Approximate Bayesian computation for censored data and its application to reliability assessment

References

• Balakrishnan, N. and Cramer, E. (2014) The Art of Progressive Censoring: Applications to Reliability and Quality, Springer, New York, NY.
   Google Scholar
• Barber, S., Voss, J. and Webster, M. (2015) The rate of convergence for approximate Bayesian computation. Electronic Journal of Statistics, 9, 80–105.
   Web of Science ®Google Scholar
• Beaumont, M. (2010) Approximate Bayesian computation in evolution and ecology. Annual Review of Ecoloyg Evolution and Systematics, 41, 379–406.
   Web of Science ®Google Scholar
• Beaumont, M., Zhang, W. and Balding, D. (2002) Approximate Bayesian computation in population genetics. Genetics, 162, 2025–2035.
   PubMed Web of Science ®Google Scholar
• Biau, G., Cerou, F. and Guyader, A. (2015) New insights into approximate Bayesian computation. Annals de l’Institut Henri Poincar, Probabilities et Statistiques, 51, 376–403.
   Web of Science ®Google Scholar
• Blum, M. (2010) Approximate Bayesian computation: A nonparametric perspective. Journal of the American Statistical Society, 105(491), 1178–1187.
   Web of Science ®Google Scholar
• Blum, M., Nunes, M., Prangle, D. and Sisson, S. (2013) A comparative review of dimension reduction methods in approximate Bayesian computation. Statistical Science, 28(2), 189–208.
   Web of Science ®Google Scholar
• Bonassi, F. and West, M. (2015) Sequential Monte Carlo with adaptive weights for approximate Bayesian computation. Bayesian Analysis, 10(1), 171–187.
   Web of Science ®Google Scholar
• Burr, T. and Skurikhin, A. (2013) Selecting summary statistics in approximate Bayesian computation for calibrating stochastic models. Biomedical Research International, 2013, e210646, 10pp.
   Google Scholar
• Csillery, K., Blum, M., Gaggiotti, O. and Francois, O. (2010) Approximate Bayesian computation (ABC) in practice. Trends in Ecology & Evolution, 25, 410–418.
   PubMed Web of Science ®Google Scholar
• Dean, T., Singh, S., Jasra, A. and Peters, G. (2014) Parameter estimation for hidden markov models with intractable likelihoods. Scandinavian Journal of Statistics, 41(4), 970–987.
   Web of Science ®Google Scholar
• Diggle, P. and Gratton, R. (1984) Monte Carlo methods of inference for implicit statistical models (with discussion). Journal of the Royal Statistics Society, Series B, 46(2), 193–227.
   Google Scholar
• Dutta, R., Corander, J., Kaski, S. and Gutmann, M. (2016) Likelihood-free inference by ratio estimation. arXiv:1611.10242.
   Google Scholar
• Ebrahimi, N. and McCullough, K. (2016) Using approximate Bayesian computation to assess the reliability of nanocomponents of a nanosystem. International Journal of Reliability, Quality and Safety Engineering, 23(2), e1650009, 28pp.
   Web of Science ®Google Scholar
• Ebrahimi, N., McCullough, K. and Xiao, Z. (2013a) Reliability of sensors based on nanowire networks. IIE Transaction, 45(2), 215–228.
   Web of Science ®Google Scholar
• Ebrahimi, N., McCullough, K. and Xiao, Z. (2013b) Reliability of sensors based on nanowire networks modeled by equilateral triangle and hexagonal lattices. IEEE Transactions on Nanotechnology, 1, 81–95.
   Google Scholar
• Ebrahimi, N. and Shehadeh, M. (2015) Assessing the reliability of components with micro- and nano-structures when they are part a multi-scale system. Reliability Engineering & System Safety, 138, 13–20.
   Web of Science ®Google Scholar
• Fearnhead, P. and Prangle, D. (2012) Constructing summary statistics for approximate Bayesian computation: Semi-automatic approximate Bayesian computation. Journal of the Royal Statistical Society, 74, 1–28.
   Google Scholar
• Frazier, D., Martin, G., Robert, C. and Rousseau, J. (2016) Asymptotic properties of approximate Bayesian computation. arXiv preprint, arXiv:1607.06903.
   Google Scholar
• Grazian, C. and Liseo, B. (2015) Approximate Bayesian computation for copula estimation. Statistica, 75(1), 111–127.
   Web of Science ®Google Scholar
• Harrison, J. and Baker, R. (2017) An automatic adaptive method to combine summary statistics in approximate Bayesian computation. arXiv preprint arXiv:1703.02341.
   Google Scholar
• Ibeh, N. and Aris-Brosou, S. (2016) Estimation of sub-epidemic dynamics by means of sequential Monte Carlo approximate Bayesian computation: An application to the Swiss HIV cohort study. BioRxiv, preprint.
   Google Scholar
• Jarvenpaa, M., Gutmann, M., Vehtari, A. and Marttinen, P. (2016) Gaussian process modeling in approximate Bayesian computation to estimate horizontal gene transfer in bacteria. arXiv:1610.06462.
   Google Scholar
• Jasra, A. (2015) Approximate Bayesian computation for a class of time series models. International Statatical Review, 83(3), 405–435.
   Web of Science ®Google Scholar
• Jiang, B., Wu, T., Zheng, C. and Wong, W. (2017) Learning summary statistic for approximate Bayesian computation via deep neural network. Statistica Sinica, 27(4), 1595–1618.
   Web of Science ®Google Scholar
• Krishnanathan, K., Anderson, S., Billings, S. and Kadirkamanathan, V. (2015) Computational system identification of continuous-time nonlinear systems using approximate Bayesian computation. International Journal of System Science, 47(15), 3537–3544.
   Web of Science ®Google Scholar
• Li, J., Nott, D., Fan, Y. and Sisson, S. (2017) Extending approximate Bayesian computation methods to high dimensions via a Gaussian copula model. Computational Statistics and Data Analysis, 106, 77–89.
   Web of Science ®Google Scholar
• Lin, D., Usher, J. and Guess, F. (1996) Bayes estimation of component-reliability from masked system-life data. IEEE Transactions on Reliability, 45(2), 233–237.
   Web of Science ®Google Scholar
• Lindqvist, H. and Skogsrud, G. (2008) Modeling of dependent competing risks by first passage times of Wiener processes. IIE Transactions, 41(1), 72–80.
   Web of Science ®Google Scholar
• Majoram, P. (2013) Approximation Bayesian computation. OA Genetics, 1(3), 853.
   Google Scholar
• Mason, P. (2016) Approximate Bayesian computation of the occurrence and size of defects in advanced gas-cooled nuclear reactor boilers. Reliability Engineering & System Safety, 146, 21–25.
   Web of Science ®Google Scholar
• Masuda, H., Ashoh, H., Watanabe, M., Nishio, K., Nakao, M. and Tamamura, T. (2001) Square and triangular nanohole array architectures in anodic alumina. Advanced Materials, 13(3), 189–192.
   Web of Science ®Google Scholar
• Meeds, E. and Welling, M. (2014) GPS-ABC: Gaussian process surrogate approximate Bayesian computation. arXiv:1401.2838v1.
   Google Scholar
• Mitrovic, J., Sejdinovic, D. and Teh, Y. (2016) DR-ABC: Approximate Bayesian computation with kernel-based distribution regression, in Proceedings of ICML 2016, JMLR W&CP, New York, volume 48, pp. 1482–1491.
   Google Scholar
• Picchini, U. and Forman, J. (2017) Bayesian inference for stochastic differential equation mixed effects models of a tumor xenography study. arXiv:1607.02633.
   Google Scholar
• Prangle, D. (2016) Lazy ABC. Statistics and Computing, 26, 171–185.
   Web of Science ®Google Scholar
• Roding, M., Zagato, E., Remaut, K. and Braeckmans, K. (2016) Approximate Bayesian computation for estimating number concentrations of monodisperse nanoparticles in suspension by optical microscopy. Physics Review E, 93(6), 063311.
   Web of Science ®Google Scholar
• Ruli, E., Sartori, N. and Ventura, L. (2016) Approximate Bayesian computation with composite score functions. Statistics and Computing, 26(3), 679–692.
   Web of Science ®Google Scholar
• Sarhan, A. (2001) Reliability estimations of components from masked system life data. Reliability Engineering & System Safety, 74(1), 107–113.
   Web of Science ®Google Scholar
• Scranton, K., Knape, J. and de Velpine, P. (2014) An approximate Bayesian computation approach to parameter estimation in a stochastic stage-structured population model. Ecology, 95(5), 1418–1428.
   Web of Science ®Google Scholar
• Sousa, V., Fritz, M., Beaumont, M. and Chikhi, L. (2009) Approximate Bayesian computation without summary statistics: The case of admixture. Genetics, 181(4), 1507–1519.
   Web of Science ®Google Scholar
• Tavare, S., Balding, D., Griffiths, R. and Donnelly, P. (1997) Inferring coalescence times from DNA sequence data. Genetics, 145(2), 505–518.
   PubMed Web of Science ®Google Scholar
• Turner, B. and Sederberg, P. (2014) A generalized, likelihood-free method for posterior estimation. Psychonomic Bulletin and Review, 21(2), 227–250.
   Web of Science ®Google Scholar
• Vakilzadeh, M., Huang, Y., Beck, J. and Abrahamsson, T. (2017) Approximate Bayesian computation by subset simulation using hierarchical state-space models. Mechanical Systems and Signal Processing, 84(B), 2–20.
   Google Scholar
• Wilkinson, R. (2012) Accelerating ABC methods using Gaussian processes, in Proceedings of AISTATS 2014, JMLR W&CP, Reykjavik, Iceland, volume 33, pp. 1015–1023.
   Google Scholar
• Wilkinson, R. (2013) Approximate Bayesian computation (ABC) gives exact results under the assumption of model error. Statistical Applications in Genetics and Molecular Biology B, 12(2), 1–13.
   Web of Science ®Google Scholar
• Yang, F., Taggart, D. and Penner, R. (2009) Fast, sensitive hydrogen gas detection using single palladium nanowires that resist fracture. Nano Letters, 9(5), 2177–2182.
   Web of Science ®Google Scholar
• Zeng, X., Latimer, M., Xiao, Z., Panuganti, S., Welp, U., Kwok, W. and Xu, T. (2011) Hydrogen gas sensing with networks of ultrasmall palladium nanowires formed on filtration membranes. Nano Letters, 11(1), 262–268.
   Web of Science ®Google Scholar
• Zeng, X., Wang, Y., Deng, H., Latimer, M., Xiao, Z., Pearson, J., Xu, T., Wang, H., Welp, U., Crabtree, G. and Kwok, W. (2011) Networks of ultrasmall Pd/Cr nanowires as high performance hydrogen sensors. ACS Nano, 5(9), 7443–7452.
   Web of Science ®Google Scholar
• Zhou, J. and Fukumizu, K. (2017) Local kernel dimension reduction in approximate Bayesian computation. arXiv:1609.01022v2.
   Google Scholar