\[ \DeclareMathOperator{\E}{E} \DeclareMathOperator{\mean}{mean} \DeclareMathOperator{\Var}{Var} \DeclareMathOperator{\Cov}{Cov} \DeclareMathOperator{\Cor}{Cor} \DeclareMathOperator{\Bias}{Bias} \DeclareMathOperator{\MSE}{MSE} \DeclareMathOperator{\RMSE}{RMSE} \DeclareMathOperator{\sd}{sd} \DeclareMathOperator{\se}{se} \DeclareMathOperator{\tr}{tr} \DeclareMathOperator{\median}{median} \DeclareMathOperator{\rank}{rank} \DeclareMathOperator*{\argmin}{arg\,min} \DeclareMathOperator*{\argmax}{arg\,max} \DeclareMathOperator{\logistic}{Logistic} \DeclareMathOperator{\logit}{Logit} \newcommand{\mat}[1]{\boldsymbol{#1}} \newcommand{\vec}[1]{\boldsymbol{#1}} \newcommand{\T}{'} % This follows BDA \newcommand{\dunif}{\mathsf{Uniform}} \newcommand{\dnorm}{\mathsf{Normal}} \newcommand{\dhalfnorm}{\mathrm{HalfNormal}} \newcommand{\dlnorm}{\mathsf{LogNormal}} \newcommand{\dmvnorm}{\mathsf{Normal}} \newcommand{\dgamma}{\mathsf{Gamma}} \newcommand{\dinvgamma}{\mathsf{InvGamma}} \newcommand{\dchisq}{\mathsf{ChiSquared}} \newcommand{\dinvchisq}{\mathsf{InvChiSquared}} \newcommand{\dexp}{\mathsf{Exponential}} \newcommand{\dlaplace}{\mathsf{Laplace}} \newcommand{\dweibull}{\mathsf{Weibull}} \newcommand{\dwishart}{\mathsf{Wishart}} \newcommand{\dinvwishart}{\mathsf{InvWishart}} \newcommand{\dlkj}{\mathsf{LkjCorr}} \newcommand{\dt}{\mathsf{StudentT}} \newcommand{\dhalft}{\mathsf{HalfStudentT}} \newcommand{\dbeta}{\mathsf{Beta}} \newcommand{\ddirichlet}{\mathsf{Dirichlet}} \newcommand{\dlogistic}{\mathsf{Logistic}} \newcommand{\dllogistic}{\mathsf{LogLogistic}} \newcommand{\dpois}{\mathsf{Poisson}} \newcommand{\dBinom}{\mathsf{Binomial}} \newcommand{\dmultinom}{\mathsf{Multinom}} \newcommand{\dnbinom}{\mathsf{NegativeBinomial}} \newcommand{\dnbinomalt}{\mathsf{NegativeBinomial2}} \newcommand{\dbetabinom}{\mathsf{BetaBinomial}} \newcommand{\dcauchy}{\mathsf{Cauchy}} \newcommand{\dhalfcauchy}{\mathsf{HalfCauchy}} \newcommand{\dbernoulli}{\mathsf{Bernoulli}} \newcommand{\R}{\mathbb{R}} \newcommand{\Reals}{\R} \newcommand{\RealPos}{\R^{+}} \newcommand{\N}{\mathbb{N}} \newcommand{\Nats}{\N} \newcommand{\cia}{\perp\!\!\!\perp} \DeclareMathOperator*{\plim}{plim} \DeclareMathOperator{\invlogit}{Inv-Logit} \DeclareMathOperator{\logit}{Logit} \DeclareMathOperator{\diag}{diag} \]

References

Aitkin, M., and N. Longford. 1986. “Statistical Modelling Issues in School Effectiveness Studies.” Journal of the Royal Statistical Society. Series A (General) 149 (1): 1–43. http://www.jstor.org/stable/2981882.

Albert, A., and J. A. Anderson. 1984. “On the Existence of Maximum Likelihood Estimates in Logistic Regression Models.” Biometrika 71 (1): 1–10. https://doi.org/10.1093/biomet/71.1.1.

Albert, Jim. 2009. Bayesian Computation with R. Use R! Springer. https://doi.org/10.1007/978-0-387-92298-0.

Andersen, Robert, and Tina Fetner. 2008. “Economic Inequality and Intolerance: Attitudes Toward Homosexuality in 35 Democracies.” American Journal of Political Science 52 (4): 942–58. https://doi.org/10.1111/j.1540-5907.2008.00352.x.

Anderson, C. J., and M. M. Singer. 2008. “The Sensitive Left and the Impervious Right: Multilevel Models and the Politics of Inequality, Ideology, and Legitimacy in Europe.” Comparative Political Studies 41 (4-5): 564–99. https://doi.org/10.1177/0010414007313113.

Arzheimer, Kai. 2009. “Contextual Factors and the Extreme Right Vote in Western Europe, 1980-2002.” American Journal of Political Science 53 (2): 259–75. https://doi.org/10.1111/j.1540-5907.2009.00369.x.

Asquith, William H. 2011. Distributional Analysis with L-Moment Statistics Using the R Environment for Statistical Computing.

Bafumi, Joseph, and Andrew Gelman. 2006. “Fitting Multilevel Models When Predictors and Group Effects Correlate.” SSRN Electronic Journal. https://doi.org/10.2139/ssrn.1010095.

Barnard, John, Robert McCulloch, and Xiao-Li Meng. 2000. “Modeling Covariance Matrices in Terms of Standard Deviations and Correlations, with Application to Shrinkage.” Statistica Sinica 10 (4): 1281–1311. http://www.jstor.org/stable/24306780.

Barrilleaux, Charles, and Carlisle Rainey. 2014. “The Politics of Need.” State Politics & Policy Quarterly 14 (4): 437–60. https://doi.org/10.1177/1532440014561644.

Bates, Douglas M. 2010. lme4: Mixed-Effects Modeling with R. http://lme4.r-forge.r-project.org/book/front.pdf.

Bates, Douglas, Martin Mächler, Ben Bolker, and Steve Walker. 2014. “Fitting Linear Mixed-Effects Models Using lme4,” June. http://arxiv.org/abs/1406.5823v1.

Beck, Nathaniel, and Jonathan N. Katz. 2007. “Random Coefficient Models for Time-Series—Cross-Section Data: Monte Carlo Experiments.” Political Analysis 15 (02): 182–95. https://doi.org/10.1093/pan/mpl001.

Beck, Nathaniel, Jonathan N. Katz, and Richard Tucker. 1998. “Taking Time Seriously: Time-Series-Cross-Section Analysis with a Binary Dependent Variable.” American Journal of Political Science 42 (4): 1260–88. http://www.jstor.org/stable/2991857.

Benoit, Dries F., and Dirk Van den Poel. 2017. “bayesQR: A Bayesian Approach to Quantile Regression.” Journal of Statistical Software 76 (7). https://doi.org/10.18637/jss.v076.i07.

Berger, James O. 1993. Statistical Decision Theory and Bayesian Analysis. Springer.

Betancourt, Michael. 2016. “Diagnosing Suboptimal Cotangent Disintegrations in Hamiltonian Monte Carlo,” April. http://arxiv.org/pdf/1604.00695v1:PDF.

———. 2017. “How the Shape of a Weakly Informative Prior Affects Inferences.” Stan Case Studies, January. http://mc-stan.org/documentation/case-studies/weakly_informative_shapes.html.

Blei, David M., Alp Kucukelbir, and Jon D. McAuliffe. 2017. “Variational Inference: A Review for Statisticians.” Journal of the American Statistical Association 112 (518): 859–77. https://doi.org/10.1080/01621459.2017.1285773.

Box, George E. P. 1976. “Science and Statistics.” Journal of the American Statistical Association 71 (356): 791–99. https://doi.org/10.1080/01621459.1976.10480949.

Carpenter, Bob, Jonah Gabry, and Ben Goodrich. 2017. “Hierarchical Partial Pooling for Repeated Binary Trials.” Stan Case Studies, January. http://mc-stan.org/documentation/case-studies/pool-binary-trials-rstanarm.html.

Carvalho, Carlos M., Michael S. Johannes, Hedibert F. Lopes, and Nicholas G. Polson. 2010. “Particle Learning and Smoothing.” Statistical Science 25 (1): 88–106. https://doi.org/10.1214/10-STS325.

Carvalho, Carlos M., Nicholas G. Polson, and James G. Scott. 2009. “Handling Sparsity via the Horseshoe.” Edited by David van Dyk and Max Welling, Proceedings of machine learning research, 5: 73–80. http://proceedings.mlr.press/v5/carvalho09a.html.

Chernoff, Herman. 1986. “Comment.” The American Statistician 40 (1): 5–6. https://doi.org/10.1080/00031305.1986.10475343.

Chung, Yeojin, Sophia Rabe-Hesketh, Vincent Dorie, Andrew Gelman, and Jingchen Liu. 2013. “A Nondegenerate Penalized Likelihood Estimator for Variance Parameters in Multilevel Models.” Psychometrika 78 (4): 685–709. https://doi.org/10.1007/s11336-013-9328-2.

Clark, Tom S., and Drew A. Linzer. 2014. “Should I Use Fixed or Random Effects?” Political Science Research and Methods 3 (02): 399–408. https://doi.org/10.1017/psrm.2014.32.

Congdon, Peter. 2014. Applied Bayesian Modelling. 2nd ed. Wiley Series in Probability and Statistics. Wiley.

Cribari-Neto, Francisco, and Achim Zeileis. 2010. “Beta Regression in R.” Journal of Statistical Software 34 (2). https://doi.org/10.18637/jss.v034.i02.

Datta, Jyotishka, and Jayanta. K. Ghosh. 2013. “Asymptotic Properties of Bayes Risk for the Horseshoe Prior.” Bayesian Analysis 8 (1): 111–32. https://doi.org/10.1214/13-BA805.

Denisova, Irina, Markus Eller, Timothy Frye, and Ekaterina Zhuravskaya. 2009. “Who Wants to Revise Privatization? The Complementarity of Market Skills and Institutions.” American Political Science Review 103 (02): 284–304. https://doi.org/10.1017/s0003055409090248.

Draper, David. 2008. “Bayesian Multilevel Analysis and MCMC.” In Handbook of Multilevel Analysis, 77–139. Springer New York. https://doi.org/10.1007/978-0-387-73186-5_2.

Duncan, O. D. 1961. “A Socioeconomic Index for All Occupations.” In Occupations and Social Status, edited by Jr. Reiss A. J. Frre Press.

Efron, B. 1986a. “Reply.” The American Statistician 40 (1): 11–11. https://doi.org/10.1080/00031305.1986.10475348.

———. 1986b. “Why Isn’t Everyone a Bayesian?” The American Statistician 40 (1): 1–5. https://doi.org/10.1080/00031305.1986.10475342.

Efron, Bradley, and Trevor Hastie. 2016. Computer Age Statistical Inference. Cambridge University Pr.

Efron, Bradley, and Carl Morris. 1975. “Data Analysis Using Stein’s Estimator and Its Generalizations.” Journal of the American Statistical Association 70 (350): 311–19. https://doi.org/10.1080/01621459.1975.10479864.

Ferrari, Silvia, and Francisco Cribari-Neto. 2004. “Beta Regression for Modelling Rates and Proportions.” Journal of Applied Statistics 31 (7): 799–815. https://doi.org/10.1080/0266476042000214501.

Fienberg, Stephen E. 2006. “When Did Bayesian Inference Become "Bayesian"?” Bayesian Analysis 1 (1): 1–40. https://doi.org/10.1214/06-BA101.

Fink, Daniel. 1997. “A Compendium of Conjugate Priors.” https://www.johndcook.com/CompendiumOfConjugatePriors.pdf.

Firth, David. 1993. “Bias Reduction of Maximum Likelihood Estimates.” Biometrika 80 (1): 27–38. https://doi.org/10.1093/biomet/80.1.27.

Flegal, James M., Murali Haran, and Galin L. Jones. 2008. “Markov Chain Monte Carlo: Can We Trust the Third Significant Figure?” Statistical Science 23 (2): 250–60. https://doi.org/10.1214/08-sts257.

Forbes, Catherine, Merran Evans, Nicholas Hastings, and Brian Peacock. 2010. Statistical Distributions. 4th ed. Wiley. https://www.wiley.com/en-us/Statistical+Distributions%2C+4th+Edition-p-9781118097823.

Fox, John. 2016. Applied Regression Analysis & Generalized Linear Models. 3rd ed. Sage.

Fragoso, Tiago M., and Francisco Louzada Neto. 2015. “Bayesian Model Averaging: A Systematic Review and Conceptual Classification,” September. http://arxiv.org/pdf/1509.08864v1:PDF.

Franchino, Fabio, and Bjørn Høyland. 2009. “Legislative Involvement in Parliamentary Systems: Opportunities, Conflict, and Institutional Constraints.” American Political Science Review 103 (04): 607–21. https://doi.org/10.1017/s0003055409990177.

Gelfand, Alan E. 1995. “Model Determination Using Sampling-Based Methods.” In.

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.

———. 2007. “A Bayesian Formulation of Exploratory Data Analysis and Goodness-of-Fit Testinga.” International Statistical Review 71 (2): 369–82. https://doi.org/10.1111/j.1751-5823.2003.tb00203.x.

———. 2009. “Confusions About Posterior Predictive Checks.” February 7, 2009. http://andrewgelman.com/2009/02/07/confusions_abou/.

———. 2014. “Discussion with Sander Greenland on Posterior Predictive Checks.” Statistical Modeling, Causal Inference, and Social Science, August. http://andrewgelman.com/2014/08/11/discussion-sander-greenland-posterior-predictive-checks/.

Gelman, Andrew, John B. Carlin, Hal S. Stern, David B. Dunson, and Aki Vehtari. 2013. Bayesian Data Analysis. Taylor & Francis Ltd.

Gelman, Andrew, and Jennifer Hill. 2007. Data Analysis Using Regression and Multilevel / Hierarchical Models. Cambridge University Pr.

Gelman, Andrew, Jessica Hwang, and Aki Vehtari. 2013. “Understanding Predictive Information Criteria for Bayesian Models.” Statistics and Computing 24 (6): 997–1016. https://doi.org/10.1007/s11222-013-9416-2.

Gelman, Andrew, Aleks Jakulin, Maria Grazia Pittau, and Yu-Sung Su. 2008. “A Weakly Informative Default Prior Distribution for Logistic and Other Regression Models.” The Annals of Applied Statistics 2 (4): 1360–83. https://doi.org/10.1214/08-aoas191.

Gelman, Andrew, and Gary King. 1993. “Why Are American Presidential Election Campaign Polls so Variable When Votes Are so Predictable?” British Journal of Political Science 23 (04): 409. https://doi.org/10.1017/s0007123400006682.

Gelman, Andrew, Xiao-Li Meng, and Hal Stern. 1996. “Posterior Predictive Assessment of Model Fitness via Realized Discrepancies.” Statistica Sinica 6 (4): 733–60. http://www.jstor.org/stable/24306036.

Gelman, Andrew, and Donald B. Rubin. 1992. “Inference from Iterative Simulation Using Multiple Sequences.” Statistical Science 7 (4): 457–72. http://www.jstor.org/stable/2246093.

Gelman, Andrew, and Cosma Shalizi. 2012a. “Rejoinder to Discussion of ‘Philosophy and the Practice of Bayesian Statistics’.” British Journal of Mathematical and Statistical Psychology 66 (1): 76–80. https://doi.org/10.1111/j.2044-8317.2012.02066.x.

Gelman, Andrew, and Cosma Rohilla Shalizi. 2012b. “Philosophy and the Practice of Bayesian Statistics.” British Journal of Mathematical and Statistical Psychology 66 (1): 8–38. https://doi.org/10.1111/j.2044-8317.2011.02037.x.

Gelman, Andrew, Boris Shor, Joseph Bafumi, and David Park. 2007. “Rich State, Poor State, Red State, Blue State: What’s the Matter with Connecticut?” Quarterly Journal of Political Science 2 (4): 345–67. https://doi.org/10.1561/100.00006026.

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, J. 1993. “Bayesian Treatment of the Independent Student-t Linear Model.” Journal of Applied Econometrics 8: S19–S40. http://www.jstor.org/stable/2285073.

Geyer, C. J. 2011. “Introduction to Markov Chain Monte Carlo.” In Handbook of Markov Chain Monte Carlo, edited by S. Brooks, Gelman, A. G. L. Jones, and X.-L. Meng. Chapman; Hall/CRC.

Ghosh, Joyee, and Andrew E. Ghattas. 2015. “Bayesian Variable Selection Under Collinearity.” The American Statistician 69 (3): 165–73. https://doi.org/10.1080/00031305.2015.1031827.

Ghosh, Joyee, Yingbo Li, and Robin Mitra. 2015. “On the Use of Cauchy Prior Distributions for Bayesian Logistic Regression,” July. http://arxiv.org/abs/1507.07170v2.

Gilardi, Fabrizio. 2010. “Who Learns from What in Policy Diffusion Processes?” American Journal of Political Science 54 (3): 650–66. http://www.jstor.org/stable/27821944.

Goldstein, H. 2011. Multilevel Statistical Models. John Wiley & Sons.

Goldstein, Harvey, Jon Rasbash, Min Yang, Geoffrey Woodhouse, Huiqi Pan, Desmond Nuttall, and Sally Thomas. 1993. “A Multilevel Analysis of School Examination Results.” Oxford Review of Education 19 (4): 425–33. https://doi.org/10.1080/0305498930190401.

Goldstein, Harvey, Min Yang, Rumana Omar, Rebecca Turner, and Simon Thompson. 2000. “Meta-Analysis Using Multilevel Models with an Application to the Study of Class Size Effects.” Journal of the Royal Statistical Society: Series C (Applied Statistics) 49 (3): 399–412. https://doi.org/10.1111/1467-9876.00200.

Greenland, Sander, and Mohammad Ali Mansournia. 2015. “Penalization, Bias Reduction, and Default Priors in Logistic and Related Categorical and Survival Regressions.” Statistics in Medicine 34 (23): 3133–43. https://doi.org/10.1002/sim.6537.

Grimmer, Justin. 2011. “An Introduction to Bayesian Inference via Variational Approximations.” Political Analysis 19 (01): 32–47. https://doi.org/10.1093/pan/mpq027.

Gross, Justin H. 2014. “Testing What Matters (If You Must Test at All): A Context-Driven Approach to Substantive and Statistical Significance.” American Journal of Political Science 59 (3): 775–88. https://doi.org/10.1111/ajps.12149.

Grün, Bettina, Ioannis Kosmidis, and Achim Zeileis. 2012. “Extended Beta Regression in R: Shaken, Stirred, Mixed, and Partitioned.” Journal of Statistical Software 48 (11). https://doi.org/10.18637/jss.v048.i11.

Heinze, Georg. 2006. “A Comparative Investigation of Methods for Logistic Regressionwith Separated or Nearly Separated Data.” Statistics in Medicine. https://doi.org/10.1002/sim.2687.

Heinze, Georg, and Michael Schemper. 2002. “A Solution to the Problem of Separation in Logistic Regression.” Statistics in Medicine. https://doi.org/10.1002/sim.1047.

Hoerl, Arthur E., and Robert W. Kennard. 1970. “Ridge Regression: Biased Estimation for Nonorthogonal Problems.” Technometrics 12 (1): 55–67. https://doi.org/10.1080/00401706.1970.10488634.

Hoff, Peter D. 2009. A First Course in Bayesian Statistical Methods. Springer Texts in Statistics. Springer-Verlag GmbH. https://doi.org/10.1007/978-0-387-92407-6.

Hooghe, Liesbet, and Gary Marks. 2004. “Does Identity or Economic Rationality Drive Public Opinion on European Integration?” PS: Political Science and Politics 37 (3): 415–20. http://www.jstor.org/stable/4488854.

Hooghe, Marc, Tim Reeskens, Dietlind Stolle, and Ann Trappers. 2009. “Ethnic Diversity and Generalized Trust in Europe.” Comparative Political Studies 42 (2): 198–223. https://doi.org/10.1177/0010414008325286.

Ishwaran, Hemant, Udaya B. Kogalur, and J. Sunil Rao. 2010. “spikeslab: Prediction and Variable Selection Using Spike and Slab Regression.” R Journal. https://journal.r-project.org/archive/2010-2/RJournal_2010-2_Ishwaran~et~al.pdf.

Ishwaran, Hemant, and J. Sunil Rao. 2005. “Spike and Slab Variable Selection: Frequentist and Bayesian Strategies.” The Annals of Statistics 33 (2): 730–73. https://doi.org/10.1214/009053604000001147.

Iversen, Torben, and Frances Rosenbluth. 2006. “The Political Economy of Gender: Explaining Cross-National Variation in the Gender Division of Labor and the Gender Voting Gap.” American Journal of Political Science 50 (1): 1–19. https://doi.org/10.1111/j.1540-5907.2006.00166.x.

Jackman, Simon. 2009. Bayesian Analysis for the Social Sciences. John Wiley; Sons Ltd.

Jiang, Jiming. 2007. Linear and Generalized Linear Mixed Models and Their Applications. Springer New York.

Johnson, Norman L., Samuel Kotz, and N. Balakrishnan. 1994. Continuous Univariate Distributions, Vol. 1. 2nd ed. Wiley Series in Probability and Statistics. Wiley-Interscience.

———. 1995. Continuous Univariate Distributions, Vol. 2. 2nd ed. Wiley Series in Probability and Statistics. Wiley-Interscience.

———. 1997. Discrete Multivariate Distributions. 1st ed. Wiley Series in Probability and Statistics. Wiley-Interscience.

Juárez, Miguel A., and Mark F. J. Steel. 2010. “Model-Based Clustering of Non-Gaussian Panel Data Based on Skew-t Distributions.” Journal of Business & Economic Statistics 28 (1): 52–66. https://doi.org/10.1198/jbes.2009.07145.

Kass, Robert E., and Adrian E. Raftery. 1995. “Bayes Factors.” Journal of the American Statistical Association 90 (430): 773–95. https://doi.org/10.1080/01621459.1995.10476572.

King, Gary. 1998. Unifying Political Methodology: The Likelihood Theory of Statistical Inference. UNIV OF MICHIGAN PR.

King, Gary, and Langche Zeng. 2001a. “Logistic Regression in Rare Events Data.” Political Analysis 9 (2): 137–63. http://www.jstor.org/stable/25791637.

———. 2001b. “Explaining Rare Events in International Relations.” International Organization 55 (3): 693–715. https://doi.org/10.1162/00208180152507597.

Kotz, Samuel, N. Balakrishnan, and Norman L. Johnson. 2000. Continuous Multivariate Distributions, Volume 1: Models and Applications. 2nd ed. Wiley Series in Probability and Statistics. Wiley-Interscience.

Kruschke, John K. 2013. “Posterior Predictive Checks Can and Should Be Bayesian: Comment on Gelman and Shalizi, ‘Philosophy and the Practice of Bayesian Statistics’.” British Journal of Mathematical and Statistical Psychology 66 (1): 45–56. https://doi.org/10.1111/j.2044-8317.2012.02063.x.

———. 2015. Doing Bayesian Data Analysis. Elsevier LTD, Oxford.

Kucukelbir, A., R. Ranganath, A. Gelman, and David M. Blei. 2015. “Automatic Variational Inference in Stan.” ArXiv E-Prints, June. https://arxiv.org/abs/1506.03431.

Lax, Jeffrey R., and Justin H. Phillips. 2009. “How Should We Estimate Public Opinion in the States?” American Journal of Political Science 53 (1): 107–21. https://doi.org/10.1111/j.1540-5907.2008.00360.x.

Lee, Peter M. 2012. Bayesian Statistics: An Introduction. Wiley.

Leemis, Lawrence M., and Jacquelyn T. McQueston. 2008. “Univariate Distribution Relationships.” The American Statistician 62 (1): 45–53. https://doi.org/10.1198/000313008X270448.

Lindley, D. V. 1986. “Comment.” The American Statistician 40 (1): 6–7. https://doi.org/10.1080/00031305.1986.10475344.

Liu, Chuanhai. 2005. “Robit Regression: A Simple Robust Alternative to Logistic and Probit Regression.” In Applied Bayesian Modeling and Causal Inference from Incomplete-Data Perspectives, 227–38. John Wiley & Sons, Ltd. https://doi.org/10.1002/0470090456.ch21.

Lopes, Hedibert F., Nicholas G. Polson, and Carlos M. Carvalho. 2012. “Bayesian Statistics with a Smile: A Resampling-Sampling Perspective.” Brazilian Journal of Probability and Statistics 26 (4): 358–71. http://www.jstor.org/stable/43601224.

Lunn, David, Chris Jackson, Nicky Best, Andrew Thomas, and David Spiegelhalter. 2012. The BUGS Book: A Practical Introduction to Bayesian Analysis. Chapman & Hall/Crc Texts in Statistical Science. CRC Press.

MacKay, David J. C. 2003. Information Theory, Inference and Learning Algorithms. Cambridge University Pr.

Marin, Jean-Michel, and Christian P. Robert. 2014. Bayesian Essentials with R. Springer. https://doi.org/10.1007/978-1-4614-8687-9.

McElreath, Richard. 2016. Statistical Rethinking. Apple Academic Press Inc.

Meer, T. W. G. van der, J. W. van Deth, and P. L. H. Scheepers. 2009. “The Politicized Participant: Ideology and Political Action in 20 Democracies.” Comparative Political Studies 42 (11): 1426–57. https://doi.org/10.1177/0010414009332136.

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.

Morris, C. N. 1986. “Comment.” The American Statistician 40 (1): 7–8. https://doi.org/10.1080/00031305.1986.10475345.

Murphy, Kevin P. 2012. Machine Learning. MIT Press Ltd.

Ntzoufras, Ioannis. 2009. Bayesian Modeling Using WinBUGS. Wiley Series in Computational Statitistics. Wiley. https://doi.org/10.1002/9780470434567.

O’Rourke, Kevin H., and Richard Sinnott. 2006. “The Determinants of Individual Attitudes Towards Immigration.” European Journal of Political Economy 22 (4): 838–61. https://doi.org/10.1016/j.ejpoleco.2005.10.005.

Park, David K., Andrew Gelman, and Joseph Bafumi. 2004. “Bayesian Multilevel Estimation with Poststratification: State-Level Estimates from National Polls.” Political Analysis 12 (04): 375–85. https://doi.org/10.1093/pan/mph024.

Pas, S. L. van der, B. J. K. Kleijn, and A. W. van der Vaart. 2014. “The Horseshoe Estimator: Posterior Concentration Around Nearly Black Vectors.” Electronic Journal of Statistics 8 (2): 2585–2618. https://doi.org/10.1214/14-ejs962.

Piironen, Juho, and Aki Vehtari. 2016. “On the Hyperprior Choice for the Global Shrinkage Parameter in the Horseshoe Prior,” October. http://arxiv.org/abs/1610.05559v1.

———. 2017. “Sparsity Information and Regularization in the Horseshoe and Other Shrinkage Priors.” Electron. J. Statist. 11 (2): 5018–51. https://doi.org/10.1214/17-EJS1337SI.

Polson, Nicholas G., and James G. Scott. 2011. “Shrink Globally, Act Locally: Sparse Bayesian Regularization and Prediction.” In Bayesian Statistics, 501–38. Oxford University Press. https://doi.org/10.1093/acprof:oso/9780199694587.003.0017.

———. 2012. “On the Half-Cauchy Prior for a Global Scale Parameter.” Bayesian Analysis 7 (4): 887–902. https://doi.org/10.1214/12-ba730.

Press, S. James. 1986. “Comment.” The American Statistician 40 (1): 9–10. https://doi.org/10.1080/00031305.1986.10475346.

Rainey, Carlisle. 2016. “Dealing with Separation in Logistic Regression Models.” Political Analysis 24 (03): 339–55. https://doi.org/10.1093/pan/mpw014.

Ranganath, R., S. Gerrish, and D. M. Blei. 2014. “Black box variational inference.” ArXiv E-Prints, December. https://arxiv.org/abs/1401.0118.

Raudenbush, Stephen W., and Anthony S. Bryk. 2001. Hierarchical Linear Models: Applications and Data Analysis Methods. SAGE PUBN.

Robert, Christian P. 2016. “The Expected Demise of the Bayes Factor.” Journal of Mathematical Psychology 72 (June): 33–37. https://doi.org/10.1016/j.jmp.2015.08.002.

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

———. 2009. Introducing Monte Carlo Methods with R. Springer. https://doi.org/10.1007/978-1-4419-1576-4.

Scott, James G., and James O. Berger. 2010. “Bayes and Empirical-Bayes Multiplicity Adjustment in the Variable-Selection Problem.” The Annals of Statistics 38 (5): 2587–2619. https://doi.org/10.1214/10-Aos792.

Smith, Adrian F. M. 1986. “Comment.” The American Statistician 40 (1): 10–10. https://doi.org/10.1080/00031305.1986.10475347.

Smith, A. F. M., and A. E. Gelfand. 1992. “Bayesian Statistics Without Tears: A Sampling/Resampling Perspective.” The American Statistician 46 (2): 84–88. https://doi.org/10.1080/00031305.1992.10475856.

Snijders, Tom A. B., and Roel Bosker. 2011. Multilevel Analysis. Sage Publications Ltd.

Stan Development Team. 2016. Stan Modeling Language Users Guide and Reference Manual, Version 2.14.0. https://github.com/stan-dev/stan/releases/download/v2.14.0/stan-reference-2.14.0.pdf.

“Stan Prior Choice Recommendations.” n.d. https://github.com/stan-dev/stan/wiki/Prior-Choice-Recommendations.

Steenbergen, Marco R., and Bradford S. Jones. 2002. “Modeling Multilevel Data Structures.” American Journal of Political Science 46 (1): 218–37. http://www.jstor.org/stable/3088424.

Stegmueller, Daniel. 2013. “How Many Countries for Multilevel Modeling? A Comparison of Frequentist and Bayesian Approaches.” American Journal of Political Science 57 (3): 748–61. https://doi.org/10.1111/ajps.12001.

Stigler, Stephen M. 1983. “Who Discovered Bayes’s Theorem?” The American Statistician 37 (4): 290–96. http://www.jstor.org/stable/2682766.

———. 2018. “Richard Price, the First Bayesian.” Statistical Science 33 (1): 117–25. https://doi.org/10.1214/17-STS635.

Tibshirani, Robert. 1996. “Regression Shrinkage and Selection via the Lasso.” Journal of the Royal Statistical Society. Series B (Methodological) 58 (1): 267–88. http://www.jstor.org/stable/2346178.

Vehtari, Aki, Andrew Gelman, and Jonah Gabry. 2015. “Pareto smoothed importance sampling.” ArXiv E-Prints, July. https://arxiv.org/abs/1507.02646.

———. 2017. “Practical Bayesian Model Evaluation Using Leave-One-Out Cross-Validation and WAIC.” Statistics and Computing 27 (5): 1413–32. https://doi.org/10.1007/s11222-016-9696-4.

Voeten, Erik. 2008. “The Impartiality of International Judges: Evidence from the European Court of Human Rights.” American Political Science Review 102 (04): 417–33. https://doi.org/10.1017/s0003055408080398.

Wechsler, Sergio, Rafael Izbicki, and Luìs Gustavo Esteves. 2013. “A Bayesian Look at Nonidentifiability: A Simple Example.” The American Statistician 67 (2): 90–93. https://doi.org/10.1080/00031305.2013.778787.

Weldon, Steven A. 2006. “The Institutional Context of Tolerance for Ethnic Minorities: A Comparative, Multilevel Analysis of Western Europe.” American Journal of Political Science 50 (2): 331–49. https://doi.org/10.1111/j.1540-5907.2006.00187.x.

West, Mike. 1987. “On Scale Mixtures of Normal Distributions.” Biometrika 74 (3): 646–48. https://doi.org/10.1093/biomet/74.3.646.

Western, Bruce. 1998. “Causal Heterogeneity in Comparative Research: A Bayesian Hierarchical Modelling Approach.” American Journal of Political Science 42 (4): 1233–59. https://doi.org/10.2307/2991856.

Western, Bruce, and Simon Jackman. 1994. “Bayesian Inference for Comparative Research.” American Political Science Review 88 (02): 412–23. https://doi.org/10.2307/2944713.

Wickham, Hadley, Dianne Cook, Heike Hofmann, and Andreas Buja. 2010. “Graphical Inference for Infovis.” IEEE Transactions on Visualization and Computer Graphics 16 (6): 973–79. https://doi.org/10.1109/tvcg.2010.161.

Wimmer, G., and G. Altmann. 1999. Thesaurus of Univariate Discrete Probability Distributions. Stamm.

Yu, Keming, and Jin Zhang. 2005. “A Three-Parameter Asymmetric Laplace Distribution and Its Extension.” Communications in Statistics - Theory and Methods 34 (9-10): 1867–79. https://doi.org/10.1080/03610920500199018.

Zorn, Christopher. 2005. “A Solution to Separation in Binary Response Models.” Political Analysis 13 (2): 157–70. https://doi.org/10.1093/pan/mpi009.