References
- Ailliot, P., Thompson, C., Thomson, P. (2011). Mixed methods for fitting the GEV distribution. Water Resources Research 47:W05551, doi:10.1029/2010WR009417.
- Andrieu, C., Doucet, A., Holenstein, R. (2010). Particle Markov chain Monte Carlo methods. Journal of the Royal Statistical Society: Series B (Statistical Methodology) 72:269–342.
- Cappe, O., Godsill, S. J., Moulines, E. (2007). An overview of existing methods and recent advances in sequential Monte Carlo. Proceedings of the IEEE 95(5):899–924.
- Carvalho, C. M., Johannes, M., Lopes, H. F., Polson, N. (2010). Particle learning and smoothing. Statistical Science 25:88–106.
- Coles, S. G., Powell, E. A. (1996). Bayesian methods in extreme value modelling: A review and new developments. International Statistical Review 64:119–136.
- Coles, S. (2001). An introduction to statistical modeling of extreme values. Springer Series in Statistics. New York: Springer-Verlag.
- Doucet, A., Freitas, N., Gordon, N. (2001). Sequential Monte Carlo methods in practice. New York: Springer.
- Doucet, A., Godsill, S., Andrieu. (2000). On sequential Monte Carlo sampling methods for Bayesian filtering. Statistics and Computing 10:197–208.
- Doucet, A., Johansen, A. (2009). A Tutorial on Particle Filtering and Smoothing: Fifteen years later. Oxford Handbook of Nonlinear Filtering 12:656–704.
- Gaetan, C., Grigoletto, M. (2004). Smoothing sample extremes with dynamic models. Extremes 7:221–236.
- Gordon, N. J., Salmond, D. J., Smith, A. F. M. (1993). Novel approach to nonlinear/non-Gaussian Bayesian state estimation. IEEE Proc. 140:107–113.
- Hastings, W. K. (1970). Monte Carlo sampling methods using markov chains and their applications. Biometrika 57(1):97–109.
- Huerta, G., Sansó, B. (2007). Time-varying models for extreme values. Journal of Environmental en Ecological Statistics 14:285–299.
- Kitagawa, J. (1996). Monte Carlo filter and smoother for non-Gaussian nonlinear state space models. Journal of Computational and Graphical Statistics 5(1):1–25.
- Klaas, M., de Freitas, N., Doucet, A. (2005). Toward Practical N2 Monte Carlo: the Marginal Particle Filter. In Proceedings of the Proceedings of the Twenty-First Conference Annual Conference on Uncertainty in Artificial Intelligence (UAI-05), Arlington, Virginia: AUAI Press, pp. 308–315. Available at http://uai.sis.pitt.edu/papers/05/p308-klaas.pdf
- Kotz, S., Nadarajah, S. (2000). Extreme value distributions: Theory and applications. London, U.K.: Imperial College Press.
- Lindsten, F., Schon, T. B., Svensson, L. (2012). A non-degenerate Rao-Blackwellised particle filter for estimating static parameters in dynamical models. Proceedings of the 16th IFAC Symposium on System Identification. Brussels, Belgium.
- Liu, J. S. (1996). Metropolized independent sampling with comparisons to rejection sampling and importance sampling. Statistics and Computing 6(2):113–119.
- Liu, J. S., Chen, R. (1998). Sequential Monte Carlo methods for dynamic systems. Journal of the American Statistical Association 93(443):1032–1044.
- Liu, J., West, M. (2001). Combined parameters and state estimation in simulation based filtering. Sequential Monte Carlo Methods in Practice. New York: Springer-Verlag, pp. 197–223.
- Lopes, H. F., Carvalho, C. M., Johannes, M., Polson, N. G. (2011). Particle learning for sequential Bayesian computation (with discussion). Bayesian Statistics. Oxford: Oxford University Press.
- Marcos, M., Calafat, F. M., Berihuete, A., Dagendorf, S. (2015). Long-term variations in global sea level extremes. Journal of Geophysical Research: Oceans 120:8115–8134, doi:10.1002/2015JC011173.
- Nakajimaa, J., Kunihamaa, T., Omori, Y., Frühwirth-Schnatter, S. (2012). Generalized extreme value distribution with time-dependence using the AR and MA models in state space. Computational Statistics & Data Analysis 56(11):3241–3259.
- Nemeth, C., Fearnhead, P., Mihaylova, L. (2013). Particle approximations of the score and observed information matrix for parameter estimation in state space models with linear computational cost. arXiv:1306.0735, submitted.
- Pitt, M., Shephard, N. (1999). Filtering via simulation: Auxiliary particle filters. Journal of the American Statistical Association 94(446):590–599.
- Prado, R., West, M. (2010). Time Series: Modeling, Computation and Inference. New York: Springer.
- Sarkka, S. (2013). Bayesian Filtering and Smoothing. Cambridge University Press.
- Smith, R. L. (1985). Maximum likelihood estimation in a class of nonregular cases. Biometrika 72:67–92.
- Storvik, G. (2002). Particle filters for state-space models with the presence of unknown static parameters. IEEE Transactions on Signal Processing 50:281–289.
- Wei, Y. (2015). Dynamic Generalized Extreme Value via Particle Filters. Ph.D. thesis. Department of Mathematics and Statistics. University of New Mexico.