Algorithmic Learning in a Random World


Book Description

Algorithmic Learning in a Random World describes recent theoretical and experimental developments in building computable approximations to Kolmogorov's algorithmic notion of randomness. Based on these approximations, a new set of machine learning algorithms have been developed that can be used to make predictions and to estimate their confidence and credibility in high-dimensional spaces under the usual assumption that the data are independent and identically distributed (assumption of randomness). Another aim of this unique monograph is to outline some limits of predictions: The approach based on algorithmic theory of randomness allows for the proof of impossibility of prediction in certain situations. The book describes how several important machine learning problems, such as density estimation in high-dimensional spaces, cannot be solved if the only assumption is randomness.













Predicting Species Occurrences


Book Description

Predictions about where different species are, where they are not, and how they move across a landscape or respond to human activities -- if timber is harvested, for instance, or stream flow altered -- are important aspects of the work of wildlife biologists, land managers, and the agencies and policymakers that govern natural resources. Despite the increased use and importance of model predictions, these predictions are seldom tested and have unknown levels of accuracy.Predicting Species Occurrences addresses those concerns, highlighting for managers and researchers the strengths and weaknesses of current approaches, as well as the magnitude of the research required to improve or test predictions of currently used models. The book is an outgrowth of an international symposium held in October 1999 that brought together scientists and researchers at the forefront of efforts to process information about species at different spatial and temporal scales. It is a comprehensive reference that offers an exhaustive treatment of the subject, with 65 chapters by leading experts from around the world that: review the history of the theory and practice of modeling and present a standard terminology examine temporal and spatial scales in terms of their influence on patterns and processes of species distribution offer detailed discussions of state-of-the-art modeling tools and descriptions of methods for assessing model accuracy discuss how to predict species presence and abundance present examples of how spatially explicit data on demographics can provide important information for managers An introductory chapter by Michael A. Huston examines the ecological context in which predictions of species occurrences are made, and a concluding chapter by John A. Wiens offers an insightful review and synthesis of the topics examined along with guidance for future directions and cautions regarding misuse of models. Other contributors include Michael P. Austin, Barry R. Noon, Alan H. Fielding, Michael Goodchild, Brian A. Maurer, John T. Rotenberry, Paul Angermeier, Pierre R. Vernier, and more than a hundred others.Predicting Species Occurrences offers important new information about many of the topics raised in the seminal volume Wildlife 2000 (University of Wisconsin Press, 1986) and will be the standard reference on this subject for years to come. Its state-of-the-art assessment will play a key role in guiding the continued development and application of tools for making accurate predictions and is an indispensable volume for anyone engaged in species management or conservation.




Random Walks and Diffusion


Book Description

This block explores the diffusion equation which is most commonly encountered in discussions of the flow of heat and of molecules moving in liquids, but diffusion equations arise from many different areas of applied mathematics. As well as considering the solutions of diffusion equations in detail, we also discuss the microscopic mechanism underlying the diffusion equation, namely that particles of matter or heat move erratically. This involves a discussion of elementary probability and statistics, which are used to develop a description of random walk processes and of the central limit theorem. These concepts are used to show that if particles follow random walk trajectories, their density obeys the diffusion equation.










Probably Not


Book Description

A revised edition that explores random numbers, probability, and statistical inference at an introductory mathematical level Written in an engaging and entertaining manner, the revised and updated second edition of Probably Not continues to offer an informative guide to probability and prediction. The expanded second edition contains problem and solution sets. In addition, the book’s illustrative examples reveal how we are living in a statistical world, what we can expect, what we really know based upon the information at hand and explains when we only think we know something. The author introduces the principles of probability and explains probability distribution functions. The book covers combined and conditional probabilities and contains a new section on Bayes Theorem and Bayesian Statistics, which features some simple examples including the Presecutor’s Paradox, and Bayesian vs. Frequentist thinking about statistics. New to this edition is a chapter on Benford’s Law that explores measuring the compliance and financial fraud detection using Benford’s Law. This book: Contains relevant mathematics and examples that demonstrate how to use the concepts presented Features a new chapter on Benford’s Law that explains why we find Benford’s law upheld in so many, but not all, natural situations Presents updated Life insurance tables Contains updates on the Gantt Chart example that further develops the discussion of random events Offers a companion site featuring solutions to the problem sets within the book Written for mathematics and statistics students and professionals, the updated edition of Probably Not: Future Prediction Using Probability and Statistical Inference, Second Edition combines the mathematics of probability with real-world examples. LAWRENCE N. DWORSKY, PhD, is a retired Vice President of the Technical Staff and Director of Motorola’s Components Research Laboratory in Schaumburg, Illinois, USA. He is the author of Introduction to Numerical Electrostatics Using MATLAB from Wiley.




Mixture Toxicity


Book Description

In the last decade and a half, great progress has been made in the development of concepts and models for mixture toxicity, both in human and environmental toxicology. However, due to their different protection goals, developments have often progressed in parallel but with little integration. Arguably the first book to clearly link ecotoxicology an