Series: Cambridge Series in Statistical and Probabilistic Mathematics (No. 23)
Hardback (ISBN-13: 9780521847032)
In fields such as biology, medical sciences, sociology, and economics researchers often face the situation where the number of available observations, or the amount of available information, is sufficiently small that approximations based on the normal distribution may be unreliable. Theoretical work over the last quarter-century has led to new likelihood-based methods that lead to very accurate approximations in finite samples, but this work has had limited impact on statistical practice. This book illustrates by means of realistic examples and case studies how to use the new theory, and investigates how and when it makes a difference to the resulting inference. The treatment is oriented towards practice and comes with code in the R language (available from the web) which enables the methods to be applied in a range of situations of interest to practitioners. The analysis includes some comparisons of higher order likelihood inference with bootstrap or Bayesian methods.
* First practical treatment of small-sample asymptotics
* Clearly illustrates the use and effect of new likelihood-based methods
with realistic examples and case studies
* Accompanied by code in the R language (available online), allowing practitioners
to apply the methods to a wide range of situations
Contents
Preface; 1. Introduction; 2. Uncertainty and approximation; 3. Simple illustrations; 4. Discrete data; 5. Regression with continuous responses; 6. Some case studies; 7. Further topics; 8. Likelihood approximations; 9. Numerical implementation; 10. Problems and further results; Appendices - some numerical techniques: Appendix 1. Convergence of sequences; Appendix 2. The sample mean; Appendix 3. Laplace approximation; Appendix 4. X2 approximations; Bibliography; Index.
Hardback (ISBN-13: 9780521876919)
Paperback (ISBN-13: 9780521670159)
C# programmers: no more translating data structures from C++ or Java to use in your programs! Mike McMillan provides a tutorial on how to use data structures and algorithms plus the first comprehensive reference for C# implementation of data structures and algorithms found in the .NET Framework library, as well as those developed by the programmer. The approach is very practical, using timing tests rather than Big O notation to analyze the efficiency of an approach. Coverage includes arrays and array lists, linked lists, hash tables, dictionaries, trees, graphs, and sorting and searching algorithms, as well as more advanced algorithms such as probabilistic algorithms and dynamic programming. This is the perfect resource for C# professionals and students alike.
* New - first C# book on implementing data structures and algorithms from the .NET framework
* Comprehensive - includes basic data structures and algorithms plus advanced algorithms such as probabilistic algorithms and dynamics programming
* Practical - features an approach to efficiency analysis thatfs useful for the working programmer
Contents
Preliminaries; 1. Collections; 2. Arrays and arraylists; 3. Basic sorting algorithms; 4. Basic searching algorithms; 5. Stacks and queues; 6. The bitarray class; 7. Strings, the string class and the stringbuilder class; 8. Pattern matching and text processing; 9. Building dictionaries - the dictionarybase class and the sortedlist class; 10. Hashing and the hashtable class; 11. Linked lists; 12. Binary trees and binary search trees; 13. Sets; 14. Advanced sorting algorithms; 15. Advanced data structures and algorithms for searching; 16. Graphs and graph algorithms; 17. Advanced algorithms.
Hardback (ISBN-13: 9780521865579)
This introductory textbook for standard undergraduate courses in thermodynamics has been completely rewritten. Starting with an overview of important quantum behaviours, the book teaches students how to calculate probabilities, in order to provide a firm foundation for later chapters. It introduces the ideas of classical thermodynamics and explores them both in general and as they are applied to specific processes and interactions. The remainder of the book deals with statistical mechanics - the study of small systems interacting with huge reservoirs. The changes to this second edition have been made after more than 10 years classroom testing and student feedback. Each topic ends with a boxed summary of ideas and results, and every chapter contains numerous homework problems, covering a broad range of difficulties. Answers are given to odd numbered problems, and solutions to even problems are available to instructors at www.cambridge.org/9780521865579.
* The entire book has been re-written and now covers more topics
* It has a greater number of homework problems which range in difficulty from warm-ups to challenges
* It is concise and has an easy reading style
Contents
Preface; Part I. Introduction: 1. Introduction; Part II. Small Systems: 2. Statistics for small systems; 3. Systems with many elements; Part III. Energy and the First Law. 4. Internal energy; 5. Interactions between systems; Part IV. States and the Second Law: 6. Internal energy and the number of accessible states; 7. Entropy and the second law; 8. Entropy and thermal interactions; Part V. Constraints: 9. Natural contraints; 10. Models; 11. Choice of variables; 12. Special processes; 13. Engines; 14. Diffusive interactions; Part VI. Classical Statistics: 15. Probabilities and microscopic behaviours; 16. Kinetic theory and transport processes in gases; 17. Magnetic properties of materials; 18. The partition function; Part VII. Quantum Statistics: 19. Introduction to quantum statisitics; 20. Quantum gases; 21. Blackbody radiation; 22. The thermal properties of solids; 23. The electrical properties of materials; 24. Low temperatures and degenerate systems; Appendices; Further reading; Problem solutions; Index.
Hardback (ISBN-13: 9780521874991)
Quantum field theory is the application of quantum mechanics to systems with infinitely many degrees of freedom. This textbook presents quantum field theoretical applications to systems out of equilibrium. It introduces the real-time approach to non-equilibrium statistical mechanics and the quantum field theory of non-equilibrium states in general. It offers two ways of learning how to study non-equilibrium states of many-body systems: the mathematical canonical way and an easy intuitive way using Feynman diagrams. The latter provides an easy introduction to the powerful functional methods of field theory, and the use of Feynman diagrams to study classical stochastic dynamics is considered in detail. The developed real-time technique is applied to study numerous phenomena in many-body systems. Complete with numerous exercises to aid self-study, this textbook is suitable for graduate students in statistical mechanics and condensed matter physics.
* Offers two ways of learning how to study non-equilibrium states of many-body systems
* Presents the universal real-time formulation of non-equilibrium states and the corresponding Feynman diagram presentation
* Shows a multitude of applications
Contents
Preface; 1. Quantum fields; 2. Operators on the multi-particle state space; 3. Quantum dynamics and Greenfs functions; 4. Non-equilibrium theory; 5. Real-time formalism; 6. Linear response theory; 7. Quantum kinetic equations; 8. Non-equilibrium superconductivity; 9. Diagrammatics and generating functionals; 10. Effective action; 11. Disordered conductors; 12. Classical statistical dynamics; Appendices: A. Path integrals; B. Retarded and advanced propagators; C. Analytic properties of Greenfs functions; Bibliography; Index.