Applied Probability (應用概率)

Lange, Kenneth

Applied Probability
  • 出版商: Springer
  • 出版日期: 2024-12-07
  • 售價: $6,360
  • 貴賓價: 9.5 折 $6,042
  • 語言: 英文
  • 頁數: 582
  • 裝訂: Hardcover - also called cloth, retail trade, or trade
  • ISBN: 1071641719
  • ISBN-13: 9781071641712

    • 海外代購書籍(需單獨結帳)

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商品描述

Applied Probability presents a unique blend of theory and applications, with special emphasis on mathematical modeling, computational techniques, and examples from the biological sciences. Chapter 1 reviews elementary probability and provides a brief survey of relevant results from measure theory. Chapter 2 is an extended essay on calculating expectations. Chapter 3 deals with probabilistic applications of convexity, inequalities, and optimization theory. Chapters 4 and 5 touch on combinatorics and combinatorial optimization. Chapters 6 through 11 present core material on stochastic processes.

If supplemented with appropriate sections from Chapters 1 and 2, there is sufficient material for a traditional semester-long course in stochastic processes covering the basics of Poisson processes, Markov chains, branching processes, martingales, and diffusion processes. This third edition includes new topics and many worked exercises. The new chapter on entropy stresses Shannon entropy and its mathematical applications. New sections in existing chapters explain the Chinese restaurant problem, the infinite alleles model, saddlepoint approximations, and recurrence relations. The extensive list of new problems pursues topics such as random graph theory omitted in the previous editions. Computational probability receives even greater emphasis than earlier. Some of the solved problems are coding exercises, and Julia code is provided.

Mathematical scientists from a variety of backgrounds will find Applied Probability appealing as a reference. This updated edition can serve as a textbook for graduate students in applied mathematics, biostatistics, computational biology, computer science, physics, and statistics. Readers should have a working knowledge of multivariate calculus, linear algebra, ordinary differential equations, and elementary probability theory.

商品描述(中文翻譯)

《應用概率》呈現了理論與應用的獨特結合，特別強調數學建模、計算技術以及來自生物科學的範例。第一章回顧了基本概率，並簡要調查了測度理論中的相關結果。第二章是一篇關於計算期望的擴展論文。第三章處理凸性、不等式和優化理論的概率應用。第四章和第五章涉及組合數學和組合優化。第六至第十一章介紹了隨機過程的核心材料。

如果補充第一章和第二章的適當部分，則有足夠的材料用於傳統的學期長隨機過程課程，涵蓋泊松過程、馬爾可夫鏈、分支過程、馬丁蓮和擴散過程的基本知識。本第三版包含了新主題和許多已解題目。新章節關於熵，強調香農熵及其數學應用。現有章節中的新部分解釋了中國餐廳問題、無限等位基因模型、鞍點近似和遞歸關係。大量的新問題探討了在先前版本中省略的隨機圖理論等主題。計算概率的強調程度比以往更高。一些已解的問題是編碼練習，並提供了Julia代碼。

來自各種背景的數學科學家會發現《應用概率》作為參考資料非常吸引人。這一更新版可以作為應用數學、生物統計學、計算生物學、計算機科學、物理學和統計學研究生的教科書。讀者應具備多變量微積分、線性代數、常微分方程和基本概率論的工作知識。

作者簡介

Kenneth Lange is the Rosenfeld Professor of Computational Genetics in the Departments of Computational Medicine, Human Genetics, and Statistics at the University of California, Los Angeles. He served as chair of the UCLA Department of Computational Medicine for 9 years and as chair of the UCLA Department of Human Genetics for 12 years. He has authored five other books, including Mathematical and Statistical Methods for Genetic Analysis (Springer, 2002), Numerical Analysis for Statisticians (Springer, 2010) and Optimization (Springer, 2013). In 2021 he was elected to the National Academy of Sciences.

作者簡介(中文翻譯)

Kenneth Lange 是加州大學洛杉磯分校計算醫學、人類遺傳學和統計學系的羅森菲爾德計算遺傳學教授。他曾擔任 UCLA 計算醫學系主任 9 年，以及 UCLA 人類遺傳學系主任 12 年。他還著有五本其他書籍，包括《遺傳分析的數學和統計方法》（Springer, 2002）、《統計學家的數值分析》（Springer, 2010）和《優化》（Springer, 2013）。他於 2021 年當選為美國國家科學院院士。

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