References
- Altman, R. M. 2004. Assessing the goodness-of-fit of hidden Markov models. Biometrics 60:444–50.
- Andrieu, C., A. Doucet, and R. Holenstein. 2010. Particle Markov chain Monte Carlo methods. Journal of the Royal Statistical Society: Series B (Statistical Methodology) 72 (3):269–342. doi:https://doi.org/10.1111/j.1467-9868.2009.00736.x.
- Barndorff-Nielsen, O., and G. Schou. 1973. On the parameterization of autoregressive models by partial autocorrelations. Journal of Multivariate Analysis 3 (4):408–19. doi:https://doi.org/10.1016/0047-259X(73)90030-4.
- Brijs, T., D. Karlis, and G. Wets. 2008. Studying the effect of weather conditions on daily crash counts using a discrete time-series model. Accident Analysis & Prevention 40 (3):1180–90. doi:https://doi.org/10.1016/j.aap.2008.01.001.
- Celeux, G., F. Forbes, C. P. Robert, and D. M. Titterington. 2006. Deviance information criteria for missing data models. Bayesian Analysis 1 (4):651–74. doi:https://doi.org/10.1214/06-BA122.
- Chopin, N., and S. S. Singh. 2015. On particle gibbs sampling. Bernoulli 21 (3):1855–83. doi:https://doi.org/10.3150/14-BEJ629.
- Collings, B. J., and B. H. Margolin. 1985. Testing goodness of fit for the Poisson assumption when observations are not identically distributed. Journal of the American Statistical Association 80 (390):411–8. doi:https://doi.org/10.2307/2287906.
- Cox, D. R. 1981. Statistical analysis of time series: Some recent developments. Scandinavian Journal of Statist 8:93–115.
- Fruhwirth-Schnatter, S., and H. Wagner. 2006. Auxiliary mixture sampling for parameter-driven models of time series of counts with applications to state space modelling. Biometrika 93 (4):827–41. doi:https://doi.org/10.1093/biomet/93.4.827.
- Fruhwirth-Schnatter, S., R. Fruhwirth, L. Held, and H. Rue. 2009. Improved auxiliary mixture sampling for hierarchical models of non-Gaussian data. Statistics and Computing 19:479–92. doi:https://doi.org/10.1007/s11222-008-9109-4.
- Gelman, A. 2006. Prior distributions for variance parameters in hierarchical models. Bayesian Analysis 1 (3):515–33. doi:https://doi.org/10.1214/06-BA117A.
- Gelman, A., X. Meng, and H. Stern. 1996. Posterior predictive assessment of model fitness via realized discrepavcies. Statistica Sinica 6:733–807.
- Ignaccolo, R. 2004. Goodness of fit tests for dependent data. Journal of Nonparametric Statistics 16 (1–2):19–38. doi:https://doi.org/10.1080/10485250310001622640.
- Jones, M. C. 1987. Randomly choosing parameters for the stationarity and invertibility region of autoregressive-moving average models. Applied Statistics 36 (2):134–8. doi:https://doi.org/10.2307/2347544.
- Jung, R. C., M. Kukuk, and R. Liesenfeld. 2006. Time series of count data: Modeling, estimation and diagnostics. Computational Statistics & Data Analysis 51 (4):2350–64. doi:https://doi.org/10.1016/j.csda.2006.08.001.
- Li, Y., T. Zeng, and J. Yu. 2012. Robust deviance information criterion for latent variable models. Research Collection School of Economics. 1–43. doi:https://doi.org/10.2139/ssrn.2316341.
- Lindsay, B. 1988. Composite likelihood methods. Contemporary Mathematics 80:220–39.
- Marjoram, P., J. Molitor, V. Plagnol, and S. Tavare. 2003. Markov chain Monte Carlo without likelihoods. Proceedings of the National Academy of Sciences 100 (26):15324–8. doi:https://doi.org/10.1073/pnas.0306899100.
- Mason, A., S. Richardson, and N. Best. 2012. Two-pronged strategy for using DIC to compare selection models with non-ignorable missing responses. Bayesian Analysis 7 (1):109–46. doi:https://doi.org/10.1214/12-BA704.
- McCullagh, P. 1986. The conditional distribution of goodness-of-fit statistics for discrete data. Journal of the American Statistical Association 81 (393):104–7. doi:https://doi.org/10.2307/2287974.
- McCulloch, C. E. 1997. Maximum likelihood algorithms for generalized linear mixed models. Journal of the American Statistical Association 92 (437):162–70. doi:https://doi.org/10.2307/2291460.
- Ng, C. T., H. Joe, D. Karlis, and J. Liu. 2011. Composite likelihood for time series models with a latent autoregressive process. Statistica Sinica 21:279–305.
- Oh, M., and Y. Lim. 2001. Bayesian analysis of time series Poisson data. Journal of Applied Statistics 82 (2):259–71. doi:https://doi.org/10.1080/02664760020016154.
- Plummer, M. 2002. Discussion of the paper by Spiegelhalter et al. JRSS (B) 64:620.
- Pritchard, J. K., M. T. Seielstad, A. Perez-Lezaun, and M. W. Feldman. 1999. Population growth of human Y chromosomes: A study of Y chromosome microsatellites. Molecular Biology and Evolution 16 (12):1791–8. doi:https://doi.org/10.1093/oxfordjournals.molbev.a026091.
- Richard, J. F., and W. Zhang. 2007. Efficient high-dimensional importance sampling. Journal of Econometrics 141 (2):1385–1411. doi:https://doi.org/10.1016/j.jeconom.2007.02.007.
- Sermaidis, G. I. 2006. Modeling time series of counts with an application on daily car accidents. Master Thesis, Athens University of Economics and Business.
- Shephard, N., and M. K. Pitt. 1997. Likelihood analysis of non-Gaussian measurement time series. Biometrika 84 (3):653–67. doi:https://doi.org/10.1093/biomet/84.3.653.
- Spiegelhalter, D. J., N. G. Best, B. P. Carlin, and A. van der Linde. 2002. Bayesian measures of model complexity and fit (with discussion). Journal of the Royal Statistical Society: Series B (Statistical Methodology) 64 (4):583–639. doi:https://doi.org/10.1111/1467-9868.00353.
- Tierney, L. 1994. Markov chain for exploring posterior distributions. The Annals of Statistics 21:1701–62. doi:https://doi.org/10.1214/aos/1176325750.
- Varin, C., N. Reid, and D. Firth. 2011. An overview of composite likelihood methods. Statistics Sinica 21:5–42.
- Zucchini, W., and I. L. Macdonald. 2009. Hidden Markov Models for Time Series. An Introduction Using R. Boca Raton, FL: CRC Press.