Mathematical Theory of Bayesian Statistics

Watanabe, Sumio

Mathematical Theory of Bayesian Statistics
  • 出版商: CRC
  • 出版日期: 2020-12-18
  • 售價: $2,500
  • 貴賓價: 9.5 折 $2,375
  • 語言: 英文
  • 頁數: 320
  • 裝訂: Quality Paper - also called trade paper
  • ISBN: 0367734818
  • ISBN-13: 9780367734817
  • 相關分類: 機率統計學 Probability-and-statistics

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商品描述

Mathematical Theory of Bayesian Statistics introduces the mathematical foundation of Bayesian inference which is well-known to be more accurate in many real-world problems than the maximum likelihood method. Recent research has uncovered several mathematical laws in Bayesian statistics, by which both the generalization loss and the marginal likelihood are estimated even if the posterior distribution cannot be approximated by any normal distribution.

 

 

 

 

 

 

 

Features

 

 

 

 

 

 

 

 

 

  • Explains Bayesian inference not subjectively but objectively.
  • Provides a mathematical framework for conventional Bayesian theorems.
  • Introduces and proves new theorems.
  • Cross validation and information criteria of Bayesian statistics are studied from the mathematical point of view.
  • Illustrates applications to several statistical problems, for example, model selection, hyperparameter optimization, and hypothesis tests.

 

 

 

 

 

 

 

 

 

This book provides basic introductions for students, researchers, and users of Bayesian statistics, as well as applied mathematicians.

 

 

 

 

 

 

 

 

 

Author

 

 

 

 

Sumio Watanabe is a professor of Department of Mathematical and Computing Science at Tokyo Institute of Technology. He studies the relationship between algebraic geometry and mathematical statistics.

 

 

 

 

 

 

 

商品描述(中文翻譯)

《貝葉斯統計的數學理論》介紹了貝葉斯推論的數學基礎，這在許多現實世界的問題中比最大概似法更準確。最近的研究揭示了貝葉斯統計中的幾個數學定律，即使後驗分佈無法以任何正態分佈逼近，也可以估計出泛化損失和邊際概率。

特點：
- 客觀地解釋貝葉斯推論，而非主觀地。
- 為傳統貝葉斯定理提供數學框架。
- 引入並證明新的定理。
- 從數學角度研究貝葉斯統計的交叉驗證和信息準則。
- 以幾個統計問題為例，例如模型選擇、超參數優化和假設檢驗，說明應用。

本書為學生、研究人員和貝葉斯統計的使用者提供基礎介紹，同時也適用於應用數學家。

作者：
渡邊澄夫（Sumio Watanabe）是東京工業大學數學與計算科學系的教授。他研究代數幾何與數學統計之間的關係。

作者簡介

Sumio Watanabe is a professor in the Department of Computational Intelligence and Systems Science at Tokyo Institute of Technology, Japan.

作者簡介(中文翻譯)

Sumio Watanabe是日本東京工業大學計算智能與系統科學系的教授。

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