Markov Processes and Random Sampling
The parameter spaces of natural patterns are so complex that inference must often proceed compositionally, successively building up more and more complex structures, as well as back-tracking, creating simpler structures from more complex versions. Inference is transformational in nature. The philosophical approach studied in this chapter is that the posterior distribution that describes the patterns contains all of the information about the underlying regular structure. Therefore, the transformations of inference are guided via the posterior in the sense that the algorithm for changing the regular structures will correspond to the sample path of a Markov process. The Markov process is constructed to push towards the posterior distribution in which the information about the patterns are stored. This provides the deepconnection between the transformational paradigm of regular structure creation, and random sampling algorithms.