International Statistical Review

Comparison of Sampling Schemes for Dynamic Linear Models

Edna A. Reis, Esther Salazar, and Dani Gamerman

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text


Hyperparameter estimation in dynamic linear models leads to inference that is not available analytically. Recently, the most common approach is through MCMC approximations. A number of sampling schemes that have been proposed in the literature are compared. They basically differ in their blocking structure. In this paper, comparison between the most common schemes is performed in terms of different efficiency criteria, including efficiency ratio and processing time. A sample of time series was simulated to reflect different relevant features such as series length and system volatility.

Article information

Internat. Statist. Rev., Volume 74, Number 2 (2006), 203-214.

First available in Project Euclid: 24 July 2006

Permanent link to this document

Bayesian inference Blocking MCMC Reparameterization State space


Reis, Edna A.; Salazar, Esther; Gamerman, Dani. Comparison of Sampling Schemes for Dynamic Linear Models. Internat. Statist. Rev. 74 (2006), no. 2, 203--214.

Export citation


  • [1] Carlin, B.P., Polson, N.G. & Stoffer, D.S. (1992). A Monte Carlo approach to nonnnormal and nonlinear state-space modeling. J. Amer. Statist. Assoc., 87, 493-500.
  • [2] Carter, C.K. & Kohn, R. (1994). On Gibbs sampling for state space models. Biometrika, 81, 541-553.
  • [3] DeJong, P. & Shephard, N. (1995). The simulation smoother for time series models. Biometrika, 82 , 339-350.
  • [4] Ehlers, R.S. & Gamerman, D. (1996). Analytic approximations for dynamic non-linear models. Braz. J. Prob. Statist., 10, 87-101.
  • [5] Frühwirth-Schnatter, S. (1994). Data augmentation and dynamic linear models. J. Time Series Anal., 15, 183-202.
  • [6] Gamerman, D. (1997). Markov Chain Monte Carlo: Stochastic Simulation for Bayesian Inference. London: Chapman & Hall.
  • [7] Gamerman, D. (1998). Markov chain Monte Carlo for dynamic generalized linear models. Biometrika, 85, 215-227.
  • [8] Gamerman, D. & Moreira, A.R.B. (2002). Bayesian analysis of econometric time series models using hybrid integration rules. Comm. in Statist., 31, 49-72.
  • [9] Godsill, S., Doucet, A. & West, M. (2004). Monte Carlo smoothing for nonlinear time series. J. Amer. Statist. Assoc., 99, 156-168.
  • [10] Gordon, N.J., Salmond, D.J. & Smith, A.F.M. (1993). Novel approach to nonlinear/non-Gaussian Bayesian state estimation. IEE Proceedings F, 140, 107-113.
  • [11] Jazwinski, A.H. (1970). Stochastic Processes and filtering Theory. San Diego: Academic Press.
  • [12] Knorr-Held, L. (1999). Conditional prior proposals in dynamic models. Scand. J. Statist., 26, 129-144.
  • [13] Lopes, H.F., Moreira, A.R.B. & Schmidt, A.M. (1999). Hyperparameter estimation in forecast models. Comput. Statist. Data Anal., 29, 387-410.
  • [14] Migon, H.S., Gamerman, D., Lopes, H.F. & Ferreira, M.A.R. (2005). Dynamic models. In Handbook of Statistics, 25, 553-588, Editors: C.R. Rao and Dipak K. Dey. Elsevier B.V.
  • [15] Muller, P. (1991). Monte Carlo integration in general dynamic models. Contemp. Math., 115, 145-163.
  • [16] Pole, A. & West, M. (1990). Efficient Bayesian learning in non-linear dynamic models. J. Forecasting, 9, 119-136.
  • [17] Rue, H. (2001). Fast sampling of Gaussian Markov random fields. J. Roy. Statist. Soc., Ser. B, 65, 325-338.
  • [18] Schmidt, A.M., Gamerman, D. & Moreira, A.R.B. (1999). An adaptive resampling scheme for cycle estimation. J. Appl. Statist., 26, 619-641.
  • [19] Shephard, N. (1994). Partial non-Gaussian state space. Biometrika, 81, 115-131.
  • [20] Shephard, N. & Pitt, M.K. (1997). Likelihood analysis of non-Gaussian measurement time series. Biometrika, 84, 653-667.
  • [21] West, M. & Harrison, J. (1997). Bayesian Forecasting and Dynamic Models. New York: Springer.