A Bayesian approach for multi-stage models with linear time-dependent hazard rate
-
Hoa Pham
und
Huong T. T. Pham
Abstract
Multi-stage models have been used to describe progression of individuals which develop through a sequence of discrete stages. We focus on the multi-stage model in which the number of individuals in each stage is assessed through destructive samples for a sequence of sampling time. Moreover, the stage duration distributions of the model are effected by a time-dependent hazard rate. The multi-stage models become complex with a stage having time-dependent hazard rate. The main aim of this paper is to derive analytically the approximation of the likelihood of the model. We apply the approximation to the Metropolis–Hastings (MH) algorithm to estimate parameters for the model. The method is demonstrated by applying to simulated data which combine non-hazard rate, stage-wise constant hazard rate and time-dependent hazard rates in stage duration distributions.
References
[1] P. Amore, Asymptotic and exact series representations for the incomplete gamma function, Europhys. Lett. 71 (2005), no. 1, 1–7. 10.1209/epl/i2005-10066-6Suche in Google Scholar
[2] J. M. Borwein and O.-Y. Chan, Uniform bounds for the complementary incomplete gamma function, Math. Inequal. Appl. 12 (2009), no. 1, 115–121. 10.7153/mia-12-10Suche in Google Scholar
[3] P. De Valpine, Stochastic development in biologically structured population models, Ecology 90 (2009), no. 10, 2889–2901. 10.1890/08-0703.1Suche in Google Scholar PubMed
[4] P. De Valpine and J. Knape, Estimation of general multistage models from cohort data, J. Agric. Biol. Environ. Stat. 20 (2015), no. 1, 140–155. 10.1007/s13253-014-0189-7Suche in Google Scholar
[5] P. De Valpine, K. Scranton, J. Knape, K. Ram and N. J. Mills, The importance of individual developmental variation in stage structured population models, Ecology Lett. 17 (2014), no. 8, 1026–1038. 10.1111/ele.12290Suche in Google Scholar PubMed
[6] S. Dutta and S. Bhattacharya, Markov chain Monte Carlo based on deterministic transformations, Stat. Methodol. 16 (2014), 100–116. 10.1016/j.stamet.2013.08.006Suche in Google Scholar
[7] P. Hoa and J. B. Alan, Exploring parameter relations for multi-stage models in stage-wise constant and time dependent hazard rates, Aust. N. Z. J. Stat. 58 (2016), no. 3, 357–376. 10.1111/anzs.12164Suche in Google Scholar
[8] J. A. Hoeting, R. L. Tweedie and C. S. Olver, Transform estimation of parameters for stage-frequency data, J. Amer. Statist. Assoc. 98 (2003), no. 463, 503–514. 10.1198/016214503000000288Suche in Google Scholar
[9] J. Knape, K. M. Daane and P. de Valpine, Estimation of stage duration distributions and mortality under repeated cohort censuses, Biometrics 70 (2014), no. 2, 346–355. 10.1111/biom.12138Suche in Google Scholar PubMed
[10] B. F. J. Manly, Stage-structured Populations: Sampling, Analysis and Simulation, Chapman and Hall, New York, 1990. 10.1007/978-94-009-0843-7_1Suche in Google Scholar
[11] E. Neuman, Inequalities and bounds for the incomplete gamma function, Results Math. 63 (2013), no. 3–4, 1209–1214. 10.1007/s00025-012-0263-9Suche in Google Scholar
[12] H. Pham, D. Nur, H. T. T. Pham and A. Branford, A Bayesian approach for parameter estimation in multi-stage models, Comm. Statist. Theory Methods 48 (2019), no. 10, 2459–2482. 10.1080/03610926.2018.1465090Suche in Google Scholar
[13] K. L. Q. Read and J. R. Ashford, A system of models for the life cycle of a biological organism, Biometrika 55 (1968), 211–221. 10.1093/biomet/55.1.211Suche in Google Scholar
[14] H.-J. Schuh and R. L. Tweedie, Parameter estimation using transform estimation in time-evolving models, Math. Biosci. 45 (1979), no. 1–2, 37–67. 10.1016/0025-5564(79)90095-6Suche in Google Scholar
[15] B. Sroysang, Inequalities for the incomplete gamma function, Math. Æterna 3 (2013), no. 3–4, 245–248. Suche in Google Scholar
© 2019 Walter de Gruyter GmbH, Berlin/Boston
Artikel in diesem Heft
- Frontmatter
- An aspect of optimal regression design for LSMC
- Equity-linked security pricing and Greeks at arbitrary intermediate times using Brownian bridge
- A Bayesian approach for multi-stage models with linear time-dependent hazard rate
- A kind of dual form for coupling from the past algorithm, to sample from Markov chain steady-state probability
- Geometry entrapment in Walk-on-Subdomains
- A second-order discretization for forward-backward SDEs using local approximations with Malliavin calculus
Artikel in diesem Heft
- Frontmatter
- An aspect of optimal regression design for LSMC
- Equity-linked security pricing and Greeks at arbitrary intermediate times using Brownian bridge
- A Bayesian approach for multi-stage models with linear time-dependent hazard rate
- A kind of dual form for coupling from the past algorithm, to sample from Markov chain steady-state probability
- Geometry entrapment in Walk-on-Subdomains
- A second-order discretization for forward-backward SDEs using local approximations with Malliavin calculus
