Mathematical Theory of Bayesian Statistics
暫譯: 貝葉斯統計的數學理論
Watanabe, Sumio
- 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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相關主題
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》介紹了貝葉斯推斷的數學基礎，這在許多現實世界的問題中被認為比最大似然法更為準確。最近的研究揭示了貝葉斯統計中的幾個數學定律，通過這些定律，即使後驗分佈無法被任何正態分佈近似，仍然可以估計一般化損失和邊際似然。
特色
- 以客觀的方式解釋貝葉斯推斷，而非主觀的。
- 提供傳統貝葉斯定理的數學框架。
- 介紹並證明新的定理。
- 從數學的角度研究貝葉斯統計的交叉驗證和信息準則。
- 說明在幾個統計問題中的應用，例如模型選擇、超參數優化和假設檢驗。
本書為貝葉斯統計的學生、研究人員和使用者，以及應用數學家提供基本介紹。
作者
渡邊澄夫是東京科技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)
渡邊澄夫是日本東京科技大學計算智慧與系統科學系的教授。
