Handbook of Numerical Analysis, Volume 20
Hardcover ISBN: 9780444641403
Imprint: North Holland
Published Date: 1st October 2019
Page Count: 525
Processing, Analyzing and Learning of Images, Shapes, and Forms: Part 2, Volume 20, surveys the contemporary developments relating to the analysis and learning of images, shapes and forms, covering mathematical models and quick computational techniques. Chapter cover Alternating Diffusion: A Geometric Approach for Sensor Fusion, Generating Structured TV-based Priors and Associated Primal-dual Methods, Graph-based Optimization Approaches for Machine Learning, Uncertainty Quantification and Networks, Extrinsic Shape Analysis from Boundary Representations, Efficient Numerical Methods for Gradient Flows and Phase-field Models, Recent Advances in Denoising of Manifold-Valued Images, Optimal Registration of Images, Surfaces and Shapes, and much more.
Covers contemporary developments relating to the analysis and learning of images, shapes and forms
Presents mathematical models and quick computational techniques relating to the topic
Provides broad coverage, with sample chapters presenting content on Alternating Diffusion and Generating Structured TV-based Priors and Associated
Researchers, developers as well as people who want to learn the most recent and advanced developments in these fields
Details
No. of pages: 525
Language: English
Copyright: c North Holland 2019
Paperback ISBN: 9780128158623
Published Date: 1st November 2019
Page Count: 352
Flexible Bayesian Regression Modeling is a step-by-step guide to the Bayesian
revolution in regression modeling that can be used in advanced econometric
and statistical analysis where datasets are characterized by complexity,
multiplicity and large sample sizes. The book reviews three forms of flexibility,
including methods which provide flexibility in their error distribution,
methods which model non-central parts of the distribution (such as quantile
regression), and models that allow the mean function to be flexible (such
as spline models). Each chapter discusses the key aspects of fitting a
regression model, including variable selection, identification of outliers,
assumptions, informative output, and interpretation of results.
This book is particularly relevant to non-specialist practitioners with
intermediate mathematical training who are seeking to apply Bayesian approaches
in economics, biology and climate change.
Introduces powerful new nonparametric Bayesian regression techniques to classically trained practitioners
Focuses on approaches offering both superior power and methodological flexibility
Supplemented with instructive and relevant R programs within the text
Covers linear regression, nonlinear regression and quantile regression techniques
Provides diverse disciplinary case studies for correlation and optimization problems drawn from Bayesian analysis ein the wildf
Applied non-specialist practitioners with intermediate mathematical training seeking to apply advanced statistical analysis of probability distributions, typically based in econometrics, biology, and climate change. Graduate students and 1st year PhD students in these areas
1. Section on mean/median (linear) regression with Bayesian nonparametric methods to model the error distributions. This include methods using
2. Section focusing on quantile regression with various approaches, this
section will describe methods which are flexible about the error distribution
as well as modelling the non-central parts of the distributions
3. Section on nonlinear regression, this section will include Bayesian methods which flexibly model the mean/quantile functions, for example Bayesian
Publication planned for: June 2019
availability: Not yet published - available from June 2019
format: Hardback
isbn: 9781108480574
This practical book is designed for applied researchers who want to use mixed models with their data. It discusses the basic principles of mixed model
analysis, including two-level and three-level structures, and covers continuous
outcome variables, dichotomous outcome variables, and categorical and survival
outcome variables. Emphasizing interpretation of results, the book develops
the most important applications of mixed models, such as the study of group
differences, longitudinal data analysis, multivariate mixed model analysis,
IPD meta-analysis, and mixed model predictions. All examples are analyzed
with STATA, and an extensive overview and comparison of alternative software
packages is provided. All datasets used in the book are available for download,
so readers can re-analyze the examples to gain a strong understanding of
the methods. Although most examples are taken from epidemiological and
clinical studies, this book is also highly recommended for researchers
working in other fields.
1. Introduction
2. Basic principles of mixed model analysis
3. What is gained by using mixed model analysis?
4. Logistic mixed model analysis
5. Mixed model analysis with other outcomes
6. Explaining differences between groups
7. Multivariable modelling
8. Predictions based on mixed model analysis
9. Mixed model analysis for longitudinal data
10. Multivariate mixed model analysis
11. Sample size calculations
12. Some loose ends.
available from September 2019
format: Paperback
isbn: 9781316636374
Doubt over the trustworthiness of published empirical results is not unwarranted and is often a result of statistical mis-specification: invalid probabilistic assumptions imposed on data. Now in its second edition, this bestselling textbook offers a comprehensive course in empirical research methods, teaching the probabilistic and statistical foundations that enable the specification and validation of statistical models, providing the basis for an informed implementation of statistical procedure to secure the trustworthiness of evidence. Each chapter has been thoroughly updated, accounting for developments in the field and the author's own research. The comprehensive scope of the textbook has been expanded by the addition of a new chapter on the Linear Regression and related statistical models. This new edition is now more accessible to students of disciplines beyond economics and includes more pedagogical features, with an increased number of examples as well as review questions and exercises at the end of each chapter.
1. An introduction to empirical modeling
2. Probability theory as a modeling framework
3. The concept of a probability model
4. A simple statistical model
5. Chance regularities and probabilistic concepts
6. Statistical models and dependence
7. Regression models
8. Introduction to stochastic processes
9. Limit theorems in probability
10. From probability theory to statistical inference
11. Estimation I: properties of estimators
12. Estimation II: methods of estimation
13. Hypothesis testing
14. Linear regression and related models
15. Mis-specification (M-S) testing.
Part of Cambridge Series in Statistical and Probabilistic Mathematics
available from July 2019
format: Hardback
isbn: 9781108494205
Cluster analysis finds groups in data automatically. Most methods have
been heuristic and leave open such central questions as: how many clusters
are there? Which method should I use? How should I handle outliers? Classification
assigns new observations to groups given previously classified observations,
and also has open questions about parameter tuning, robustness and uncertainty
assessment. This book frames cluster analysis and classification in terms
of statistical models, thus yielding principled estimation, testing and
prediction methods, and sound answers to the central questions. It builds
the basic ideas in an accessible but rigorous way, with extensive data
examples and R code; describes modern approaches to high-dimensional data
and networks; and explains such recent advances as Bayesian regularization,
non-Gaussian model-based clustering, cluster merging, variable selection,
semi-supervised and robust classification, clustering of functional data,
text and images, and co-clustering. Written for advanced undergraduates
in data science, as well as researchers and practitioners, it assumes basic
knowledge of multivariate calculus, linear algebra, probability and statistics.
'Bouveyron, Celeux, Murphy, and Raftery pioneered the theory, computation,
and application of modern model-based clustering and discriminant analysis.
Here they have produced an exhaustive yet accessible text, covering both
the field's state of the art as well as its intellectual development. The
authors develop a unified vision of cluster analysis, rooted in the theory
and computation of mixture models. Embedded R code points the way for applied
readers,
while graphical displays develop intuition about both model construction
and the critical but often-neglected estimation process. Building on a
series of running examples, the authors gradually and methodically extend
their core insights into a variety of exciting data structures, including
networks and functional data. This text will serve as a backbone for graduate
study as well as an important reference for applied data scientists interested
in working with
cutting-edge tools in semi- and unsupervised machine learning.' John S. Ahlquist, University of California, San Diego
1. Introduction
2. Model-based clustering: basic ideas
3. Dealing with difficulties
4. Model-based classification
5. Semi-supervised clustering and classification
6. Discrete data clustering
7. Variable selection
8. High-dimensional data
9. Non-Gaussian model-based clustering
10. Network data
11. Model-based clustering with covariates
12. Other topics
List of R packages
Bibliography
Index.