Bounding the lumping error in Markov chain dynamics
نویسندگان
چکیده
منابع مشابه
Bounding the lumping error in Markov chain dynamics
Forming lumped states in a Markov chain is a very useful device leading to a coarser level of description. The Markov chain on these lumped states is often taken as an approximation for the time evolution of the unlumped chain. In the present work we derive a bound on the error in this approximation.
متن کاملInference of higher order substitution dynamics by Markov chain lumping
We apply Markov chain lumping techniques to aggregate codons from an empirical substitution matrix. The standard genetic code as well as higher order amino acid substitution groups are identified. Since the aggregates are derived from first principles they do not rely on system dependent assumptions made beforehand, e.g. regarding criteria on what should constitute an amino acid group. We there...
متن کاملA Symbolic Algorithm for Optimal Markov Chain Lumping
Many approaches to tackle the state explosion problem of Markov chains are based on the notion of lumpability, which allows computation of measures using the quotient Markov chain, which, in some cases, has much smaller state space than the original one. We present, for the first time, a symbolic algorithm and its implementation for the lumping of Markov chains that are represented using Multi-...
متن کاملOptimal state-space lumping in Markov chains
We prove that the optimal lumping quotient of a finite Markov chain can be constructd in O(m lg n) time, where n is the number of states and m is the number of transitions. The proof relies on the use of splay trees [18] to sort transition weights.
متن کاملDiscrepancy estimates for variance bounding Markov chain quasi-Monte Carlo
Markov chain Monte Carlo (MCMC) simulations are modeled as driven by true random numbers. We consider variance bounding Markov chains driven by a deterministic sequence of numbers. The star-discrepancy provides a measure of efficiency of such Markov chain quasi-Monte Carlo methods. We define a pull-back discrepancy of the driver sequence and state a close relation to the star-discrepancy of the...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Applied Mathematics Letters
سال: 2009
ISSN: 0893-9659
DOI: 10.1016/j.aml.2009.03.016