Agrawal, Nikhar, Anton Bikineev, Paul Bristow, Marco Guazzone, Christopher Kormanyos, Hubert Holin, Bruno Lalande, et al. 2017. “Double-Exponential Quadrature.” https://www.boost.org/doc/libs/1_66_0/libs/math/doc/html/math_toolkit/double_exponential.html.
Aguilar, Omar, and Mike West. 2000. “Bayesian Dynamic Factor Models and Portfolio Allocation.” Journal of Business & Economic Statistics 18 (3): 338–57.
Ahnert, Karsten, and Mario Mulansky. 2011. “Odeint—Solving Ordinary Differential Equations in C++.” arXiv 1110.3397.
Albert, J. H., and S. Chib. 1993. “Bayesian Analysis of Binary and Polychotomous Response Data.” Journal of the American Statistical Association 88: 669–79.
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, 1281–311.
Bayarri, MJ, and James O Berger. 2000. “P Values for Composite Null Models.” Journal of the American Statistical Association 95 (452): 1127–42.
Betancourt, Michael. 2012. “A General Metric for Riemannian Manifold Hamiltonian Monte Carlo.” arXiv 1212.4693. http://arxiv.org/abs/1212.4693.
Betancourt, Michael, and Mark Girolami. 2013. “Hamiltonian Monte Carlo for Hierarchical Models.” arXiv 1312.0906. http://arxiv.org/abs/1312.0906.
Blackwell, David. 1947. “Conditional Expectation and Unbiased Sequential Estimation.” The Annals of Mathematical Statistics 18 (1): 105–10. https://doi.org/10.1214/aoms/1177730497.
Blei, David M., and John D. Lafferty. 2007. “A Correlated Topic Model of Science.” The Annals of Applied Statistics 1 (1): 17–37.
Blei, David M., Andrew Y. Ng, and Michael I. Jordan. 2003. “Latent Dirichlet Allocation.” Journal of Machine Learning Research 3: 993–1022.
Breiman, Leo. 1996. “Bagging Predictors.” Machine Learning 24 (2): 123–40.
Brenan, K. E., S. L. Campbell, and L. R. Petzold. 1995. Numerical Solution of Initial-Value Problems in Differential-Algebraic Equations. SIAM Classics in Applied Mathematics 14. Philadelphia: Society for Industrial; Applied Mathematics.
Cash, J. R., and Alan H. Karp. 1990. “A Variable Order Runge-Kutta Method for Initial Value Problems with Rapidly Varying Right-Hand Sides.” ACM Transactions on Mathematical Software 16 (3): 201–22. https://doi.org/10.1145/79505.79507.
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.
Clayton, D. G. 1992. “Models for the Analysis of Cohort and Case-Control Studies with Inaccurately Measured Exposures.” In Statistical Models for Longitudinal Studies of Exposure and Health, edited by James H. Dwyer, Manning Feinleib, Peter Lippert, and Hans Hoffmeister, 301–31. New York: Oxford University Press.
Cohen, Scott D, and Alan C Hindmarsh. 1996. “CVODE, a Stiff/Nonstiff ODE Solver in C.” Computers in Physics 10 (2): 138–43.
Cook, Samantha R., Andrew Gelman, and Donald B Rubin. 2006. “Validation of Software for Bayesian Models Using Posterior Quantiles.” Journal of Computational and Graphical Statistics 15 (3): 675–92. https://doi.org/10.1198/106186006X136976.
Cormack, R. M. 1964. “Estimates of Survival from the Sighting of Marked Animals.” Biometrika 51 (3/4): 429–38.
Curtis, S. McKay. 2010. “BUGS Code for Item Response Theory.” Journal of Statistical Software 36 (1): 1–34.
Dawid, A Philip. 1982. “The Well-Calibrated Bayesian.” Journal of the American Statistical Association 77 (379): 605–10.
Dawid, A. P., and A. M. Skene. 1979. “Maximum Likelihood Estimation of Observer Error-Rates Using the EM Algorithm.” Journal of the Royal Statistical Society. Series C (Applied Statistics) 28 (1): 20–28.
Dempster, A. P., N. M. Laird, and D. B. Rubin. 1977. “Maximum Likelihood from Incomplete Data via the EM Algorithm.” Journal of the Royal Statistical Society. Series B (Methodological) 39 (1): 1–38.
Dormand, John R, and Peter J Prince. 1980. “A Family of Embedded Runge-Kutta Formulae.” Journal of Computational and Applied Mathematics 6 (1): 19–26.
Efron, Bradley, and Robert Tibshirani. 1986. “Bootstrap Methods for Standard Errors, Confidence Intervals, and Other Measures of Statistical Accuracy.” Statistical Science 1 (1): 54–75.
Efron, Bradley, and Robert J Tibshirani. 1994. An Introduction to the Bootstrap. Chapman & Hall/CRC.
Engle, Robert F. 1982. “Autoregressive Conditional Heteroscedasticity with Estimates of Variance of United Kingdom Inflation.” Econometrica 50: 987–1008.
Field, Christopher B, Michael J Behrenfeld, James T Randerson, and Paul Falkowski. 1998. “Primary Production of the Biosphere: Integrating Terrestrial and Oceanic Components.” Science 281 (5374): 237–40.
Fonnesbeck, Chris, Anand Patil, David Huard, and John Salvatier. 2013. PyMC User’s Guide.
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.
Gelman, A. 2006. “Prior Distributions for Variance Parameters in Hierarchical Models.” Bayesian Analysis 1 (3): 515–34.
Gelman, Andrew. 2004. “Parameterization and Bayesian Modeling.” Journal of the American Statistical Association 99: 537–45.
Gelman, Andrew, J. B. Carlin, Hal S. Stern, David B. Dunson, Aki Vehtari, and Donald B. Rubin. 2013. Bayesian Data Analysis. Third Edition. London: Chapman & Hall / CRC Press.
Gelman, Andrew, and Jennifer Hill. 2007. Data Analysis Using Regression and Multilevel-Hierarchical Models. Cambridge, United Kingdom: Cambridge University Press.
Gelman, Andrew, Xiao-Li Meng, and Hal Stern. 1996. “Posterior Predictive Assessment of Model Fitness via Realized Discrepancies.” Statistica Sinica, 733–60.
Girolami, Mark, and Ben Calderhead. 2011. “Riemann Manifold Langevin and Hamiltonian Monte Carlo Methods.” Journal of the Royal Statistical Society: Series B (Statistical Methodology) 73 (2): 123–214.
Gneiting, Tilmann, Fadoua Balabdaoui, and Adrian E Raftery. 2007. “Probabilistic Forecasts, Calibration and Sharpness.” Journal of the Royal Statistical Society: Series B (Statistical Methodology) 69 (2): 243–68.
Gneiting, Tilmann, and Adrian E Raftery. 2007. “Strictly Proper Scoring Rules, Prediction, and Estimation.” Journal of the American Statistical Association 102 (477): 359–78.
Greene, William H. 2011. Econometric Analysis. 7th ed. Prentice-Hall.
Hairer, Ernst, Syvert P. Nørsett, and Gerhard Wanner. 1993. Solving Ordinary Differential Equations I: Nonstiff Problems. 2nd ed. Springer Series in Computational Mathematics, Springer Ser.Comp.Mathem. Hairer,E.:Solving Ordinary Diff. Berlin Heidelberg: Springer-Verlag.
Hindmarsh, Alan C, Peter N Brown, Keith E Grant, Steven L Lee, Radu Serban, Dan E Shumaker, and Carol S Woodward. 2005. “SUNDIALS: Suite of Nonlinear and Differential/Algebraic Equation Solvers.” ACM Transactions on Mathematical Software (TOMS) 31 (3): 363–96.
Hoeting, Jennifer A., David Madigan, Adrian E Raftery, and Chris T. Volinsky. 1999. “Bayesian Model Averaging: A Tutorial.” Statistical Science 14 (4): 382–417.
Hoffman, Matthew D., and Andrew Gelman. 2014. “The No-U-Turn Sampler: Adaptively Setting Path Lengths in Hamiltonian Monte Carlo.” Journal of Machine Learning Research 15: 1593–623. http://jmlr.org/papers/v15/hoffman14a.html.
Huggins, Jonathan H, and Jeffrey W Miller. 2019. “Using Bagged Posteriors for Robust Inference and Model Criticism.” arXiv, no. 1912.07104.
Jarrett, R. G. 1979. “A Note on the Intervals Between Coal-Mining Disasters.” Biometrika 66 (1): 191–93.
Jolly, G. M. 1965. “Explicit Estimates from Capture-Recapture Data with Both Death and Immigration-Stochastic Model.” Biometrika 52 (1/2): 225–47.
Kennedy, Lauren, and Andrew Gelman. 2019. “Know Your Population and Know Your Model: Using Model-Based Regression and Poststratification to Generalize Findings Beyond the Observed Sample.” arXiv, no. 1906.11323.
Kim, Sangjoon, Neil Shephard, and Siddhartha Chib. 1998. “Stochastic Volatility: Likelihood Inference and Comparison with ARCH Models.” Review of Economic Studies 65: 361–93.
Lambert, Diane. 1992. “Zero-Inflated Poisson Regression, with an Application to Defects in Manufacturing.” Technometrics 34 (1).
Lewandowski, Daniel, Dorota Kurowicka, and Harry Joe. 2009. “Generating Random Correlation Matrices Based on Vines and Extended Onion Method.” Journal of Multivariate Analysis 100: 1989–2001.
Lincoln, F. C. 1930. “Calculating Waterfowl Abundance on the Basis of Banding Returns.” United States Department of Agriculture Circular 118: 1–4.
Little, Roderick JA. 1993. “Post-Stratification: A Modeler’s Perspective.” Journal of the American Statistical Association 88 (423): 1001–12.
Lunn, David, Christopher Jackson, Nicky Best, Andrew Thomas, and David Spiegelhalter. 2012. The BUGS Book: A Practical Introduction to Bayesian Analysis. CRC Press/Chapman & Hall.
Marsaglia, George. 1972. “Choosing a Point from the Surface of a Sphere.” The Annals of Mathematical Statistics 43 (2): 645–46.
Mazzia, F., J. R. Cash, and K. Soetaert. 2012. “A Test Set for Stiff Initial Value Problem Solvers in the Open Source Software R: Package deTestSet.” Journal of Computational and Applied Mathematics 236 (16): 4119–31.
Montenbruck, Oliver, and Eberhard Gill. 2000. Satellite Orbits: Models, Methods and Applications. Berlin Heidelberg: Springer-Verlag. https://doi.org/10.1007/978-3-642-58351-3.
Neal, Radford M. 1996a. Bayesian Learning for Neural Networks. Lecture Notes in Statistics 118. New York: Springer.
———. 1996b. “Sampling from Multimodal Distributions Using Tempered Transitions.” Statistics and Computing 6 (4): 353–66.
———. 1997. “Monte Carlo Implementation of Gaussian Process Models for Bayesian Regression and Classification.” 9702. University of Toronto, Department of Statistics.
———. 2003. “Slice Sampling.” Annals of Statistics 31 (3): 705–67.
Papaspiliopoulos, Omiros, Gareth O. Roberts, and Martin Sköld. 2007. “A General Framework for the Parametrization of Hierarchical Models.” Statistical Science 22 (1): 59–73.
Park, David K, Andrew Gelman, and Joseph Bafumi. 2004. “Bayesian Multilevel Estimation with Poststratification: State-Level Estimates from National Polls.” Political Analysis 12 (4): 375–85.
Paustian, Keith, Elissa Levine, Wilfred M Post, and Irene M Ryzhova. 1997. “The Use of Models to Integrate Information and Understanding of Soil C at the Regional Scale.” Geoderma 79 (1-4): 227–60.
Petersen, C. G. J. 1896. “The Yearly Immigration of Young Plaice into the Limfjord from the German Sea.” Report of the Danish Biological Station 6: 5–84.
Piironen, Juho, and Aki Vehtari. 2016. “Projection Predictive Model Selection for Gaussian Processes.” In Machine Learning for Signal Processing (MLSP), 2016 IEEE 26th International Workshop on. IEEE.
Powell, Michael J. D. 1970. “A Hybrid Method for Nonlinear Equations.” In Numerical Methods for Nonlinear Algebraic Equations, edited by P. Rabinowitz. Gordon; Breach.
Rao, C. Radhakrishna. 1945. “Information and Accuracy Attainable in the Estimation of Statistical Parameters.” Bulletin of the Calcutta Math Society 37 (3): 81–91.
Rasmussen, Carl Edward, and Christopher K. I. Williams. 2006. Gaussian Processes for Machine Learning. MIT Press.
Richardson, Sylvia, and Walter R. Gilks. 1993. “A Bayesian Approach to Measurement Error Problems in Epidemiology Using Conditional Independence Models.” American Journal of Epidemiology 138 (6): 430–42.
Rubin, Donald B. 1984. “Bayesianly Justifiable and Relevant Frequency Calculations for the Applied Statistician.” The Annals of Statistics, 1151–72.
Rubin, Donald B. 1981. “Estimation in Parallel Randomized Experiments.” Journal of Educational Statistics 6: 377–401.
Schofield, Matthew R. 2007. “Hierarchical Capture-Recapture Models.” PhD thesis, Department of Statistics, University of Otago, Dunedin.
Seber, G. A. F. 1965. “A Note on the Multiple-Recapture Census.” Biometrika 52 (1/2): 249–59.
Serban, Radu, and Alan C Hindmarsh. 2005. “CVODES: The Sensitivity-Enabled ODE Solver in SUNDIALS.” In ASME 2005 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, 257–69. American Society of Mechanical Engineers.
Smith, Teresa C., David J. Spiegelhalter, and Andrew Thomas. 1995. “Bayesian Approaches to Random-Effects Meta-Analysis: A Comparative Study.” Statistics in Medicine 14 (24): 2685–99.
Swendsen, Robert H., and Jian-Sheng Wang. 1986. “Replica Monte Carlo Simulation of Spin Glasses.” Physical Review Letters 57: 2607–9.
Talts, Sean, Michael Betancourt, Daniel Simpson, Aki Vehtari, and Andrew Gelman. 2018. “Validating Bayesian Inference Algorithms with Simulation-Based Calibration.” arXiv, no. 1804.06788.
Vehtari, Aki, Andrew Gelman, and Jonah Gabry. 2017. “Practical Bayesian Model Evaluation Using Leave-One-Out Cross-Validation and WAIC.” Statistics and Computing 27 (5): 1413–32.
Warn, David E., S. G. Thompson, and David J. Spiegelhalter. 2002. “Bayesian Random Effects Meta-Analysis of Trials with Binary Outcomes: Methods for the Absolute Risk Difference and Relative Risk Scales.” Statistics in Medicine 21: 1601–23.
Zellner, Arnold. 1962. “An Efficient Method of Estimating Seemingly Unrelated Regression Equations and Tests for Aggregation Bias.” Journal of the American Statistical Association 57: 348–68.
Zhang, Hao. 2004. “Inconsistent Estimation and Asymptotically Equal Interpolations in Model-Based Geostatistics.” Journal of the American Statistical Association 99 (465): 250–61.
Zyczkowski, K., and H. J. Sommers. 2001. “Induced Measures in the Space of Mixed Quantum States.” Journal of Physics A: Mathematical and General 34 (35): 7111.