Estimating and Correcting the Effects of Model Selection Uncertainty


Book Description

Most applied statistical analyses are carried out under model uncertainty, meaning that the model which generated the observations is unknown, and so the data are first used to select one of a set of plausible models by means of some selection criterion. Generally the data are then used to make inferences about some quantity of interest, ignoring model selection uncertainty, i.e. the fact that the selection step was carried out using the same data, and despite the known fact that this leads to invalid inferences. This thesis investigates several issues relating to this problem from both the Bayesian and the frequentist points of view, and offers new suggestions for dealing with it. We examine Bayesian model averaging (BMA) and point out that its frequentist performance is not always well-defined because, in some cases, it is unclear whether BMA methodology is truly Bayesian. We illustrate the point with a “fully Bayesian model averaging" that is applicable when the quantity of interest is parametric.




Risk Analysis Foundations, Models, and Methods


Book Description

Risk Analysis: Foundations, Models, and Methods fully addresses the questions of "What is health risk analysis?" and "How can its potentialities be developed to be most valuable to public health decision-makers and other health risk managers?" Risk analysis provides methods and principles for answering these questions. It is divided into methods for assessing, communicating, and managing health risks. Risk assessment quantitatively estimates the health risks to individuals and to groups from hazardous exposures and from the decisions or activities that create them. It applies specialized models and methods to quantify likely exposures and their resulting health risks. Its goal is to produce information to improve decisions. It does this by relating alternative decisions to their probable consequences and by identifying those decisions that make preferred outcomes more likely. Health risk assessment draws on explicit engineering, biomathematical, and statistical consequence models to describe or simulate the causal relations between actions and their probable effects on health. Risk communication characterizes and presents information about health risks and uncertainties to decision-makers and stakeholders. Risk management applies principles for choosing among alternative decision alternatives or actions that affect exposure, health risks, or their consequences.




Model Averaging


Book Description

This book provides a concise and accessible overview of model averaging, with a focus on applications. Model averaging is a common means of allowing for model uncertainty when analysing data, and has been used in a wide range of application areas, such as ecology, econometrics, meteorology and pharmacology. The book presents an overview of the methods developed in this area, illustrating many of them with examples from the life sciences involving real-world data. It also includes an extensive list of references and suggestions for further research. Further, it clearly demonstrates the links between the methods developed in statistics, econometrics and machine learning, as well as the connection between the Bayesian and frequentist approaches to model averaging. The book appeals to statisticians and scientists interested in what methods are available, how they differ and what is known about their properties. It is assumed that readers are familiar with the basic concepts of statistical theory and modelling, including probability, likelihood and generalized linear models.




The New Palgrave Dictionary of Economics


Book Description

The award-winning The New Palgrave Dictionary of Economics, 2nd edition is now available as a dynamic online resource. Consisting of over 1,900 articles written by leading figures in the field including Nobel prize winners, this is the definitive scholarly reference work for a new generation of economists. Regularly updated! This product is a subscription based product.




Rainfall-Runoff Modelling


Book Description

Rainfall-Runoff Modelling: The Primer, Second Edition is the follow-up of this popular and authoritative text, first published in 2001. The book provides both a primer for the novice and detailed descriptions of techniques for more advanced practitioners, covering rainfall-runoff models and their practical applications. This new edition extends these aims to include additional chapters dealing with prediction in ungauged basins, predicting residence time distributions, predicting the impacts of change and the next generation of hydrological models. Giving a comprehensive summary of available techniques based on established practices and recent research the book offers a thorough and accessible overview of the area. Rainfall-Runoff Modelling: The Primer Second Edition focuses on predicting hydrographs using models based on data and on representations of hydrological process. Dealing with the history of the development of rainfall-runoff models, uncertainty in mode predictions, good and bad practice and ending with a look at how to predict future catchment hydrological responses this book provides an essential underpinning of rainfall-runoff modelling topics. Fully revised and updated version of this highly popular text Suitable for both novices in the area and for more advanced users and developers Written by a leading expert in the field Guide to internet sources for rainfall-runoff modelling software




Bayesian Models


Book Description

Bayesian modeling has become an indispensable tool for ecological research because it is uniquely suited to deal with complexity in a statistically coherent way. This textbook provides a comprehensive and accessible introduction to the latest Bayesian methods—in language ecologists can understand. Unlike other books on the subject, this one emphasizes the principles behind the computations, giving ecologists a big-picture understanding of how to implement this powerful statistical approach. Bayesian Models is an essential primer for non-statisticians. It begins with a definition of probability and develops a step-by-step sequence of connected ideas, including basic distribution theory, network diagrams, hierarchical models, Markov chain Monte Carlo, and inference from single and multiple models. This unique book places less emphasis on computer coding, favoring instead a concise presentation of the mathematical statistics needed to understand how and why Bayesian analysis works. It also explains how to write out properly formulated hierarchical Bayesian models and use them in computing, research papers, and proposals. This primer enables ecologists to understand the statistical principles behind Bayesian modeling and apply them to research, teaching, policy, and management. Presents the mathematical and statistical foundations of Bayesian modeling in language accessible to non-statisticians Covers basic distribution theory, network diagrams, hierarchical models, Markov chain Monte Carlo, and more Deemphasizes computer coding in favor of basic principles Explains how to write out properly factored statistical expressions representing Bayesian models




Handbook of Meta-Analysis


Book Description

Meta-analysis is the application of statistics to combine results from multiple studies and draw appropriate inferences. Its use and importance have exploded over the last 25 years as the need for a robust evidence base has become clear in many scientific areas, including medicine and health, social sciences, education, psychology, ecology, and economics. Recent years have seen an explosion of methods for handling complexities in meta-analysis, including explained and unexplained heterogeneity between studies, publication bias, and sparse data. At the same time, meta-analysis has been extended beyond simple two-group comparisons of continuous and binary outcomes to comparing and ranking the outcomes from multiple groups, to complex observational studies, to assessing heterogeneity of effects, and to survival and multivariate outcomes. Many of these methods are statistically complex and are tailored to specific types of data. Key features Rigorous coverage of the full range of current statistical methodology used in meta-analysis Comprehensive, coherent, and unified overview of the statistical foundations behind meta-analysis Detailed description of the primary methods for both univariate and multivariate data Computer code to reproduce examples in chapters Thorough review of the literature with thousands of references Applications to specific types of biomedical and social science data This book is for a broad audience of graduate students, researchers, and practitioners interested in the theory and application of statistical methods for meta-analysis. It is written at the level of graduate courses in statistics, but will be of interest to and readable for quantitative scientists from a range of disciplines. The book can be used as a graduate level textbook, as a general reference for methods, or as an introduction to specialized topics using state-of-the art methods.




Measurement of Higgs Boson Production Cross Sections in the Diphoton Channel


Book Description

This thesis presents the measurement of the Higgs boson cross section in the diphoton decay channel. The measurement relies on proton-proton collision data at a center-of-mass energy √s = 13 TeV recorded by the ATLAS experiment at the Large Hadron Collider (LHC). The collected data correspond to the full Run-2 dataset with an integrated luminosity of 139 fb-1. The measured cross sections are used to constrain anomalous Higgs boson interactions in the Effective Field Theory (EFT) framework. The results presented in this thesis represent a reduction by a factor 2 of the different photon and jet energy scale and resolution systematic uncertainties with respect to the previous ATLAS publication. The thesis details the calibration of electron and photon energies in ATLAS, in particular the measurement of the presampler energy scale and the estimation of its systematic uncertainty. This calibration was used to perform a measurement of the Higgs boson mass in the H → γγ and H → 4l channels using the 36 fb−1 dataset.




Wildlife Research


Book Description




Mixed-Effects Models and Small Area Estimation


Book Description

This book provides a self-contained introduction of mixed-effects models and small area estimation techniques. In particular, it focuses on both introducing classical theory and reviewing the latest methods. First, basic issues of mixed-effects models, such as parameter estimation, random effects prediction, variable selection, and asymptotic theory, are introduced. Standard mixed-effects models used in small area estimation, known as the Fay-Herriot model and the nested error regression model, are then introduced. Both frequentist and Bayesian approaches are given to compute predictors of small area parameters of interest. For measuring uncertainty of the predictors, several methods to calculate mean squared errors and confidence intervals are discussed. Various advanced approaches using mixed-effects models are introduced, from frequentist to Bayesian approaches. This book is helpful for researchers and graduate students in fields requiring data analysis skills as well as in mathematical statistics.