Stanとrでベイズ統計モデリング pdf epub mobi txt 电子书 下载 2025

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图书标签:

• 贝叶斯统计
• Stan
• R
• 概率编程
• 统计建模
• 数据分析
• 马尔可夫链蒙特卡洛
• 层次模型
• R语言
• 贝叶斯推断

出版社： 共立出版

ISBN：9784320112421

商品编码：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.

评分☆☆☆☆☆

终于有机会入手了这本《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质感，迫不及待地翻开，光是目录就让人对即将开启的贝叶斯之旅充满了期待。作为一名对数据分析有着浓厚兴趣，但又常常在传统统计方法中感到束缚的研究者，我一直渴望找到一种能够更灵活、更深入地理解数据背后机制的工具。这本书，正如其名，将Stan强大的模型构建能力与R丰富的生态系统相结合，这无疑是为我量身打造的。虽然我还没有深入到每个章节的具体细节，但从前言和一些引用的示例来看，作者显然对贝叶斯统计建模有着深刻的理解，并且能够用清晰易懂的方式将其传达给读者。我尤其关注书中关于模型选择、模型诊断以及如何解释贝叶斯模型输出的部分，这些都是在实际应用中至关重要但又常常令人困惑的环节。我预感，这本书将不仅仅是一本技术手册，更是一次启发思考的旅程，帮助我突破传统统计的藩篱，用更加直观和强大的方式来解读数据。

评分☆☆☆☆☆

终于等到了《Stanとrでベイズ統計モデリング》这本书，拿到手里就爱不释手。我一直认为，统计建模不应该是一个黑盒子，而应该是一个可以被理解、被操纵的工具。贝叶斯方法恰恰提供了这样一种可能性，它允许我们将先验知识融入模型，并且能够清晰地量化不确定性。这本书选择Stan作为建模工具，我认为是一个非常明智的决定，因为Stan以其灵活性和高效性而闻名。我特别期待书中关于如何诊断贝叶斯模型的后验分布、如何进行模型比较以及如何进行模型泛化的部分。这些都是在实际应用中非常关键但又常常容易被忽略的环节。我相信，通过这本书的学习，我不仅能够掌握使用Stan和R进行贝叶斯建模的技巧，更重要的是，能够建立起一种更加深刻的统计思维方式，从而更自信地应对各种复杂的数据分析挑战。

评分☆☆☆☆☆

当我收到《Stanとrでベイズ統計モデリング》这本书时，我的内心是充满好奇和期待的。我一直对贝叶斯统计方法抱有浓厚的兴趣，因为它提供了一种更加符合人类认知直觉的建模方式。然而，在实际操作中，尤其是涉及到复杂的模型时，总会遇到一些技术上的瓶颈。我希望这本书能够提供一套系统性的解决方案，让我能够将贝叶斯建模的理论知识转化为可执行的代码。从我粗略翻阅的章节来看，这本书的结构安排非常合理，从基础概念入手，逐步深入到各种高级模型，并且贯穿始终的是对Stan语言的教学。我非常欣赏作者在介绍Stan语法时，能够清晰地解释其背后的统计学意义，而不是仅仅罗列代码。这对于我这种既想掌握工具又想理解原理的读者来说，无疑是巨大的福音。我期待着这本书能够带领我进入一个全新的统计建模世界。

评分☆☆☆☆☆

这本《Stanとrでベイズ統計モデリング》的出现，对我来说简直是及时雨。我一直在尝试将贝叶斯方法应用到我的工作中，但总是感觉有些力不从心，尤其是在需要自定义模型或者处理复杂数据结构时。这本书的重点在于将Stan和R这两个强大的工具结合起来，这正是许多统计从业者所需要的。我特别期待书中关于层次模型、广义线性模型以及时间序列模型等内容的讲解。这些都是我在实际工作中经常遇到的问题，而传统的统计软件往往在处理这些问题时显得不够灵活。我希望通过这本书，能够学习到如何利用Stan来构建更加精细、更加符合实际情况的模型，并且能够通过R来方便地进行数据预处理、结果可视化和模型评估。我坚信，掌握了Stan和R的结合运用，我将能更有效地从数据中提取有价值的信息。

评分☆☆☆☆☆

最近我一直在学习这本《Stanとrでベイズ統計モデリング》，读起来真的非常有启发。我最喜欢的是它不拘泥于理论的死板讲解，而是非常注重实践，通过大量的代码示例来展示如何构建和应用各种贝叶斯模型。特别是那些关于如何将现实世界的问题转化为统计模型，以及如何利用Stan进行灵活定制的部分，让我茅塞顿开。我一直觉得，学习统计方法的目的不仅仅是掌握算法，更重要的是能够用这些工具去解决实际问题。这本书恰好做到了这一点，它并没有止步于展示“如何做”，而是引导你去思考“为什么这么做”，以及在不同的情境下，我们应该如何选择和调整模型。对我来说，这就像是获得了一把能够打开更多数据宝藏的金钥匙，我迫不及待地想将书中学到的知识应用到我的研究项目中，去探索那些隐藏在数据深处的规律。