Abstract
This paper deals with the class of bisexual branching processes with population-size dependent mating introduced in Molina et al. (2002, Bisexual Galton–Watson branching process with population-size dependent mating. J Appl Probab 39:479–490). We determine Bayes estimators for the main moments of such processes in both situations: assuming offspring distribution belonging to the bivariate power series family and considering that no assumption is made about the underlying offspring distribution. As illustration we provide several examples, in particular, considering some classical offspring distributions, we explicitly determine the proposed Bayes estimators and, through simulation, we show the evolution of their estimates and of the corresponding high posterior density credibility sets.
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References
Bernardo JM, Smith AFM (1994) Bayesian theory. Wiley, Chichester
Bruss FT (1984) A note on extinction criteria for bisexual Galton–Watson processes. J Appl Probab 21:915–919
Daley DJ (1968) Extinction conditions for certain bisexual Galton–Watson branching processes. Z Wahrscheinlichkeitstheorie 9:315–322
Gentleman R, Ihaka R (1996) A language for data analysis and graphics. J Comput Graph Stat 5:299–314
Guttorp P (1991) Statistical inference for branching processes. Wiley, New York
Hull DM (1982) A necessary condition for extinction in those bisexual Galton–Watson branching processes governed by superadditive mating functions. J Appl Probab 19:847–850
Khatri CG (1959) On certain properties of power-series distributions. Biometrika 46:486–490
Mendoza M, Gutiérrez-Peña E (2000) Bayesian conjugate analysis of the Galton–Watson process. Test 9:149–172
Molina M, Mota M, Ramos A (2002) Bisexual Galton–Watson branching process with population-size dependent mating. J Appl Probab 39:479–490
Molina M, Mota M, Ramos A (2004a) Limit behavior for a supercritical bisexual Galton–Watson branching process with population-size dependent mating. Stoch Process Appl 112:309–317
Molina M, Mota M, Ramos A (2004b) Some theoretical results for a bisexual Galton–Watson process with population-size dependent mating. J Math Sci 121:2681–2687
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Molina, M., Mota, M. & Ramos, A. Bayesian estimation in the class of bisexual branching processes with population-size dependent mating. TEST 17, 179–196 (2008). https://doi.org/10.1007/s11749-006-0029-3
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DOI: https://doi.org/10.1007/s11749-006-0029-3
Keywords
- Bisexual branching processes
- Population-size dependent processes
- Bayesian inference
- Bivariate power series distributions family