Probability and Statistical Inference: From Basic Principles to Advanced Models

Mavrakakis, Miltiadis C., Penzer, Jeremy

Probability and Statistical Inference: From Basic Principles to Advanced Models

商品描述

Probability and Statistical Inference: From Basic Principles to Advanced Models covers aspects of probability, distribution theory, and inference that are fundamental to a proper understanding of data analysis and statistical modelling. It presents these topics in an accessible manner without sacrificing mathematical rigour, bridging the gap between the many excellent introductory books and the more advanced, graduate-level texts. The book introduces and explores techniques that are relevant to modern practitioners, while being respectful to the history of statistical inference. It seeks to provide a thorough grounding in both the theory and application of statistics, with even the more abstract parts placed in the context of a practical setting.

Features:

-Complete introduction to mathematical probability, random variables, and distribution theory.
-Concise but broad account of statistical modelling, covering topics such as generalised linear models, survival analysis, time series, and random processes.
-Extensive discussion of the key concepts in classical statistics (point estimation, interval estimation, hypothesis testing) and the main techniques in likelihood-based inference.
-Detailed introduction to Bayesian statistics and associated topics.
-Practical illustration of some of the main computational methods used in modern statistical inference (simulation, boostrap, MCMC).

This book is for students who have already completed a first course in probability and statistics, and now wish to deepen and broaden their understanding of the subject. It can serve as a foundation for advanced undergraduate or postgraduate courses. Our aim is to challenge and excite the more mathematically able students, while providing explanations of statistical concepts that are more detailed and approachable than those in advanced texts. This book is also useful for data scientists, researchers, and other applied practitioners who want to understand the theory behind the statistical methods used in their fields.

商品描述(中文翻譯)

《機率與統計推論：從基本原則到進階模型》涵蓋了機率、分佈理論和推論的各個方面，這些都是正確理解數據分析和統計建模的基礎。它以易於理解的方式呈現這些主題，同時不犧牲數學的嚴謹性，彌合了許多優秀的入門書籍與更高級的研究生級文本之間的差距。該書介紹並探討了與現代實務相關的技術，同時尊重統計推論的歷史。它旨在提供統計學理論和應用的全面基礎，即使是較為抽象的部分也置於實際情境中。

特色：

- 完整介紹數學機率、隨機變數和分佈理論。
- 簡明但廣泛的統計建模概述，涵蓋一般化線性模型、生存分析、時間序列和隨機過程等主題。
- 對經典統計學中的關鍵概念（點估計、區間估計、假設檢定）及基於似然推論的主要技術進行廣泛討論。
- 詳細介紹貝葉斯統計及相關主題。
- 實用示範現代統計推論中使用的一些主要計算方法（模擬、重抽樣、MCMC）。

本書適合已完成第一門機率與統計課程的學生，並希望深化和擴展對該主題的理解。它可以作為高級本科或研究生課程的基礎。我們的目標是挑戰並激發數學能力較強的學生，同時提供比高級文本中更詳細且易於理解的統計概念解釋。本書對於數據科學家、研究人員及其他應用實務者也非常有用，幫助他們理解其領域中使用的統計方法背後的理論。

作者簡介

Miltiadis Mavrakakis obtained his PhD in Statistics at LSE under the supervision of Jeremy Penzer. His first job was as a teaching fellow at LSE, taking over course ST202 and completing this book in the process. He splits his time between lecturing (at LSE, Imperial College London, and the University of London International Programme) and his applied statistical work. Milt is currently a Senior Analyst at Smartodds, a sports betting consultancy, where he focuses on the statistical modelling of sports and financial markets. He lives in London with his wife, son, and daughter.

Jeremy Penzer first post-doc job was as a research assistant at the London School of Economics. Jeremy went on to become a lecturer at LSE and to teach the second year statistical inference course (ST202) that formed the starting point for this book. While working at LSE, his research interests were time series analysis and computational statistics. After 12 years as an academic, Jeremy shifted career to work in financial services. He is currently Chief Marketing and Analytics Officer for Capital One Europe (plc). Jeremy lives just outside Nottingham with his wife and two daughters.

作者簡介(中文翻譯)

Miltiadis Mavrakakis 在倫敦政治經濟學院（LSE）獲得統計學博士學位，指導教授為 Jeremy Penzer。他的第一份工作是在 LSE 擔任教學助理，負責 ST202 課程並在此過程中完成本書。他的時間分配在講授（於 LSE、倫敦帝國學院及倫敦大學國際課程）和應用統計工作之間。Milt 目前是 Smartodds 的高級分析師，這是一家體育博彩顧問公司，他專注於體育和金融市場的統計建模。他與妻子、兒子和女兒住在倫敦。

Jeremy Penzer 的第一份博士後工作是在倫敦政治經濟學院擔任研究助理。Jeremy 隨後成為 LSE 的講師，教授第二年統計推斷課程（ST202），這也是本書的起點。在 LSE 工作期間，他的研究興趣包括時間序列分析和計算統計。經過 12 年的學術生涯，Jeremy 轉行進入金融服務業。他目前是 Capital One Europe（plc）的首席市場與分析官。Jeremy 與妻子和兩個女兒住在諾丁漢郊外。

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