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Crawford FW, Stutz TC, Lange K. Coupling bounds for approximating birth-death processes by truncation. Stat Probab Lett. 2016;109:30-38doi: 10.1016/j.spl.2015.10.013.
Crawford, F. W., Stutz, T. C., & Lange, K. (2016). Coupling bounds for approximating birth-death processes by truncation. Statistics & probability letters, 10930-38. https://doi.org/10.1016/j.spl.2015.10.013
Crawford, Forrest W, et al. "Coupling bounds for approximating birth-death processes by truncation." Statistics & probability letters vol. 109 (2016): 30-38. doi: https://doi.org/10.1016/j.spl.2015.10.013
Crawford FW, Stutz TC, Lange K. Coupling bounds for approximating birth-death processes by truncation. Stat Probab Lett. 2016 Feb 01;109:30-38. doi: 10.1016/j.spl.2015.10.013. PMID: 26622074; PMCID: PMC4662656.
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Stat Probab Lett. 2016 Feb 01;109:30-38. doi: 10.1016/j.spl.2015.10.013.

Coupling bounds for approximating birth-death processes by truncation.

Statistics & probability letters

Forrest W Crawford, Timothy C Stutz, Kenneth Lange

Affiliations

  1. Departments of Biostatistics and Ecology & Evolutionary Biology, Yale University, 60 College St, PO Box 208034 New Haven, CT 06510 USA, phone: (203) 785-6125.
  2. Department of Biomathematics, University of California, Los Angeles.
  3. Department of Biomathematics, University of California, Los Angeles ; Departments of Human Genetics and Statistics, University of California, Los Angeles.

PMID: 26622074 PMCID: PMC4662656 DOI: 10.1016/j.spl.2015.10.013

Abstract

Birth-death processes are continuous-time Markov counting processes. Approximate moments can be computed by truncating the transition rate matrix. Using a coupling argument, we derive bounds for the total variation distance between the process and its finite approximation.

References

  1. Theor Popul Biol. 2003 Mar;63(2):159-68 - PubMed
  2. Brief Bioinform. 2006 Mar;7(1):70-85 - PubMed
  3. J Math Biol. 2012 Sep;65(3):553-80 - PubMed
  4. J Am Stat Assoc. 2014 Apr;109(506):730-747 - PubMed

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Grant support