Stanとrでベイズ統計モデリング pdf epub mobi txt 電子書 下載 2025

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圖書標籤:

• 貝葉斯統計
• Stan
• R
• 概率編程
• 統計建模
• 數據分析
• 馬爾可夫鏈濛特卡洛
• 層次模型
• R語言
• 貝葉斯推斷

齣版社： 共立齣版

ISBN：9784320112421

商品編碼：19874597

Bayesian Statistical Modeling: A Comprehensive Guide This book offers a deep dive into the principles and practical applications of Bayesian statistical modeling, a powerful framework for understanding data and making informed decisions in the face of uncertainty. We will embark on a journey from the foundational concepts of probability and statistical inference to the sophisticated techniques employed in modern data analysis. Our aim is to equip readers with the theoretical understanding and hands-on skills necessary to tackle complex modeling challenges across a wide range of disciplines. The core of Bayesian statistics lies in its subjective interpretation of probability, where probability represents a degree of belief. This perspective, contrasted with the frequentist approach, allows for the incorporation of prior knowledge and the sequential updating of beliefs as new evidence becomes available. We will meticulously explore this fundamental difference, illustrating how it shapes the way we approach statistical problems and interpret results. The book will guide you through the construction of probabilistic models, emphasizing the importance of clearly defining the relationships between observed data and underlying latent processes. I. Foundations of Bayesian Inference Our exploration begins with the bedrock of Bayesian statistics: Bayes' Theorem. We will not only present the theorem but also dissect its components – the prior probability, the likelihood function, and the posterior probability – with rigorous mathematical exposition and intuitive explanations. Understanding how the posterior distribution arises from the interplay of prior beliefs and observed data is paramount. We will delve into various scenarios illustrating Bayes' Theorem in action, from simple coin-flipping experiments to more intricate real-world applications. Central to Bayesian inference is the concept of prior distributions. This section will be dedicated to understanding their role, types, and selection. We will discuss informative priors, which encode strong pre-existing knowledge, and non-informative or weakly informative priors, which exert minimal influence on the posterior, allowing the data to speak for itself. The subjective nature of prior selection will be addressed, along with strategies for ensuring robustness and sensitivity analysis to gauge the impact of different prior choices. We will explore conjugate priors, which simplify posterior calculations, and more general approaches when conjugate families are not applicable. The likelihood function is the bridge between our model and the observed data. We will examine common likelihood distributions, such as the Bernoulli, Binomial, Poisson, Normal, and Exponential distributions, and their suitability for different types of data. The process of defining a likelihood that accurately reflects the data-generating mechanism will be a key focus. The ultimate goal of Bayesian inference is to obtain the posterior distribution. Since analytical solutions for the posterior are often intractable, we will dedicate significant attention to computational methods. Markov Chain Monte Carlo (MCMC) algorithms, particularly Gibbs Sampling and Metropolis-Hastings, will be explained in detail. We will explore the theoretical underpinnings of these methods, their convergence diagnostics, and practical implementation considerations. The advantages of MCMC in exploring complex, high-dimensional posterior distributions will be highlighted. We will also introduce Variational Inference as an alternative approximate inference technique, discussing its strengths and weaknesses compared to MCMC. II. Building Bayesian Statistical Models Moving beyond the theoretical foundations, we will transition to the art and science of model building. This section will focus on translating research questions and data characteristics into formal Bayesian models. We will discuss different types of models, starting with simple linear regression models within a Bayesian framework. This will include understanding how to specify priors for regression coefficients and error variances, and how to interpret the resulting posterior distributions. The concept of hierarchical modeling will be a significant topic. We will explain how to model group-level effects and individual-level variations simultaneously, allowing for borrowing strength across groups and capturing complex dependencies. Examples will range from analyzing repeated measures data to modeling spatial or temporal correlations. We will explore the advantages of hierarchical models in situations with limited data for some groups. Generalized Linear Models (GLMs) will be extended to the Bayesian realm. We will cover models for binary outcomes (logistic regression), count data (Poisson regression), and other non-normal response variables. The focus will be on specifying appropriate likelihood functions and priors for the model parameters. The book will also introduce non-parametric Bayesian methods. While traditional parametric models assume a fixed functional form, non-parametric approaches offer greater flexibility by allowing the model to adapt to the data. We will touch upon concepts like Gaussian Processes for regression and classification, and Dirichlet Processes for flexible mixture modeling. III. Model Assessment and Selection A crucial aspect of any modeling endeavor is model assessment and model selection. We will explore various techniques for evaluating the fit of a Bayesian model to the data. This includes: Posterior Predictive Checks: Simulating data from the fitted model and comparing it to the observed data to assess model plausibility. Information Criteria: Discussing Bayesian extensions of AIC and BIC, such as the Deviance Information Criterion (DIC) and the Watanabe-Akaike Information Criterion (WAIC), and their interpretation in model comparison. Leave-One-Out Cross-Validation (LOO-CV): A robust method for estimating out-of-sample predictive accuracy. We will emphasize the importance of model averaging when there is substantial uncertainty about the true model, allowing us to incorporate evidence from multiple models. IV. Advanced Topics and Applications The latter part of the book will delve into more advanced topics and illustrate the broad applicability of Bayesian modeling through diverse examples. We will explore: Time Series Analysis: Applying Bayesian methods to model time-dependent data, including autoregressive models and state-space models. Causal Inference: Discussing how Bayesian approaches can be used to estimate causal effects, particularly in observational studies, by incorporating prior knowledge and accounting for confounding. Missing Data Imputation: Utilizing Bayesian hierarchical models for principled imputation of missing data. Bayesian Networks: Introducing graphical models for representing probabilistic relationships between variables, enabling complex reasoning and inference. Hierarchical Models for Mixed-Effects Designs: A deeper dive into the application of hierarchical models in experimental designs with both fixed and random effects. Throughout the book, practical implementation will be a key theme. We will guide readers through the use of popular statistical software packages and libraries for Bayesian modeling, such as Stan and R. This will involve providing code examples, demonstrating how to set up models, run MCMC simulations, visualize results, and interpret output. The intention is to bridge the gap between theoretical understanding and practical application, empowering readers to confidently apply Bayesian methods to their own research problems. Target Audience This book is intended for researchers, students, and practitioners in fields such as statistics, machine learning, biostatistics, econometrics, psychology, ecology, and any discipline that involves data analysis and modeling. Prior exposure to basic probability and statistics is assumed, but a comprehensive review of fundamental concepts will be provided to ensure accessibility. The book aims to cater to individuals who are either new to Bayesian statistics or seeking to deepen their understanding and computational proficiency. By the end of this journey, readers will possess a robust understanding of Bayesian statistical modeling, the ability to construct and evaluate complex models, and the practical skills to implement these techniques using modern software tools. We believe this comprehensive approach will foster a deeper appreciation for the power and flexibility of the Bayesian paradigm in unraveling the complexities of data and informing critical decisions.

評分☆☆☆☆☆

終於等到瞭《Stanとrでベイズ統計モデリング》這本書，拿到手裏就愛不釋手。我一直認為，統計建模不應該是一個黑盒子，而應該是一個可以被理解、被操縱的工具。貝葉斯方法恰恰提供瞭這樣一種可能性，它允許我們將先驗知識融入模型，並且能夠清晰地量化不確定性。這本書選擇Stan作為建模工具，我認為是一個非常明智的決定，因為Stan以其靈活性和高效性而聞名。我特彆期待書中關於如何診斷貝葉斯模型的後驗分布、如何進行模型比較以及如何進行模型泛化的部分。這些都是在實際應用中非常關鍵但又常常容易被忽略的環節。我相信，通過這本書的學習，我不僅能夠掌握使用Stan和R進行貝葉斯建模的技巧，更重要的是，能夠建立起一種更加深刻的統計思維方式，從而更自信地應對各種復雜的數據分析挑戰。

評分☆☆☆☆☆

終於有機會入手瞭這本《Stanとrでベイズ統計モデリング》，拿到手的那一刻就感受到它厚重的質感，迫不及待地翻開，光是目錄就讓人對即將開啓的貝葉斯之旅充滿瞭期待。作為一名對數據分析有著濃厚興趣，但又常常在傳統統計方法中感到束縛的研究者，我一直渴望找到一種能夠更靈活、更深入地理解數據背後機製的工具。這本書，正如其名，將Stan強大的模型構建能力與R豐富的生態係統相結閤，這無疑是為我量身打造的。雖然我還沒有深入到每個章節的具體細節，但從前言和一些引用的示例來看，作者顯然對貝葉斯統計建模有著深刻的理解，並且能夠用清晰易懂的方式將其傳達給讀者。我尤其關注書中關於模型選擇、模型診斷以及如何解釋貝葉斯模型輸齣的部分，這些都是在實際應用中至關重要但又常常令人睏惑的環節。我預感，這本書將不僅僅是一本技術手冊，更是一次啓發思考的旅程，幫助我突破傳統統計的藩籬，用更加直觀和強大的方式來解讀數據。

評分☆☆☆☆☆

這本《Stanとrでベイズ統計モデリング》的齣現，對我來說簡直是及時雨。我一直在嘗試將貝葉斯方法應用到我的工作中，但總是感覺有些力不從心，尤其是在需要自定義模型或者處理復雜數據結構時。這本書的重點在於將Stan和R這兩個強大的工具結閤起來，這正是許多統計從業者所需要的。我特彆期待書中關於層次模型、廣義綫性模型以及時間序列模型等內容的講解。這些都是我在實際工作中經常遇到的問題，而傳統的統計軟件往往在處理這些問題時顯得不夠靈活。我希望通過這本書，能夠學習到如何利用Stan來構建更加精細、更加符閤實際情況的模型，並且能夠通過R來方便地進行數據預處理、結果可視化和模型評估。我堅信，掌握瞭Stan和R的結閤運用，我將能更有效地從數據中提取有價值的信息。

評分☆☆☆☆☆

當我收到《Stanとrでベイズ統計モデリング》這本書時，我的內心是充滿好奇和期待的。我一直對貝葉斯統計方法抱有濃厚的興趣，因為它提供瞭一種更加符閤人類認知直覺的建模方式。然而，在實際操作中，尤其是涉及到復雜的模型時，總會遇到一些技術上的瓶頸。我希望這本書能夠提供一套係統性的解決方案，讓我能夠將貝葉斯建模的理論知識轉化為可執行的代碼。從我粗略翻閱的章節來看，這本書的結構安排非常閤理，從基礎概念入手，逐步深入到各種高級模型，並且貫穿始終的是對Stan語言的教學。我非常欣賞作者在介紹Stan語法時，能夠清晰地解釋其背後的統計學意義，而不是僅僅羅列代碼。這對於我這種既想掌握工具又想理解原理的讀者來說，無疑是巨大的福音。我期待著這本書能夠帶領我進入一個全新的統計建模世界。

評分☆☆☆☆☆

最近我一直在學習這本《Stanとrでベイズ統計モデリング》，讀起來真的非常有啓發。我最喜歡的是它不拘泥於理論的死闆講解，而是非常注重實踐，通過大量的代碼示例來展示如何構建和應用各種貝葉斯模型。特彆是那些關於如何將現實世界的問題轉化為統計模型，以及如何利用Stan進行靈活定製的部分，讓我茅塞頓開。我一直覺得，學習統計方法的目的不僅僅是掌握算法，更重要的是能夠用這些工具去解決實際問題。這本書恰好做到瞭這一點，它並沒有止步於展示“如何做”，而是引導你去思考“為什麼這麼做”，以及在不同的情境下，我們應該如何選擇和調整模型。對我來說，這就像是獲得瞭一把能夠打開更多數據寶藏的金鑰匙，我迫不及待地想將書中學到的知識應用到我的研究項目中，去探索那些隱藏在數據深處的規律。