A distance function for stochastic matrices
This provides a tool for comparing healthcare processes, but it is incremental as it builds on existing information geometry concepts.
The paper tackles the problem of comparing Markov chain models by introducing a new distance function for stochastic matrices, which is shown to be efficient and equivalent to the Bhattacharyya angle for ergodic chains.
Motivated by information geometry, a distance function on the space of stochastic matrices is advocated. Starting with sequences of Markov chains the Bhattacharyya angle is advocated as the natural tool for comparing both short and long term Markov chain runs. Bounds on the convergence of the distance and mixing times are derived. Guided by the desire to compare different Markov chain models, especially in the setting of healthcare processes, a new distance function on the space of stochastic matrices is presented. It is a true distance measure which has a closed form and is efficient to implement for numerical evaluation. In the case of ergodic Markov chains, it is shown that considering either the Bhattacharyya angle on Markov sequences or the new stochastic matrix distance leads to the same distance between models.