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Information criteria and statistical modeling
One of the main objectives of this book is to provide comprehensive explanations of the concepts and derivations of the AIC and related criteria, including Schwarz’s Bayesian information criterion (BIC), together with a wide range of practical examples of model selection and evaluation criteria. A secondary objective is to provide a theoretical basis for the analysis and extension of information criteria via a statistical functional approach. A generalized information criterion (GIC) and a bootstrap information criterion are presented, which provide unified tools for modeling and model evaluation for a diverse range of models, including various types of nonlinear models and model estimation procedures such as robust estimation, the maximum penalized likelihood method and a Bayesian approach.
Information and Complexity in Statistical Modeling
The main theme in this book is to teach modeling based on the principle that the objective is to extract the information from data that can be learned with suggested classes of probability models. The intuitive and fundamental concepts of complexity, learnable information, and noise are formalized, which provides a firm information theoretic foundation for statistical modeling.
Inference in Hidden Markov Models
This book is a comprehensive treatment of inference for hidden Markov models, including both algorithms and statistical theory. Topics range from filtering and smoothing of the hidden Markov chain to parameter estimation, Bayesian methods and estimation of the number of states.In a unified way the book covers both models with finite state spaces, which allow for exact algorithms for filtering, estimation etc. and models with continuous state spaces (also called state-space models) requiring approximate simulation-based algorithms that are also described in detail. Simulation in hidden Markov models is addressed in five different chapters that cover both Markov chain Monte Carlo and sequential Monte Carlo approaches. Many examples illustrate the algorithms and theory. The book also carefully treats Gaussian linear state-space models and their extensions and it contains a chapter on general Markov chain theory and probabilistic aspects of hidden Markov models.
In and Out of Equilibrium 2
The intersection of probability and physics has been a rich and explosive area of growth in the past three decades, specifically covering such subjects as percolation theory, random walks in random environment, disordered systems, interacting particle systems and their many connections to statistical mechanics. The last decade was particularly fruitful for all these topics. This book reflects this development and marks also the first decade of the Brazilian School of Probability. This volume consists of a collection of invited articles, written by some of the most distinguished probabilists, most of whom have been personally responsible for advances in the various subfields of probability.
Heavy-Tail Phenomena : Probabilistic and Statistical Modeling
This comprehensive text gives an interesting and useful blend of the mathematical, probabilistic and statistical tools used in heavy-tail analysis. Heavy tails are characteristic of phenomena where there is a significant probability of a single huge value impacting system behavior. Record-breaking insurance losses, financial returns, sizes of files stored on a server, transmission rates of files are all examples of heavy-tailed phenomena.
Growth Dynamics of Conifer Tree Rings : Images of Past and Future Environments
Each tree ring contains an image of the time when the ring formed, projected onto the ring's size, structure, and composition. Tree rings thus are natural archives of past environments, and contain records of past climate. While dendrochronologists have investigated the impact of climate on tree-ring growth by empirical–statistical methods, this volume presents a process-based model complementing previous approaches. Basic ideas concerning the biology of tree-ring growth and its control by environmental factors are treated, especially for conifers. The use of the model is illustrated by means of several examples from widely differing environments, and possible future directions for model development and application are discussed. The volume provides an improved mechanistic basis for the interpretation of tree rings as records of past climate. It advances process understanding of the large-scale environmental control of wood growth. As forests are the main carbon sink on land, the results are of great importance for all global change studies.
Geometry and Topology in Hamiltonian Dynamics and Statistical Mechanics
This book explores the foundations of hamiltonian dynamical systems and statistical mechanics, in particular phase transition, from the point of view of geometry and topology. A broad participation of topology in these fields has been lacking and this book will provide a welcome overview of the current research in the area, in which the author himself is a pioneer. Using geometrical thinking to solve fundamental problems in these areas, compared to the purely analytical methods usually used in physics could be highly productive. The author skillfully guides the reader, whether mathematician or physicists through the background needed to understand and use these techniques.
Geodetic Deformation Monitoring : From Geophysical to Engineering Roles ; IAG Symposium Jaén, Spain, March 7-19,2005
Geodesy is the science dealing with the determination of the position of points in space, the shape and gravity field of the Earth and with their time variations. A consequence is that geodesists feel as a permanent subject of research, the detection, analysis and interpretation of spatial deformation as well as gravity field variation. This book collects 36 selected papers from the International Symposium on Geodetic Deformation Monitoring held in Jaén (Spain) from 17th to 19th March 2005. The main topics covered in the symposium were: mathematical and statistical models for crustal deformation analysis, deformation monitoring from GPS and InSAR data: analysis and geophysical interpretation, geodetic monitoring of movements in civil engineering, integration of spatial and terrestrial techniques in deformation studies, geodynamical applications of gravimetric observations and present-day geodetic instrumentation for deformation monitoring. This volume is a good overview of theoretical matters, models and results.
Genetic programming : Theory and practice II
This volume explores the emerging interaction between theory and practice in the cutting-edge, machine learning method of Genetic Programming (GP). The contributions developed from a second workshop at the University of Michigan's Center for the Study of Complex Systems where leading international genetic programming theorists from major universities and active practitioners from leading industries and businesses met to examine how GP theory informs practice and how GP practice impacts GP theory. Chapters include such topics as financial trading rules, industrial statistical model building, population sizing, the roles of structure in problem solving by computer, stock picking, automated design of industrial-strength analog circuits, topological synthesis of robust systems, algorithmic chemistry, supply chain reordering policies, post docking filtering, an evolved antenna for a NASA mission and incident detection on highways.
Fuzzy logic with engineering applications
With numerous examples and end-of-chapter problems, this book is essential reading for graduates and senior undergraduate students in civil, chemical, mechanical and electrical engineering as wells as researchers and practitioners working with fuzzy logic in industry.
Frontiers in Statistical Quality Control 8
The proportion of nonconforming meters in a lot has traditionally defined lot quality for utility meter sampling inspection purposes. However, lot quality is usually measured on the basis of two criteria for such products: the proportion of nonc- forming packages in the lot and the lot mean quantity.
From microphysics to macrophysics : Methods and applications of statistical physics ; Vol.2
Volume 2 applies statistical methods to systems governed by quantum effects, in particular to solid state physics, explaining properties due to the crystal structure or to the lattice excitations or to the electrons. Liquid helium is discussed and radiative equilibrium and transport are studied. The last chapters are devoted to non-equilibrium processes and to kinetic equations, with many applications included.
Free Energy and Self-Interacting Particles
This book examines a system of parabolic-elliptic partial differential eq- tions proposed in mathematical biology, statistical mechanics, and chemical kinetics. In the context of biology, this system of equations describes the chemotactic feature of cellular slime molds and also the capillary formation of blood vessels in angiogenesis. There are several methods to derive this system. One is the biased random walk of the individual, and another is the reinforced random walk of one particle modelled on the cellular automaton. In the context of statistical mechanics or chemical kinetics, this system of equations describes the motion of a mean field of many particles, interacting under the gravitational inner force or the chemical reaction
Forest Mensuration
Van Laar and Akça’s popular text book, Forest Mensuration, was first published in 1997. Like that first edition, this modern update is based on extensive research, teaching and practical experience in both Europe, and the tropics and subtropics. However, it has also been extensively revised, and now includes chapters on remote sensing and the application of aerial photographs and satellite imagery. As with its predecessor, this book assumes no advanced knowledge of statistical methods, and combines practical techniques with important historical and disciplinary context. The result is a strong balance between a handbook on traditional mensuration methods, and a valuable reference on the many recent research and inventory-related innovations which have emerged in recent years.
Finite Mixture and Markov Switching Models
The prominence of finite mixture modelling is greater than ever. Many important statistical topics like clustering data, outlier treatment, or dealing with unobserved heterogeneity involve finite mixture models in some way or other. The area of potential applications goes beyond simple data analysis and extends to regression analysis and to non-linear time series analysis using Markov switching models.It is the first time that the Bayesian perspective of finite mixture modelling is systematically presented in book form. It is argued that the Bayesian approach provides much insight in this context and is easily implemented in practice. Although the main focus is on Bayesian inference, the author reviews several frequentist techniques, especially selecting the number of components of a finite mixture model, and discusses some of their shortcomings compared to the Bayesian approach. The aim of this book is to impart the finite mixture and Markov switching approach to statistical modelling to a wide-ranging community. This includes not only statisticians, but also biologists, economists, engineers, financial agents, market researcher, medical researchers or any other frequent user of statistical models. This book should help newcomers to the field to understand how finite mixture and Markov switching models are formulated, what structures they imply on the data, what they could be used for, and how they are estimated.
Existence and Regularity Properties of the Integrated Density of States of Random Schrödinger Operators
The theory of random Schrödinger operators is devoted to the mathematical analysis of quantum mechanical Hamiltonians modeling disordered solids. Apart from its importance in physics, it is a multifaceted subject in its own right, drawing on ideas and methods from various mathematical disciplines like functional analysis, selfadjoint operators, PDE, stochastic processes and multiscale methods. The present text describes in detail a quantity encoding spectral features of random operators: the integrated density of states or spectral distribution function. Various approaches to the construction of the integrated density of states and the proof of its regularity properties are presented.
Equilibrium statistical physics : Phases of matter and phase transitions
This is a textbook which gradually introduces the student to the statistical mechanical study of the different phases of matter and to the phase transitions between them. Throughout, only simple models of both ordinary and soft matter are used but these are studied in full detail. The subject is developed in a pedagogical manner, starting from the basics, going from the simple ideal systems to the interacting systems, and ending with the more modern topics. The latter include the renormalisation group approach to critical phenomena, the density functional theory of interfaces, the topological defects of nematic liquid crystals and the kinematic aspects of the phase transformation process. This textbook provides the student with a complete overview, intentionally at an introductory level, of the theory of phase transitions. References include suggestions for more detailed treatments and four appendices supply overviews of the mathematical tools employed in the text.
Engineering self-organising systems ; 4th International Workshop, ESOA 2006, Hakodate, Japan, May 9, 2006, Revised and Invited Papers
This book discusses a broad variety of topics in an effort to allow room for new ideas and discussion, and eventually a better understanding of the important directions and techniques of Engineering Self-Organizing.This book raises the important question of whether there are underlying statistical mechanics-like principles that apply to emergent multi-agent systems. Answering this question will in the long run provide an important part of the underlying theory of emergent distributed systems.
Econophysics of Trade and Business Networks
This book reviews the current econophysics researches in the structure and functioning of these complex financial network systems. Leading researchers in the respective fields will report on their recent researches and review on the contemporary developments.
Econophysics of Stock and other Markets ; Proceedings of the Econophys-Kolkata II
This book reviews the latest econophysics researches on the fluctuations in stock, forex and other markets. The statistical modeling of markets, using various agent-based game theoretical approaches, and their scaling analysis have been discussed. The leading researchers in these fields have reported on their recent work and also reviewed the contemporary literature. Some historical perspectives as well as some comments and debates on recent issues in econophysics research have also been included.
