ABSTRACT
This chapter adds coverage of recent developments, particularly on auxiliary likelihood methods and ABC model choice. It focuses on summary statistic selection methods which can be used with standard ABC algorithms. The chapter discusses issues which are common to many summary statistic selection methods, and reviews the theoretical results motivating the use of summary statistics in ABC. It describes why methods for selecting summary statistics are necessary in more theoretical detail. The chapter discusses the curse of dimensionality, showing that low dimensional informative summaries are needed. It splits summary statistic selection methods into three strategies: subset selection, projection, and auxiliary likelihood. The chapter gives an overview of each and introduces some useful general terminology. In practice, the categories overlap, with some methods applying a combination of the strategies. The chapter concentrates on using summary statistics to reduce the ABC curse of dimensionality and approximate the true posterior.
