Fundamentals of Nonparametric Bayesian Inference (Hardcover)

Subhashis Ghosal, Aad van der Vaart

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商品描述

Explosive growth in computing power has made Bayesian methods for infinite-dimensional models - Bayesian nonparametrics - a nearly universal framework for inference, finding practical use in numerous subject areas. Written by leading researchers, this authoritative text draws on theoretical advances of the past twenty years to synthesize all aspects of Bayesian nonparametrics, from prior construction to computation and large sample behavior of posteriors. Because understanding the behavior of posteriors is critical to selecting priors that work, the large sample theory is developed systematically, illustrated by various examples of model and prior combinations. Precise sufficient conditions are given, with complete proofs, that ensure desirable posterior properties and behavior. Each chapter ends with historical notes and numerous exercises to deepen and consolidate the reader's understanding, making the book valuable for both graduate students and researchers in statistics and machine learning, as well as in application areas such as econometrics and biostatistics.

商品描述(中文翻譯)

計算能力的爆炸性增長使得貝葉斯方法在無限維模型中的應用——貝葉斯非參數統計——成為一個幾乎普遍的推理框架,在許多學科領域中找到實際應用。這本權威性的書籍由領先的研究人員撰寫,借鑒了過去二十年的理論進展,綜合了貝葉斯非參數統計的所有方面,從先驗構建到計算和後驗的大樣本行為。由於理解後驗的行為對於選擇有效的先驗至關重要,大樣本理論被系統地發展,並通過各種模型和先驗組合的示例進行了說明。給出了精確的充分條件,並附有完整的證明,以確保後驗具有理想的性質和行為。每章結束時都有歷史注釋和大量練習題,以加深和鞏固讀者的理解,使本書對統計學和機器學習的研究生和研究人員以及應用領域(如計量經濟學和生物統計學)的研究人員都具有價值。