Waic And Wbic With R Stan
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Waic And Wbic With R Stan
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Author : Joe Suzuki
language : en
Publisher: Springer Nature
Release Date : 2023-10-24
Waic And Wbic With R Stan written by Joe Suzuki and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-10-24 with Computers categories.
Master the art of machine learning and data science by diving into the essence of mathematical logic with this comprehensive textbook. This book focuses on the widely applicable information criterion (WAIC), also described as the Watanabe-Akaike information criterion, and the widely applicable Bayesian information criterion (WBIC), also described as the Watanabe Bayesian information criterion. This book expertly guides you through relevant mathematical problems while also providing hands-on experience with programming in R and Stan. Whether you’re a data scientist looking to refine your model selection process or a researcher who wants to explore the latest developments in Bayesian statistics, this accessible guide will give you a firm grasp of Watanabe Bayesian Theory. The key features of this indispensable book include: A clear and self-contained writing style, ensuring ease of understanding for readers at various levels of expertise. 100 carefully selected exercises accompanied by solutions in the main text, enabling readers to effectively gauge their progress and comprehension. A comprehensive guide to Sumio Watanabe’s groundbreaking Bayes theory, demystifying a subject once considered too challenging even for seasoned statisticians. Detailed source programs and Stan codes that will enhance readers’ grasp of the mathematical concepts presented. A streamlined approach to algebraic geometry topics in Chapter 6, making Bayes theory more accessible and less daunting. Embark on your machine learning and data science journey with this essential textbook and unlock the full potential of WAIC and WBIC today!
Waic And Wbic With Python Stan
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Author : Joe Suzuki
language : en
Publisher: Springer Nature
Release Date : 2023-12-20
Waic And Wbic With Python Stan written by Joe Suzuki and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-12-20 with Computers categories.
Master the art of machine learning and data science by diving into the essence of mathematical logic with this comprehensive textbook. This book focuses on the widely applicable information criterion (WAIC), also described as the Watanabe-Akaike information criterion, and the widely applicable Bayesian information criterion (WBIC), also described as the Watanabe Bayesian information criterion. The book expertly guides you through relevant mathematical problems while also providing hands-on experience with programming in Python and Stan. Whether you’re a data scientist looking to refine your model selection process or a researcher who wants to explore the latest developments in Bayesian statistics, this accessible guide will give you a firm grasp of Watanabe Bayesian Theory. The key features of this indispensable book include: A clear and self-contained writing style, ensuring ease of understanding for readers at various levels of expertise. 100 carefully selected exercises accompanied by solutions in the main text, enabling readers to effectively gauge their progress and comprehension. A comprehensive guide to Sumio Watanabe’s groundbreaking Bayes theory, demystifying a subject once considered too challenging even for seasoned statisticians. Detailed source programs and Stan codes that will enhance readers’ grasp of the mathematical concepts presented. A streamlined approach to algebraic geometry topics in Chapter 6, making Bayes theory more accessible and less daunting. Embark on your machine learning and data science journey with this essential textbook and unlock the full potential of WAIC and WBIC today!
Bayesian Statistical Modeling With Stan R And Python
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Author : Kentaro Matsuura
language : en
Publisher: Springer Nature
Release Date : 2023-01-24
Bayesian Statistical Modeling With Stan R And Python written by Kentaro Matsuura and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-01-24 with Computers categories.
This book provides a highly practical introduction to Bayesian statistical modeling with Stan, which has become the most popular probabilistic programming language. The book is divided into four parts. The first part reviews the theoretical background of modeling and Bayesian inference and presents a modeling workflow that makes modeling more engineering than art. The second part discusses the use of Stan, CmdStanR, and CmdStanPy from the very beginning to basic regression analyses. The third part then introduces a number of probability distributions, nonlinear models, and hierarchical (multilevel) models, which are essential to mastering statistical modeling. It also describes a wide range of frequently used modeling techniques, such as censoring, outliers, missing data, speed-up, and parameter constraints, and discusses how to lead convergence of MCMC. Lastly, the fourth part examines advanced topics for real-world data: longitudinal data analysis, state space models, spatial data analysis, Gaussian processes, Bayesian optimization, dimensionality reduction, model selection, and information criteria, demonstrating that Stan can solve any one of these problems in as little as 30 lines. Using numerous easy-to-understand examples, the book explains key concepts, which continue to be useful when using future versions of Stan and when using other statistical modeling tools. The examples do not require domain knowledge and can be generalized to many fields. The book presents full explanations of code and math formulas, enabling readers to extend models for their own problems. All the code and data are on GitHub.
Advancements In Bayesian Methods And Implementations
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Author :
language : en
Publisher: Academic Press
Release Date : 2022-10-06
Advancements In Bayesian Methods And Implementations written by and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-10-06 with Mathematics categories.
Advancements in Bayesian Methods and Implementation, Volume 47 in the Handbook of Statistics series, highlights new advances in the field, with this new volume presenting interesting chapters on a variety of timely topics, including Fisher Information, Cramer-Rao and Bayesian Paradigm, Compound beta binomial distribution functions, MCMC for GLMMS, Signal Processing and Bayesian, Mathematical theory of Bayesian statistics where all models are wrong, Machine Learning and Bayesian, Non-parametric Bayes, Bayesian testing, and Data Analysis with humans, Variational inference or Functional horseshoe, Generalized Bayes. - Provides the authority and expertise of leading contributors from an international board of authors - Presents the latest release in the Handbook of Statistics series - Updated release includes the latest information on Advancements in Bayesian Methods and Implementation
Bayesian Hierarchical Models
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Author : Peter D. Congdon
language : en
Publisher: CRC Press
Release Date : 2019-09-16
Bayesian Hierarchical Models written by Peter D. Congdon and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-09-16 with Mathematics categories.
An intermediate-level treatment of Bayesian hierarchical models and their applications, this book demonstrates the advantages of a Bayesian approach to data sets involving inferences for collections of related units or variables, and in methods where parameters can be treated as random collections. Through illustrative data analysis and attention to statistical computing, this book facilitates practical implementation of Bayesian hierarchical methods. The new edition is a revision of the book Applied Bayesian Hierarchical Methods. It maintains a focus on applied modelling and data analysis, but now using entirely R-based Bayesian computing options. It has been updated with a new chapter on regression for causal effects, and one on computing options and strategies. This latter chapter is particularly important, due to recent advances in Bayesian computing and estimation, including the development of rjags and rstan. It also features updates throughout with new examples. The examples exploit and illustrate the broader advantages of the R computing environment, while allowing readers to explore alternative likelihood assumptions, regression structures, and assumptions on prior densities. Features: Provides a comprehensive and accessible overview of applied Bayesian hierarchical modelling Includes many real data examples to illustrate different modelling topics R code (based on rjags, jagsUI, R2OpenBUGS, and rstan) is integrated into the book, emphasizing implementation Software options and coding principles are introduced in new chapter on computing Programs and data sets available on the book’s website
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Author : 片平 健太郎
language : ja
Publisher: 株式会社 オーム社
Release Date : 2018-09-25
written by 片平 健太郎 and has been published by 株式会社 オーム社 this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-09-25 with Computers categories.
人や動物の行動データの背後にある計算過程をモデル化し，行動の理解と予測につなげる。 本書は，主に行動データの計算論モデリングの方法やその理論を初学者に向けて丁寧に解説します。実例として，心理学や神経科学の実験課題として良く用いられる，ギャンブル課題における選択行動データを扱います。本文では自分ではプログラミングをしない読者も想定して，プログラムは用いずに計算論モデリングの概要がイメージできるような解説をこころがけました。実際に計算論モデリングをするためのRコードやStanコードは付録やサポートページで解説しています。 はじめに 第1部 基礎編 第1章 計算論モデリングとは 1.1 計算論モデルとは何か 1.2 計算論モデリングとは何か 1.3 計算論モデリングにより何が得られるのか 1.4 シミュレーション 1.5 おわりに 第2章 計算論モデリングの基礎 2.1 強化学習モデル 2.1.1 数学的表記法 2.1.2 Rescorla-Wagnerモデル 2.1.3 行動選択 2.2 パラメータ推定 2.2.1 モデルで次の選択を予測する 2.2.2 最尤推定 2.3 モデルを比較する 2.4 おわりに 第3章 強化学習モデルを用いたデータ解析の事例 3.1 報酬予測誤差に対応する脳活動の解析 3.2 選択・学習における社会的影響 3.3 主観的価値の推定 3.4 人種偏見の効果 3.5 疾患に関する行動特性の計算論モデリング 3.5.1 抑うつと強化学習 3.5.2 アイオワギャンブリング課題 3.6 おわりに 第2部 実践編 第4章 パラメータ推定 4.1 最尤推定とベイズの定理に基づく推定 4.1.1 最尤推定 4.1.2 ベイズの定理 4.1.3 MAP推定 4.1.4 ベイズ推定 4.2 Q 学習モデルへの適用例 4.3 集団データ分析 4.3.1 個人レベル分析 4.3.2 固定効果分析 4.3.3 階層モデル 4.4 Q学習モデルを用いた集団データ分析のシミュレーション 4.5 どの推定法を選ぶか 4.6 おわりに 第5章 モデル選択 5.1 モデル選択の例 5.2 AICとBIC 5.3 モデル選択の考え方 5.4 予測の良さに基づくモデル選択 5.4.1 AIC 5.4.2 交差検証法 5.4.3 WAIC 5.5 ベイズ的なモデル選択法 5.5.1 モデルの事後確率 5.5.2 周辺尤度とは何か 5.5.3 周辺尤度では過剰に複雑なモデルにペナルティがかかる 5.5.4 周辺尤度の近似法 5.5.5 周辺尤度とベイズファクター 5.6 尤度比検定 5.7 集団データからモデル選択をする方法 5.7.1 個人レベル分析に基づくモデル選択 5.7.2 固定効果分析に基づくモデル選択 5.7.3 階層モデルに基づくモデル選択 5.7.4 モデルをランダム効果とした分析 5.8 おわりに 第6章 計算論モデリングに基づく統計分析 6.1 計算論モデリングに基づく統計分析の目的と方法 6.2 パラメータの群間比較 6.2.1 パラメータの点推定値を「観測値」として用いる方法 6.2.2 固定効果分析のモデル選択による群間比較 6.2.3 階層ベイズ法による群間比較 6.3 パラメータと連続的な特性との相関分析，回帰分析 6.3.1 パラメータの点推定値を「観測値」として用いる方法 6.3.2 階層モデルによる方法 6.4 モデル内のパラメータ間の比較 6.5 モデルの要素が必要か否かの検討 6.6 潜在変数をリグレッサーとして用いる 6.7 おわりに 第3部 理論・発展編 第7章 結果の解釈，計算論モデルの統計的性質の理解 7.1 パラメータの解釈 7.1.1 パラメータの推定可能性 7.2 シミュレーションでパラメータの効果を調べる 7.3 報酬履歴，選択履歴の効果 7.3.1 ロジスティック回帰モデル 7.3.2 ロジスティック回帰モデルとQ学習モデルの関係 7.4 モデルの誤設定の影響 7.5 おわりに 第8章 強化学習モデルの拡張・ベイズ推論モデル 8.1 行動選択ルールのバリエーション 8.2 選択の自己相関 8.3 価値計算についてのバリエーション 8.3.1 アクター・クリティック学習 8.3.2 Q学習とアクター・クリティック学習の相違点 8.4 状態遷移，遅延報酬を扱う 8.4.1 報酬関数 8.4.2 TD誤差学習 8.4.3 SARSA 8.4.4 Q学習 8.4.5 適格度トレース 8.5 モデルフリー強化学習とモデルベース強化学習 8.5.1 二段階マルコフ決定課題 8.6 パラメータを時間的に変化させる 8.7 ベイズ推定を計算論モデルとして用いる 8.7.1 1次元正規分布モデルのベイズ推論 8.7.2 カルマンフィルター 8.7.3 その他のベイズ推論モデル 8.8 おわりに 第9章 計算論モデリングの課題と発展 9.1 計算論モデルの役割 9.2 扱えるデータのタイプ 9.3 頻度主義とベイズ主義 9.4 新たな計算論モデルを構築する方法 9.4.1 規範的アプローチ 9.4.2 心理学的な理論に基づくアプローチ 9.4.3 神経科学的知見に基づくアプローチ 9.4.4 既存の計算論モデルを組み合わせる 9.5 モデルの統計的構造の理解 9.6 計算論モデリングの応用に向けて 9.7 計算論モデリングのためのソフトウェア，パッケージ 9.8 おわりに 付録A 数学的な補足 A.1 期待値 A.2 対数と指数関数 A.3 本書で用いる確率分布 A.3.1 正規分布 A.3.2 ベータ分布 A.3.3 ガンマ分布 A.4 コイントスに関する計算 A.4.1 μの最尤推定値の導出 A.4.2 μの事後分布の導出 A.5 WAIC A.6 WBIC A.7 周辺尤度のラプラス近似 A.7.1 パラメータが一つの場合 A.7.2 パラメータが複数ある場合 A.8 信頼区間 A.9 正規分布モデルの事後分布の計算 A.10 正規分布の周辺化 付録B Rコード，シミュレーションの詳細 B.1 Rescorla-Wagnerモデルのシミュレーション B.2 Q学習モデルのシミュレーション B.3 MAP推定 B.4 ベイズ推定によるQ学習の推定 B.5 集団データのシミュレーション B.6 階層ベイズ B.7 WAIC, WBICの計算 文献案内 参考文献 索引
100 With R Stan
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Author : 鈴木讓
language : ja
Publisher:
Release Date : 2023-09-12
100 With R Stan written by 鈴木讓 and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-09-12 with categories.
WAICおよびWBICの理論的根拠を与えるとともに、RやStanを用いてその有効性を実証。略解はサポートページに掲載予定。