{"id":24702243,"url":"https://github.com/storopoli/Bayesian-Statistics","last_synced_at":"2025-10-09T09:30:21.765Z","repository":{"id":45588077,"uuid":"479514103","full_name":"storopoli/Bayesian-Statistics","owner":"storopoli","description":"Bayesian statistics graduate 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Bayesian Statistics\n\n[![CC BY-SA 4.0](https://img.shields.io/badge/License-CC%20BY--SA%204.0-lightgrey.svg)](http://creativecommons.org/licenses/by-sa/4.0/)\n\n\u003cdiv class=\"figure\" style=\"text-align: center\"\u003e\n\n\u003cimg src=\"slides/images/memes/main.jpg\" alt=\"Bayesian for Everyone!\" width=\"500\" /\u003e\n\u003cp class=\"caption\"\u003e\nBayesian for Everyone!\n\u003c/p\u003e\n\n\u003c/div\u003e\n\nThis repository holds slides and code for a full Bayesian statistics graduate course.\n\n**Bayesian statistics** is an approach to inferential statistics based on Bayes' theorem,\nwhere available knowledge about parameters in a statistical model is updated with the information in observed data.\nThe background knowledge is expressed as a prior distribution and combined with observational data in the form of a likelihood function to determine the posterior distribution.\nThe posterior can also be used for making predictions about future events.\n\n**Bayesian statistics** is a departure from classical inferential statistics that prohibits probability statements about parameters and is based on asymptotically sampling infinite samples from a theoretical population and finding parameter values that maximize the likelihood function.\nMostly notorious is null-hypothesis significance testing (NHST) based on _p_-values.\nBayesian statistics **incorporate uncertainty** (and prior knowledge) by allowing probability statements about parameters,\nand the process of parameter value inference is a direct result of the **Bayes' theorem**.\n\n## Content\n\nThe whole content is a set of several slides found at [`the latest release`](https://github.com/storopoli/Bayesian-Statistics/releases/latest/download/slides.pdf) (382 slides).\nHere is a brief table of contents:\n\n1. **What is Bayesian Statistics?**\n1. **Common Probability Distributions**\n1. **Priors**\n1. **Bayesian Workflow**\n1. **Bayesian Linear Regression**\n1. **Bayesian Logistic Regression**\n1. **Bayesian Ordinal Regression**\n1. **Bayesian Regression with Count Data: Poisson Regression**\n1. **Robust Bayesian Regression**\n1. **Bayesian Sparse Regression**\n1. **Hierarchical Models**\n1. **Markov Chain Monte Carlo (MCMC) and Model Metrics**\n1. **Model Comparison: Cross-Validation and Other Metrics**\n\n## Probabilistic Programming Languages (PPLs)\n\nAlong with slides for the content, this repository also holds Stan code and also Turing code for all models.\nStan and Turing represents, respectively, the present and future of [probabilistic programming](https://en.wikipedia.org/wiki/Probabilistic_programming) languages.\n\nAll model files are tested in [GitHub Actions](https://github.com/storopoli/Bayesian-Statistics/actions/workflows/models.yml)\nagainst the latest Stan and Julia/Turing versions.\n\n### Stan\n\n[**Stan**](https://mc-stan.org) (Carpenter et al., 2017) Stan is a state-of-the-art platform for statistical modeling and high-performance statistical computation.\nThousands of users rely on Stan for statistical modeling, data analysis, and prediction in the social, biological, and physical sciences, engineering, and business.\n\nStan models are specified in its own language (similar to C++) and compiled into an executable binary that can generate Bayesian statistical inferences using a high-performance Markov Chain Montecarlo (MCMC).\n\nYou can find Stan models for all the content discussed in the slides at [`stan/`](stan/) folder.\n\n### Turing\n\n[**Turing**](http://turinglang.org/) (Ge, Xu \u0026 Ghahramani, 2018) is an ecosystem of [**Julia**](https://www.julialang.org) packages for Bayesian Inference using [probabilistic programming](https://en.wikipedia.org/wiki/Probabilistic_programming).\nModels specified using Turing are easy to read and write — models work the way you write them.\nLike everything in Julia, Turing is [fast](https://arxiv.org/abs/2002.02702).\n\nYou can find Turing models for all the content discussed in the slides at [`turing/`](turing/) folder.\n\n## Datasets\n\n- `kidiq` (linear regression): data from a survey of adult American women and their children\n  (a subsample from the National Longitudinal Survey of Youth).\n  Source: Gelman and Hill (2007).\n- `wells` (logistic regression): a survey of 3200 residents in a small area of Bangladesh suffering\n  from arsenic contamination of groundwater.\n  Respondents with elevated arsenic levels in their wells had been encouraged to switch their water source\n  to a safe public or private well in the nearby area\n  and the survey was conducted several years later to\n  learn which of the affected residents had switched wells.\n  Source: Gelman and Hill (2007).\n- `esoph` (ordinal regression): data from a case-control study of (o)esophageal cancer in Ille-et-Vilaine, France.\n  Source: Breslow and Day (1980).\n- `roaches` (Poisson regression): data on the efficacy of a pest management system at reducing the number of roaches in urban apartments.\n  Source: Gelman and Hill (2007).\n- `duncan` (robust regression): data from occupation's prestige filled with outliers.\n  Source: Duncan (1961).\n- `sparse_regression` (sparse regression): simulated data from the [`glmnet` R package](https://cran.r-project.org/package=glmnet).\n  Source: Tay, Narasimhan and Hastie (2023).\n- `cheese` (hierarchical models): data from cheese ratings.\n  A group of 10 rural and 10 urban raters rated 4 types of different cheeses (A, B, C and D) in two samples.\n  Source: Boatwright, McCulloch and Rossi (1999).\n\n## Author\n\nJose Storopoli, PhD - [ORCID](https://orcid.org/0000-0002-0559-5176) - \u003chttps://storopoli.io\u003e\n\n## How to use the content?\n\nThe content is licensed under a very permissive Creative Commons license (CC BY-SA).\nYou are mostly welcome to contribute with [issues](https://www.github.com/storopoli/Bayesian-Statistics/issues)\nand [pull requests](https://github.com/storopoli/Bayesian-Statistics/pulls).\nMy hope is to have **more people into Bayesian statistics**.\nThe content is aimed towards PhD candidates in applied sciences.\nI chose to provide an **intuitive approach** along with some rigorous mathematical formulations.\nI've made it to be how I would have liked to be introduced to Bayesian statistics.\n\nIf you want to build the slides locally without having to worry with [Typst](https://typst.app)\npackages, [install Nix](https://nixos.org/download.html) and run:\n\n```shell\nnix build github:storopoli/Bayesian-Statistics\n```\n\n## References\n\nThe references are divided in **books**, **papers**, **software**, and **datasets**.\n\n### Books\n\n- Gelman, A., Carlin, J. B., Stern, H. S., Dunson, D. B., Vehtari, A.,\n  \u0026 Rubin, D. B. (2013). _Bayesian Data Analysis_. Chapman and\n  Hall/CRC.\n- McElreath, R. (2020). _Statistical rethinking: A Bayesian course\n  with examples in R and Stan_. CRC press.\n- Gelman, A., Hill, J., \u0026 Vehtari, A. (2020). _Regression and other\n  stories_. Cambridge University Press.\n- Brooks, S., Gelman, A., Jones, G., \u0026 Meng, X.-L. (2011). _Handbook\n  of Markov Chain Monte Carlo_. CRC Press.\n  \u003chttp://books.google.com?id=qfRsAIKZ4rIC\u003e\n  - Geyer, C. J. (2011). Introduction to markov chain monte carlo.\n    In S. Brooks, A. Gelman, G. L. Jones, \u0026 X.-L. Meng (Eds.),\n    _Handbook of markov chain monte carlo_.\n\n### Papers\n\nThe papers section of the references are divided into **required** and **complementary**.\n\n#### Required\n\n- van de Schoot, R., Depaoli, S., King, R., Kramer, B., Märtens, K.,\n  Tadesse, M. G., Vannucci, M., Gelman, A., Veen, D., Willemsen, J., \u0026\n  Yau, C. (2021). Bayesian statistics and modelling. _Nature Reviews\n  Methods Primers_, _1_(1, 1), 1–26.\n  https://doi.org/[10.1038/s43586-020-00001-2](https://doi.org/10.1038/s43586-020-00001-2)\n- Gabry, J., Simpson, D., Vehtari, A., Betancourt, M., \u0026 Gelman, A.\n  (2019). Visualization in Bayesian workflow. _Journal of the Royal\n  Statistical Society: Series A (Statistics in Society)_, _182_(2),\n  389–402.\n  https://doi.org/[10.1111/rssa.12378](https://doi.org/10.1111/rssa.12378)\n- Gelman, A., Vehtari, A., Simpson, D., Margossian, C. C., Carpenter,\n  B., Yao, Y., Kennedy, L., Gabry, J., Bürkner, P.-C., \u0026 Modr’ak, M.\n  (2020, November 3). _Bayesian Workflow_.\n  \u003chttp://arxiv.org/abs/2011.01808\u003e\n- Benjamin, D. J., Berger, J. O., Johannesson, M., Nosek, B. A.,\n  Wagenmakers, E.-J., Berk, R., Bollen, K. A., Brembs, B., Brown, L.,\n  Camerer, C., Cesarini, D., Chambers, C. D., Clyde, M., Cook, T. D.,\n  De Boeck, P., Dienes, Z., Dreber, A., Easwaran, K., Efferson, C., …\n  Johnson, V. E. (2018). Redefine statistical significance. _Nature\n  Human Behaviour_, _2_(1), 6–10.\n  https://doi.org/[10.1038/s41562-017-0189-z](https://doi.org/10.1038/s41562-017-0189-z)\n- Etz, A. (2018). Introduction to the Concept of Likelihood and Its\n  Applications. _Advances in Methods and Practices in Psychological\n  Science_, _1_(1), 60–69.\n  https://doi.org/[10.1177/2515245917744314](https://doi.org/10.1177/2515245917744314)\n- Etz, A., Gronau, Q. F., Dablander, F., Edelsbrunner, P. A., \u0026\n  Baribault, B. (2018). How to become a Bayesian in eight easy steps:\n  An annotated reading list. _Psychonomic Bulletin \u0026 Review_, _25_(1),\n  219–234.\n  https://doi.org/[10.3758/s13423-017-1317-5](https://doi.org/10.3758/s13423-017-1317-5)\n- McShane, B. B., Gal, D., Gelman, A., Robert, C., \u0026 Tackett, J. L.\n  (2019). Abandon Statistical Significance. _American Statistician_,\n  _73_, 235–245.\n  https://doi.org/[10.1080/00031305.2018.1527253](https://doi.org/10.1080/00031305.2018.1527253)\n- Amrhein, V., Greenland, S., \u0026 McShane, B. (2019). Scientists rise up\n  against statistical significance. _Nature_, _567_(7748), 305–307.\n  https://doi.org/[10.1038/d41586-019-00857-9](https://doi.org/10.1038/d41586-019-00857-9)\n- Piironen, J. \u0026 Vehtari, A. (2017). Sparsity information and regularization in the\n  horseshoe and other shrinkage priors.\n  _Electronic Journal of Statistics_. _11_(2), 5018-5051.\n  https://doi.org/10.1214/17-EJS1337SI\n- van Ravenzwaaij, D., Cassey, P., \u0026 Brown, S. D. (2018). A simple\n  introduction to Markov Chain Monte–Carlo sampling. _Psychonomic\n  Bulletin and Review_, _25_(1), 143–154.\n  https://doi.org/[10.3758/s13423-016-1015-8](https://doi.org/10.3758/s13423-016-1015-8)\n- Vandekerckhove, J., Matzke, D., Wagenmakers, E.-J., \u0026 others.\n  (2015). Model comparison and the principle of parsimony. In J. R.\n  Busemeyer, Z. Wang, J. T. Townsend, \u0026 A. Eidels (Eds.), _Oxford\n  handbook of computational and mathematical psychology_ (pp.\n  300–319). Oxford University Press Oxford.\n- van de Schoot, R., Kaplan, D., Denissen, J., Asendorpf, J. B.,\n  Neyer, F. J., \u0026 van Aken, M. A. G. (2014). A Gentle Introduction to\n  Bayesian Analysis: Applications to Developmental Research. _Child\n  Development_, _85_(3), 842–860.\n  https://doi.org/[10.1111/cdev.12169](https://doi.org/10.1111/cdev.12169)\n  \u003cspan class=\"csl-block\"\u003e\\_eprint:\n  https://srcd.onlinelibrary.wiley.com/doi/pdf/10.1111/cdev.12169\u003c/span\u003e\n- Wagenmakers, E.-J. (2007). A practical solution to the pervasive\n  problems of p values. _Psychonomic Bulletin \u0026 Review_, _14_(5),\n  779–804.\n  https://doi.org/[10.3758/BF03194105](https://doi.org/10.3758/BF03194105)\n- Vandekerckhove, J., Matzke, D., Wagenmakers, E.-J., \u0026 others. (2015).\n  Model comparison and the principle of parsimony.\n  In J. R. Busemeyer, Z. Wang, J. T. Townsend, \u0026 A. Eidels (Eds.),\n  Oxford handbook of computational and mathematical psychology (pp. 300–319).\n  Oxford University Press Oxford.\n- Vehtari, A., Gelman, A., \u0026 Gabry, J. (2015). Practical Bayesian model evaluation\n  using leave-one-out cross-validation and WAIC.\n  https://doi.org/10.1007/s11222-016-9696-4\n\n#### Complementary\n\n- Cohen, J. (1994). The earth is round (p \u0026lt; .05). _American\n  Psychologist_, _49_(12), 997–1003.\n  https://doi.org/[10.1037/0003-066X.49.12.997](https://doi.org/10.1037/0003-066X.49.12.997)\n- Dienes, Z. (2011). Bayesian Versus Orthodox Statistics: Which Side\n  Are You On? _Perspectives on Psychological Science_, _6_(3),\n  274–290.\n  https://doi.org/[10.1177/1745691611406920](https://doi.org/10.1177/1745691611406920)\n- Etz, A., \u0026 Vandekerckhove, J. (2018). Introduction to Bayesian\n  Inference for Psychology. _Psychonomic Bulletin \u0026 Review_, _25_(1),\n  5–34.\n  https://doi.org/[10.3758/s13423-017-1262-3](https://doi.org/10.3758/s13423-017-1262-3)\n- J’unior, C. A. M. (2020). Quanto vale o valor-p? _Arquivos de\n  Ciências Do Esporte_, _7_(2).\n- Kerr, N. L. (1998). HARKing: Hypothesizing after the results are\n  known. _Personality and Social Psychology Review_, _2_(3), 196–217.\n  https://doi.org/[10.1207/s15327957pspr0203\\_4](https://doi.org/10.1207/s15327957pspr0203_4)\n- Kruschke, J. K., \u0026 Vanpaemel, W. (2015). Bayesian estimation in\n  hierarchical models. In J. R. Busemeyer, Z. Wang, J. T. Townsend,\n  \u0026 A. Eidels (Eds.), _The Oxford handbook of computational and\n  mathematical psychology_ (pp. 279–299). Oxford University Press\n  Oxford, UK.\n- Kruschke, J. K., \u0026 Liddell, T. M. (2018). Bayesian data analysis for\n  newcomers. _Psychonomic Bulletin \u0026 Review_, _25_(1), 155–177.\n  https://doi.org/[10.3758/s13423-017-1272-1](https://doi.org/10.3758/s13423-017-1272-1)\n- Kruschke, J. K., \u0026 Liddell, T. M. (2018). The Bayesian New\n  Statistics: Hypothesis testing, estimation, meta-analysis, and power\n  analysis from a Bayesian perspective. _Psychonomic Bulletin \u0026\n  Review_, _25_(1), 178–206.\n  https://doi.org/[10.3758/s13423-016-1221-4](https://doi.org/10.3758/s13423-016-1221-4)\n- Lakens, D., Adolfi, F. G., Albers, C. J., Anvari, F., Apps, M. A.\n  J., Argamon, S. E., Baguley, T., Becker, R. B., Benning, S. D.,\n  Bradford, D. E., Buchanan, E. M., Caldwell, A. R., Van Calster, B.,\n  Carlsson, R., Chen, S. C., Chung, B., Colling, L. J., Collins, G.\n  S., Crook, Z., … Zwaan, R. A. (2018). Justify your alpha. _Nature\n  Human Behaviour_, _2_(3), 168–171.\n  https://doi.org/[10.1038/s41562-018-0311-x](https://doi.org/10.1038/s41562-018-0311-x)\n- Morey, R. D., Hoekstra, R., Rouder, J. N., Lee, M. D., \u0026\n  Wagenmakers, E.-J. (2016). \u003cspan class=\"nocase\"\u003eThe fallacy of\n  placing confidence in confidence intervals\u003c/span\u003e. _Psychonomic\n  Bulletin \u0026 Review_, _23_(1), 103–123.\n  https://doi.org/[10.3758/s13423-015-0947-8](https://doi.org/10.3758/s13423-015-0947-8)\n- Murphy, K. R., \u0026 Aguinis, H. (2019). HARKing: How Badly Can\n  Cherry-Picking and Question Trolling Produce Bias in Published\n  Results? _Journal of Business and Psychology_, _34_(1).\n  https://doi.org/[10.1007/s10869-017-9524-7](https://doi.org/10.1007/s10869-017-9524-7)\n- Stark, P. B., \u0026 Saltelli, A. (2018). Cargo-cult statistics and\n  scientific crisis. _Significance_, _15_(4), 40–43.\n  https://doi.org/[10.1111/j.1740-9713.2018.01174.x](https://doi.org/10.1111/j.1740-9713.2018.01174.x)\n\n### Software\n\n- Carpenter, B., Gelman, A., Hoffman, M. D., Lee, D., Goodrich, B.,\n  Betancourt, M., Brubaker, M., Guo, J., Li, P., \u0026 Riddell, A. (2017).\n  Stan : A Probabilistic Programming Language. _Journal of Statistical\n  Software_, _76_(1).\n  https://doi.org/[10.18637/jss.v076.i01](https://doi.org/10.18637/jss.v076.i01)\n- Ge, H., Xu, K., \u0026 Ghahramani, Z. (2018). Turing: A Language for Flexible Probabilistic Inference. International Conference on Artificial Intelligence and Statistics, 1682–1690. http://proceedings.mlr.press/v84/ge18b.html\n- Tarek, M., Xu, K., Trapp, M., Ge, H., \u0026 Ghahramani, Z. (2020). DynamicPPL: Stan-like Speed for Dynamic Probabilistic Models. ArXiv:2002.02702 [Cs, Stat]. http://arxiv.org/abs/2002.02702\n- Xu, K., Ge, H., Tebbutt, W., Tarek, M., Trapp, M., \u0026 Ghahramani, Z. (2020). AdvancedHMC.jl: A robust, modular and efficient implementation of advanced HMC algorithms. Symposium on Advances in Approximate Bayesian Inference, 1–10. http://proceedings.mlr.press/v118/xu20a.html\n\n### Datasets\n\n- Boatwright, P., McCulloch, R., \u0026 Rossi, P. (1999). Account-level modeling for trade promotion: An application of a constrained parameter hierarchical model. _Journal of the American Statistical Association_, 94(448), 1063–1073.\n- Breslow, N. E. \u0026 Day, N. E. (1980). **Statistical Methods in Cancer Research. Volume 1: The Analysis of Case-Control Studies**. IARC Lyon / Oxford University Press.\n- Duncan, O. D. (1961). A socioeconomic index for all occupations. Class: Critical Concepts, 1, 388–426.\n- Tay JK, Narasimhan B, Hastie T (2023). Elastic Net Regularization Paths for All Generalized Linear Models. _Journal of Statistical Software_, 106(1), 1–31. doi:10.18637/jss.v106.i01.\n- Gelman, A., \u0026 Hill, J. (2007). **Data analysis using regression and\n  multilevel/hierarchical models**. Cambridge university press.\n\n## How to cite\n\nTo cite this course, please use:\n\n    Storopoli (2022). Bayesian Statistics: a graduate course. https://github.com/storopoli/Bayesian-Statistics.\n\nOr in BibTeX format ($\\LaTeX$):\n\n    @misc{storopoli2022bayesian,\n      author = {Storopoli, Jose},\n      title = {Bayesian Statistics: a graduate course},\n      url = {https://github.com/storopoli/Bayesian-Statistics},\n      year = {2022}\n    }\n\n## License\n\nThis content is licensed under [Creative Commons Attribution-ShareAlike 4.0 International](http://creativecommons.org/licenses/by-sa/4.0/).\n\n[![CC BY-SA 4.0](https://licensebuttons.net/l/by-sa/4.0/88x31.png)](http://creativecommons.org/licenses/by-sa/4.0/)\n","funding_links":["https://github.com/sponsors/storopoli"],"categories":["Uncategorized"],"sub_categories":["Uncategorized"],"project_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Fstoropoli%2FBayesian-Statistics","html_url":"https://awesome.ecosyste.ms/projects/github.com%2Fstoropoli%2FBayesian-Statistics","lists_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Fstoropoli%2FBayesian-Statistics/lists"}