Risks : Prediction and Assessment Beyond the Fukushima Accident
This book covers seismic probabilistic risk assessment (S-PRA) and related studies which have become more important to increase the safety of nuclear facilities against earthquakes and tsunamis in the face of the many uncertainties after the Fukushima accident. The topics are (1) Active faults and active tectonics important for seismic hazard assessment of nuclear facilities,(2) Seismic source modeling and simulation and modeling techniques indispensable for strong ground motion prediction, and (3) PRA with external hazard and risk communication.
Design of Observational Studies
This book introduction to statistical inference in observational studies and a detailed discussion of the principles that guide the design of observational studies. An observational study is an empiric investigation of effects caused by treatments when randomized experimentation is unethical or infeasible. Observational studies are common in most fields that study the effects of treatments on people, including medicine, economics, epidemiology, education, psychology, political science and sociology. The quality and strength of evidence provided by an observational study is determined largely by its design. Design of Observational Studies is organized into five parts. Chapters 2, 3, and 5 of Part I cover concisely many of the ideas discussed in Rosenbaum’s Observational Studies. Part II discusses the practical aspects of using propensity scores and other tools to create a matched comparison that balances many covariates, and includes an updated chapter on matching in R. In Part III, the concept of design sensitivity is used to appraise the relative ability of competing designs to distinguish treatment effects from biases due to unmeasured covariates. Part IV discusses evidence factors and the computerized construction of more than one comparison group. Part V discusses planning the analysis of an observational study, with particular reference to Sir Ronald Fisher’s striking advice for observational studies: "make your theories elaborate."
Decision Making under Deep Uncertainty : From Theory to Practice
Focuses on both the theory and practice associated with the tools and approaches for decisionmaking in the face of deep uncertainty. It explores approaches and tools supporting the design of strategic plans under deep uncertainty, and their testing in the real world, including barriers and enablers for their use in practice. The book broadens traditional approaches and tools to include the analysis of actors and networks related to the problem at hand. It also shows how lessons learned in the application process can be used to improve the approaches and tools used in the design process. The book offers guidance in identifying and applying appropriate approaches and tools to design plans, as well as advice on implementing these plans in the real world. For decisionmakers and practitioners, the book includes realistic examples and practical guidelines that should help them understand what decisionmaking under deep uncertainty is and how it may be of assistance to them.
Control Theory in Physics and other Fields of Science : Concepts, Tools, and Applications
This book covers systematically and in a simple language the mathematical and physical foundations of controlling deterministic and stochastic evolutionary processes in systems with a high degree of complexity. Strong emphasis is placed on concepts, methods and techniques for modelling, assessment and the solution or estimation of control problems in an attempt to understand the large variability of these problems in several branches of physics, chemistry and biology as well as in technology and economics. The main focus of the book is on a clear physical and mathematical understanding of the dynamics and kinetics behind several kinds of control problems and their relation to self-organizing principles in complex systems. The book is a modern introduction and a helpful tool for researchers, engineers as well as post-docs and graduate students interested in an application oriented control theory and related topics.
Mathematical Methods for Engineers and Geoscientists
This book introduces and explains classical and modern mathematical procedures as applied to the real problems confronting engineers and geoscientists. Written in a manner that is understandable for students across the breadth of their studies, it lays out the foundations for mastering difficult and sometimes confusing mathematical methods.
Linear and Generalized Linear Mixed Models and Their Applications
This book covers two major classes of mixed effects models—linear mixed models and generalized linear mixed models—and it presents an up-to-date account of theory and methods in analysis of these models as well as their applications in various fields. It offers a systematic approach to inference about non-Gaussian linear mixed models. Furthermore, it discusses the latest developments and methods in the field, incorporating relevant updates since publication of the first edition. These include advances in high-dimensional linear mixed models in genome-wide association studies (GWAS), advances in inference about generalized linear mixed models with crossed random effects, new methods in mixed model prediction, mixed model selection, and mixed model diagnostics.
Le raisonnement bayésien : Modélisation et inférence = Bayesian reasoning : Modeling and inference
Describes in detail the practice of the Bayesian statistical approach using many examples chosen for their educational interest. The first part gives the general principles of statistical modeling making it possible to supervise but also to come to the aid of the imagination of the apprentice modeler. By examining examples of increasing difficulty, the reader forges the keys to building their own model. The second part presents the most useful calculation algorithms for estimating the unknowns of the model. Each inference method is presented and illustrated by numerous application cases.
Chance : The life of games and the game of life
With its many easy-to-follow mathematical examples, this book takes the reader on an almost chronological trip through the fascinating and amazing laws of chance, omnipresent in the natural world and in our daily lives. Along the route many fascinating topics are discussed, such as: challenging probability paradoxes; "paranormal" coincidences; game odds; causes and effects; interpretation of opinion polls; winning chances as a game proceeds; the nature of randomness; entropy and randomness; randomness in life; algorithmic complexity and the undecidability of randomness; possibilities and limitations of learning the laws of a Universe immersed in chance events. This charming book will inform and entertain the scientist and non-scientist alike.
Bayesian Methods in the Search for MH370
This book demonstrates how nonlinear/non-Gaussian Bayesian time series estimation methods were used to produce a probability distribution of potential MH370 flight paths. It provides details of how the probabilistic models of aircraft flight dynamics, satellite communication system measurements, environmental effects and radar data were constructed and calibrated. The probability distribution was used to define the search zone in the southern Indian Ocean. The book describes particle-filter based numerical calculation of the aircraft flight-path probability distribution and validates the method using data from several of the involved aircraft’s previous flights. Finally it is shown how the Reunion Island flaperon debris find affects the search probability distribution.
Bayesian core : A practical approach to computational Bayesian statistics
This Bayesian modeling book provides an operational methodology for conducting Bayesian inference, rather than focusing on its theoretical justifications. Special attention is paid to the derivation of prior distributions in each case and specific reference solutions are given for each of the models.
Applied Stochastic Processes
Applied Stochastic Processes uses a distinctly applied framework to present the most important topics in the field of stochastic processes.
Applied Stochastic Control of Jump Diffusions
The main purpose of the book is to give a rigorous, yet mostly nontechnical, introduction to the most important and useful solution methods of various types of stochastic control problems for jump diffusions and its applications.
Applied Statistics Using SPSS, STATISTICA, MATLAB and R
The book provides a comprehensive coverage of the main statistical analysis topics important for practical applications such as data description, statistical inference, classification and regression, factor analysis, survival data and directional statistics.
