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This book emphasizes the importance of the likelihood function in statistical theory and applications and discusses it in the context of biology and ecology. Bayesian and frequentist methods both use the likelihood function and provide differing but related insights. This is examined here both through review of basic methodology and also the integr
The interest in using Bayesian methods in ecology is increasing, however many ecologists have difficulty with conducting the required analyses. McCarthy bridges that gap, using a clear and accessible style. The text also incorporates case studies to demonstrate mark-recapture analysis, development of population models and the use of subjective judgement. The advantages of Bayesian methods, are also described here, for example, the incorporation of any relevant prior information and the ability to assess the evidence in favour of competing hypotheses. Free software is available as well as an accompanying web-site containing the data files and WinBUGS codes. Bayesian Methods for Ecology will appeal to academic researchers, upper undergraduate and graduate students of Ecology.
Offering a rich diversity of models, Bayesian phylogenetics allows evolutionary biologists, systematists, ecologists, and epidemiologists to obtain answers to very detailed phylogenetic questions. Suitable for graduate-level researchers in statistics and biology, Bayesian Phylogenetics: Methods, Algorithms, and Applications presents a snapshot of current trends in Bayesian phylogenetic research. Encouraging interdisciplinary research, this book introduces state-of-the-art phylogenetics to the Bayesian statistical community and, likewise, presents state-of-the-art Bayesian statistics to the phylogenetics community. The book emphasizes model selection, reflecting recent interest in accurately estimating marginal likelihoods. It also discusses new approaches to improve mixing in Bayesian phylogenetic analyses in which the tree topology varies. In addition, the book covers divergence time estimation, biologically realistic models, and the burgeoning interface between phylogenetics and population genetics.
This richly illustrated textbook covers modern statistical methods with applications in medicine, epidemiology and biology. Firstly, it discusses the importance of statistical models in applied quantitative research and the central role of the likelihood function, describing likelihood-based inference from a frequentist viewpoint, and exploring the properties of the maximum likelihood estimate, the score function, the likelihood ratio and the Wald statistic. In the second part of the book, likelihood is combined with prior information to perform Bayesian inference. Topics include Bayesian updating, conjugate and reference priors, Bayesian point and interval estimates, Bayesian asymptotics and empirical Bayes methods. It includes a separate chapter on modern numerical techniques for Bayesian inference, and also addresses advanced topics, such as model choice and prediction from frequentist and Bayesian perspectives. This revised edition of the book “Applied Statistical Inference” has been expanded to include new material on Markov models for time series analysis. It also features a comprehensive appendix covering the prerequisites in probability theory, matrix algebra, mathematical calculus, and numerical analysis, and each chapter is complemented by exercises. The text is primarily intended for graduate statistics and biostatistics students with an interest in applications.
Introduction and background; Exploratory data analysis and graphics; Deterministic functions for ecological modeling; Probability and stochastic distributions for ecological modeling; Stochatsic simulation and power analysis; Likelihood and all that; Optimization and all that; Likelihood examples; Standar statistics revisited; Modeling variance; Dynamic models.
An essential guide to quantitative research methods in ecology and conservation biology, accessible for even the most math-averse student or professional. Quantitative research techniques have become increasingly important in ecology and conservation biology, but the sheer breadth of methods that must be understood—from population modeling and probabilistic thinking to modern statistics, simulation, and data science—and a lack of computational or mathematics training have hindered quantitative literacy in these fields. In this book, ecologist Justin Kitzes addresses those challenges for students and practicing scientists alike. Requiring only basic algebra and the ability to use a spreadsheet, Handbook of Quantitative Ecology is designed to provide a practical, intuitive, and integrated introduction to widely used quantitative methods. Kitzes builds each chapter around a specific ecological problem and arrives, step by step, at a general principle through the process of solving that problem. Grouped into five broad categories—difference equations, probability, matrix models, likelihood statistics, and other numerical methods—the book introduces basic concepts, starting with exponential and logistic growth, and helps readers to understand the field’s more advanced subjects, such as bootstrapping, stochastic optimization, and cellular automata. Complete with online solutions to all numerical problems, Kitzes’s Handbook of Quantitative Ecology is an ideal coursebook for both undergraduate and graduate students of ecology, as well as a useful and necessary resource for mathematically out-of-practice scientists.
Thirty years ago, biologists could get by with a rudimentary grasp of mathematics and modeling. Not so today. In seeking to answer fundamental questions about how biological systems function and change over time, the modern biologist is as likely to rely on sophisticated mathematical and computer-based models as traditional fieldwork. In this book, Sarah Otto and Troy Day provide biology students with the tools necessary to both interpret models and to build their own. The book starts at an elementary level of mathematical modeling, assuming that the reader has had high school mathematics and first-year calculus. Otto and Day then gradually build in depth and complexity, from classic models in ecology and evolution to more intricate class-structured and probabilistic models. The authors provide primers with instructive exercises to introduce readers to the more advanced subjects of linear algebra and probability theory. Through examples, they describe how models have been used to understand such topics as the spread of HIV, chaos, the age structure of a country, speciation, and extinction. Ecologists and evolutionary biologists today need enough mathematical training to be able to assess the power and limits of biological models and to develop theories and models themselves. This innovative book will be an indispensable guide to the world of mathematical models for the next generation of biologists. A how-to guide for developing new mathematical models in biology Provides step-by-step recipes for constructing and analyzing models Interesting biological applications Explores classical models in ecology and evolution Questions at the end of every chapter Primers cover important mathematical topics Exercises with answers Appendixes summarize useful rules Labs and advanced material available
This textbook introduces a science philosophy called "information theoretic" based on Kullback-Leibler information theory. It focuses on a science philosophy based on "multiple working hypotheses" and statistical models to represent them. The text is written for people new to the information-theoretic approaches to statistical inference, whether graduate students, post-docs, or professionals. Readers are however expected to have a background in general statistical principles, regression analysis, and some exposure to likelihood methods. This is not an elementary text as it assumes reasonable competence in modeling and parameter estimation.
Written in simple language with relevant examples, this illustrative introductory book presents best practices in experimental design and simple data analysis. Taking a practical and intuitive approach, it only uses mathematical formulae to formalize the methods where necessary and appropriate. The text features extended discussions of examples that include real data sets arising from research. The authors analyze data in detail to illustrate the use of basic formulae for simple examples while using the GenStat statistical package for more complex examples. Each chapter offers instructions on how to obtain the example analyses in GenStat and R.
Meta-analysis is a powerful statistical methodology for synthesizing research evidence across independent studies. This is the first comprehensive handbook of meta-analysis written specifically for ecologists and evolutionary biologists, and it provides an invaluable introduction for beginners as well as an up-to-date guide for experienced meta-analysts. The chapters, written by renowned experts, walk readers through every step of meta-analysis, from problem formulation to the presentation of the results. The handbook identifies both the advantages of using meta-analysis for research synthesis and the potential pitfalls and limitations of meta-analysis (including when it should not be used). Different approaches to carrying out a meta-analysis are described, and include moment and least-square, maximum likelihood, and Bayesian approaches, all illustrated using worked examples based on real biological datasets. This one-of-a-kind resource is uniquely tailored to the biological sciences, and will provide an invaluable text for practitioners from graduate students and senior scientists to policymakers in conservation and environmental management. Walks you through every step of carrying out a meta-analysis in ecology and evolutionary biology, from problem formulation to result presentation Brings together experts from a broad range of fields Shows how to avoid, minimize, or resolve pitfalls such as missing data, publication bias, varying data quality, nonindependence of observations, and phylogenetic dependencies among species Helps you choose the right software Draws on numerous examples based on real biological datasets