I am familiar with the concept of stochastic ordering for two random variables and how we can say if a markov matrix is stochastically monotone. What I'm interested in is if there is a concept for ranking two separate markov matrices.
To illustrate suppose we have two stochastically monotone markov matrices A and B which preserve the ordering of x≿y. Under what circumstances can we say (if any) that matrix A is preferred to matrix B in stochastic order?
Note: The definitions I am using are from this slide deck: http://polaris.imag.fr/jean-marc.vincent/index.html/Slides/asmta09.pdf
Have a look at : https://wmassey.princeton.edu/20th%20Century/stochord.pdf
In any case a good, excellent, paper , to start with.
Kind regards, J.W.Nieuwenhuis.
``Preferred'' comes afterwards. Having an order isn't enough; what's necessary is defining quantities that are sensitive to it.
Depends on what your mean by two different matrices. If the two different matrices are derived from two different data sets, then no, the comparison is completely meaningless. If your matrices are using the same data but different sets of model parameters then of course you can compare the matrices since this is simple a test of of the fit of one set of parameters vs. another set.
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