## Summary statistics for end-point conditioned continuous-time Markov chains

Publikation: Working paperForskning

### Dokumenter

• T.N. Thiele Centre
• Institut for Matematiske Fag
• Center for Bioinformatik (BiRC)
Continuous-time Markov chains are a widely used modelling tool. Applications include DNA sequence evolution, ion channel gating behavior and mathematical finance. We consider the problem of calculating properties of summary statistics (e.g. mean time spent in a state, mean number of jumps between two states and the distribution of the total number of jumps) for discretely observed continuous time Markov chains. Three alternative methods for calculating properties of summary statistics are described and the pros and cons of the methods are discussed. The methods are based on (i) an eigenvalue decomposition of the rate matrix, (ii) the uniformization method, and (iii) integrals of matrix exponentials. In particular we develop a framework that allows for analyses of rather general summary statistics using the uniformization method.
Originalsprog Engelsk Århus Thiele Centre, Institut for Matematiske Fag, Aarhus Universitet 17 Udgivet - 7 aug. 2010

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