Bayesian statistics for the social sciences by Ben Goodrich (provides a nice background to logic, probability as an extension to logic, the different schools of statistical inference, and subjectivity/objectivity)
Bayesian multiplicity control by Jim Berger. Contains a formal proof that sequential monitoring requires no multiplicity adjustment in the Bayesian context (slide 30).
# Resources* [fharrell.com](https://www.fharrell.com/#category=bayes)## Interactive Demonstrations {-}* [Interactive demo 1](http://rpsychologist.com/d3/bayes)* [Interactive demo 2](http://sumsar.net/best_online)* [Interactive demo of Bayesian decision theory](http://www.statsathome.com/2017/10/12/bayesian-decision-theory-made-ridiculously-simple)* [Bayesian inference for published clinical trials](http://medstats.atspace.cc/bayes.html)* [Bayesian analysis: two proportions](https://argoshare.is.ed.ac.uk/bayesian_two_proportions)* [Bayesian and Frequentist Side by Side](https://iupbsapps.shinyapps.io/KruschkeFreqAndBayesApp) interactive app by John Kruschke## Probability {-}* [Let's talk about probability](https://youtu.be/H5WjVgL6Nh4?si=O8-y1UXVCXE_OFPP) 25m video by Bill Press (**highly recommended**)* [Introduction to Probability](https://www.edx.org/course/introduction-to-probability-0), a free online course from Harvard by Joseph Blitzstein* [Introduction to probability and statistics](https://ocw.mit.edu/courses/mathematics/18-05-introduction-to-probability-and-statistics-spring-2014) from MIT by Jeremy Orloff and Jonathan Bloom* [Epistemological interpretation of probability](https://stats.stackexchange.com/a/643443/4253)## General {-}* [Application of Bayesian approaches in drug development: starting a virtuous cycle](https://www.nature.com/articles/s41573-023-00638-0) by Steve Ruberg et al* [Bayesian analytical methods in cardiovascular clinical trials: Why, when, and how](https://onlinecjc.ca/article/S0828-282X(24)01130-9/fulltext) by Samuel Heuts et al* [Statistical Remedies for Medical Researchers](https://link.springer.com/book/10.1007%2F978-3-030-43714-5) by Peter Thall* [A gentle introduction to the comparison between null hypothesis testing and Bayesian analysis: Reanalysis of two randomized controlled trials](https://www.jmir.org/2018/10/e10873) by Marcus Bendtsen* [Introductory Video: Frequentist vs. Bayes](https://www.youtube.com/watch?v=85lLfUHmmYQ)* [Resources](http://www.bayesianscientific.org) from the DIA Bayesian Scientific Working Group* [Bayes](https://youtu.be/FROAk4AFKHk?si=oiYI_CA3QodkDK_W) 32m video by Bill Press* [Bayesian statistics without frequentist language](https://youtu.be/yakg94HyWdE) talk by Richard McElreath* [Bayesian statistics for the social sciences](https://courseworks2.columbia.edu/courses/54170/files/folder/LectureMaterial/Week01) by Ben Goodrich (provides a nice background to logic, probability as an extension to logic, the different schools of statistical inference, and subjectivity/objectivity)* [Thomas Bayes and the crisis in science](https://www.the-tls.co.uk/articles/public/thomas-bayes-science-crisis) by David Papineau* [How to become a Bayesian in eight easy steps](https://psyarxiv.com/ph6sw) annotated reading list* [Web resource for Bayesian methods in drug development](http://trialdesign.org) especially for Phase 1 and 2 studies* [R scripts](https://github.com/avehtari/BDA_R_demos) illustrating Bayesian analyses* [Bayesian estimation supersedes the t test](http://www.indiana.edu/~kruschke/articles/Kruschke2013JEPG.pdf) by John Kruschke* [Bayesian t-tests](https://vuorre.netlify.com/post/2017/how-to-compare-two-groups-with-robust-bayesian-estimation-using-r-stan-and-brms)* Michael Clark's [Bayesian Basics](http://m-clark.github.io/bayesian-basics)* Michael Clark's [Become a Bayesian with R and Stan](http://m-clark.github.io/workshops/bayesian)* Scripts with nice workflow for analyzing [fentanyl trends using multilevel Bayesian models](https://github.com/peterphalen/code-for-publications/tree/master/Phalen-Ray-Watson-Huynh-Greene)* Bayesian [sequential testing calculator](https://yanirs.github.io/tools/split-test-calculator)* [Bayesian posteriors are calibrated by definition](http://andrewgelman.com/2017/04/12/bayesian-posteriors-calibrated) by Andrew Gelman* [Verifying posterior distribution calculations](http://andrewgelman.com/2018/04/18/better-check-yo-self-wreck-yo-self)* [Bayesian statistics without frequentist language](https://youtu.be/yakg94HyWdE) video by Richard McElreath* [Tutorials](https://www.youtube.com/playlist?list=PLuwyh42iHquU4hUBQs20hkBsKSMrp6H0J) from StanCon 2018 Helsinki* [Bayesian perspective on proposed FDA adaptive trial guideline](https://www.bayesianspectacles.org/a-bayesian-perspective-on-the-proposed-fda-guidelines-for-adaptive-clinical-trials)* [A student's guide to Bayesian statistics](https://youtu.be/P_og8H-VkIY) by Ben Lambert* [Book for Lambert's _A Student's Guide to Bayesian Statistics_](http://ben-lambert.com/a-students-guide-to-bayesian-statistics)* [Data analysis: A Bayesian tutorial](https://www.amazon.com/gp/product/0198568320/ref=ppx_yo_dt_b_asin_title_o08_s00?ie=UTF8&psc=1) by Devinderjit Sivia and John Skilling* [What is Bayesian/frequentist inference?](https://normaldeviate.wordpress.com/2012/11/17/what-is-bayesianfrequentist-inference) by Larry Wasserman* [Lawrence Joseph's Bayesian courses](https://www.medicine.mcgill.ca/epidemiology/Joseph/courses/EPIB-651/main.html)* [Analytix Thinking Blog](https://analytixthinking.blog) by Steve Ruberg* [Bayesian Inference](https://youtu.be/OwQnUr6rLHA) 54m video by Ben Vincent* [Bayesian Inference is Just Counting](https://youtu.be/_NEMHM1wDfI) 2h video by Richard McElreath* [Teaching Bayesian and Frequentist Methods Side by Side](https://youtu.be/kG43ZKBEqNw) 1 hour video by John Kruschke, and [presentation and interactive app](https://jkkweb.sitehost.iu.edu/KruschkeFreqAndBayesAppTutorial.html)* [Détente: A Practical Understanding of P‐values and Bayesian Posterior Probabilities](https://ascpt.onlinelibrary.wiley.com/doi/abs/10.1002/cpt.2004) by Stephen Ruberg* [Bayesian Data Analysis](http://www.stat.columbia.edu/~gelman/book) by Gelman et al (book available for free for non-commercial purposes)* [Improving transparency and replication in Bayesian statistics: The WAMBS checklist](https://pubmed.ncbi.nlm.nih.gov/26690773) by Depaoli and van de Schoot* [hbiostat.org/bayes](https://hbiostat.org/bayes)* [Reasons confidence intervals and credible intervals may not be equated](https://online.ucpress.edu/collabra/article/5/1/13/112982/Pragmatism-should-Not-be-a-Substitute-for) by Ladislas Nalborczyk, Paul-Christian Bürkner, Donald R. Williams* [Bayesian workflow](https://arxiv.org/abs/2011.01808) by A Gelman et al* [Bayesian methods in human drug and biological products development in CDER and CBER](https://link.springer.com/article/10.1007/s43441-022-00483-0)* Mark Lai's [Course handouts for Bayesian Data Analysis](https://bookdown.org/marklhc/notes_bookdown)* [Introduction to Bayesian Statistics by Woody Lewenstein](https://youtu.be/NIqeFYUhSzU?si=fECV43EcRCMM6KXI) video* [Bayesian Thinking in Biostatistics](https://www.routledge.com/Bayesian-Thinking-in-Biostatistics/Rosner-Laud-Johnson/p/book/9781439800089) by Gary L Rosner, Purushottam W. Laud, Wesley O. Johnson* [Bayes Rules! An Introduction to Applied Bayesian Modeling](https://www.bayesrulesbook.com) by Alicia A. Johnson, Miles Q. Ott, Mine Dogucu## Choice of Priors {-}* [Prior choice recommendations wiki](http://andrewgelman.com/2017/04/28/prior-choice-recommendations-wiki)* [How are Bayesian priors decided in real life?](https://stats.stackexchange.com/questions/548972)* [Zero-excluding priors for variance parameters](http://andrewgelman.com/2018/05/04/zero-excluding-priors-hierarchical-variance-parameters-improve-computation-full-bayesian-inference)* [Prior distributions and the Australia principle](http://andrewgelman.com/2018/05/20/prior-distributions-australia-principle)* [There is always prior information](http://elevanth.org/blog/2017/08/22/there-is-always-prior-information) by Richard McElreath* [What are credible priors and what are skeptical priors?](https://discourse.datamethods.org/t/what-are-credible-priors-and-what-are-skeptical-priors) - discussion on [datamethods.org](http://datamethods.org)* [A weakly informative default prior distribution for logistic and other regression models](https://projecteuclid.org/euclid.aoas/1231424214)* [Predictively consistent prior effective sample sizes](https://arxiv.org/pdf/1907.04185.pdf) by Beat Neuenschwander et al* [Quantification of prior impact in terms of effective current sample size](https://onlinelibrary.wiley.com/doi/abs/10.1111/biom.13124) by Manuel Wiesenfarth and Silvia Calderazzo* [Is ignorance bliss?](https://www.slideshare.net/StephenSenn1/is-ignorance-bliss-230843523) by Stephen Senn (describes logic of linking random effects variance to size of average treatment effect)* [Why optional stopping can be a problem for Bayesians](https://link.springer.com/article/10.3758/s13423-020-01803-x) by Rianne de Heide and Peter Grünwald. (has an interesting taxonomy of types of priors)* [Sensitivity analysis using different priors](https://x.com/ahmed_sayed_98/status/1726581615005147611?s=20)* [Shrinkage priors for regression models](https://doi.org/10.1016/j.jmp.2018.12.004) by van Erp, Oberski, and Mulder* [Effects of sceptical priors on the performance of adaptive clinical trials with binary outcomes](https://doi.org/10.1002/pst.2387) by Granholm, Lange, Harhay, et al## Design and Sample Size {-}* [A review of Bayesian perspectives on sample size derivation for confirmatory trials](https://www.tandfonline.com/doi/full/10.1080/00031305.2021.1901782) by K Kunzmann et al.* [Joint control of consensus and evidence in Bayesian design of clinical trials](https://onlinelibrary.wiley.com/doi/10.1002/bimj.202100035) by F De Santis and S Gubbiotti. Covers how to compute a sample size to achieve consensus in posteriors when priors conflict.* [Bayesian power analysis](https://solomonkurz.netlify.app/blog/bayesian-power-analysis-part-i/) by A. Solomon Kurz* [Improving clinical trials using Bayesian adaptive designs: a breast cancer example](https://bmcmedresmethodol.biomedcentral.com/articles/10.1186/s12874-022-01603-y) by Wei Hong et al.## Multiplicity {-}* [Bayesian multiplicity control](http://www.mpe.mpg.de/~aws/Berger.pdf) by Jim Berger. Contains a formal proof that sequential monitoring requires no multiplicity adjustment in the Bayesian context (slide 30).* [Of Amazons, Martingales, rogue traders and sequential analysis](https://www.linkedin.com/pulse/amazons-martingales-rogue-traders-sequential-analysis-stephen-senn) by Stephen Senn* [Interim analysis for early stopping during the study](https://davidbock.netlify.app/post/2021/07/29/interim-analysis-for-early-stopping-during-the-study) by David Bock* [Why optional stopping can be a problem for Bayesians](https://link.springer.com/article/10.3758/s13423-020-01803-x) by Rianne de Heide and Peter Grünwald. (But focuses on Bayes' factors)* [Bayesian inference completely solves the multiple comparisons problem](https://statmodeling.stat.columbia.edu/2016/08/22) by Andrew Gelman## `brms` Package in R (uses Stan) {-}* [Statistical Rethinking](http://xcelab.net/rm/statistical-rethinking) examples with [R brms](https://osf.io/97t6w)* [Statistical Rethinking with brms, ggplot2, and the tidyverse](http://blogdown.org/connect/#/apps/1850) by AS Kurz* [Blog posts](https://paul-buerkner.github.io/blog) about the R brms package for regression models using Stan* [Handling missing values with brms](https://github.com/paul-buerkner/brms/blob/master/vignettes/brms_missings.Rmd)* [brms vignettes](https://github.com/paul-buerkner/brms/tree/master/vignettes)* [Generalized additive models](https://www.fromthebottomoftheheap.net/2018/04/21/fitting-gams-with-brms)* [Ordinal predictors](https://psyarxiv.com/9qkhj)* [Hands-on example of Bayesian mixed models with brms](https://bayesat.github.io/lund2018) by Andrey Anikin* [BRMS Demos](https://avehtari.github.io/BDA_R_demos/demos_rstan/brms_demo.html) by Aki Vehtari## Other Software {-}* [Plotting Posterior Distributions with ggdistribute](https://cran.r-project.org/web/packages/ggdistribute/vignettes/geom_posterior.html)* [Building Models in PyMC3](https://nbviewer.jupyter.org/github/fonnesbeck/Bios8366/blob/master/notebooks/Section4_5-Model-Building-with-PyMC3.ipynb)* [Simulation Practices for Adaptive Trial Designs in Drug and Device Development](https://www.tandfonline.com/doi/abs/10.1080/19466315.2018.1560359) by Mayer et al* [Bayesian survival analysis using the `rstanarm` R package](https://arxiv.org/abs/2002.09633)* [When MCMC fails: The advice we’re giving is wrong. Here’s what we you should be doing instead](https://statmodeling.stat.columbia.edu/2021/06/10/when-mcmc-fails-the-advice-were-giving-is-wrong-heres-what-we-you-should-be-doing-instead-hint-its-all-about-the-folk-theorem) by Andrew Gelman## Regression Modeling {-}* [Dealing with co-linearities](http://mc-stan.org/users/documentation/case-studies/qr_regression.html) and [here](http://mc-stan.org/rstanarm/reference/QR-argument.html)* [Sparse regression and penalization](http://betanalpha.github.io/assets/case_studies/bayes_sparse_regression.html)* [Monotonic effects: a principled approach for including ordinal predictors in regression models](https://psyarxiv.com/9qkhj)* [Polynomial regression and basis splines](https://youtu.be/ENxTrFf9a7c) by Richard McElreath* [Ordinal regression](https://bookdown.org/ajkurz/Statistical_Rethinking_recoded/monsters-and-mixtures.html#ordered-categorical-outcomes) by A Solomon Kurz## Reporting and Graphics for Bayesian Analyses {-}* [Bayesian Analysis Reporting Guidelines](https://discourse.mc-stan.org/t/help-in-reply-to-reviewer-regarding-ci/33416/5)* [Tidy data and Bayesian analysis make uncertainty visualization fun](http://www.mjskay.com/presentations/openvisconf2018-bayes-uncertainty-2.pdf) by Matthew Kay* [Estimating treatment effects and ICCs from (G)LMMs on the observed scale using Bayes, Part 1: lognormal models](http://rpsychologist.com/GLMM-part1-lognormal)* [Bayesian reanalyses from summary statistics: A guide for academic consumers](http://journals.sagepub.com/doi/10.1177/2515245918779348) (perhaps too much emphasis on Bayes factors and point hypotheses)## Philosophy {-}* [Properties of uncertainty](https://www.edge.org/response-detail/27137) by Jason Wilkes* [Why is it so hard to do good science?](http://eneuro.org/content/early/2018/09/04/ENEURO.0188-18.2018) by Ray Dingledine; discusses decision making and downsides of not using Bayesian thinking* [The Flawed Reasoning Behind the Replication Crisis](http://nautil.us/issue/74/networks/the-flawed-reasoning-behind-the-replication-crisis) by Aubrey Clayton* [Miscellaneous videos](https://discourse.datamethods.org/t/are-there-situations-in-which-a-frequentist-approach-is-inherently-better-than-bayesian/7172/10?u=f2harrell) including material related to ET Jaynes