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The following books have example models translated to Stan
BUGS example models volumes 1--3.
David Lunn, Christopher Jackson, Nicky Best, Andrew Thomas, and David Spiegelhalter (2012) The BUGS Book: A Practical Introduction to Bayesian Analysis. CRC Press.
Applied regression modeling examples from
Andrew Gelman and Jennifer Hill (2006) Data Analysis Using Regression and Multilevel/Hierarchical Models. Cambridge University Press.
Bayesian Cognitive Modeling Examples
Bayesian models of cognition, examples from:
Michael Lee and Eric-Jan Wagenmakers (2013) Bayesian Modeling for Cognitive Science: A Practical Course. Cambridge Univesity Press.
Bayesian Population Analysis Examples
Bayesian models for ecology, translated from examples in:
Marc Kéry and Michael Schaub (2012) Bayesian Population Analysis using WinBUGS --- A Hierarchical Perspective. Academic Press.
There are also examples available in the manual.