Random Patterns and Structures in Spatial Data
暫譯: 空間數據中的隨機模式與結構

Stoica, Radu

Random Patterns and Structures in Spatial Data
  • 出版商: CRC
  • 出版日期: 2025-04-02
  • 售價: $4,910
  • 貴賓價: 9.5 折 $4,665
  • 語言: 英文
  • 頁數: 281
  • 裝訂: Hardcover - also called cloth, retail trade, or trade
  • ISBN: 1032459360
  • ISBN-13: 9781032459363

    • 海外代購書籍(需單獨結帳)

商品描述

The book presents a general mathematical framework able to detect and to characterize, from a morphological and statistical perspective, patterns hidden in spatial data. The mathematical tool employed is a Gibbs point process with interaction, which permits us to reduce the complexity of the pattern. It presents the framework, step by step, in three major parts: modeling, simulation, and inference. Each of these parts contains a theoretical development followed by applications and examples.

Features:

  • Presents mathematical foundations for tackling pattern detection and characterisation in spatial data using marked Gibbs point processes with interactions
  • Proposes a general methodology for morphological and statistical characterisation of patterns based on three branches, probabilistic modeling, stochastic simulation, and statistical inference
  • Includes application examples from cosmology, environmental sciences, geology, and social networks
  • Presents theoretical and practical details for the presented algorithms in order to be correctly and efficiently used
  • Provides access to C]+ and R code to encourage the reader to experiment and to develop new ideas
  • Includes references and pointers to mathematical and applied literature to encourage further study

The book is primarily aimed at researchers in mathematics, statistics, and the above-mentioned application domains. It is accessible for advanced undergraduate and graduate students, so could be used to teach a course. It will be of interest to any scientific researcher interested in formulating a mathematical answer to the always challenging question: what is the pattern hidden in the data?

商品描述(中文翻譯)

本書提供了一個通用的數學框架，能夠從形態學和統計的角度檢測和描述隱藏在空間數據中的模式。所使用的數學工具是具有互動性的Gibbs點過程，這使我們能夠降低模式的複雜性。本書分為三個主要部分：建模、模擬和推斷，逐步介紹該框架。每個部分都包含理論發展，隨後是應用和示例。

**特色：**
- 提供使用帶有互動的標記Gibbs點過程來處理空間數據中模式檢測和描述的數學基礎
- 提出基於三個分支的通用方法論，用於模式的形態學和統計描述，包括概率建模、隨機模擬和統計推斷
- 包含來自宇宙學、環境科學、地質學和社交網絡的應用示例
- 提供所呈現算法的理論和實踐細節，以便正確和高效地使用
- 提供C]+和R代碼，鼓勵讀者進行實驗並發展新想法
- 包含參考文獻和數學及應用文獻的指引，以鼓勵進一步學習

本書主要針對數學、統計學及上述應用領域的研究人員。對於高年級本科生和研究生來說也很容易理解，因此可以用來教授課程。對於任何希望為始終具有挑戰性的問題——數據中隱藏的模式是什麼？——提供數學解答的科學研究者都會感興趣。

作者簡介

Radu S. Stoica is a full professor in mathematics at the University of Lorraine, France. His research activity connects stochastic geometry, spatial statistics, and Bayesian inference for probabilistic modeling and statistical description of random structures and patterns. The results of his work consist of tailored to the data methodologies based on Gibbs Markov models, Monte Carlo algorithms, and inference procedures, which can characterise and detect structures and patterns either hidden or directly observed in the data. The tackled application domains are astronomy, geosciences, image analysis, and network sciences. Prior to his current position, Dr. Stoica was an associate professor at University of Lille, France. He also worked as a researcher for INRAe Avignon, France, University Jaume I, Spain, and CWI Amsterdam, The Netherlands.

作者簡介(中文翻譯)

Radu S. Stoica 是法國洛林大學的數學全職教授。他的研究活動結合了隨機幾何、空間統計學和貝葉斯推斷，用於隨機結構和模式的概率建模及統計描述。他的研究成果包括基於 Gibbs Markov 模型、蒙地卡羅算法和推斷程序的數據專屬方法，這些方法能夠表徵和檢測數據中隱藏或直接觀察到的結構和模式。所涉及的應用領域包括天文學、地球科學、影像分析和網絡科學。在擔任目前職位之前，Stoica 博士曾是法國里爾大學的副教授。他還曾在法國阿維尼翁的 INRAe、 西班牙的哈梅一世大學以及荷蘭的 CWI 阿姆斯特丹擔任研究員。

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