The complexity of large-scale data sets (“Big Data”) has stimulated the development of advanced computational methods for analysing them. There are two different kinds of methods to aid this. The model-based method uses probability models and likelihood and Bayesian theory, while the model-free method does not require a probability model, likelihood or Bayesian theory. These two approaches are based on different philosophical principles of probability theory, espoused by the famous statisticians Ronald Fisher and Jerzy Neyman. Introduction to Statistical Modelling and Inference covers simple experimental and survey designs, and probability models up to and including generalised linear (regression) models and some extensions of these, including finite mixtures. A wide range of examples from different application fields are also discussed and analysed. No special software is used, beyond that needed for maximum likelihood analysis of generalised linear models. Students are expected to have a basic mathematical background in algebra, coordinate geometry and calculus. Features • Probability models are developed from the shape of the sample empirical cumulative distribution function (cdf) or a transformation of it. • Bounds for the value of the population cumulative distribution function are obtained from the Beta distribution at each point of the empirical cdf. • Bayes’s theorem is developed from the properties of the screening test for a rare condition. • The multinomial distribution provides an always-true model for any randomly sampled data. • The model-free bootstrap method for finding the precision of a sample estimate has a model-based parallel – the Bayesian bootstrap – based on the always-true multinomial distribution. • The Bayesian posterior distributions of model parameters can be obtained from the maximum likelihood analysis of the model. This book is aimed at students in a wide range of disciplines including Data Science. The book is based on the model-based theory, used widely by scientists in many fields, and compares it, in less detail, with the model-free theory, popular in computer science, machine learning and official survey analysis. The development of the model-based theory is accelerated by recent developments in Bayesian analysis.

Directly oriented towards real practical application, this book develops both the basic theoretical framework of extreme value models and the statistical inferential techniques for using these models in practice. Intended for statisticians and non-statisticians alike, the theoretical treatment is elementary, with heuristics often replacing detailed mathematical proof. Most aspects of extreme modeling techniques are covered, including historical techniques (still widely used) and contemporary techniques based on point process models. A wide range of worked examples, using genuine datasets, illustrate the various modeling procedures and a concluding chapter provides a brief introduction to a number of more advanced topics, including Bayesian inference and spatial extremes. All the computations are carried out using S-PLUS, and the corresponding datasets and functions are available via the Internet for readers to recreate examples for themselves. An essential reference for students and researchers in statistics and disciplines such as engineering, finance and environmental science, this book will also appeal to practitioners looking for practical help in solving real problems. Stuart Coles is Reader in Statistics at the University of Bristol, UK, having previously lectured at the universities of Nottingham and Lancaster. In 1992 he was the first recipient of the Royal Statistical Society's research prize. He has published widely in the statistical literature, principally in the area of extreme value modeling.

A Hands-On Approach to Teaching Introductory Statistics Expanded with over 100 more pages, Introduction to Statistical Data Analysis for the Life Sciences, Second Edition presents the right balance of data examples, statistical theory, and computing to teach introductory statistics to students in the life sciences. This popular textbook covers the mathematics underlying classical statistical analysis, the modeling aspects of statistical analysis and the biological interpretation of results, and the application of statistical software in analyzing real-world problems and datasets. New to the Second Edition A new chapter on non-linear regression models A new chapter that contains examples of complete data analyses, illustrating how a full-fledged statistical analysis is undertaken Additional exercises in most chapters A summary of statistical formulas related to the specific designs used to teach the statistical concepts This text provides a computational toolbox that enables students to analyze real datasets and gain the confidence and skills to undertake more sophisticated analyses. Although accessible with any statistical software, the text encourages a reliance on R. For those new to R, an introduction to the software is available in an appendix. The book also includes end-of-chapter exercises as well as an entire chapter of case exercises that help students apply their knowledge to larger datasets and learn more about approaches specific to the life sciences.

Any practical introduction to statistics in the life sciences requires a focus on applications and computational statistics combined with a reasonable level of mathematical rigor. It must offer the right combination of data examples, statistical theory, and computing required for analysis today. And it should involve R software, the lingua franca of statistical computing. Introduction to Statistical Data Analysis for the Life Sciences covers all the usual material but goes further than other texts to emphasize: Both data analysis and the mathematics underlying classical statistical analysis Modeling aspects of statistical analysis with added focus on biological interpretations Applications of statistical software in analyzing real-world problems and data sets Developed from their courses at the University of Copenhagen, the authors imbue readers with the ability to model and analyze data early in the text and then gradually fill in the blanks with needed probability and statistics theory. While the main text can be used with any statistical software, the authors encourage a reliance on R. They provide a short tutorial for those new to the software and include R commands and output at the end of each chapter. Data sets used in the book are available on a supporting website. Each chapter contains a number of exercises, half of which can be done by hand. The text also contains ten case exercises where readers are encouraged to apply their knowledge to larger data sets and learn more about approaches specific to the life sciences. Ultimately, readers come away with a computational toolbox that enables them to perform actual analysis for real data sets as well as the confidence and skills to undertake more sophisticated analyses as their careers progress.

A comprehensive text and reference bringing together advances in the theory of probability and statistics and relating them to applications. The three major categories of statistical models that relate dependent variables to explanatory variables are covered: univariate regression models, multivariate regression models, and simultaneous equations models. Methods are illustrated with worked examples, complete with figures that display code and output.

David A. Freedman presents a definitive synthesis of his approach to statistical modeling and causal inference in the social sciences.

Model inference is often based on a single best models, despite modern computers easily can process many models concurrently. One reason is the manual labour involved. Managing model ensembles can become tedious when performed manually. This work presents the software design and a prototype that is concerned to facilitate that task. Requirements are discussed and examples given. Practitioners who do not shy away from interactive ensemble model management will certainly benefit from these ideas. Other readers are welcome to re-check with model ensembles and see the myth of tedious labour dissolving.

Applied Statistical Modelling for Ecologists provides a gentle introduction to the essential models of applied statistics: linear models, generalized linear models, mixed and hierarchical models. All models are fit with both a likelihood and a Bayesian approach, using several powerful software packages widely used in research publications: JAGS, NIMBLE, Stan, and TMB. In addition, the foundational method of maximum likelihood is explained in a manner that ecologists can really understand. This book is the successor of the widely used Introduction to WinBUGS for Ecologists (Kéry, Academic Press, 2010). Like its parent, it is extremely effective for both classroom use and self-study, allowing students and researchers alike to quickly learn, understand, and carry out a very wide range of statistical modelling tasks. The examples in Applied Statistical Modelling for Ecologists come from ecology and the environmental sciences, but the underlying statistical models are very widely used by scientists across many disciplines. This book will be useful for anybody who needs to learn and quickly become proficient in statistical modelling, with either a likelihood or a Bayesian focus, and in the model-fitting engines covered, including the three latest packages NIMBLE, Stan, and TMB. - Contains a concise and gentle introduction to probability and applied statistics as needed in ecology and the environmental sciences - Covers the foundations of modern applied statistical modelling - Gives a comprehensive, applied introduction to what currently are the most widely used and most exciting, cutting-edge model fitting software packages: JAGS, NIMBLE, Stan, and TMB - Provides a highly accessible applied introduction to the two dominant methods of fitting parametric statistical models: maximum likelihood and Bayesian posterior inference - Details the principles of model building, model checking and model selection - Adopts a "Rosetta Stone" approach, wherein understanding of one software, and of its associated language, will be greatly enhanced by seeing the analogous code in other engines - Provides all code available for download for students, at https://www.elsevier.com/books-and-journals/book-companion/9780443137150

The contributions collected in this book have been written by well-known statisticians to acknowledge Ludwig Fahrmeir's far-reaching impact on Statistics as a science, while celebrating his 65th birthday. The contributions cover broad areas of contemporary statistical model building, including semiparametric and geoadditive regression, Bayesian inference in complex regression models, time series modelling, statistical regularization, graphical models and stochastic volatility models.