A random sequence is a sequence-valued outcome whose elements are generated according to a probability model. Its length may be finite or infinite, and its values may be discrete or continuous. section 16.6
A Markov process constructs a random sequence one state at a time:
- Choose the first state by sampling from an initial distribution. section 16.6
- Choose each later state by applying a transition function to the most recent state and sampling from the resulting distribution. section 16.6
- Allow states to be anything, including words, so the resulting sequence can become text. section 16.6
From words to posterior samples
Recording initial-word and word-pair distributions from existing sentences produces a simple random text generator. The Metropolis algorithm instead constructs a Markov process whose sequence of states samples a target continuous posterior distribution. section 16.0 section 16.6
