Cross-Fertilizing Strategies for Better EM Mountain Climbing and DA Field Exploration: A Graphical Guide Book

In recent years, a variety of extensions and refinements have been developed for data augmentation based model fitting routines. These developments aim to extend the application, improve the speed, and/or simplify the implementation of data augmentation methods, such as the deterministic EM algorithm for mode finding and stochastic Gibbs sampler and other auxiliary-variable based methods for posterior sampling. In this overview article we graphically illustrate and compare a number of these extensions all of which aim to maintain the simplicity and computation stability of their predecessors. We particularly emphasize the usefulness of identifying similarities between the deterministic and stochastic counterparts as we seek more efficient computational strategies. We also demonstrate the applicability of data augmentation methods for handling complex models Professor van Dyk’s research was supported in part by NSF grants DMS-04-06085, SES-05-50980, DMS-09-07522. Professor Meng’s research was supported in part by NSF grants DMS-04-05953, DMS-05-05595, DMS-06-52743, and DMS-09-07185 1 with highly hierarchical structure, using a high-energy high-resolution spectral imaging model for data from a new generation of satellite telescopes, such as the Chandra X-ray Observatory.