Hamiltonian Monte Carlo for Hierarchical Models

• Published in: Current Trends in Bayesian Methodology with Applications pp. 119 - 142
• Format: Book Chapter
• Language: English
• Published: United Kingdom Chapman and Hall/CRC 2015; CRC Press LLC
• Subjects: BIOLOGY, LIFE SCIENCES; Probability & statistics; Random Walk Metropolis; Non-centered Parameterizations; Step Size; Random Walk Behavior; Momenta Distribution; Acceptance Probability; Stan Models; MCMC; Pe Rc; Generalized Linear Model; Markov Chain Monte Carlo Techniques; Variance Τ2; Int; Hierarchical Models; Characteristic Length Scale; Random Walk; Latent Parameters; Gibbs Sampler; Potential Scale Reduction Factor; Target Distribution; Markov Chain Monte Carlo Algorithms; Marginal Variances; Ge A; Optimal Integration Time
• ISBN: 1482235110; 9781482235111
• DOI: 10.1201/b18502-11

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.