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1. Shard Calculation

Query:

Response:

Calculated Shard: 115 (from laksa146)

2. Crawled Status Check

Query:

curl -X POST \
  'http://laksa115.int.ahrefs:8124/' \
  -H 'Content-Type: text/plain' \
  -H 'X-ClickHouse-Database: crawler3' \
  -H 'Authorization: Basic YXBpOg==' \
  -d 'SELECT getAhrefsURLFromUnparsed(src_unparsed) AS found_url, ifNull(toUnixTimestamp(download_stamp), 0) AS crawl_time, ifNull(toUnixTimestamp(props_url_first_seen), 0) AS first_indexed_time, download_http_code AS http_code, src_unparsed AS src_unparsed, src_root_hash AS src_root_hash, history_drop_reason AS history_drop_reason, meta_title AS meta_title, meta_descriptions AS meta_descriptions, attrs_boilerpipe_text AS attrs_boilerpipe_text, attrs_markdown AS attrs_markdown, attrs_readable_markdown AS attrs_readable_markdown, meta_canonical AS meta_canonical FROM crawler3.page_info_local FINAL PREWHERE (src_root_hash, src_unparsed) IN ((getAhrefsRootHashFromUnparsed(getAhrefsUnparsedNoserviceFromURL(\'https://www.oreilly.com/library/view/bayesian-statistics-an/9781118359778/\')), getAhrefsUnparsedNoserviceFromURL(\'https://www.oreilly.com/library/view/bayesian-statistics-an/9781118359778/\'))) FORMAT JSONEachRow'

Response:

{"found_url":"https:\/\/www.oreilly.com\/library\/view\/bayesian-statistics-an\/9781118359778\/","crawl_time":1775697710,"first_indexed_time":1539254486,"http_code":200,"src_unparsed":"com,oreilly!www,\/library\/view\/bayesian-statistics-an\/9781118359778\/ s443","src_root_hash":"3309313061461398115","history_drop_reason":null,"meta_title":"Bayesian Statistics: An Introduction, 4th Edition [Book]","meta_descriptions":["Bayesian Statistics is the school of thought that combines prior beliefs with the likelihood of a hypothesis to arrive at posterior beliefs. The first edition of Peter Lee's book... - Selection from Bayesian Statistics: An Introduction, 4th Edition [Book]"],"attrs_boilerpipe_text":"Overview\nBayesian Statistics is the school of thought that combines prior beliefs with the likelihood of a hypothesis to arrive at posterior beliefs. The first edition of Peter Lee's book appeared in 1989, but the subject has moved ever onwards, with increasing emphasis on Monte Carlo based techniques.\nThis new fourth edition looks at recent techniques such as variational methods, Bayesian importance sampling, approximate Bayesian computation and Reversible Jump Markov Chain Monte Carlo (RJMCMC), providing a concise account of the way in which the Bayesian approach to statistics develops as well as how it contrasts with the conventional approach. The theory is built up step by step, and important notions such as sufficiency are brought out of a discussion of the salient features of specific examples.\nThis edition:\nIncludes expanded coverage of Gibbs sampling, including more numerical examples and treatments of OpenBUGS, R2WinBUGS and R2OpenBUGS.\nPresents significant new material on recent techniques such as Bayesian importance sampling, variational Bayes, Approximate Bayesian Computation (ABC) and Reversible Jump Markov Chain Monte Carlo (RJMCMC).\nProvides extensive examples throughout the book to complement the theory presented.\nAccompanied by a supporting website featuring new material and solutions.\nMore and more students are realizing that they need to learn Bayesian statistics to meet their academic and professional goals. This book is best suited for use as a main text in courses on Bayesian statistics for third and fourth year undergraduates and postgraduate students.\nBecome an O’Reilly member and get unlimited access to this title plus top books and audiobooks from O’Reilly and nearly 200 top publishers, thousands of courses curated by job role, 150+ live events each month,\nand much more.\nRead now\nUnlock full access\nMore than 5,000 organizations count on O’Reilly\nO’Reilly covers everything we've got, with content to help us build a world-class technology community, upgrade the capabilities and competencies of our teams, and improve overall team performance as well as their engagement.\nJulian F.\nI wanted to learn C and C++, but it didn't click for me until I picked up an O'Reilly book. When I went on the O’Reilly platform, I was astonished to find all the books there, plus live events and sandboxes so you could play around with the technology.\nAddison B.\nI’ve been on the O’Reilly platform for more than eight years. I use a couple of learning platforms, but I'm on O'Reilly more than anybody else. When you're there, you start learning. I'm never disappointed.\nAmir M.\nI'm always learning. So when I got on to O'Reilly, I was like a kid in a candy store. There are playlists. There are answers. There's on-demand training. It's worth its weight in gold, in terms of what it allows me to do.\nMark W.\nYou might also like","attrs_markdown":"[Skip to Content](https:\/\/www.oreilly.com\/library\/view\/bayesian-statistics-an\/9781118359778\/#main)\n\n- [For Enterprise](https:\/\/www.oreilly.com\/online-learning\/teams.html)\n- [For Government](https:\/\/www.oreilly.com\/online-learning\/government.html)\n- [For Higher Ed](https:\/\/www.oreilly.com\/online-learning\/academic.html)\n- [For Individuals](https:\/\/www.oreilly.com\/online-learning\/individuals.html)\n- [For Content Marketing](https:\/\/www.oreilly.com\/content-marketing-solutions.html)\n\n- Explore Skills\n  - Cloud Computing\n    - [Microsoft Azure](https:\/\/www.oreilly.com\/search\/skills\/microsoft-azure\/)\n    - [Amazon Web Services (AWS)](https:\/\/www.oreilly.com\/search\/skills\/amazon-web-services-aws\/)\n    - [Google Cloud](https:\/\/www.oreilly.com\/search\/skills\/google-cloud\/)\n    - [Cloud Migration](https:\/\/www.oreilly.com\/search\/skills\/cloud-migration\/)\n    - [Cloud Deployment](https:\/\/www.oreilly.com\/search\/skills\/cloud-deployment\/)\n    - [Cloud Platforms](https:\/\/www.oreilly.com\/search\/skills\/cloud-platforms\/)\n    \n    [View all](https:\/\/www.oreilly.com\/library\/view\/bayesian-statistics-an\/9781118359778\/)\n  - Data Engineering\n    - [Data Warehouse](https:\/\/www.oreilly.com\/search\/skills\/data-warehouse\/)\n    - [SQL](https:\/\/www.oreilly.com\/search\/skills\/sql\/)\n    - [Apache Spark](https:\/\/www.oreilly.com\/search\/skills\/apache-spark\/)\n    - [Microsoft SQL Server](https:\/\/www.oreilly.com\/search\/skills\/microsoft-sql-server\/)\n    - [MySQL](https:\/\/www.oreilly.com\/search\/skills\/mysql\/)\n    - [Kafka](https:\/\/www.oreilly.com\/search\/skills\/kafka\/)\n    - [Data Lake](https:\/\/www.oreilly.com\/search\/skills\/data-lake\/)\n    - [Streaming & Messaging](https:\/\/www.oreilly.com\/search\/skills\/streaming-messaging\/)\n    - [NoSQL Databases](https:\/\/www.oreilly.com\/search\/skills\/nosql-databases\/)\n    - [Relational Databases](https:\/\/www.oreilly.com\/search\/skills\/relational-databases\/)\n    \n    [View all](https:\/\/www.oreilly.com\/library\/view\/bayesian-statistics-an\/9781118359778\/)\n  - Data Science\n    - [Pandas](https:\/\/www.oreilly.com\/search\/topics\/pandas\/)\n    - [R](https:\/\/www.oreilly.com\/search\/topics\/r\/)\n    - [MATLAB](https:\/\/www.oreilly.com\/search\/topics\/matlab\/)\n    - [SAS](https:\/\/www.oreilly.com\/search\/topics\/sas\/)\n    - [D3](https:\/\/www.oreilly.com\/search\/topics\/d3\/)\n    - [Power BI](https:\/\/www.oreilly.com\/search\/topics\/power-bi\/)\n    - [Tableau](https:\/\/www.oreilly.com\/search\/topics\/tableau\/)\n    - [Statistics](https:\/\/www.oreilly.com\/search\/topics\/statistics\/)\n    - [Exploratory Data Analysis](https:\/\/www.oreilly.com\/search\/topics\/exploratory-data-analysis\/)\n    - [Data Visualization](https:\/\/www.oreilly.com\/search\/topics\/data-visualization\/)\n    \n    [View all](https:\/\/www.oreilly.com\/library\/view\/bayesian-statistics-an\/9781118359778\/)\n  - 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[Design Tools](https:\/\/www.oreilly.com\/search\/skills\/design-tools\/)\n    \n    [View all](https:\/\/www.oreilly.com\/library\/view\/bayesian-statistics-an\/9781118359778\/)\n  - Business\n    - [Agile](https:\/\/www.oreilly.com\/search\/skills\/agile\/)\n    - [Project Management](https:\/\/www.oreilly.com\/search\/skills\/project-management\/)\n    - [Product Management](https:\/\/www.oreilly.com\/search\/skills\/product-management\/)\n    - [Marketing](https:\/\/www.oreilly.com\/search\/skills\/marketing\/)\n    - [Human Resources](https:\/\/www.oreilly.com\/search\/skills\/human-resources\/)\n    - [Finance](https:\/\/www.oreilly.com\/search\/skills\/finance\/)\n    - [Team Management](https:\/\/www.oreilly.com\/search\/skills\/team-management\/)\n    - [Business Strategy](https:\/\/www.oreilly.com\/search\/skills\/business-strategy\/)\n    - [Digital Transformation](https:\/\/www.oreilly.com\/search\/skills\/digital-transformation\/)\n    - [Organizational Leadership](https:\/\/www.oreilly.com\/search\/skills\/organizational-leadership\/)\n    \n    [View all](https:\/\/www.oreilly.com\/library\/view\/bayesian-statistics-an\/9781118359778\/)\n  - Soft Skills\n    - [Professional Communication](https:\/\/www.oreilly.com\/search\/skills\/professional-communication\/)\n    - [Emotional Intelligence](https:\/\/www.oreilly.com\/search\/skills\/emotional-intelligence\/)\n    - [Presentation Skills](https:\/\/www.oreilly.com\/search\/skills\/presentation-skills\/)\n    - [Innovation](https:\/\/www.oreilly.com\/search\/skills\/innovation\/)\n    - [Critical Thinking](https:\/\/www.oreilly.com\/search\/skills\/critical-thinking\/)\n    - [Public Speaking](https:\/\/www.oreilly.com\/search\/skills\/public-speaking\/)\n    - [Collaboration](https:\/\/www.oreilly.com\/search\/skills\/collaboration\/)\n    - [Personal Productivity](https:\/\/www.oreilly.com\/search\/skills\/personal-productivity\/)\n    - [Confidence \/ Motivation](https:\/\/www.oreilly.com\/search\/skills\/confidence-motivation\/)\n    \n    [View all](https:\/\/www.oreilly.com\/library\/view\/bayesian-statistics-an\/9781118359778\/)\n  \n  [View all](https:\/\/www.oreilly.com\/search\/skills)\n- Features\n  - 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Cloud Computing\n    ## Cloud Computing\n    - [Microsoft Azure](https:\/\/www.oreilly.com\/search\/skills\/microsoft-azure\/)\n    - [Amazon Web Services (AWS)](https:\/\/www.oreilly.com\/search\/skills\/amazon-web-services-aws\/)\n    - [Google Cloud](https:\/\/www.oreilly.com\/search\/skills\/google-cloud\/)\n    - [Cloud Migration](https:\/\/www.oreilly.com\/search\/skills\/cloud-migration\/)\n    - [Cloud Deployment](https:\/\/www.oreilly.com\/search\/skills\/cloud-deployment\/)\n    - [Cloud Platforms](https:\/\/www.oreilly.com\/search\/skills\/cloud-platforms\/)\n    \n    Back\n  - Data Engineering\n    ## Data Engineering\n    - [Data Warehouse](https:\/\/www.oreilly.com\/search\/skills\/data-warehouse\/)\n    - [SQL](https:\/\/www.oreilly.com\/search\/skills\/sql\/)\n    - [Apache Spark](https:\/\/www.oreilly.com\/search\/skills\/apache-spark\/)\n    - [Microsoft SQL Server](https:\/\/www.oreilly.com\/search\/skills\/microsoft-sql-server\/)\n    - [MySQL](https:\/\/www.oreilly.com\/search\/skills\/mysql\/)\n    - [Kafka](https:\/\/www.oreilly.com\/search\/skills\/kafka\/)\n    - [Data Lake](https:\/\/www.oreilly.com\/search\/skills\/data-lake\/)\n    - [Streaming & Messaging](https:\/\/www.oreilly.com\/search\/skills\/streaming-messaging\/)\n    - [NoSQL Databases](https:\/\/www.oreilly.com\/search\/skills\/nosql-databases\/)\n    - [Relational Databases](https:\/\/www.oreilly.com\/search\/skills\/relational-databases\/)\n    \n    Back\n  - Data Science\n    ## Data Science\n    - [Pandas](https:\/\/www.oreilly.com\/search\/topics\/pandas\/)\n    - [R](https:\/\/www.oreilly.com\/search\/topics\/r\/)\n    - [MATLAB](https:\/\/www.oreilly.com\/search\/topics\/matlab\/)\n    - [SAS](https:\/\/www.oreilly.com\/search\/topics\/sas\/)\n    - [D3](https:\/\/www.oreilly.com\/search\/topics\/d3\/)\n    - [Power BI](https:\/\/www.oreilly.com\/search\/topics\/power-bi\/)\n    - [Tableau](https:\/\/www.oreilly.com\/search\/topics\/tableau\/)\n    - [Statistics](https:\/\/www.oreilly.com\/search\/topics\/statistics\/)\n    - [Exploratory Data Analysis](https:\/\/www.oreilly.com\/search\/topics\/exploratory-data-analysis\/)\n    - [Data Visualization](https:\/\/www.oreilly.com\/search\/topics\/data-visualization\/)\n    \n    Back\n  - AI & ML\n    ## AI & ML\n    - [Generative AI](https:\/\/www.oreilly.com\/search\/skills\/generative-ai\/)\n    - [Machine Learning](https:\/\/www.oreilly.com\/search\/skills\/machine-learning\/)\n    - [Artificial Intelligence (AI)](https:\/\/www.oreilly.com\/search\/skills\/artificial-intelligence-ai\/)\n    - [Deep Learning](https:\/\/www.oreilly.com\/search\/skills\/deep-learning\/)\n    - [Reinforcement Learning](https:\/\/www.oreilly.com\/search\/skills\/reinforcement-learning\/)\n    - [Natural Language Processing](https:\/\/www.oreilly.com\/search\/skills\/natural-language-processing\/)\n    - [TensorFlow](https:\/\/www.oreilly.com\/search\/skills\/tensorflow\/)\n    - [Scikit-Learn](https:\/\/www.oreilly.com\/search\/skills\/scikit-learn\/)\n    - [Hyperparameter Tuning](https:\/\/www.oreilly.com\/search\/skills\/hyperparameter-tuning\/)\n    - [MLOps](https:\/\/www.oreilly.com\/search\/skills\/mlops\/)\n    \n    Back\n  - Programming Languages\n    ## Programming Languages\n    - [Java](https:\/\/www.oreilly.com\/search\/skills\/java\/)\n    - [JavaScript](https:\/\/www.oreilly.com\/search\/skills\/javascript\/)\n    - [Spring](https:\/\/www.oreilly.com\/search\/skills\/spring\/)\n    - [Python](https:\/\/www.oreilly.com\/search\/skills\/python\/)\n    - [Go](https:\/\/www.oreilly.com\/search\/skills\/go\/)\n    - [C\\#](https:\/\/www.oreilly.com\/search\/skills\/c-sharp\/)\n    - [C++](https:\/\/www.oreilly.com\/search\/skills\/c-plus-plus\/)\n    - [C](https:\/\/www.oreilly.com\/search\/skills\/c\/)\n    - [Swift](https:\/\/www.oreilly.com\/search\/skills\/swift\/)\n    - [Rust](https:\/\/www.oreilly.com\/search\/skills\/rust\/)\n    - [Functional Programming](https:\/\/www.oreilly.com\/search\/skills\/functional-programming\/)\n    \n    Back\n  - Software Architecture\n    ## Software Architecture\n    - [Object-Oriented](https:\/\/www.oreilly.com\/search\/skills\/object-oriented-architecture\/)\n    - [Distributed Systems](https:\/\/www.oreilly.com\/search\/skills\/distributed-systems\/)\n    - [Domain-Driven Design](https:\/\/www.oreilly.com\/search\/skills\/domain-driven-design\/)\n    - [Architectural Patterns](https:\/\/www.oreilly.com\/search\/skills\/architectural-patterns\/)\n    \n    Back\n  - IT\/Ops\n    ## IT\/Ops\n    - [Kubernetes](https:\/\/www.oreilly.com\/search\/topics\/kubernetes\/)\n    - [Docker](https:\/\/www.oreilly.com\/search\/topics\/docker\/)\n    - [GitHub](https:\/\/www.oreilly.com\/search\/topics\/github\/)\n    - [Terraform](https:\/\/www.oreilly.com\/search\/topics\/terraform\/)\n    - [Continuous Delivery](https:\/\/www.oreilly.com\/search\/topics\/continuous-delivery\/)\n    - [Continuous Integration](https:\/\/www.oreilly.com\/search\/topics\/continuous-integration\/)\n    - [Database Administration](https:\/\/www.oreilly.com\/search\/topics\/database-administration\/)\n    - [Computer Networking](https:\/\/www.oreilly.com\/search\/topics\/computer-networking\/)\n    - 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[Security Engineering](https:\/\/www.oreilly.com\/search\/skills\/security-engineering\/)\n    - [Security Certifications](https:\/\/www.oreilly.com\/search\/skills\/security-certifications\/)\n    \n    Back\n  - Design\n    ## Design\n    - [Web Design](https:\/\/www.oreilly.com\/search\/skills\/web-design\/)\n    - [Graphic Design](https:\/\/www.oreilly.com\/search\/skills\/graphic-design\/)\n    - [Interaction Design](https:\/\/www.oreilly.com\/search\/skills\/interaction-design\/)\n    - [Film & Video](https:\/\/www.oreilly.com\/search\/skills\/film-video\/)\n    - [User Experience (UX)](https:\/\/www.oreilly.com\/search\/skills\/user-experience-ux\/)\n    - [Design Process](https:\/\/www.oreilly.com\/search\/skills\/design-process\/)\n    - [Design Tools](https:\/\/www.oreilly.com\/search\/skills\/design-tools\/)\n    \n    Back\n  - Business\n    ## Business\n    - [Agile](https:\/\/www.oreilly.com\/search\/skills\/agile\/)\n    - [Project Management](https:\/\/www.oreilly.com\/search\/skills\/project-management\/)\n    - 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[Interactive learning](https:\/\/www.oreilly.com\/online-learning\/intro-interactive-learning.html)\n  - [Live events](https:\/\/www.oreilly.com\/online-learning\/live-events.html)\n  - [Superstreams](https:\/\/www.oreilly.com\/products\/superstreams.html)\n  - [Answers](https:\/\/www.oreilly.com\/online-learning\/feature-answers.html)\n  - [Insights reporting](https:\/\/www.oreilly.com\/online-learning\/insights-dashboard.html)\n  \n  Back\n- [Radar Blog](https:\/\/www.oreilly.com\/radar\/)\n- [Buy Courses](https:\/\/www.oreilly.com\/live\/)\n***\n- [Plans](https:\/\/www.oreilly.com\/online-learning\/pricing.html)\n- [Sign In](https:\/\/www.oreilly.com\/member\/login\/)\n- [Try Now](https:\/\/www.oreilly.com\/online-learning\/try-now.html)\n\n![Bayesian Statistics: An Introduction, 4th Edition](https:\/\/www.oreilly.com\/covers\/urn:orm:book:9781118359778\/300w\/)\n\nbook\n\n# Bayesian Statistics: An Introduction, 4th Edition\n##### by [Peter M. Lee](https:\/\/www.oreilly.com\/search\/?query=author:\"Peter%20M.%20Lee\"&sort=relevance&highlight=true)\n\nSeptember 2012\n\nIntermediate to advanced\n\n486 pages\n\n10h 41m\n\nEnglish\n\n[Wiley](https:\/\/www.oreilly.com\/publisher\/36d782fd-353a-4200-acec-dab22ff9a53c\/)\n\n[Read nowUnlock full access](https:\/\/www.oreilly.com\/start-trial\/?next=\/library\/view\/bayesian-statistics-an\/9781118359778\/)\n\n### Contents\n- ### [Cover](https:\/\/www.oreilly.com\/library\/view\/bayesian-statistics-an\/9781118359778\/OEBPS\/9781118359778_epub_cov.htm)\n- ### [Title Page](https:\/\/www.oreilly.com\/library\/view\/bayesian-statistics-an\/9781118359778\/OEBPS\/9781118359778_epub_fm_01.htm)\n- ### [Copyright](https:\/\/www.oreilly.com\/library\/view\/bayesian-statistics-an\/9781118359778\/OEBPS\/9781118359778_epub_fm_02.htm)\n- ### [Dedication](https:\/\/www.oreilly.com\/library\/view\/bayesian-statistics-an\/9781118359778\/OEBPS\/9781118359778_epub_fm_03.htm)\n- ### [Preface](https:\/\/www.oreilly.com\/library\/view\/bayesian-statistics-an\/9781118359778\/OEBPS\/9781118359778_epub_fm_04.htm)\n- ### [Preface to the First Edition](https:\/\/www.oreilly.com\/library\/view\/bayesian-statistics-an\/9781118359778\/OEBPS\/9781118359778_epub_fm_05.htm)\n- ### [Chapter 1: Preliminaries](https:\/\/www.oreilly.com\/library\/view\/bayesian-statistics-an\/9781118359778\/OEBPS\/9781118359778_epub_ch_01.htm)\n- ### [1\\.1 Probability and Bayes’ Theorem](https:\/\/www.oreilly.com\/library\/view\/bayesian-statistics-an\/9781118359778\/OEBPS\/c01-sec1-0001.htm)\n- ### [1\\.2 Examples on Bayes’ Theorem](https:\/\/www.oreilly.com\/library\/view\/bayesian-statistics-an\/9781118359778\/OEBPS\/c01-sec1-0002.htm)\n- ### [1\\.3 Random variables](https:\/\/www.oreilly.com\/library\/view\/bayesian-statistics-an\/9781118359778\/OEBPS\/c01-sec1-0003.htm)\n- ### [1\\.4 Several random variables](https:\/\/www.oreilly.com\/library\/view\/bayesian-statistics-an\/9781118359778\/OEBPS\/c01-sec1-0004.htm)\n- ### [1\\.5 Means and variances](https:\/\/www.oreilly.com\/library\/view\/bayesian-statistics-an\/9781118359778\/OEBPS\/c01-sec1-0005.htm)\n- ### [1\\.6 Exercises on Chapter 1](https:\/\/www.oreilly.com\/library\/view\/bayesian-statistics-an\/9781118359778\/OEBPS\/c01-sec1-0006.htm)\n- ### [Chapter 2: Bayesian inference for the normal distribution](https:\/\/www.oreilly.com\/library\/view\/bayesian-statistics-an\/9781118359778\/OEBPS\/9781118359778_epub_ch_02.htm)\n- ### [2\\.1 Nature of Bayesian inference](https:\/\/www.oreilly.com\/library\/view\/bayesian-statistics-an\/9781118359778\/OEBPS\/c02-sec1-0001.htm)\n- ### [2\\.2 Normal prior and likelihood](https:\/\/www.oreilly.com\/library\/view\/bayesian-statistics-an\/9781118359778\/OEBPS\/c02-sec1-0002.htm)\n- ### [2\\.3 Several normal observations with a normal prior](https:\/\/www.oreilly.com\/library\/view\/bayesian-statistics-an\/9781118359778\/OEBPS\/c02-sec1-0003.htm)\n- ### [2\\.4 Dominant likelihoods](https:\/\/www.oreilly.com\/library\/view\/bayesian-statistics-an\/9781118359778\/OEBPS\/c02-sec1-0004.htm)\n- ### [2\\.5 Locally uniform priors](https:\/\/www.oreilly.com\/library\/view\/bayesian-statistics-an\/9781118359778\/OEBPS\/c02-sec1-0005.htm)\n- ### [2\\.6 Highest density regions](https:\/\/www.oreilly.com\/library\/view\/bayesian-statistics-an\/9781118359778\/OEBPS\/c02-sec1-0006.htm)\n- ### [2\\.7 Normal variance](https:\/\/www.oreilly.com\/library\/view\/bayesian-statistics-an\/9781118359778\/OEBPS\/c02-sec1-0007.htm)\n- ### [2\\.8 HDRs for the normal variance](https:\/\/www.oreilly.com\/library\/view\/bayesian-statistics-an\/9781118359778\/OEBPS\/c02-sec1-0008.htm)\n- ### [2\\.9 The role of sufficiency](https:\/\/www.oreilly.com\/library\/view\/bayesian-statistics-an\/9781118359778\/OEBPS\/c02-sec1-0009.htm)\n- ### [2\\.10 Conjugate prior distributions](https:\/\/www.oreilly.com\/library\/view\/bayesian-statistics-an\/9781118359778\/OEBPS\/c02-sec1-0010.htm)\n- ### [2\\.11 The exponential family](https:\/\/www.oreilly.com\/library\/view\/bayesian-statistics-an\/9781118359778\/OEBPS\/c02-sec1-0011.htm)\n- ### [2\\.12 Normal mean and variance both unknown](https:\/\/www.oreilly.com\/library\/view\/bayesian-statistics-an\/9781118359778\/OEBPS\/c02-sec1-0012.htm)\n- ### [2\\.13 Conjugate joint prior for the normal distribution](https:\/\/www.oreilly.com\/library\/view\/bayesian-statistics-an\/9781118359778\/OEBPS\/c02-sec1-0013.htm)\n- ### [2\\.14 Exercises on Chapter 2](https:\/\/www.oreilly.com\/library\/view\/bayesian-statistics-an\/9781118359778\/OEBPS\/c02-sec1-0014.htm)\n- ### [Chapter 3: Some other common distributions](https:\/\/www.oreilly.com\/library\/view\/bayesian-statistics-an\/9781118359778\/OEBPS\/9781118359778_epub_ch_03.htm)\n- ### [3\\.1 The binomial distribution](https:\/\/www.oreilly.com\/library\/view\/bayesian-statistics-an\/9781118359778\/OEBPS\/c03-sec1-0001.htm)\n- ### [3\\.2 Reference prior for the binomial likelihood](https:\/\/www.oreilly.com\/library\/view\/bayesian-statistics-an\/9781118359778\/OEBPS\/c03-sec1-0002.htm)\n- ### [3\\.3 Jeffreys’ rule](https:\/\/www.oreilly.com\/library\/view\/bayesian-statistics-an\/9781118359778\/OEBPS\/c03-sec1-0003.htm)\n- ### [3\\.4 The Poisson distribution](https:\/\/www.oreilly.com\/library\/view\/bayesian-statistics-an\/9781118359778\/OEBPS\/c03-sec1-0004.htm)\n- ### [3\\.5 The uniform distribution](https:\/\/www.oreilly.com\/library\/view\/bayesian-statistics-an\/9781118359778\/OEBPS\/c03-sec1-0005.htm)\n- ### [3\\.6 Reference prior for the uniform distribution](https:\/\/www.oreilly.com\/library\/view\/bayesian-statistics-an\/9781118359778\/OEBPS\/c03-sec1-0006.htm)\n- ### [3\\.7 The tramcar problem](https:\/\/www.oreilly.com\/library\/view\/bayesian-statistics-an\/9781118359778\/OEBPS\/c03-sec1-0007.htm)\n- ### [3\\.8 The first digit problem; invariant priors](https:\/\/www.oreilly.com\/library\/view\/bayesian-statistics-an\/9781118359778\/OEBPS\/c03-sec1-0008.htm)\n- ### [3\\.9 The circular normal distribution](https:\/\/www.oreilly.com\/library\/view\/bayesian-statistics-an\/9781118359778\/OEBPS\/c03-sec1-0009.htm)\n- ### [3\\.10 Approximations based on the likelihood](https:\/\/www.oreilly.com\/library\/view\/bayesian-statistics-an\/9781118359778\/OEBPS\/c03-sec1-0010.htm)\n- ### [3\\.11 Reference posterior distributions](https:\/\/www.oreilly.com\/library\/view\/bayesian-statistics-an\/9781118359778\/OEBPS\/c03-sec1-0011.htm)\n- ### [3\\.12 Exercises on Chapter 3](https:\/\/www.oreilly.com\/library\/view\/bayesian-statistics-an\/9781118359778\/OEBPS\/c03-sec1-0012.htm)\n- ### [Chapter 4: Hypothesis testing](https:\/\/www.oreilly.com\/library\/view\/bayesian-statistics-an\/9781118359778\/OEBPS\/9781118359778_epub_ch_04.htm)\n- ### [4\\.1 Hypothesis testing](https:\/\/www.oreilly.com\/library\/view\/bayesian-statistics-an\/9781118359778\/OEBPS\/c04-sec1-0001.htm)\n- ### [4\\.2 One-sided hypothesis tests](https:\/\/www.oreilly.com\/library\/view\/bayesian-statistics-an\/9781118359778\/OEBPS\/c04-sec1-0002.htm)\n- ### [4\\.3 Lindley’s method](https:\/\/www.oreilly.com\/library\/view\/bayesian-statistics-an\/9781118359778\/OEBPS\/c04-sec1-0003.htm)\n- ### [4\\.4 Point (or sharp) null hypotheses with prior information](https:\/\/www.oreilly.com\/library\/view\/bayesian-statistics-an\/9781118359778\/OEBPS\/c04-sec1-0004.htm)\n- ### [4\\.5 Point null hypotheses for the normal distribution](https:\/\/www.oreilly.com\/library\/view\/bayesian-statistics-an\/9781118359778\/OEBPS\/c04-sec1-0005.htm)\n- ### [4\\.6 The Doogian philosophy](https:\/\/www.oreilly.com\/library\/view\/bayesian-statistics-an\/9781118359778\/OEBPS\/c04-sec1-0006.htm)\n- ### [4\\.7 Exercises on Chapter 4](https:\/\/www.oreilly.com\/library\/view\/bayesian-statistics-an\/9781118359778\/OEBPS\/c04-sec1-0007.htm)\n- ### [Chapter 5: Two-sample problems](https:\/\/www.oreilly.com\/library\/view\/bayesian-statistics-an\/9781118359778\/OEBPS\/9781118359778_epub_ch_05.htm)\n- ### [5\\.1 Two-sample problems – both variances unknown](https:\/\/www.oreilly.com\/library\/view\/bayesian-statistics-an\/9781118359778\/OEBPS\/c05-sec1-0001.htm)\n- ### [5\\.2 Variances unknown but equal](https:\/\/www.oreilly.com\/library\/view\/bayesian-statistics-an\/9781118359778\/OEBPS\/c05-sec1-0002.htm)\n- ### [5\\.3 Variances unknown and unequal (Behrens–Fisher problem)](https:\/\/www.oreilly.com\/library\/view\/bayesian-statistics-an\/9781118359778\/OEBPS\/c05-sec1-0003.htm)\n- ### [5\\.4 The Behrens–Fisher controversy](https:\/\/www.oreilly.com\/library\/view\/bayesian-statistics-an\/9781118359778\/OEBPS\/c05-sec1-0004.htm)\n- ### [5\\.5 Inferences concerning a variance ratio](https:\/\/www.oreilly.com\/library\/view\/bayesian-statistics-an\/9781118359778\/OEBPS\/c05-sec1-0005.htm)\n- ### [5\\.6 Comparison of two proportions; the \\$2\\\\times 2\\$ table](https:\/\/www.oreilly.com\/library\/view\/bayesian-statistics-an\/9781118359778\/OEBPS\/c05-sec1-0006.htm)\n- ### [5\\.7 Exercises on Chapter 5](https:\/\/www.oreilly.com\/library\/view\/bayesian-statistics-an\/9781118359778\/OEBPS\/c05-sec1-0007.htm)\n- ### [Chapter 6: Correlation, regression and the analysis of variance](https:\/\/www.oreilly.com\/library\/view\/bayesian-statistics-an\/9781118359778\/OEBPS\/9781118359778_epub_ch_06.htm)\n- ### [6\\.1 Theory of the correlation coefficient](https:\/\/www.oreilly.com\/library\/view\/bayesian-statistics-an\/9781118359778\/OEBPS\/c06-sec1-0001.htm)\n- ### [6\\.2 Examples on the use of the correlation coefficient](https:\/\/www.oreilly.com\/library\/view\/bayesian-statistics-an\/9781118359778\/OEBPS\/c06-sec1-0007.htm)\n- ### [6\\.3 Regression and the bivariate normal model](https:\/\/www.oreilly.com\/library\/view\/bayesian-statistics-an\/9781118359778\/OEBPS\/c06-sec1-0011.htm)\n- ### [6\\.4 Conjugate prior for the bivariate regression model](https:\/\/www.oreilly.com\/library\/view\/bayesian-statistics-an\/9781118359778\/OEBPS\/c06-sec1-0021.htm)\n- ### [6\\.5 Comparison of several means – the one way model](https:\/\/www.oreilly.com\/library\/view\/bayesian-statistics-an\/9781118359778\/OEBPS\/c06-sec1-0025.htm)\n- ### [6\\.6 The two way layout](https:\/\/www.oreilly.com\/library\/view\/bayesian-statistics-an\/9781118359778\/OEBPS\/c06-sec1-0033.htm)\n- ### [6\\.7 The general linear model](https:\/\/www.oreilly.com\/library\/view\/bayesian-statistics-an\/9781118359778\/OEBPS\/c06-sec1-0037.htm)\n- ### [6\\.8 Exercises on Chapter 6](https:\/\/www.oreilly.com\/library\/view\/bayesian-statistics-an\/9781118359778\/OEBPS\/c06-sec1-0042.htm)\n- ### [Chapter 7: Other topics](https:\/\/www.oreilly.com\/library\/view\/bayesian-statistics-an\/9781118359778\/OEBPS\/9781118359778_epub_ch_07.htm)\n- ### [7\\.1 The likelihood principle](https:\/\/www.oreilly.com\/library\/view\/bayesian-statistics-an\/9781118359778\/OEBPS\/c07-sec1-0001.htm)\n- ### [7\\.2 The stopping rule principle](https:\/\/www.oreilly.com\/library\/view\/bayesian-statistics-an\/9781118359778\/OEBPS\/c07-sec1-0002.htm)\n- ### [7\\.3 Informative stopping rules](https:\/\/www.oreilly.com\/library\/view\/bayesian-statistics-an\/9781118359778\/OEBPS\/c07-sec1-0003.htm)\n- ### [7\\.4 The likelihood principle and reference priors](https:\/\/www.oreilly.com\/library\/view\/bayesian-statistics-an\/9781118359778\/OEBPS\/c07-sec1-0004.htm)\n- ### [7\\.5 Bayesian decision theory](https:\/\/www.oreilly.com\/library\/view\/bayesian-statistics-an\/9781118359778\/OEBPS\/c07-sec1-0005.htm)\n- ### [7\\.6 Bayes linear methods](https:\/\/www.oreilly.com\/library\/view\/bayesian-statistics-an\/9781118359778\/OEBPS\/c07-sec1-0006.htm)\n- ### [7\\.7 Decision theory and hypothesis testing](https:\/\/www.oreilly.com\/library\/view\/bayesian-statistics-an\/9781118359778\/OEBPS\/c07-sec1-0007.htm)\n- ### [7\\.8 Empirical Bayes methods](https:\/\/www.oreilly.com\/library\/view\/bayesian-statistics-an\/9781118359778\/OEBPS\/c07-sec1-0008.htm)\n- ### [7\\.9 Exercises on Chapter 7](https:\/\/www.oreilly.com\/library\/view\/bayesian-statistics-an\/9781118359778\/OEBPS\/c07-sec1-0009.htm)\n- ### [Chapter 8: Hierarchical models](https:\/\/www.oreilly.com\/library\/view\/bayesian-statistics-an\/9781118359778\/OEBPS\/9781118359778_epub_ch_08.htm)\n- ### [8\\.1 The idea of a hierarchical model](https:\/\/www.oreilly.com\/library\/view\/bayesian-statistics-an\/9781118359778\/OEBPS\/c08-sec1-0001.htm)\n- ### [8\\.2 The hierarchical normal model](https:\/\/www.oreilly.com\/library\/view\/bayesian-statistics-an\/9781118359778\/OEBPS\/c08-sec1-0002.htm)\n- ### [8\\.3 The baseball example](https:\/\/www.oreilly.com\/library\/view\/bayesian-statistics-an\/9781118359778\/OEBPS\/c08-sec1-0003.htm)\n- ### [8\\.4 The Stein estimator](https:\/\/www.oreilly.com\/library\/view\/bayesian-statistics-an\/9781118359778\/OEBPS\/c08-sec1-0004.htm)\n- ### [8\\.5 Bayesian analysis for an unknown overall mean](https:\/\/www.oreilly.com\/library\/view\/bayesian-statistics-an\/9781118359778\/OEBPS\/c08-sec1-0005.htm)\n- ### [8\\.6 The general linear model revisited](https:\/\/www.oreilly.com\/library\/view\/bayesian-statistics-an\/9781118359778\/OEBPS\/c08-sec1-0006.htm)\n- ### [8\\.7 Exercises on Chapter 8](https:\/\/www.oreilly.com\/library\/view\/bayesian-statistics-an\/9781118359778\/OEBPS\/c08-sec1-0007.htm)\n- ### [Chapter 9: The Gibbs sampler and other numerical methods](https:\/\/www.oreilly.com\/library\/view\/bayesian-statistics-an\/9781118359778\/OEBPS\/9781118359778_epub_ch_09.htm)\n- ### [9\\.1 Introduction to numerical methods](https:\/\/www.oreilly.com\/library\/view\/bayesian-statistics-an\/9781118359778\/OEBPS\/c09-sec1-0001.htm)\n- ### [9\\.2 The EM algorithm](https:\/\/www.oreilly.com\/library\/view\/bayesian-statistics-an\/9781118359778\/OEBPS\/c09-sec1-0002.htm)\n- ### [9\\.3 Data augmentation by Monte Carlo](https:\/\/www.oreilly.com\/library\/view\/bayesian-statistics-an\/9781118359778\/OEBPS\/c09-sec1-0003.htm)\n- ### [9\\.4 The Gibbs sampler](https:\/\/www.oreilly.com\/library\/view\/bayesian-statistics-an\/9781118359778\/OEBPS\/c09-sec1-0004.htm)\n- ### [9\\.5 Rejection sampling](https:\/\/www.oreilly.com\/library\/view\/bayesian-statistics-an\/9781118359778\/OEBPS\/c09-sec1-0005.htm)\n- ### [9\\.6 The Metropolis–Hastings algorithm](https:\/\/www.oreilly.com\/library\/view\/bayesian-statistics-an\/9781118359778\/OEBPS\/c09-sec1-0006.htm)\n- ### [9\\.7 Introduction to WinBUGS and OpenBUGS](https:\/\/www.oreilly.com\/library\/view\/bayesian-statistics-an\/9781118359778\/OEBPS\/c09-sec1-0007.htm)\n- ### [9\\.8 Generalized linear models](https:\/\/www.oreilly.com\/library\/view\/bayesian-statistics-an\/9781118359778\/OEBPS\/c09-sec1-0008.htm)\n- ### [9\\.9 Exercises on Chapter 9](https:\/\/www.oreilly.com\/library\/view\/bayesian-statistics-an\/9781118359778\/OEBPS\/c09-sec1-0009.htm)\n- ### [Chapter 10: Some approximate methods](https:\/\/www.oreilly.com\/library\/view\/bayesian-statistics-an\/9781118359778\/OEBPS\/9781118359778_epub_ch_10.htm)\n- ### [10\\.1 Bayesian importance sampling](https:\/\/www.oreilly.com\/library\/view\/bayesian-statistics-an\/9781118359778\/OEBPS\/c10-sec1-0001.htm)\n- ### [10\\.2 Variational Bayesian methods: simple case](https:\/\/www.oreilly.com\/library\/view\/bayesian-statistics-an\/9781118359778\/OEBPS\/c10-sec1-0002.htm)\n- ### [10\\.3 Variational Bayesian methods: general case](https:\/\/www.oreilly.com\/library\/view\/bayesian-statistics-an\/9781118359778\/OEBPS\/c10-sec1-0003.htm)\n- ### [10\\.4 ABC: Approximate Bayesian Computation](https:\/\/www.oreilly.com\/library\/view\/bayesian-statistics-an\/9781118359778\/OEBPS\/c10-sec1-0004.htm)\n- ### [10\\.5 Reversible jump Markov chain Monte Carlo](https:\/\/www.oreilly.com\/library\/view\/bayesian-statistics-an\/9781118359778\/OEBPS\/c10-sec1-0005.htm)\n- ### [10\\.6 Exercises on Chapter 10](https:\/\/www.oreilly.com\/library\/view\/bayesian-statistics-an\/9781118359778\/OEBPS\/c10-sec1-0006.htm)\n- ### [Appendix A: Common statistical distributions](https:\/\/www.oreilly.com\/library\/view\/bayesian-statistics-an\/9781118359778\/OEBPS\/9781118359778_epub_bm_01.htm)\n- ### [A.1 Normal distribution](https:\/\/www.oreilly.com\/library\/view\/bayesian-statistics-an\/9781118359778\/OEBPS\/c1-sec1-0001.htm)\n- ### [A.2 Chi-squared distribution](https:\/\/www.oreilly.com\/library\/view\/bayesian-statistics-an\/9781118359778\/OEBPS\/c1-sec1-0002.htm)\n- ### [A.3 Normal approximation to chi-squared](https:\/\/www.oreilly.com\/library\/view\/bayesian-statistics-an\/9781118359778\/OEBPS\/c1-sec1-0003.htm)\n- ### [A.4 Gamma distribution](https:\/\/www.oreilly.com\/library\/view\/bayesian-statistics-an\/9781118359778\/OEBPS\/c1-sec1-0004.htm)\n- ### [A.5 Inverse chi-squared distribution](https:\/\/www.oreilly.com\/library\/view\/bayesian-statistics-an\/9781118359778\/OEBPS\/c1-sec1-0005.htm)\n- ### [A.6 Inverse chi distribution](https:\/\/www.oreilly.com\/library\/view\/bayesian-statistics-an\/9781118359778\/OEBPS\/c1-sec1-0006.htm)\n- ### [A.7 Log chi-squared distribution](https:\/\/www.oreilly.com\/library\/view\/bayesian-statistics-an\/9781118359778\/OEBPS\/c1-sec1-0007.htm)\n- ### [A.8 Student’s t distribution](https:\/\/www.oreilly.com\/library\/view\/bayesian-statistics-an\/9781118359778\/OEBPS\/c1-sec1-0008.htm)\n- ### [A.9 Normal\/chi-squared distribution](https:\/\/www.oreilly.com\/library\/view\/bayesian-statistics-an\/9781118359778\/OEBPS\/c1-sec1-0009.htm)\n- ### [A.10 Beta distribution](https:\/\/www.oreilly.com\/library\/view\/bayesian-statistics-an\/9781118359778\/OEBPS\/c1-sec1-00010.htm)\n- ### [A.11 Binomial distribution](https:\/\/www.oreilly.com\/library\/view\/bayesian-statistics-an\/9781118359778\/OEBPS\/c1-sec1-00011.htm)\n- ### [A.12 Poisson distribution](https:\/\/www.oreilly.com\/library\/view\/bayesian-statistics-an\/9781118359778\/OEBPS\/c1-sec1-00012.htm)\n- ### [A.13 Negative binomial distribution](https:\/\/www.oreilly.com\/library\/view\/bayesian-statistics-an\/9781118359778\/OEBPS\/c1-sec1-00013.htm)\n- ### [A.14 Hypergeometric distribution](https:\/\/www.oreilly.com\/library\/view\/bayesian-statistics-an\/9781118359778\/OEBPS\/c1-sec1-00014.htm)\n- ### [A.15 Uniform distribution](https:\/\/www.oreilly.com\/library\/view\/bayesian-statistics-an\/9781118359778\/OEBPS\/c1-sec1-00015.htm)\n- ### [A.16 Pareto distribution](https:\/\/www.oreilly.com\/library\/view\/bayesian-statistics-an\/9781118359778\/OEBPS\/c1-sec1-00016.htm)\n- ### [A.17 Circular normal distribution](https:\/\/www.oreilly.com\/library\/view\/bayesian-statistics-an\/9781118359778\/OEBPS\/c1-sec1-00017.htm)\n- ### [A.18 Behrens’ distribution](https:\/\/www.oreilly.com\/library\/view\/bayesian-statistics-an\/9781118359778\/OEBPS\/c1-sec1-00018.htm)\n- ### [A.19 Snedecor’s F distribution](https:\/\/www.oreilly.com\/library\/view\/bayesian-statistics-an\/9781118359778\/OEBPS\/c1-sec1-00019.htm)\n- ### [A.20 Fisher’s z distribution](https:\/\/www.oreilly.com\/library\/view\/bayesian-statistics-an\/9781118359778\/OEBPS\/c1-sec1-00020.htm)\n- ### [A.21 Cauchy distribution](https:\/\/www.oreilly.com\/library\/view\/bayesian-statistics-an\/9781118359778\/OEBPS\/c1-sec1-00021.htm)\n- ### [A.22 The probability that one beta variable is greater than another](https:\/\/www.oreilly.com\/library\/view\/bayesian-statistics-an\/9781118359778\/OEBPS\/c1-sec1-00022.htm)\n- ### [A.23 Bivariate normal distribution](https:\/\/www.oreilly.com\/library\/view\/bayesian-statistics-an\/9781118359778\/OEBPS\/c1-sec1-00023.htm)\n- ### [A.24 Multivariate normal distribution](https:\/\/www.oreilly.com\/library\/view\/bayesian-statistics-an\/9781118359778\/OEBPS\/c1-sec1-00024.htm)\n- ### [A.25 Distribution of the correlation coefficient](https:\/\/www.oreilly.com\/library\/view\/bayesian-statistics-an\/9781118359778\/OEBPS\/c1-sec1-00025.htm)\n- ### [Appendix B: Tables](https:\/\/www.oreilly.com\/library\/view\/bayesian-statistics-an\/9781118359778\/OEBPS\/9781118359778_epub_bm_02.htm)\n- ### [Appendix C: R programs](https:\/\/www.oreilly.com\/library\/view\/bayesian-statistics-an\/9781118359778\/OEBPS\/9781118359778_epub_bm_03.htm)\n- ### [Appendix D: Further reading](https:\/\/www.oreilly.com\/library\/view\/bayesian-statistics-an\/9781118359778\/OEBPS\/9781118359778_epub_bm_04.htm)\n- ### [D.1 Robustness](https:\/\/www.oreilly.com\/library\/view\/bayesian-statistics-an\/9781118359778\/OEBPS\/FR-sec1-0001.htm)\n- ### [D.2 Nonparametric methods](https:\/\/www.oreilly.com\/library\/view\/bayesian-statistics-an\/9781118359778\/OEBPS\/FR-sec1-0002.htm)\n- ### [D.3 Multivariate estimation](https:\/\/www.oreilly.com\/library\/view\/bayesian-statistics-an\/9781118359778\/OEBPS\/FR-sec1-0003.htm)\n- ### [D.4 Time series and forecasting](https:\/\/www.oreilly.com\/library\/view\/bayesian-statistics-an\/9781118359778\/OEBPS\/FR-sec1-0004.htm)\n- ### [D.5 Sequential methods](https:\/\/www.oreilly.com\/library\/view\/bayesian-statistics-an\/9781118359778\/OEBPS\/FR-sec1-0005.htm)\n- ### [D.6 Numerical methods](https:\/\/www.oreilly.com\/library\/view\/bayesian-statistics-an\/9781118359778\/OEBPS\/FR-sec1-0006.htm)\n- ### [D.7 Bayesian networks](https:\/\/www.oreilly.com\/library\/view\/bayesian-statistics-an\/9781118359778\/OEBPS\/FR-sec1-0007.htm)\n- ### [D.8 General reading](https:\/\/www.oreilly.com\/library\/view\/bayesian-statistics-an\/9781118359778\/OEBPS\/FR-sec1-0008.htm)\n- ### [References](https:\/\/www.oreilly.com\/library\/view\/bayesian-statistics-an\/9781118359778\/OEBPS\/9781118359778_epub_bm_05.htm)\n- ### [Index](https:\/\/www.oreilly.com\/library\/view\/bayesian-statistics-an\/9781118359778\/OEBPS\/9781118359778_epub_bm_06.htm)\n\nShow More\n\n### Overview\nBayesian Statistics is the school of thought that combines prior beliefs with the likelihood of a hypothesis to arrive at posterior beliefs. The first edition of Peter Lee's book appeared in 1989, but the subject has moved ever onwards, with increasing emphasis on Monte Carlo based techniques.\n\nThis new fourth edition looks at recent techniques such as variational methods, Bayesian importance sampling, approximate Bayesian computation and Reversible Jump Markov Chain Monte Carlo (RJMCMC), providing a concise account of the way in which the Bayesian approach to statistics develops as well as how it contrasts with the conventional approach. The theory is built up step by step, and important notions such as sufficiency are brought out of a discussion of the salient features of specific examples.\n\n*This edition:*\n\n- Includes expanded coverage of Gibbs sampling, including more numerical examples and treatments of OpenBUGS, R2WinBUGS and R2OpenBUGS.\n- Presents significant new material on recent techniques such as Bayesian importance sampling, variational Bayes, Approximate Bayesian Computation (ABC) and Reversible Jump Markov Chain Monte Carlo (RJMCMC).\n- Provides extensive examples throughout the book to complement the theory presented.\n- Accompanied by a supporting website featuring new material and solutions.\n\nMore and more students are realizing that they need to learn Bayesian statistics to meet their academic and professional goals. This book is best suited for use as a main text in courses on Bayesian statistics for third and fourth year undergraduates and postgraduate students.\n\n##### Become an O’Reilly member and get unlimited access to this title plus top books and audiobooks from O’Reilly and nearly 200 top publishers, thousands of courses curated by job role, 150+ live events each month, and much more.\n[Read nowUnlock full access](https:\/\/www.oreilly.com\/start-trial\/?next=\/library\/view\/bayesian-statistics-an\/9781118359778\/)\n\n### More than 5,000 organizations count on O’Reilly\n![AirBnb](https:\/\/www.oreilly.com\/library\/view\/dist\/AirBnb-DGMKJRKH.svg)![BlueOrigin](https:\/\/www.oreilly.com\/library\/view\/dist\/BlueOrigin-4RWFILGY.svg)![Electronic Arts](https:\/\/www.oreilly.com\/library\/view\/dist\/EA-7HTQJYZU.svg)![HomeDepot](https:\/\/www.oreilly.com\/library\/view\/dist\/HomeDepot-WLPY677N.svg)![Nasdaq](https:\/\/www.oreilly.com\/library\/view\/dist\/Nasdaq-4FUP2MSJ.svg)![Rakuten](https:\/\/www.oreilly.com\/library\/view\/dist\/Rakuten-BLMSPBIO.svg)![Tata Consultancy Services](https:\/\/www.oreilly.com\/library\/view\/dist\/TCS-NRQ65RC6.svg)\n***\n![QuotationMark](https:\/\/www.oreilly.com\/library\/view\/dist\/QuotationMark-QYP5HNGW.svg)O’Reilly covers everything we've got, with content to help us build a world-class technology community, upgrade the capabilities and competencies of our teams, and improve overall team performance as well as their engagement.\n\n##### Julian F.\nHead of Cybersecurity\n\n![QuotationMark](https:\/\/www.oreilly.com\/library\/view\/dist\/QuotationMark-QYP5HNGW.svg)I wanted to learn C and C++, but it didn't click for me until I picked up an O'Reilly book. 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It's worth its weight in gold, in terms of what it allows me to do.\n\n##### Mark W.\nEmbedded Software Engineer\n\n### You might also like\n[![Statistical Rethinking, 2nd Edition](https:\/\/www.oreilly.com\/library\/cover\/9780429639142\/300w\/)](https:\/\/www.oreilly.com\/library\/view\/-\/9780429639142\/)\n\n[Statistical Rethinking, 2nd Edition](https:\/\/www.oreilly.com\/library\/view\/-\/9780429639142\/)\n\nRichard McElreath\n\n[![Bayesian Data Analysis, Third Edition, 3rd Edition](https:\/\/www.oreilly.com\/library\/cover\/9781439898222\/300w\/)](https:\/\/www.oreilly.com\/library\/view\/-\/9781439898222\/)\n\n[Bayesian Data Analysis, Third Edition, 3rd Edition](https:\/\/www.oreilly.com\/library\/view\/-\/9781439898222\/)\n\nAndrew Gelman, John B. Carlin, Hal S. Stern, David B. Dunson, Aki Vehtari, Donald B. Rubin\n\n[![Bayesian Statistics the Fun Way](https:\/\/www.oreilly.com\/library\/cover\/9781098122492\/300w\/)](https:\/\/www.oreilly.com\/library\/view\/-\/9781098122492\/)\n\n[Bayesian Statistics the Fun Way](https:\/\/www.oreilly.com\/library\/view\/-\/9781098122492\/)\n\nWill Kurt\n\n[![Statistical Rethinking](https:\/\/www.oreilly.com\/library\/cover\/9781482253481\/300w\/)](https:\/\/www.oreilly.com\/library\/view\/-\/9781482253481\/)\n\n[Statistical Rethinking](https:\/\/www.oreilly.com\/library\/view\/-\/9781482253481\/)\n\nRichard McElreath\n\n### Publisher Resources\nISBN: 9781118359778[Purchase book](http:\/\/www.wiley.com\/remtitle.cgi?isbn=1118332571)\n\nFollow us\n\n## [About O'Reilly](https:\/\/www.oreilly.com\/about\/)\n- [Teach\/Write\/Train](https:\/\/www.oreilly.com\/work-with-us.html)\n- [Careers](https:\/\/www.oreilly.com\/careers\/)\n- [O'Reilly News](https:\/\/www.oreilly.com\/press\/)\n- [Media Coverage](https:\/\/www.oreilly.com\/press\/media-coverage.html)\n- [Community Partners](https:\/\/www.oreilly.com\/partner\/signup.csp)\n- [Affiliate Program](https:\/\/www.oreilly.com\/affiliates\/)\n- [Submit an RFP](https:\/\/www.oreilly.com\/online-learning\/rfp.html)\n- [Diversity](https:\/\/www.oreilly.com\/diversity\/)\n- [Content Sponsorship](https:\/\/www.oreilly.com\/content-marketing-solutions.html)\n\n## [Support](https:\/\/www.oreilly.com\/online-learning\/support\/)\n- [Contact Us](https:\/\/www.oreilly.com\/about\/contact.html)\n- [Newsletters](https:\/\/www.oreilly.com\/emails\/newsletters\/)\n- [Privacy Policy](https:\/\/www.oreilly.com\/privacy.html)\n- [AI Policy](https:\/\/www.oreilly.com\/about\/oreilly-approach-to-generative-ai.html)\n\n## [International](https:\/\/www.oreilly.com\/library\/view\/bayesian-statistics-an\/9781118359778\/)\n- [Australia & New Zealand](https:\/\/www.oreilly.com\/online-learning\/anz.html)\n- [Japan](https:\/\/www.oreilly.co.jp\/index.shtml)\n\n## Download the O'Reilly App\nTake O'Reilly with you and learn anywhere, anytime on your phone and tablet.\n\n- [![Apple app store](https:\/\/cdn.oreillystatic.com\/oreilly\/images\/app-store-logo.png)](https:\/\/itunes.apple.com\/us\/app\/safari-to-go\/id881697395 \"Download in the Apple App Store\")\n- [![Google play store](https:\/\/cdn.oreillystatic.com\/oreilly\/images\/google-play-logo.png)](https:\/\/play.google.com\/store\/apps\/details?id=com.safariflow.queue)\n\n## Watch on Your Big Screen\nView all O'Reilly videos, virtual conferences, and live events on your home TV.\n\n- [![Roku Players and TVs](https:\/\/cdn.oreillystatic.com\/oreilly\/images\/roku-tv-logo.png)](https:\/\/channelstore.roku.com\/details\/c9d25fa651f0ad84e484b0dfd4b20172:856a240ad268961983e91ae52c1e1e5c\/oreilly \"O'Reilly on Roku\")\n- [![Amazon appstore](https:\/\/cdn.oreillystatic.com\/oreilly\/images\/amazon-appstore-logo.png)](https:\/\/www.amazon.com\/OReilly-Media-Inc\/dp\/B087YYHL5C\/ref=sr_1_2?dchild=1&keywords=oreilly&qid=1604964116&s=mobile-apps&sr=1-2 \"O'Reilly on Amazon Fire TV\")\n\n[![O'Reilly home](https:\/\/cdn.oreillystatic.com\/images\/sitewide-headers\/oreilly_logo_mark_red.svg)](https:\/\/www.oreilly.com\/ \"home page\")\n\n[Do not sell or share my personal information](https:\/\/www.oreilly.com\/privacy.html?donotsell=show).\n\n© 2025, O'Reilly Media, Inc. 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This new fourth edition looks at recent techniques such as variational methods, Bayesian importance sampling, approximate Bayesian computation and Reversible Jump Markov Chain Monte Carlo (RJMCMC), providing a concise account of the way in which the Bayesian approach to statistics develops as well as how it contrasts with the conventional approach. The theory is built up step by step, and important notions such as sufficiency are brought out of a discussion of the salient features of specific examples. *This edition:* Includes expanded coverage of Gibbs sampling, including more numerical examples and treatments of OpenBUGS, R2WinBUGS and R2OpenBUGS. Presents significant new material on recent techniques such as Bayesian importance sampling, variational Bayes, Approximate Bayesian Computation (ABC) and Reversible Jump Markov Chain Monte Carlo (RJMCMC). Provides extensive examples throughout the book to complement the theory presented. Accompanied by a supporting website featuring new material and solutions. More and more students are realizing that they need to learn Bayesian statistics to meet their academic and professional goals. This book is best suited for use as a main text in courses on Bayesian statistics for third and fourth year undergraduates and postgraduate students.\n\n##### Become an O’Reilly member and get unlimited access to this title plus top books and audiobooks from O’Reilly and nearly 200 top publishers, thousands of courses curated by job role, 150+ live events each month, and much more.\n[Read nowUnlock full access](https:\/\/www.oreilly.com\/start-trial\/?next=\/library\/view\/bayesian-statistics-an\/9781118359778\/)\n\n### More than 5,000 organizations count on O’Reilly\n![AirBnb](https:\/\/www.oreilly.com\/library\/view\/dist\/AirBnb-DGMKJRKH.svg)![BlueOrigin](https:\/\/www.oreilly.com\/library\/view\/dist\/BlueOrigin-4RWFILGY.svg)![Electronic Arts](https:\/\/www.oreilly.com\/library\/view\/dist\/EA-7HTQJYZU.svg)![HomeDepot](https:\/\/www.oreilly.com\/library\/view\/dist\/HomeDepot-WLPY677N.svg)![Nasdaq](https:\/\/www.oreilly.com\/library\/view\/dist\/Nasdaq-4FUP2MSJ.svg)![Rakuten](https:\/\/www.oreilly.com\/library\/view\/dist\/Rakuten-BLMSPBIO.svg)![Tata Consultancy Services](https:\/\/www.oreilly.com\/library\/view\/dist\/TCS-NRQ65RC6.svg)\n***\n![QuotationMark](https:\/\/www.oreilly.com\/library\/view\/dist\/QuotationMark-QYP5HNGW.svg)O’Reilly covers everything we've got, with content to help us build a world-class technology community, upgrade the capabilities and competencies of our teams, and improve overall team performance as well as their engagement.\n\n##### Julian F.\n\n![QuotationMark](https:\/\/www.oreilly.com\/library\/view\/dist\/QuotationMark-QYP5HNGW.svg)I wanted to learn C and C++, but it didn't click for me until I picked up an O'Reilly book. 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It's worth its weight in gold, in terms of what it allows me to do.\n\n##### Mark W.\n\n### You might also like\n[![Statistical Rethinking, 2nd Edition](https:\/\/www.oreilly.com\/library\/cover\/9780429639142\/300w\/)](https:\/\/www.oreilly.com\/library\/view\/-\/9780429639142\/)\n\n[![Bayesian Data Analysis, Third Edition, 3rd Edition](https:\/\/www.oreilly.com\/library\/cover\/9781439898222\/300w\/)](https:\/\/www.oreilly.com\/library\/view\/-\/9781439898222\/)\n\n[![Bayesian Statistics the Fun Way](https:\/\/www.oreilly.com\/library\/cover\/9781098122492\/300w\/)](https:\/\/www.oreilly.com\/library\/view\/-\/9781098122492\/)\n\n[![Statistical Rethinking](https:\/\/www.oreilly.com\/library\/cover\/9781482253481\/300w\/)](https:\/\/www.oreilly.com\/library\/view\/-\/9781482253481\/)","meta_canonical":null}

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Boilerpipe Text	Overview Bayesian Statistics is the school of thought that combines prior beliefs with the likelihood of a hypothesis to arrive at posterior beliefs. The first edition of Peter Lee's book appeared in 1989, but the subject has moved ever onwards, with increasing emphasis on Monte Carlo based techniques. This new fourth edition looks at recent techniques such as variational methods, Bayesian importance sampling, approximate Bayesian computation and Reversible Jump Markov Chain Monte Carlo (RJMCMC), providing a concise account of the way in which the Bayesian approach to statistics develops as well as how it contrasts with the conventional approach. The theory is built up step by step, and important notions such as sufficiency are brought out of a discussion of the salient features of specific examples. This edition: Includes expanded coverage of Gibbs sampling, including more numerical examples and treatments of OpenBUGS, R2WinBUGS and R2OpenBUGS. Presents significant new material on recent techniques such as Bayesian importance sampling, variational Bayes, Approximate Bayesian Computation (ABC) and Reversible Jump Markov Chain Monte Carlo (RJMCMC). Provides extensive examples throughout the book to complement the theory presented. Accompanied by a supporting website featuring new material and solutions. More and more students are realizing that they need to learn Bayesian statistics to meet their academic and professional goals. This book is best suited for use as a main text in courses on Bayesian statistics for third and fourth year undergraduates and postgraduate students. Become an O’Reilly member and get unlimited access to this title plus top books and audiobooks from O’Reilly and nearly 200 top publishers, thousands of courses curated by job role, 150+ live events each month, and much more. Read now Unlock full access More than 5,000 organizations count on O’Reilly O’Reilly covers everything we've got, with content to help us build a world-class technology community, upgrade the capabilities and competencies of our teams, and improve overall team performance as well as their engagement. Julian F. I wanted to learn C and C++, but it didn't click for me until I picked up an O'Reilly book. When I went on the O’Reilly platform, I was astonished to find all the books there, plus live events and sandboxes so you could play around with the technology. Addison B. I’ve been on the O’Reilly platform for more than eight years. I use a couple of learning platforms, but I'm on O'Reilly more than anybody else. When you're there, you start learning. I'm never disappointed. Amir M. I'm always learning. So when I got on to O'Reilly, I was like a kid in a candy store. There are playlists. There are answers. There's on-demand training. It's worth its weight in gold, in terms of what it allows me to do. Mark W. You might also like
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[Radar Blog](https://www.oreilly.com/radar/) - [Buy Courses](https://www.oreilly.com/live/) * - [Plans](https://www.oreilly.com/online-learning/pricing.html) - [Sign In](https://www.oreilly.com/member/login/) - [Try Now](https://www.oreilly.com/online-learning/try-now.html) ![Bayesian Statistics: An Introduction, 4th Edition](https://www.oreilly.com/covers/urn:orm:book:9781118359778/300w/) book # Bayesian Statistics: An Introduction, 4th Edition ##### by [Peter M. Lee](https://www.oreilly.com/search/?query=author:"Peter%20M.%20Lee"&sort=relevance&highlight=true) September 2012 Intermediate to advanced 486 pages 10h 41m English [Wiley](https://www.oreilly.com/publisher/36d782fd-353a-4200-acec-dab22ff9a53c/) [Read nowUnlock full access](https://www.oreilly.com/start-trial/?next=/library/view/bayesian-statistics-an/9781118359778/) ### Contents - ### [Cover](https://www.oreilly.com/library/view/bayesian-statistics-an/9781118359778/OEBPS/9781118359778_epub_cov.htm) - ### [Title Page](https://www.oreilly.com/library/view/bayesian-statistics-an/9781118359778/OEBPS/9781118359778_epub_fm_01.htm) - ### [Copyright](https://www.oreilly.com/library/view/bayesian-statistics-an/9781118359778/OEBPS/9781118359778_epub_fm_02.htm) - ### [Dedication](https://www.oreilly.com/library/view/bayesian-statistics-an/9781118359778/OEBPS/9781118359778_epub_fm_03.htm) - ### [Preface](https://www.oreilly.com/library/view/bayesian-statistics-an/9781118359778/OEBPS/9781118359778_epub_fm_04.htm) - ### [Preface to the First Edition](https://www.oreilly.com/library/view/bayesian-statistics-an/9781118359778/OEBPS/9781118359778_epub_fm_05.htm) - ### [Chapter 1: Preliminaries](https://www.oreilly.com/library/view/bayesian-statistics-an/9781118359778/OEBPS/9781118359778_epub_ch_01.htm) - ### [1\.1 Probability and Bayes’ Theorem](https://www.oreilly.com/library/view/bayesian-statistics-an/9781118359778/OEBPS/c01-sec1-0001.htm) - ### [1\.2 Examples on Bayes’ Theorem](https://www.oreilly.com/library/view/bayesian-statistics-an/9781118359778/OEBPS/c01-sec1-0002.htm) - ### [1\.3 Random variables](https://www.oreilly.com/library/view/bayesian-statistics-an/9781118359778/OEBPS/c01-sec1-0003.htm) - ### [1\.4 Several random variables](https://www.oreilly.com/library/view/bayesian-statistics-an/9781118359778/OEBPS/c01-sec1-0004.htm) - ### [1\.5 Means and variances](https://www.oreilly.com/library/view/bayesian-statistics-an/9781118359778/OEBPS/c01-sec1-0005.htm) - ### [1\.6 Exercises on Chapter 1](https://www.oreilly.com/library/view/bayesian-statistics-an/9781118359778/OEBPS/c01-sec1-0006.htm) - ### [Chapter 2: Bayesian inference for the normal distribution](https://www.oreilly.com/library/view/bayesian-statistics-an/9781118359778/OEBPS/9781118359778_epub_ch_02.htm) - ### [2\.1 Nature of Bayesian inference](https://www.oreilly.com/library/view/bayesian-statistics-an/9781118359778/OEBPS/c02-sec1-0001.htm) - ### [2\.2 Normal prior and likelihood](https://www.oreilly.com/library/view/bayesian-statistics-an/9781118359778/OEBPS/c02-sec1-0002.htm) - ### [2\.3 Several normal observations with a normal prior](https://www.oreilly.com/library/view/bayesian-statistics-an/9781118359778/OEBPS/c02-sec1-0003.htm) - ### [2\.4 Dominant likelihoods](https://www.oreilly.com/library/view/bayesian-statistics-an/9781118359778/OEBPS/c02-sec1-0004.htm) - ### [2\.5 Locally uniform priors](https://www.oreilly.com/library/view/bayesian-statistics-an/9781118359778/OEBPS/c02-sec1-0005.htm) - ### [2\.6 Highest density regions](https://www.oreilly.com/library/view/bayesian-statistics-an/9781118359778/OEBPS/c02-sec1-0006.htm) - ### [2\.7 Normal variance](https://www.oreilly.com/library/view/bayesian-statistics-an/9781118359778/OEBPS/c02-sec1-0007.htm) - ### [2\.8 HDRs for the normal variance](https://www.oreilly.com/library/view/bayesian-statistics-an/9781118359778/OEBPS/c02-sec1-0008.htm) - ### [2\.9 The role of sufficiency](https://www.oreilly.com/library/view/bayesian-statistics-an/9781118359778/OEBPS/c02-sec1-0009.htm) - ### [2\.10 Conjugate prior distributions](https://www.oreilly.com/library/view/bayesian-statistics-an/9781118359778/OEBPS/c02-sec1-0010.htm) - ### [2\.11 The exponential family](https://www.oreilly.com/library/view/bayesian-statistics-an/9781118359778/OEBPS/c02-sec1-0011.htm) - ### [2\.12 Normal mean and variance both unknown](https://www.oreilly.com/library/view/bayesian-statistics-an/9781118359778/OEBPS/c02-sec1-0012.htm) - ### [2\.13 Conjugate joint prior for the normal distribution](https://www.oreilly.com/library/view/bayesian-statistics-an/9781118359778/OEBPS/c02-sec1-0013.htm) - ### [2\.14 Exercises on Chapter 2](https://www.oreilly.com/library/view/bayesian-statistics-an/9781118359778/OEBPS/c02-sec1-0014.htm) - ### [Chapter 3: Some other common distributions](https://www.oreilly.com/library/view/bayesian-statistics-an/9781118359778/OEBPS/9781118359778_epub_ch_03.htm) - ### [3\.1 The binomial distribution](https://www.oreilly.com/library/view/bayesian-statistics-an/9781118359778/OEBPS/c03-sec1-0001.htm) - ### [3\.2 Reference prior for the binomial likelihood](https://www.oreilly.com/library/view/bayesian-statistics-an/9781118359778/OEBPS/c03-sec1-0002.htm) - ### [3\.3 Jeffreys’ rule](https://www.oreilly.com/library/view/bayesian-statistics-an/9781118359778/OEBPS/c03-sec1-0003.htm) - ### [3\.4 The Poisson distribution](https://www.oreilly.com/library/view/bayesian-statistics-an/9781118359778/OEBPS/c03-sec1-0004.htm) - ### [3\.5 The uniform distribution](https://www.oreilly.com/library/view/bayesian-statistics-an/9781118359778/OEBPS/c03-sec1-0005.htm) - ### [3\.6 Reference prior for the uniform distribution](https://www.oreilly.com/library/view/bayesian-statistics-an/9781118359778/OEBPS/c03-sec1-0006.htm) - ### [3\.7 The tramcar problem](https://www.oreilly.com/library/view/bayesian-statistics-an/9781118359778/OEBPS/c03-sec1-0007.htm) - ### [3\.8 The first digit problem; invariant priors](https://www.oreilly.com/library/view/bayesian-statistics-an/9781118359778/OEBPS/c03-sec1-0008.htm) - ### [3\.9 The circular normal distribution](https://www.oreilly.com/library/view/bayesian-statistics-an/9781118359778/OEBPS/c03-sec1-0009.htm) - ### [3\.10 Approximations based on the likelihood](https://www.oreilly.com/library/view/bayesian-statistics-an/9781118359778/OEBPS/c03-sec1-0010.htm) - ### [3\.11 Reference posterior distributions](https://www.oreilly.com/library/view/bayesian-statistics-an/9781118359778/OEBPS/c03-sec1-0011.htm) - ### [3\.12 Exercises on Chapter 3](https://www.oreilly.com/library/view/bayesian-statistics-an/9781118359778/OEBPS/c03-sec1-0012.htm) - ### [Chapter 4: Hypothesis testing](https://www.oreilly.com/library/view/bayesian-statistics-an/9781118359778/OEBPS/9781118359778_epub_ch_04.htm) - ### [4\.1 Hypothesis testing](https://www.oreilly.com/library/view/bayesian-statistics-an/9781118359778/OEBPS/c04-sec1-0001.htm) - ### [4\.2 One-sided hypothesis tests](https://www.oreilly.com/library/view/bayesian-statistics-an/9781118359778/OEBPS/c04-sec1-0002.htm) - ### [4\.3 Lindley’s method](https://www.oreilly.com/library/view/bayesian-statistics-an/9781118359778/OEBPS/c04-sec1-0003.htm) - ### [4\.4 Point (or sharp) null hypotheses with prior information](https://www.oreilly.com/library/view/bayesian-statistics-an/9781118359778/OEBPS/c04-sec1-0004.htm) - ### [4\.5 Point null hypotheses for the normal distribution](https://www.oreilly.com/library/view/bayesian-statistics-an/9781118359778/OEBPS/c04-sec1-0005.htm) - ### [4\.6 The Doogian philosophy](https://www.oreilly.com/library/view/bayesian-statistics-an/9781118359778/OEBPS/c04-sec1-0006.htm) - ### [4\.7 Exercises on Chapter 4](https://www.oreilly.com/library/view/bayesian-statistics-an/9781118359778/OEBPS/c04-sec1-0007.htm) - ### [Chapter 5: Two-sample problems](https://www.oreilly.com/library/view/bayesian-statistics-an/9781118359778/OEBPS/9781118359778_epub_ch_05.htm) - ### [5\.1 Two-sample problems – both variances unknown](https://www.oreilly.com/library/view/bayesian-statistics-an/9781118359778/OEBPS/c05-sec1-0001.htm) - ### [5\.2 Variances unknown but equal](https://www.oreilly.com/library/view/bayesian-statistics-an/9781118359778/OEBPS/c05-sec1-0002.htm) - ### [5\.3 Variances unknown and unequal (Behrens–Fisher problem)](https://www.oreilly.com/library/view/bayesian-statistics-an/9781118359778/OEBPS/c05-sec1-0003.htm) - ### [5\.4 The Behrens–Fisher controversy](https://www.oreilly.com/library/view/bayesian-statistics-an/9781118359778/OEBPS/c05-sec1-0004.htm) - ### [5\.5 Inferences concerning a variance ratio](https://www.oreilly.com/library/view/bayesian-statistics-an/9781118359778/OEBPS/c05-sec1-0005.htm) - ### [5\.6 Comparison of two proportions; the \$2\\times 2\$ table](https://www.oreilly.com/library/view/bayesian-statistics-an/9781118359778/OEBPS/c05-sec1-0006.htm) - ### [5\.7 Exercises on Chapter 5](https://www.oreilly.com/library/view/bayesian-statistics-an/9781118359778/OEBPS/c05-sec1-0007.htm) - ### [Chapter 6: Correlation, regression and the analysis of variance](https://www.oreilly.com/library/view/bayesian-statistics-an/9781118359778/OEBPS/9781118359778_epub_ch_06.htm) - ### [6\.1 Theory of the correlation coefficient](https://www.oreilly.com/library/view/bayesian-statistics-an/9781118359778/OEBPS/c06-sec1-0001.htm) - ### [6\.2 Examples on the use of the correlation coefficient](https://www.oreilly.com/library/view/bayesian-statistics-an/9781118359778/OEBPS/c06-sec1-0007.htm) - ### [6\.3 Regression and the bivariate normal model](https://www.oreilly.com/library/view/bayesian-statistics-an/9781118359778/OEBPS/c06-sec1-0011.htm) - ### [6\.4 Conjugate prior for the bivariate regression model](https://www.oreilly.com/library/view/bayesian-statistics-an/9781118359778/OEBPS/c06-sec1-0021.htm) - ### [6\.5 Comparison of several means – the one way model](https://www.oreilly.com/library/view/bayesian-statistics-an/9781118359778/OEBPS/c06-sec1-0025.htm) - ### [6\.6 The two way layout](https://www.oreilly.com/library/view/bayesian-statistics-an/9781118359778/OEBPS/c06-sec1-0033.htm) - ### [6\.7 The general linear model](https://www.oreilly.com/library/view/bayesian-statistics-an/9781118359778/OEBPS/c06-sec1-0037.htm) - ### [6\.8 Exercises on Chapter 6](https://www.oreilly.com/library/view/bayesian-statistics-an/9781118359778/OEBPS/c06-sec1-0042.htm) - ### [Chapter 7: Other topics](https://www.oreilly.com/library/view/bayesian-statistics-an/9781118359778/OEBPS/9781118359778_epub_ch_07.htm) - ### [7\.1 The likelihood principle](https://www.oreilly.com/library/view/bayesian-statistics-an/9781118359778/OEBPS/c07-sec1-0001.htm) - ### [7\.2 The stopping rule principle](https://www.oreilly.com/library/view/bayesian-statistics-an/9781118359778/OEBPS/c07-sec1-0002.htm) - ### [7\.3 Informative stopping rules](https://www.oreilly.com/library/view/bayesian-statistics-an/9781118359778/OEBPS/c07-sec1-0003.htm) - ### [7\.4 The likelihood principle and reference priors](https://www.oreilly.com/library/view/bayesian-statistics-an/9781118359778/OEBPS/c07-sec1-0004.htm) - ### [7\.5 Bayesian decision theory](https://www.oreilly.com/library/view/bayesian-statistics-an/9781118359778/OEBPS/c07-sec1-0005.htm) - ### [7\.6 Bayes linear methods](https://www.oreilly.com/library/view/bayesian-statistics-an/9781118359778/OEBPS/c07-sec1-0006.htm) - ### [7\.7 Decision theory and hypothesis testing](https://www.oreilly.com/library/view/bayesian-statistics-an/9781118359778/OEBPS/c07-sec1-0007.htm) - ### [7\.8 Empirical Bayes methods](https://www.oreilly.com/library/view/bayesian-statistics-an/9781118359778/OEBPS/c07-sec1-0008.htm) - ### [7\.9 Exercises on Chapter 7](https://www.oreilly.com/library/view/bayesian-statistics-an/9781118359778/OEBPS/c07-sec1-0009.htm) - ### [Chapter 8: Hierarchical models](https://www.oreilly.com/library/view/bayesian-statistics-an/9781118359778/OEBPS/9781118359778_epub_ch_08.htm) - ### [8\.1 The idea of a hierarchical model](https://www.oreilly.com/library/view/bayesian-statistics-an/9781118359778/OEBPS/c08-sec1-0001.htm) - ### [8\.2 The hierarchical normal model](https://www.oreilly.com/library/view/bayesian-statistics-an/9781118359778/OEBPS/c08-sec1-0002.htm) - ### [8\.3 The baseball example](https://www.oreilly.com/library/view/bayesian-statistics-an/9781118359778/OEBPS/c08-sec1-0003.htm) - ### [8\.4 The Stein estimator](https://www.oreilly.com/library/view/bayesian-statistics-an/9781118359778/OEBPS/c08-sec1-0004.htm) - ### [8\.5 Bayesian analysis for an unknown overall mean](https://www.oreilly.com/library/view/bayesian-statistics-an/9781118359778/OEBPS/c08-sec1-0005.htm) - ### [8\.6 The general linear model revisited](https://www.oreilly.com/library/view/bayesian-statistics-an/9781118359778/OEBPS/c08-sec1-0006.htm) - ### [8\.7 Exercises on Chapter 8](https://www.oreilly.com/library/view/bayesian-statistics-an/9781118359778/OEBPS/c08-sec1-0007.htm) - ### [Chapter 9: The Gibbs sampler and other numerical methods](https://www.oreilly.com/library/view/bayesian-statistics-an/9781118359778/OEBPS/9781118359778_epub_ch_09.htm) - ### [9\.1 Introduction to numerical methods](https://www.oreilly.com/library/view/bayesian-statistics-an/9781118359778/OEBPS/c09-sec1-0001.htm) - ### [9\.2 The EM algorithm](https://www.oreilly.com/library/view/bayesian-statistics-an/9781118359778/OEBPS/c09-sec1-0002.htm) - ### [9\.3 Data augmentation by Monte Carlo](https://www.oreilly.com/library/view/bayesian-statistics-an/9781118359778/OEBPS/c09-sec1-0003.htm) - ### [9\.4 The Gibbs sampler](https://www.oreilly.com/library/view/bayesian-statistics-an/9781118359778/OEBPS/c09-sec1-0004.htm) - ### [9\.5 Rejection sampling](https://www.oreilly.com/library/view/bayesian-statistics-an/9781118359778/OEBPS/c09-sec1-0005.htm) - ### [9\.6 The Metropolis–Hastings algorithm](https://www.oreilly.com/library/view/bayesian-statistics-an/9781118359778/OEBPS/c09-sec1-0006.htm) - ### [9\.7 Introduction to WinBUGS and OpenBUGS](https://www.oreilly.com/library/view/bayesian-statistics-an/9781118359778/OEBPS/c09-sec1-0007.htm) - ### [9\.8 Generalized linear models](https://www.oreilly.com/library/view/bayesian-statistics-an/9781118359778/OEBPS/c09-sec1-0008.htm) - ### [9\.9 Exercises on Chapter 9](https://www.oreilly.com/library/view/bayesian-statistics-an/9781118359778/OEBPS/c09-sec1-0009.htm) - ### [Chapter 10: Some approximate methods](https://www.oreilly.com/library/view/bayesian-statistics-an/9781118359778/OEBPS/9781118359778_epub_ch_10.htm) - ### [10\.1 Bayesian importance sampling](https://www.oreilly.com/library/view/bayesian-statistics-an/9781118359778/OEBPS/c10-sec1-0001.htm) - ### [10\.2 Variational Bayesian methods: simple case](https://www.oreilly.com/library/view/bayesian-statistics-an/9781118359778/OEBPS/c10-sec1-0002.htm) - ### [10\.3 Variational Bayesian methods: general case](https://www.oreilly.com/library/view/bayesian-statistics-an/9781118359778/OEBPS/c10-sec1-0003.htm) - ### [10\.4 ABC: Approximate Bayesian Computation](https://www.oreilly.com/library/view/bayesian-statistics-an/9781118359778/OEBPS/c10-sec1-0004.htm) - ### [10\.5 Reversible jump Markov chain Monte Carlo](https://www.oreilly.com/library/view/bayesian-statistics-an/9781118359778/OEBPS/c10-sec1-0005.htm) - ### [10\.6 Exercises on Chapter 10](https://www.oreilly.com/library/view/bayesian-statistics-an/9781118359778/OEBPS/c10-sec1-0006.htm) - ### [Appendix A: Common statistical distributions](https://www.oreilly.com/library/view/bayesian-statistics-an/9781118359778/OEBPS/9781118359778_epub_bm_01.htm) - ### [A.1 Normal distribution](https://www.oreilly.com/library/view/bayesian-statistics-an/9781118359778/OEBPS/c1-sec1-0001.htm) - ### [A.2 Chi-squared distribution](https://www.oreilly.com/library/view/bayesian-statistics-an/9781118359778/OEBPS/c1-sec1-0002.htm) - ### [A.3 Normal approximation to chi-squared](https://www.oreilly.com/library/view/bayesian-statistics-an/9781118359778/OEBPS/c1-sec1-0003.htm) - ### [A.4 Gamma distribution](https://www.oreilly.com/library/view/bayesian-statistics-an/9781118359778/OEBPS/c1-sec1-0004.htm) - ### [A.5 Inverse chi-squared distribution](https://www.oreilly.com/library/view/bayesian-statistics-an/9781118359778/OEBPS/c1-sec1-0005.htm) - ### [A.6 Inverse chi distribution](https://www.oreilly.com/library/view/bayesian-statistics-an/9781118359778/OEBPS/c1-sec1-0006.htm) - ### [A.7 Log chi-squared distribution](https://www.oreilly.com/library/view/bayesian-statistics-an/9781118359778/OEBPS/c1-sec1-0007.htm) - ### [A.8 Student’s t distribution](https://www.oreilly.com/library/view/bayesian-statistics-an/9781118359778/OEBPS/c1-sec1-0008.htm) - ### [A.9 Normal/chi-squared distribution](https://www.oreilly.com/library/view/bayesian-statistics-an/9781118359778/OEBPS/c1-sec1-0009.htm) - ### [A.10 Beta distribution](https://www.oreilly.com/library/view/bayesian-statistics-an/9781118359778/OEBPS/c1-sec1-00010.htm) - ### [A.11 Binomial distribution](https://www.oreilly.com/library/view/bayesian-statistics-an/9781118359778/OEBPS/c1-sec1-00011.htm) - ### [A.12 Poisson distribution](https://www.oreilly.com/library/view/bayesian-statistics-an/9781118359778/OEBPS/c1-sec1-00012.htm) - ### [A.13 Negative binomial distribution](https://www.oreilly.com/library/view/bayesian-statistics-an/9781118359778/OEBPS/c1-sec1-00013.htm) - ### [A.14 Hypergeometric distribution](https://www.oreilly.com/library/view/bayesian-statistics-an/9781118359778/OEBPS/c1-sec1-00014.htm) - ### [A.15 Uniform distribution](https://www.oreilly.com/library/view/bayesian-statistics-an/9781118359778/OEBPS/c1-sec1-00015.htm) - ### [A.16 Pareto distribution](https://www.oreilly.com/library/view/bayesian-statistics-an/9781118359778/OEBPS/c1-sec1-00016.htm) - ### [A.17 Circular normal distribution](https://www.oreilly.com/library/view/bayesian-statistics-an/9781118359778/OEBPS/c1-sec1-00017.htm) - ### [A.18 Behrens’ distribution](https://www.oreilly.com/library/view/bayesian-statistics-an/9781118359778/OEBPS/c1-sec1-00018.htm) - ### [A.19 Snedecor’s F distribution](https://www.oreilly.com/library/view/bayesian-statistics-an/9781118359778/OEBPS/c1-sec1-00019.htm) - ### [A.20 Fisher’s z distribution](https://www.oreilly.com/library/view/bayesian-statistics-an/9781118359778/OEBPS/c1-sec1-00020.htm) - ### [A.21 Cauchy distribution](https://www.oreilly.com/library/view/bayesian-statistics-an/9781118359778/OEBPS/c1-sec1-00021.htm) - ### [A.22 The probability that one beta variable is greater than another](https://www.oreilly.com/library/view/bayesian-statistics-an/9781118359778/OEBPS/c1-sec1-00022.htm) - ### [A.23 Bivariate normal distribution](https://www.oreilly.com/library/view/bayesian-statistics-an/9781118359778/OEBPS/c1-sec1-00023.htm) - ### [A.24 Multivariate normal distribution](https://www.oreilly.com/library/view/bayesian-statistics-an/9781118359778/OEBPS/c1-sec1-00024.htm) - ### [A.25 Distribution of the correlation coefficient](https://www.oreilly.com/library/view/bayesian-statistics-an/9781118359778/OEBPS/c1-sec1-00025.htm) - ### [Appendix B: Tables](https://www.oreilly.com/library/view/bayesian-statistics-an/9781118359778/OEBPS/9781118359778_epub_bm_02.htm) - ### [Appendix C: R programs](https://www.oreilly.com/library/view/bayesian-statistics-an/9781118359778/OEBPS/9781118359778_epub_bm_03.htm) - ### [Appendix D: Further reading](https://www.oreilly.com/library/view/bayesian-statistics-an/9781118359778/OEBPS/9781118359778_epub_bm_04.htm) - ### [D.1 Robustness](https://www.oreilly.com/library/view/bayesian-statistics-an/9781118359778/OEBPS/FR-sec1-0001.htm) - ### [D.2 Nonparametric methods](https://www.oreilly.com/library/view/bayesian-statistics-an/9781118359778/OEBPS/FR-sec1-0002.htm) - ### [D.3 Multivariate estimation](https://www.oreilly.com/library/view/bayesian-statistics-an/9781118359778/OEBPS/FR-sec1-0003.htm) - ### [D.4 Time series and forecasting](https://www.oreilly.com/library/view/bayesian-statistics-an/9781118359778/OEBPS/FR-sec1-0004.htm) - ### [D.5 Sequential methods](https://www.oreilly.com/library/view/bayesian-statistics-an/9781118359778/OEBPS/FR-sec1-0005.htm) - ### [D.6 Numerical methods](https://www.oreilly.com/library/view/bayesian-statistics-an/9781118359778/OEBPS/FR-sec1-0006.htm) - ### [D.7 Bayesian networks](https://www.oreilly.com/library/view/bayesian-statistics-an/9781118359778/OEBPS/FR-sec1-0007.htm) - ### [D.8 General reading](https://www.oreilly.com/library/view/bayesian-statistics-an/9781118359778/OEBPS/FR-sec1-0008.htm) - ### [References](https://www.oreilly.com/library/view/bayesian-statistics-an/9781118359778/OEBPS/9781118359778_epub_bm_05.htm) - ### [Index](https://www.oreilly.com/library/view/bayesian-statistics-an/9781118359778/OEBPS/9781118359778_epub_bm_06.htm) Show More ### Overview Bayesian Statistics is the school of thought that combines prior beliefs with the likelihood of a hypothesis to arrive at posterior beliefs. The first edition of Peter Lee's book appeared in 1989, but the subject has moved ever onwards, with increasing emphasis on Monte Carlo based techniques. This new fourth edition looks at recent techniques such as variational methods, Bayesian importance sampling, approximate Bayesian computation and Reversible Jump Markov Chain Monte Carlo (RJMCMC), providing a concise account of the way in which the Bayesian approach to statistics develops as well as how it contrasts with the conventional approach. The theory is built up step by step, and important notions such as sufficiency are brought out of a discussion of the salient features of specific examples. This edition: - Includes expanded coverage of Gibbs sampling, including more numerical examples and treatments of OpenBUGS, R2WinBUGS and R2OpenBUGS. - Presents significant new material on recent techniques such as Bayesian importance sampling, variational Bayes, Approximate Bayesian Computation (ABC) and Reversible Jump Markov Chain Monte Carlo (RJMCMC). - Provides extensive examples throughout the book to complement the theory presented. - Accompanied by a supporting website featuring new material and solutions. More and more students are realizing that they need to learn Bayesian statistics to meet their academic and professional goals. 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Readable Markdown	### Overview Bayesian Statistics is the school of thought that combines prior beliefs with the likelihood of a hypothesis to arrive at posterior beliefs. The first edition of Peter Lee's book appeared in 1989, but the subject has moved ever onwards, with increasing emphasis on Monte Carlo based techniques. This new fourth edition looks at recent techniques such as variational methods, Bayesian importance sampling, approximate Bayesian computation and Reversible Jump Markov Chain Monte Carlo (RJMCMC), providing a concise account of the way in which the Bayesian approach to statistics develops as well as how it contrasts with the conventional approach. The theory is built up step by step, and important notions such as sufficiency are brought out of a discussion of the salient features of specific examples. This edition: Includes expanded coverage of Gibbs sampling, including more numerical examples and treatments of OpenBUGS, R2WinBUGS and R2OpenBUGS. Presents significant new material on recent techniques such as Bayesian importance sampling, variational Bayes, Approximate Bayesian Computation (ABC) and Reversible Jump Markov Chain Monte Carlo (RJMCMC). Provides extensive examples throughout the book to complement the theory presented. Accompanied by a supporting website featuring new material and solutions. More and more students are realizing that they need to learn Bayesian statistics to meet their academic and professional goals. This book is best suited for use as a main text in courses on Bayesian statistics for third and fourth year undergraduates and postgraduate students. ##### Become an O’Reilly member and get unlimited access to this title plus top books and audiobooks from O’Reilly and nearly 200 top publishers, thousands of courses curated by job role, 150+ live events each month, and much more. [Read nowUnlock full access](https://www.oreilly.com/start-trial/?next=/library/view/bayesian-statistics-an/9781118359778/) ### More than 5,000 organizations count on O’Reilly ![AirBnb](https://www.oreilly.com/library/view/dist/AirBnb-DGMKJRKH.svg)![BlueOrigin](https://www.oreilly.com/library/view/dist/BlueOrigin-4RWFILGY.svg)![Electronic Arts](https://www.oreilly.com/library/view/dist/EA-7HTQJYZU.svg)![HomeDepot](https://www.oreilly.com/library/view/dist/HomeDepot-WLPY677N.svg)![Nasdaq](https://www.oreilly.com/library/view/dist/Nasdaq-4FUP2MSJ.svg)![Rakuten](https://www.oreilly.com/library/view/dist/Rakuten-BLMSPBIO.svg)![Tata Consultancy Services](https://www.oreilly.com/library/view/dist/TCS-NRQ65RC6.svg) *** ![QuotationMark](https://www.oreilly.com/library/view/dist/QuotationMark-QYP5HNGW.svg)O’Reilly covers everything we've got, with content to help us build a world-class technology community, upgrade the capabilities and competencies of our teams, and improve overall team performance as well as their engagement. ##### Julian F. ![QuotationMark](https://www.oreilly.com/library/view/dist/QuotationMark-QYP5HNGW.svg)I wanted to learn C and C++, but it didn't click for me until I picked up an O'Reilly book. When I went on the O’Reilly platform, I was astonished to find all the books there, plus live events and sandboxes so you could play around with the technology. ##### Addison B. ![QuotationMark](https://www.oreilly.com/library/view/dist/QuotationMark-QYP5HNGW.svg)I’ve been on the O’Reilly platform for more than eight years. I use a couple of learning platforms, but I'm on O'Reilly more than anybody else. When you're there, you start learning. I'm never disappointed. ##### Amir M. ![QuotationMark](https://www.oreilly.com/library/view/dist/QuotationMark-QYP5HNGW.svg)I'm always learning. So when I got on to O'Reilly, I was like a kid in a candy store. There are playlists. There are answers. There's on-demand training. It's worth its weight in gold, in terms of what it allows me to do. ##### Mark W. ### You might also like [![Statistical Rethinking, 2nd Edition](https://www.oreilly.com/library/cover/9780429639142/300w/)](https://www.oreilly.com/library/view/-/9780429639142/) [![Bayesian Data Analysis, Third Edition, 3rd Edition](https://www.oreilly.com/library/cover/9781439898222/300w/)](https://www.oreilly.com/library/view/-/9781439898222/) [![Bayesian Statistics the Fun Way](https://www.oreilly.com/library/cover/9781098122492/300w/)](https://www.oreilly.com/library/view/-/9781098122492/) [![Statistical Rethinking](https://www.oreilly.com/library/cover/9781482253481/300w/)](https://www.oreilly.com/library/view/-/9781482253481/)
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