Journal of Applied Probability

Summary statistics for endpoint-conditioned continuous-time Markov chains

Asger Hobolth and Jens Ledet Jensen

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Abstract

Continuous-time Markov chains are a widely used modelling tool. Applications include DNA sequence evolution, ion channel gating behaviour, 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.

Article information

Source
J. Appl. Probab., Volume 48, Number 4 (2011), 911-924.

Dates
First available in Project Euclid: 16 December 2011

Permanent link to this document
https://projecteuclid.org/euclid.jap/1324046009

Digital Object Identifier
doi:10.1239/jap/1324046009

Mathematical Reviews number (MathSciNet)
MR2896658

Zentralblatt MATH identifier
1231.60071

Subjects
Primary: 60-08: Computational methods (not classified at a more specific level) [See also 65C50]
Secondary: 60J22: Computational methods in Markov chains [See also 65C40] 60J25: Continuous-time Markov processes on general state spaces 60J27: Continuous-time Markov processes on discrete state spaces

Keywords
Continuous-time Markov chain dwelling time EM algorithm transition number uniformization

Citation

Hobolth, Asger; Jensen, Jens Ledet. Summary statistics for endpoint-conditioned continuous-time Markov chains. J. Appl. Probab. 48 (2011), no. 4, 911--924. doi:10.1239/jap/1324046009. https://projecteuclid.org/euclid.jap/1324046009


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