Generating Patterns

Summary

We are trying to recognise patterns in time, and in order to do so we attempt to model the process that could have generated the pattern. We use discrete time steps, discrete states, and we may make the Markov assumption. Having made these assumptions, the system producing the patterns can be described as a Markov process consisting of a vector and a state transition matrix. An important point about the assumption is that the state transition probabilites do not vary in time - the matrix is fixed throughout the life of the system.