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# References

Bailey, David H., Karthik Jeyabalan, and Xiaoye S. Li. 2005. “A Comparison of Three High-Precision Quadrature Schemes.” Experiment. Math. 14 (3): 317–29. https://projecteuclid.org:443/euclid.em/1128371757.

Bowling, Shannon R., Mohammad T. Khasawneh, Sittichai Kaewkuekool, and Byung Rae Cho. 2009. “A Logistic Approximation to the Cumulative Normal Distribution.” Journal of Industrial Engineering and Management 2 (1): 114–27.

Durbin, J., and S. J. Koopman. 2001. Time Series Analysis by State Space Methods. New York: Oxford University Press.

Feller, William. 1968. An Introduction to Probability Theory and Its Applications. Vol. 1. 3. Wiley, New York.

Gelman, Andrew, J. B. Carlin, Hal S. Stern, David B. Dunson, Aki Vehtari, and Donald B. Rubin. 2013. Bayesian Data Analysis. Third. London: Chapman &Hall/CRC Press.

Guennebaud, Gaël, Benoît Jacob, and others. 2010. “Eigen V3.” http://eigen.tuxfamily.org.

Jorge J. More, Kenneth E. Hillstrom, Burton S. Garbow. 1980. User Guide for Minpack-1. 9700 South Cass Avenue, Argonne, Illinois 60439: Argonne National Laboratory.

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.

Lunn, D. J., J. Wakefield, A. Thomas, N. Best, and D. Spiegelhalter. 1999. PKBugs User Guide.

Mori, Masatake. 1978. “An Imt-Type Double Exponential Formula for Numerical Integration.” Publications of the Research Institute for Mathematical Sciences 14 (3): 713–29. https://doi.org/10.2977/prims/1195188835.

Navarro, Daniel J, and Ian G Fuss. 2009. “Fast and Accurate Calculations for First-Passage Times in Wiener Diffusion Models.” Journal of Mathematical Psychology 53 (4): 222–30.

Powell, Michael J. D. 1970. “A Hybrid Method for Nonlinear Equations.” In Numerical Methods for Nonlinear Algebraic Equations, edited by P. Rabinowitz. Gordon; Breach.

Takahasi, Hidetosi, and Masatake Mori. 1974. “Double Exponential Formulas for Numerical Integration.” Publications of the Research Institute for Mathematical Sciences 9 (3): 721–41. https://doi.org/10.2977/prims/1195192451.

Tanaka, Ken’ichiro, Masaaki Sugihara, Kazuo Murota, and Masatake Mori. 2009. “Function Classes for Double Exponential Integration Formulas.” Numerische Mathematik 111 (4): 631–55. https://doi.org/10.1007/s00211-008-0195-1.

Vandekerckhove, Joachim, and Dominik Wabersich. 2014. “The RWiener Package: An R Package Providing Distribution Functions for the Wiener Diffusion Model.” The R Journal 6/1. http://journal.r-project.org/archive/2014-1/vandekerckhove-wabersich.pdf.

1. This function used to be called get_lp(), but that name has been deprecated; using it will print a warning. The function get_lp() will be removed in a future release.↩︎

2. Dividing by $$N$$ rather than $$(N-1)$$ produces a maximum likelihood estimate of variance, which is biased to underestimate variance.↩︎

3. The softmax function is so called because in the limit as $$y_n \rightarrow \infty$$ with $$y_m$$ for $$m \neq n$$ held constant, the result tends toward the “one-hot” vector $$\theta$$ with $$\theta_n = 1$$ and $$\theta_m = 0$$ for $$m \neq n$$, thus providing a “soft” version of the maximum function.↩︎

4. It is possible to build up a valid L within Stan, but that would then require Jacobian adjustments to imply the intended posterior.↩︎