Hamiltonian Monte Carlo for Hierarchical Models (Current Trends in Bayesian Methodology with Applications, 2015)
Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97 4.6 Appendix: Stan Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97Funnel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97 Generate One-Way Normal Pseudo-data . . . . . . . . . . . . . . . . . . . . . . . . 98 One-Way Normal (Centered) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99 One-Way Normal (Non-Centered) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99 Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100Many of the most exciting problems in applied statistics involve intricate, typically high-dimensional, models and, at least relative to the model complexity, sparse data. With the data alone unable to identify the model, valid inference in these circumstances requires signiﬁcant prior information. Such information, however, is not limited to the choice of an explicit prior distribution: it can be encoded in the construction of the model itself.