12  References

Albert, Jim. 2009. Bayesian Computation with R. 2nd ed. New York: Springer. https://doi.org/10.1007/978-0-387-92298-0.

Alexander, Rohan. 2023. Telling Stories with Data: With Applications in R. Boca Raton, FL: CRC Press.

Andrieu, Christophe, and Gareth O. Roberts. 2009. “The Pseudo-Marginal Approach for Efficient Monte Carlo Computations.” The Annals of Statistics 37 (2): 697–725. https://doi.org/10.1214/07-AOS574.

Andrieu, Christophe, and Johannes Thoms. 2008. “A Tutorial on Adaptive MCMC.” Statistics and Computing 18 (4): 343–73. https://doi.org/10.1007/s11222-008-9110-y.

Beaumont, Mark A. 2003. “Estimation of Population Growth or Decline in Genetically Monitored Populations.” Genetics 164 (3): 1139–60. https://doi.org/10.1093/genetics/164.3.1139.

Bishop, Christopher M. 2006. Pattern Recognition and Machine Learning. New York, NY: Springer. https://www.microsoft.com/en-us/research/publication/pattern-recognition-machine-learning/.

Bolin, David, Alexandre B. Simas, and Zhen Xiong. 2023. “Wasserstein Complexity Penalization Priors: A New Class of Penalizing Complexity Priors.” arXiv e-Prints, arXiv:2312.04481. https://doi.org/10.48550/arXiv.2312.04481.

Botev, Zdravko, and Pierre L’Écuyer. 2017. “Simulation from the Normal Distribution Truncated to an Interval in the Tail.” In Proceedings of the 10th EAI International Conference on Performance Evaluation Methodologies and Tools on 10th EAI International Conference on Performance Evaluation Methodologies and Tools, 23–29. https://doi.org/10.4108/eai.25-10-2016.2266879.

Box, G. E. P., and D. R. Cox. 1964. “An Analysis of Transformations.” Journal of the Royal Statistical Society: Series B (Methodological) 26 (2): 211–43. https://doi.org/10.1111/j.2517-6161.1964.tb00553.x.

Boyd, Stephen, and Lieven Vandenberghe. 2004. Convex Optimization. Cambridge, UK: Cambridge University Press. https://doi.org/10.1017/CBO9780511804441.

Brodeur, Mathieu, Perrine Ruer, Pierre-Majorique Léger, and Sylvain Sénécal. 2021. “Smartwatches Are More Distracting Than Mobile Phones While Driving: Results from an Experimental Study.” Accident Analysis & Prevention 149: 105846. https://doi.org/10.1016/j.aap.2020.105846.

Carpenter, Bob, Andrew Gelman, Matthew D. Hoffman, Daniel Lee, Ben Goodrich, Michael Betancourt, Marcus Brubaker, Jiqiang Guo, Peter Li, and Allen Riddell. 2017. “Stan: A Probabilistic Programming Language.” Journal of Statistical Software 76 (1): 1–32. https://doi.org/10.18637/jss.v076.i01.

Carvalho, Carlos M., Nicholas G. Polson, and James G. Scott. 2010. “The Horseshoe Estimator for Sparse Signals.” Biometrika 97 (2): 465–80. https://doi.org/10.1093/biomet/asq017.

Coles, Stuart G., and Jonathan A. Tawn. 1996. “A Bayesian Analysis of Extreme Rainfall Data.” Journal of the Royal Statistical Society. Series C (Applied Statistics) 45 (4): 463–78. https://doi.org/10.2307/2986068.

Cseke, Botond, and Tom Heskes. 2011. “Approximate Marginals in Latent Gaussian Models.” Journal of Machine Learning Research 12 (13): 417–54. http://jmlr.org/papers/v12/cseke11a.html.

Davison, A. C. 2003. Statistical Models. Cambridge, UK: Cambridge University Press.

Dehaene, Guillaume, and Simon Barthelmé. 2018. “Expectation Propagation in the Large Data Limit.” Journal of the Royal Statistical Society: Series B (Statistical Methodology) 80 (1): 199–217. https://doi.org/10.1111/rssb.12241.

Devroye, L. 1986. Non-Uniform Random Variate Generation. New York: Springer. http://www.nrbook.com/devroye/.

Duke, Kristen E., and On Amir. 2023. “The Importance of Selling Formats: When Integrating Purchase and Quantity Decisions Increases Sales.” Marketing Science 42 (1): 87–109. https://doi.org/10.1287/mksc.2022.1364.

Dyk, David A van, and Xiao-Li Meng. 2001. “The Art of Data Augmentation.” Journal of Computational and Graphical Statistics 10 (1): 1–50. https://doi.org/10.1198/10618600152418584.

Eaton, Morris L. 2007. Multivariate Statistics: A Vector Space Approach. Institute for Mathematical Statistics. https://doi.org/10.1214/lnms/1196285102.

Finetti, Bruno de. 1974. Theory of Probability: A Critical Introductory Treatment. Vol. 1. New York: Wiley.

Gabry, Jonah, Daniel Simpson, Aki Vehtari, Michael Betancourt, and Andrew Gelman. 2019. “Visualization in Bayesian Workflow.” Journal of the Royal Statistical Society Series A: Statistics in Society 182 (2): 389–402. https://doi.org/10.1111/rssa.12378.

Gelfand, Alan E., and Adrian F. M. Smith. 1990. “Sampling-Based Approaches to Calculating Marginal Densities.” Journal of the American Statistical Association 85 (410): 398–409. https://doi.org/10.1080/01621459.1990.10476213.

Gelman, Andrew. 2006. “Prior Distributions for Variance Parameters in Hierarchical Models (Comment on Article by Browne and Draper).” Bayesian Analysis 1 (3): 515–34. https://doi.org/10.1214/06-ba117a.

Gelman, Andrew, John B. Carlin, Hal S. Stern, David B. Dunson, Aki Vehtari, and Donald B. Rubin. 2013. Bayesian Data Analysis. 3rd ed. New York: Chapman; Hall/CRC. https://doi.org/10.1201/b16018.

Gelman, Andrew, and Donald B. Rubin. 1992. “Inference from Iterative Simulation Using Multiple Sequences.” Statistical Science 7 (4): 457–72. https://doi.org/10.1214/ss/1177011136.

Gelman, Andrew, Aki Vehtari, Daniel Simpson, Charles C Margossian, Bob Carpenter, Yuling Yao, Lauren Kennedy, Jonah Gabry, Paul-Christian Bürkner, and Martin Modrák. 2020. “Bayesian Workflow.” arXiv. https://doi.org/https://doi.org/10.48550/arXiv.2011.01808.

Geman, Stuart, and Donald Geman. 1984. “Stochastic Relaxation, Gibbs Distributions, and the Bayesian Restoration of Images.” IEEE Transactions on Pattern Analysis and Machine Intelligence Pami-6 (6): 721–41. https://doi.org/10.1109/tpami.1984.4767596.

George, Edward I., and Robert E. McCulloch. 1993. “Variable Selection via Gibbs Sampling.” Journal of the American Statistical Association 88 (423): 881–89. https://doi.org/10.1080/01621459.1993.10476353.

Geweke, John. 1992. “Evaluating the Accuracy of Sampling-Based Approaches to the Calculation of Posterior Moments.” In Bayesian Statistics 4: Proceedings of the Fourth Valencia International Meeting, Dedicated to the Memory of Morris h. DeGroot, 1931–1989. Oxford University Press. https://doi.org/10.1093/oso/9780198522669.003.0010.

———. 2004. “Getting It Right: Joint Distribution Tests of Posterior Simulators.” Journal of the American Statistical Association 99 (467): 799–804. https://doi.org/10.1198/016214504000001132.

Geyer, Charles J. 2011. “Introduction to Markov Chain Monte Carlo.” In Handbook of Markov Chain Monte Carlo, edited by S. Brooks, A. Gelman, G. Jones, and X. L. Meng, 3–48. Boca Raton: CRC Press. https://doi.org/10.1201/b10905-3.

Gosset, William Sealy. 1908. “The Probable Error of a Mean.” Biometrika 6 (1): 1–25. https://doi.org/10.1093/biomet/6.1.1.

Gradshteyn, I. S., and I. M. Ryzhik. 2014. Table of Integrals, Series, and Products. 8th ed. Academic Press. https://doi.org/10.1016/c2010-0-64839-5.

Green, Peter J. 1995. “Reversible Jump Markov Chain Monte Carlo Computation and Bayesian Model Determination.” Biometrika 82 (4): 711–32. https://doi.org/10.1093/biomet/82.4.711.

———. 2001. “A Primer on Markov Chain Monte Carlo.” Monographs on Statistics and Applied Probability 87: 1–62.

Hastings, W. K. 1970. “Monte Carlo sampling methods using Markov chains and their applications.” Biometrika 57 (1): 97–109. https://doi.org/10.1093/biomet/57.1.97.

Held, Leonhard, and Daniel Sabanés Bové. 2020. Likelihood and Bayesian Inference: With Applications in Biology and Medicine. 2nd ed. Heidelberg: Springer Berlin. https://doi.org/10.1007/978-3-662-60792-3.

Hobert, James. 2011. “The Data Augmentation Algorithm: Theory and Methodology.” In Handbook of Markov Chain Monte Carlo, edited by S. Brooks, A. Gelman, G. Jones, and X. L. Meng, 253–93. Boca Raton: CRC Press. https://doi.org/10.1201/b10905-11.

Hoffman, Matthew D., David M. Blei, Chong Wang, and John Paisley. 2013. “Stochastic Variational Inference.” Journal of Machine Learning Research 14 (40): 1303–47. http://jmlr.org/papers/v14/hoffman13a.html.

Holmes, C. C., D. G. T. Denison, and B. K. Mallick. 2002. “Accounting for Model Uncertainty in Seemingly Unrelated Regressions.” Journal of Computational and Graphical Statistics 11 (3): 533–51. http://www.jstor.org/stable/1391112.

Jasra, A., C. C. Holmes, and D. A. Stephens. 2005. “Markov Chain Monte Carlo Methods and the Label Switching Problem in Bayesian Mixture Modeling.” Statistical Science 20 (1): 50–67. https://doi.org/10.1214/088342305000000016.

Jegerlehner, Sabrina, Franziska Suter-Riniker, Philipp Jent, Pascal Bittel, and Michael Nagler. 2021. “Diagnostic Accuracy of a SARS-CoV-2 Rapid Antigen Test in Real-Life Clinical Settings.” International Journal of Infectious Diseases 109: 118–22. https://doi.org/10.1016/j.ijid.2021.07.010.

Kinderman, Albert J, and John F Monahan. 1977. “Computer Generation of Random Variables Using the Ratio of Uniform Deviates.” ACM Transactions on Mathematical Software (TOMS) 3 (3): 257–60.

Kitagawa, Genshiro. 1987. “Non-Gaussian State—Space Modeling of Nonstationary Time Series.” Journal of the American Statistical Association 82 (400): 1032–41. https://doi.org/10.1080/01621459.1987.10478534.

Kucukelbir, Alp, Dustin Tran, Rajesh Ranganath, Andrew Gelman, and David M. Blei. 2017. “Automatic Differentiation Variational Inference.” Journal of Machine Learning Research 18 (14): 1–45. http://jmlr.org/papers/v18/16-107.html.

Lewandowski, Daniel, Dorota Kurowicka, and Harry Joe. 2009. “Generating Random Correlation Matrices Based on Vines and Extended Onion Method.” Journal of Multivariate Analysis 100 (9): 1989–2001. https://doi.org/10.1016/j.jmva.2009.04.008.

Lin, Jason D, Nicole You Jeung Kim, Esther Uduehi, and Anat Keinan. 2024. “Culture for Sale: Unpacking Consumer Perceptions of Cultural Appropriation.” Journal of Consumer Research. https://doi.org/10.1093/jcr/ucad076.

Liu, Jun S. 1994. “Siegel’s Formula via Stein’s Identities.” Statistics & Probability Letters 21 (3): 247–51. https://doi.org/10.1016/0167-7152(94)90121-X.

Marshall, Albert W., and Ingram Olkin. 1985. “A Family of Bivariate Distributions Generated by the Bivariate Bernoulli Distribution.” Journal of the American Statistical Association 80 (390): 332–38. https://doi.org/10.1080/01621459.1985.10478116.

Martins, Eduardo S., and Jery R. Stedinger. 2000. “Generalized Maximum-Likelihood Generalized Extreme-Value Quantile Estimators for Hydrologic Data.” Water Resources Research 36 (3): 737–44. https://doi.org/10.1029/1999WR900330.

Mathieu, Edouard, Hannah Ritchie, Lucas Rodés-Guirao, Cameron Appel, Charlie Giattino, Joe Hasell, Bobbie Macdonald, et al. 2020. “Coronavirus Pandemic (COVID-19).” Our World in Data.

Matias, J. Nathan, Kevin Munger, Marianne Aubin Le Quere, and Charles Ebersole. 2021. “The Upworthy Research Archive, a Time Series of 32,487 Experiments in U.S. Media.” Scientific Data 8 (195). https://doi.org/10.1038/s41597-021-00934-7.

McNeil, A. J., R. Frey, and P. Embrechts. 2005. Quantitative Risk Management: Concepts, Techniques, and Tools. 1st ed. Princeton, NJ: Princeton University Press.

Metropolis, Nicholas, Arianna W. Rosenbluth, Marshall N. Rosenbluth, Augusta H. Teller, and Edward Teller. 1953. “Equation of State Calculations by Fast Computing Machines.” The Journal of Chemical Physics 21 (6): 1087–92. https://doi.org/10.1063/1.1699114.

Minka, Thomas P. 2001. “A Family of Algorithms for Approximate Bayesian Inference.” PhD thesis, Massachusetts Institute of Technology. http://hdl.handle.net/1721.1/86583.

Mitchell, T. J., and J. J. Beauchamp. 1988. “Bayesian Variable Selection in Linear Regression.” Journal of the American Statistical Association 83 (404): 1023–32. https://doi.org/10.1080/01621459.1988.10478694.

Nadarajah, Saralees. 2008. “Marshall and Olkin’s Distributions.” Acta Applicandae Mathematicae 103 (1): 87–100. https://doi.org/10.1007/s10440-008-9221-7.

Neal, Radford M. 2011. “MCMC Using Hamiltonian Dynamics.” In Handbook of Markov Chain Monte Carlo, edited by S. Brooks, A. Gelman, G. Jones, and X. L. Meng, 113–62. Boca Raton: CRC Press. https://doi.org/10.1201/b10905-5.

Northrop, Paul J. 2024. rust: Ratio-of-Uniforms Simulation with Transformation. https://doi.org/10.32614/CRAN.package.rust.

Northrop, Paul J., and Nicolas Attalides. 2016. “Posterior Propriety in Bayesian Extreme Value Analyses Using Reference Priors.” Statistica Sinica 26 (2): 721–43. https://doi.org/10.5705/ss.2014.034.

Nychka, Douglas, Soutir Bandyopadhyay, Dorit Hammerling, Finn Lindgren, and Stephan Sain. 2015. “A Multiresolution Gaussian Process Model for the Analysis of Large Spatial Datasets.” Journal of Computational and Graphical Statistics 24 (2): 579–99.

Ormerod, J. T., and M. P. Wand. 2010. “Explaining Variational Approximations.” The American Statistician 64 (2): 140–53. https://doi.org/10.1198/tast.2010.09058.

Park, Trevor, and George Casella. 2008. “The Bayesian Lasso.” Journal of the American Statistical Association 103 (482): 681–86. https://doi.org/10.1198/016214508000000337.

Peskun, P. H. 1973. “Optimum Monte-Carlo Sampling Using Markov Chains.” Biometrika 60 (3): 607–12. https://doi.org/10.1093/biomet/60.3.607.

Piironen, Juho, and Aki Vehtari. 2017. “Sparsity Information and Regularization in the Horseshoe and Other Shrinkage Priors.” Electronic Journal of Statistics 11 (2): 5018–51. https://doi.org/10.1214/17-ejs1337si.

Plummer, Martyn, Nicky Best, Kate Cowles, and Karen Vines. 2006. “CODA: Convergence Diagnosis and Output Analysis for MCMC.” R News 6 (1): 7–11. https://doi.org/10.32614/CRAN.package.coda.

Raftery, Adrian E. 1995. “Bayesian Model Selection in Social Research.” Sociological Methodology 25: 111–63. https://doi.org/10.2307/271063.

Ranganath, Rajesh, Sean Gerrish, and David Blei. 2014. “Black Box Variational Inference.” In Proceedings of the Seventeenth International Conference on Artificial Intelligence and Statistics, edited by Samuel Kaski and Jukka Corander, 33:814–22. Proceedings of Machine Learning Research. Reykjavik, Iceland: PMLR. https://proceedings.mlr.press/v33/ranganath14.html.

Robert, Christian P., and George Casella. 2004. Monte Carlo Statistical Methods. 2nd ed. New York, NY: Springer. https://doi.org/10.1007/978-1-4757-4145-2.

Roberts, Gareth O., and Jeffrey S. Rosenthal. 2001. “Optimal Scaling for Various Metropolis–Hastings Algorithms.” Statistical Science 16 (4): 351–67. https://doi.org/10.1214/ss/1015346320.

Rue, Håvard, Sara Martino, and Nicolas Chopin. 2009. “Approximate Bayesian Inference for Latent Gaussian Models by Using Integrated Nested Laplace Approximations.” Journal of the Royal Statistical Society: Series B (Statistical Methodology) 71 (2): 319–92. https://doi.org/10.1111/j.1467-9868.2008.00700.x.

Rue, H., and L. Held. 2005. Gaussian Markov Random Fields: Theory and Applications. Chapman & Hall/CRC Monographs on Statistics & Applied Probability. Boca Raton: CRC Press.

Säilynoja, Teemu, Paul-Christian Bürkner, and Aki Vehtari. 2022. “Graphical Test for Discrete Uniformity and Its Applications in Goodness-of-Fit Evaluation and Multiple Sample Comparison.” Statistics and Computing 32 (2): 32. https://doi.org/10.1007/s11222-022-10090-6.

Sherlock, Chris. 2013. “Optimal Scaling of the Random Walk Metropolis: General Criteria for the 0.234 Acceptance Rule.” Journal of Applied Probability 50 (1): 1–15. https://doi.org/10.1239/jap/1363784420.

Simpson, Daniel, Håvard Rue, Andrea Riebler, Thiago G. Martins, and Sigrunn H. Sørbye. 2017. “Penalising Model Component Complexity: A Principled, Practical Approach to Constructing Priors.” Statistical Science 32 (1): 1–28. https://doi.org/10.1214/16-sts576.

Smith, Richard L. 1985. “Maximum Likelihood Estimation in a Class of Nonregular Cases.” Biometrika 72 (1): 67–90. https://doi.org/10.1093/biomet/72.1.67.

Sørbye, Sigrunn Holbek, and Håvard Rue. 2017. “Penalised Complexity Priors for Stationary Autoregressive Processes.” Journal of Time Series Analysis 38 (6): 923–35. https://doi.org/10.1111/jtsa.12242.

Spiegelhalter, David J., Nicola G. Best, Bradley P. Carlin, and Angelika Linde. 2014. “The Deviance Information Criterion: 12 Years On.” Journal of the Royal Statistical Society Series B: Statistical Methodology 76 (3): 485–93. https://doi.org/10.1111/rssb.12062.

Spiegelhalter, David J., Nicola G. Best, Bradley P. Carlin, and Angelika Van Der Linde. 2002. “Bayesian Measures of Model Complexity and Fit.” Journal of the Royal Statistical Society: Series B (Statistical Methodology) 64 (4): 583–639. https://doi.org/10.1111/1467-9868.00353.

Stephens, Matthew. 2002. “Dealing with Label Switching in Mixture Models.” Journal of the Royal Statistical Society Series B: Statistical Methodology 62 (4): 795–809. https://doi.org/10.1111/1467-9868.00265.

Talts, Sean, Michael Betancourt, Daniel Simpson, Aki Vehtari, and Andrew Gelman. 2020. “Validating Bayesian Inference Algorithms with Simulation-Based Calibration.” https://doi.org/10.48550/arXiv.1804.06788.

Tanner, Martin A., and Wing Hung Wong. 1987. “The Calculation of Posterior Distributions by Data Augmentation.” Journal of the American Statistical Association 82 (398): 528–40. https://doi.org/10.1080/01621459.1987.10478458.

Tierney, Luke, and Joseph B. Kadane. 1986. “Accurate Approximations for Posterior Moments and Marginal Densities.” Journal of the American Statistical Association 81 (393): 82–86. https://doi.org/10.1080/01621459.1986.10478240.

van Niekerk, Janet, and Håavard Rue. 2024. “Low-Rank Variational Bayes Correction to the Laplace Method.” Journal of Machine Learning Research 25 (62): 1–25. http://jmlr.org/papers/v25/21-1405.html.

Villani, Mattias. 2023. “Bayesian Learning: A Gentle Introduction.” https://mattiasvillani.com/BayesianLearningBook/.

Wakefield, J. C., A. E. Gelfand, and A. F. M. Smith. 1991. “Efficient Generation of Random Variates via the Ratio-of-Uniforms Method.” Statistics and Computing 1 (2): 129–33. https://doi.org/10.1007/BF01889987.

Watanabe, Sumio. 2010. “Asymptotic Equivalence of Bayes Cross Validation and Widely Applicable Information Criterion in Singular Learning Theory.” Journal of Machine Learning Research 11 (116): 3571–94. http://jmlr.org/papers/v11/watanabe10a.html.

Wood, Simon N. 2019. “Simplified Integrated Nested Laplace Approximation.” Biometrika 107 (1): 223–30. https://doi.org/10.1093/biomet/asz044.

Zellner, Arnold. 1971. An Introduction to Bayesian Inference in Econometrics. Wiley.

———. 1986. “On Assessing Prior Distributions and Bayesian Regression Analysis with g-Prior Distributions.” In Bayesian Inference and Decision Techniques: Essays in Honor of Bruno de Finetti, 233–43. North-Holland/Elsevier.