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

TL;DR

This paper provides a graphical overview of various data augmentation techniques for EM and DA methods, highlighting their similarities, extensions, and applications to complex hierarchical models in astrophysics.

Contribution

It introduces a comparative graphical guide to data augmentation strategies, emphasizing their extensions and applicability to complex hierarchical models.

Findings

Extensions improve computational stability and speed.

Graphical comparisons clarify similarities between methods.

Application demonstrated on satellite telescope spectral imaging.

Abstract

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 with highly hierarchical structure, using a high-energy high-resolution spectral imaging model for data from satellite telescopes, such as the Chandra X-ray Observatory.