Peter Mörters, Roger Moser, Mathew Penrose, Hartmut Schwetlick, and Johannes Zimmer (eds)
- Published in print:
- 2008
- Published Online:
- September 2008
- ISBN:
- 9780199239252
- eISBN:
- 9780191716911
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199239252.001.0001
- Subject:
- Mathematics, Probability / Statistics, Analysis
There has been a significant increase recently in activities on the interface between applied analysis and probability theory. With the potential of a combined approach to the study of various ...
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There has been a significant increase recently in activities on the interface between applied analysis and probability theory. With the potential of a combined approach to the study of various physical systems in view, this book is a collection of topical survey articles by leading researchers in both fields, working on the mathematical description of growth phenomena in the broadest sense. The main aim of the book is to foster interaction between researchers in probability and analysis, and to inspire joint efforts to attack important physical problems. Mathematical methods discussed in the book comprise large deviation theory, lace expansion, harmonic analysis, multi-scale techniques, and homogenization of partial differential equations. Models based on the physics of individual particles are discussed alongside models based on the continuum description of large collections of particles, and the mathematical theories are used to describe physical phenomena such as droplet formation, Bose–Einstein condensation, Anderson localization, Ostwald ripening, or the formation of the early universe.Less
There has been a significant increase recently in activities on the interface between applied analysis and probability theory. With the potential of a combined approach to the study of various physical systems in view, this book is a collection of topical survey articles by leading researchers in both fields, working on the mathematical description of growth phenomena in the broadest sense. The main aim of the book is to foster interaction between researchers in probability and analysis, and to inspire joint efforts to attack important physical problems. Mathematical methods discussed in the book comprise large deviation theory, lace expansion, harmonic analysis, multi-scale techniques, and homogenization of partial differential equations. Models based on the physics of individual particles are discussed alongside models based on the continuum description of large collections of particles, and the mathematical theories are used to describe physical phenomena such as droplet formation, Bose–Einstein condensation, Anderson localization, Ostwald ripening, or the formation of the early universe.
Ludwig Fahrmeir and Thomas Kneib
- Published in print:
- 2011
- Published Online:
- September 2011
- ISBN:
- 9780199533022
- eISBN:
- 9780191728501
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199533022.001.0001
- Subject:
- Mathematics, Probability / Statistics, Biostatistics
Several recent advances in smoothing and semiparametric regression are presented in this book from a unifying, Bayesian perspective. Simulation-based full Bayesian Markov chain Monte Carlo (MCMC) ...
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Several recent advances in smoothing and semiparametric regression are presented in this book from a unifying, Bayesian perspective. Simulation-based full Bayesian Markov chain Monte Carlo (MCMC) inference, as well as empirical Bayes procedures closely related to penalized likelihood estimation and mixed models, are considered here. Throughout, the focus is on semiparametric regression and smoothing based on basis expansions of unknown functions and effects in combination with smoothness priors for the basis coefficients. Beginning with a review of basic methods for smoothing and mixed models, longitudinal data, spatial data, and event history data are treated in separate chapters. Worked examples from various fields such as forestry, development economics, medicine, and marketing are used to illustrate the statistical methods covered in this book. Most of these examples have been analysed using implementations in the Bayesian software, BayesX, and some with R Codes.Less
Several recent advances in smoothing and semiparametric regression are presented in this book from a unifying, Bayesian perspective. Simulation-based full Bayesian Markov chain Monte Carlo (MCMC) inference, as well as empirical Bayes procedures closely related to penalized likelihood estimation and mixed models, are considered here. Throughout, the focus is on semiparametric regression and smoothing based on basis expansions of unknown functions and effects in combination with smoothness priors for the basis coefficients. Beginning with a review of basic methods for smoothing and mixed models, longitudinal data, spatial data, and event history data are treated in separate chapters. Worked examples from various fields such as forestry, development economics, medicine, and marketing are used to illustrate the statistical methods covered in this book. Most of these examples have been analysed using implementations in the Bayesian software, BayesX, and some with R Codes.
José M. Bernardo, M. J. Bayarri, James O. Berger, A. P. Dawid, David Heckerman, Adrian F. M. Smith, and Mike West (eds)
- Published in print:
- 2011
- Published Online:
- January 2012
- ISBN:
- 9780199694587
- eISBN:
- 9780191731921
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199694587.001.0001
- Subject:
- Mathematics, Probability / Statistics
The Valencia International Meetings on Bayesian Statistics – established in 1979 and held every four years – have been the forum for a definitive overview of current concerns and activities in ...
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The Valencia International Meetings on Bayesian Statistics – established in 1979 and held every four years – have been the forum for a definitive overview of current concerns and activities in Bayesian statistics. These are the edited Proceedings of the Ninth meeting, and contain the invited papers each followed by their discussion and a rejoinder by the author(s). In the tradition of the earlier editions, this encompasses an enormous range of theoretical and applied research, highlighting the breadth, vitality and impact of Bayesian thinking in interdisciplinary research across many fields as well as the corresponding growth and vitality of core theory and methodology. The Valencia 9 invited papers cover a broad range of topics, including foundational and core theoretical issues in statistics, the continued development of new and refined computational methods for complex Bayesian modelling, substantive applications of flexible Bayesian modelling, and new developments in the theory and methodology of graphical modelling. They also describe advances in methodology for specific applied fields, including financial econometrics and portfolio decision making, public policy applications for drug surveillance, studies in the physical and environmental sciences, astronomy and astrophysics, climate change studies, molecular biosciences, statistical genetics or stochastic dynamic networks in systems biology.Less
The Valencia International Meetings on Bayesian Statistics – established in 1979 and held every four years – have been the forum for a definitive overview of current concerns and activities in Bayesian statistics. These are the edited Proceedings of the Ninth meeting, and contain the invited papers each followed by their discussion and a rejoinder by the author(s). In the tradition of the earlier editions, this encompasses an enormous range of theoretical and applied research, highlighting the breadth, vitality and impact of Bayesian thinking in interdisciplinary research across many fields as well as the corresponding growth and vitality of core theory and methodology. The Valencia 9 invited papers cover a broad range of topics, including foundational and core theoretical issues in statistics, the continued development of new and refined computational methods for complex Bayesian modelling, substantive applications of flexible Bayesian modelling, and new developments in the theory and methodology of graphical modelling. They also describe advances in methodology for specific applied fields, including financial econometrics and portfolio decision making, public policy applications for drug surveillance, studies in the physical and environmental sciences, astronomy and astrophysics, climate change studies, molecular biosciences, statistical genetics or stochastic dynamic networks in systems biology.
Paul Damien, Petros Dellaportas, Nicholas G. Polson, and David A. Stephens (eds)
- Published in print:
- 2013
- Published Online:
- May 2013
- ISBN:
- 9780199695607
- eISBN:
- 9780191744167
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199695607.001.0001
- Subject:
- Mathematics, Probability / Statistics
The development of hierarchical models and Markov chain Monte Carlo (MCMC) techniques forms one of the most profound advances in Bayesian analysis since the 1970s and provides the basis for advances ...
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The development of hierarchical models and Markov chain Monte Carlo (MCMC) techniques forms one of the most profound advances in Bayesian analysis since the 1970s and provides the basis for advances in virtually all areas of applied and theoretical Bayesian statistics. This book travels on a statistical journey that begins with the basic structure of Bayesian theory, and then provides details on most of the past and present advances in this field. The book honours the contributions of Sir Adrian F. M. Smith, one of the seminal Bayesian researchers, with his work on hierarchical models, sequential Monte Carlo, and Markov chain Monte Carlo and his mentoring of numerous graduate students.Less
The development of hierarchical models and Markov chain Monte Carlo (MCMC) techniques forms one of the most profound advances in Bayesian analysis since the 1970s and provides the basis for advances in virtually all areas of applied and theoretical Bayesian statistics. This book travels on a statistical journey that begins with the basic structure of Bayesian theory, and then provides details on most of the past and present advances in this field. The book honours the contributions of Sir Adrian F. M. Smith, one of the seminal Bayesian researchers, with his work on hierarchical models, sequential Monte Carlo, and Markov chain Monte Carlo and his mentoring of numerous graduate students.
A. C. Davison, Yadolah Dodge, and N. Wermuth (eds)
- Published in print:
- 2005
- Published Online:
- September 2007
- ISBN:
- 9780198566540
- eISBN:
- 9780191718038
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198566540.001.0001
- Subject:
- Mathematics, Probability / Statistics
Sir David Cox is among the most important statisticians of the past half-century, making pioneering and highly influential contributions to a wide range of topics in statistics and applied ...
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Sir David Cox is among the most important statisticians of the past half-century, making pioneering and highly influential contributions to a wide range of topics in statistics and applied probability. This book contains summaries of the invited talks at a meeting held at the University of Neuchâtel in July 2004 to celebrate David Cox’s 80th birthday. The chapters describe current developments across a wide range of topics, ranging from statistical theory and methods, through applied probability and modelling, to applications in areas including finance, epidemiology, hydrology, medicine, and social science. The book contains chapters by numerous well-known statisticians. It provides a summary of current thinking across a wide front by leading statistical thinkers.Less
Sir David Cox is among the most important statisticians of the past half-century, making pioneering and highly influential contributions to a wide range of topics in statistics and applied probability. This book contains summaries of the invited talks at a meeting held at the University of Neuchâtel in July 2004 to celebrate David Cox’s 80th birthday. The chapters describe current developments across a wide range of topics, ranging from statistical theory and methods, through applied probability and modelling, to applications in areas including finance, epidemiology, hydrology, medicine, and social science. The book contains chapters by numerous well-known statisticians. It provides a summary of current thinking across a wide front by leading statistical thinkers.
Geoffrey Grimmett and Colin McDiarmid (eds)
- Published in print:
- 2007
- Published Online:
- September 2007
- ISBN:
- 9780198571278
- eISBN:
- 9780191718885
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198571278.001.0001
- Subject:
- Mathematics, Probability / Statistics
Professor Dominic Welsh has made significant contributions to the fields of combinatorics and discrete probability, including matroids, complexity, and percolation. He has taught, influenced, and ...
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Professor Dominic Welsh has made significant contributions to the fields of combinatorics and discrete probability, including matroids, complexity, and percolation. He has taught, influenced, and inspired generations of students and researchers in mathematics. This book summarizes and reviews the consistent themes from his work through a series of articles written by renowned experts. These articles, presented as chapters, contain original research work, set in a broader context by the inclusion of review material.Less
Professor Dominic Welsh has made significant contributions to the fields of combinatorics and discrete probability, including matroids, complexity, and percolation. He has taught, influenced, and inspired generations of students and researchers in mathematics. This book summarizes and reviews the consistent themes from his work through a series of articles written by renowned experts. These articles, presented as chapters, contain original research work, set in a broader context by the inclusion of review material.
Stéphane Boucheron, Gábor Lugosi, and Pascal Massart
- Published in print:
- 2013
- Published Online:
- May 2013
- ISBN:
- 9780199535255
- eISBN:
- 9780191747106
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199535255.001.0001
- Subject:
- Mathematics, Probability / Statistics, Applied Mathematics
This monograph presents a mathematical theory of concentration inequalities for functions of independent random variables. The basic phenomenon under investigation is that if a function of many ...
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This monograph presents a mathematical theory of concentration inequalities for functions of independent random variables. The basic phenomenon under investigation is that if a function of many independent random variables does not depend too much on any of them then it is concentrated around its expected value. This book offers a host of inequalities to quantify this statement. The authors describe the interplay between the probabilistic structure (independence) and a variety of tools ranging from functional inequalities, transportation arguments, to information theory. Applications to the study of empirical processes, random projections, random matrix theory, and threshold phenomena are presented. The book offers a self-contained introduction to concentration inequalities, including a survey of concentration of sums of independent random variables, variance bounds, the entropy method, and the transportation method. Deep connections with isoperimetric problems are revealed. Special attention is paid to applications to the supremum of empirical processes.Less
This monograph presents a mathematical theory of concentration inequalities for functions of independent random variables. The basic phenomenon under investigation is that if a function of many independent random variables does not depend too much on any of them then it is concentrated around its expected value. This book offers a host of inequalities to quantify this statement. The authors describe the interplay between the probabilistic structure (independence) and a variety of tools ranging from functional inequalities, transportation arguments, to information theory. Applications to the study of empirical processes, random projections, random matrix theory, and threshold phenomena are presented. The book offers a self-contained introduction to concentration inequalities, including a survey of concentration of sums of independent random variables, variance bounds, the entropy method, and the transportation method. Deep connections with isoperimetric problems are revealed. Special attention is paid to applications to the supremum of empirical processes.
Jon Williamson
- Published in print:
- 2010
- Published Online:
- September 2010
- ISBN:
- 9780199228003
- eISBN:
- 9780191711060
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199228003.001.0001
- Subject:
- Mathematics, Probability / Statistics, Logic / Computer Science / Mathematical Philosophy
Bayesian epistemology aims to answer the following question: How strongly should an agent believe the various propositions expressible in her language? Subjective Bayesians hold that.it is largely ...
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Bayesian epistemology aims to answer the following question: How strongly should an agent believe the various propositions expressible in her language? Subjective Bayesians hold that.it is largely (though not entirely) up to the agent as to which degrees of belief to adopt. Objective Bayesians, on the other hand, maintain that appropriate degrees of belief are largely (though not entirely) determined by the agent's evidence. This book states and defends a version of objective Bayesian epistemology. According to this version, objective Bayesianism is characterized by three norms: (i) Probability: degrees of belief should be probabilities; (ii) Calibration: they should be calibrated with evidence; and (iii) Equivocation: they should otherwise equivocate between basic outcomes. Objective Bayesianism has been challenged on a number of different fronts: for example, it has been accused of being poorly motivated, of failing to handle qualitative evidence, of yielding counter‐intuitive degrees of belief after updating, of suffering from a failure to learn from experience, of being computationally intractable, of being susceptible to paradox, of being language dependent, and of not being objective enough. The book argues that these criticisms can be met and that objective Bayesianism is a promising theory with an exciting agenda for further research.Less
Bayesian epistemology aims to answer the following question: How strongly should an agent believe the various propositions expressible in her language? Subjective Bayesians hold that.it is largely (though not entirely) up to the agent as to which degrees of belief to adopt. Objective Bayesians, on the other hand, maintain that appropriate degrees of belief are largely (though not entirely) determined by the agent's evidence. This book states and defends a version of objective Bayesian epistemology. According to this version, objective Bayesianism is characterized by three norms: (i) Probability: degrees of belief should be probabilities; (ii) Calibration: they should be calibrated with evidence; and (iii) Equivocation: they should otherwise equivocate between basic outcomes. Objective Bayesianism has been challenged on a number of different fronts: for example, it has been accused of being poorly motivated, of failing to handle qualitative evidence, of yielding counter‐intuitive degrees of belief after updating, of suffering from a failure to learn from experience, of being computationally intractable, of being susceptible to paradox, of being language dependent, and of not being objective enough. The book argues that these criticisms can be met and that objective Bayesianism is a promising theory with an exciting agenda for further research.
Ray Chambers and Robert Clark
- Published in print:
- 2012
- Published Online:
- May 2012
- ISBN:
- 9780198566625
- eISBN:
- 9780191738449
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198566625.001.0001
- Subject:
- Mathematics, Probability / Statistics
This book is an introduction to the model-based approach to survey sampling. It consists of three parts, with Part I focusing on estimation of population totals. Chapters 1 and 2 introduce survey ...
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This book is an introduction to the model-based approach to survey sampling. It consists of three parts, with Part I focusing on estimation of population totals. Chapters 1 and 2 introduce survey sampling, and the model-based approach, respectively. Chapter 3 considers the simplest possible model, the homogenous population model, which is then extended to stratified populations in Chapter 4. Chapter 5 discusses simple linear regression models for populations, and Chapter 6 considers clustered populations. The general linear population model is then used to integrate these results in Chapter 7. Part II of this book considers the properties of estimators based on incorrectly specified models. Chapter 8 develops robust sample designs that lead to unbiased predictors under model misspecification, and shows how flexible modelling methods like non-parametric regression can be used in survey sampling. Chapter 9 extends this development to misspecfication robust prediction variance estimators and Chapter 10 completes Part II of the book with an exploration of outlier robust sample survey estimation. Chapters 11 to 17 constitute Part III of the book and show how model-based methods can be used in a variety of problem areas of modern survey sampling. They cover (in order) prediction of non-linear population quantities, sub-sampling approaches to prediction variance estimation, design and estimation for multipurpose surveys, prediction for domains, small area estimation, efficient prediction of population distribution functions and the use of transformations in survey inference. The book is designed to be accessible to undergraduate and graduate level students with a good grounding in statistics and applied survey statisticians seeking an introduction to model-based survey design and estimation.Less
This book is an introduction to the model-based approach to survey sampling. It consists of three parts, with Part I focusing on estimation of population totals. Chapters 1 and 2 introduce survey sampling, and the model-based approach, respectively. Chapter 3 considers the simplest possible model, the homogenous population model, which is then extended to stratified populations in Chapter 4. Chapter 5 discusses simple linear regression models for populations, and Chapter 6 considers clustered populations. The general linear population model is then used to integrate these results in Chapter 7. Part II of this book considers the properties of estimators based on incorrectly specified models. Chapter 8 develops robust sample designs that lead to unbiased predictors under model misspecification, and shows how flexible modelling methods like non-parametric regression can be used in survey sampling. Chapter 9 extends this development to misspecfication robust prediction variance estimators and Chapter 10 completes Part II of the book with an exploration of outlier robust sample survey estimation. Chapters 11 to 17 constitute Part III of the book and show how model-based methods can be used in a variety of problem areas of modern survey sampling. They cover (in order) prediction of non-linear population quantities, sub-sampling approaches to prediction variance estimation, design and estimation for multipurpose surveys, prediction for domains, small area estimation, efficient prediction of population distribution functions and the use of transformations in survey inference. The book is designed to be accessible to undergraduate and graduate level students with a good grounding in statistics and applied survey statisticians seeking an introduction to model-based survey design and estimation.
Peter Grindrod
- Published in print:
- 2014
- Published Online:
- March 2015
- ISBN:
- 9780198725091
- eISBN:
- 9780191792526
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198725091.001.0001
- Subject:
- Mathematics, Analysis, Probability / Statistics
This book presents analytics within a framework of mathematical theory and concepts, building upon firm theory and foundations of probability theory, graphs, and networks, random matrices, linear ...
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This book presents analytics within a framework of mathematical theory and concepts, building upon firm theory and foundations of probability theory, graphs, and networks, random matrices, linear algebra, optimization, forecasting, discrete dynamical systems, and more. Following on from the theoretical considerations, applications are given to data from commercially relevant interests: supermarket baskets; loyalty cards; mobile phone call records; smart meters; ‘omic‘ data; sales promotions; social media; and microblogging. Each chapter tackles a topic in analytics: social networks and digital marketing; forecasting; clustering and segmentation; inverse problems; Markov models of behavioural changes; multiple hypothesis testing and decision-making; and so on. Chapters start with background mathematical theory explained with a strong narrative and then give way to practical considerations and then to exemplar applications.Less
This book presents analytics within a framework of mathematical theory and concepts, building upon firm theory and foundations of probability theory, graphs, and networks, random matrices, linear algebra, optimization, forecasting, discrete dynamical systems, and more. Following on from the theoretical considerations, applications are given to data from commercially relevant interests: supermarket baskets; loyalty cards; mobile phone call records; smart meters; ‘omic‘ data; sales promotions; social media; and microblogging. Each chapter tackles a topic in analytics: social networks and digital marketing; forecasting; clustering and segmentation; inverse problems; Markov models of behavioural changes; multiple hypothesis testing and decision-making; and so on. Chapters start with background mathematical theory explained with a strong narrative and then give way to practical considerations and then to exemplar applications.
