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|Title:||Similar states in continuous-time Markov chains|
Lumped Markov chain
|Citation:||Yap, V.B. (2009-06). Similar states in continuous-time Markov chains. Journal of Applied Probability 46 (2) : 497-506. ScholarBank@NUS Repository. https://doi.org/10.1239/jap/1245676102|
|Abstract:||In a homogeneous continuous-time Markov chain on a finite state space, two states that jump to every other state with the same rate are called similar. By partitioning states into similarity classes, the algebraic derivation of the transition matrix can be simplified, using hidden holding times and lumped Markov chains. When the rate matrix is reversible, the transition matrix is explicitly related in an intuitive way to that of the lumped chain. The theory provides a unified derivation for a whole range of useful DNA base substitution models, and a number of amino acid substitution models. © Applied Probability Trust 2009.|
|Source Title:||Journal of Applied Probability|
|Appears in Collections:||Staff Publications|
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