Analytic convergence rates and parameterization issues for the Gibbs sampler applied to state space models

Journal of Time Series Analysis

Volumn 20, Issue 1, 1999, Pages 63-85

  Pitt, Michael K ^a   Shephard, Neil ^a  

^a NONE

Author keywords

Blocking; Convergence rates; Gibbs sampling; Markov chain Monte Carlo; Parameterization; Simulation smoother; Stochastic volatility

Indexed keywords

EID: 0040291797     PISSN: 01439782     EISSN: None     Source Type: Journal    
DOI: 10.1111/1467-9892.00126     Document Type: Article

References (24)

1. CARLIN, B. P., POLSON, N. G. and STOFFER, D. (1992) A Monte Carlo approach to nonnormal and nonlinear state-space modelling. J. Am. Stat. Assoc. 87, 493-500.
2. CARTER, C. K. and KOHN, R. (1994) On Gibbs sampling for state space models. Biometrika 81, 541-53.
3. FRUHWIRTH-SCHNATTER, S. (1994) Data augmentation and dynamic linear models. J. Time Ser. Anal. 15, 183-202.
4. GELFAND, A. and SMITH, A. F. M. (1990) Sampling-based approaches to calculating marginal densities. J. Am. Stat. Assoc. 85, 398-409.
5. _, SAHU, S. K. and CARLIN, B. P. (1995) Efficient parameterisations for normal linear mixed models. Biometrika 82, 479-88.
6. GEMAN, S. and GEMAN, D. (1984) Stochastic relaxation, Gibbs distribution and the Bayesian restoration of images. IEEE Trans. PAMI 6, 721-41.
7. GILKS, W. K. and ROBERTS, G. O. (1996) Strategies for improving MCMC. In Markov Chain Monte Carlo in Practice (eds W. R. Gilks, S. Richardson and D. J. Spiegelhalter). London: Chapman and Hall.
8. _, RICHARDSON, S. and SPIEGELHALTER, D. J. (1996) Markov Chain Monte Carlo in Practice. London: Chapman and Hall.
9. HARVEY, A. C. (1989) Forecasting, Structural Time Series Models and the Kalman Filter. Cambridge: Cambridge University Press.
10. _, (1993) Time Series Models, 2nd Edn. Hemel Hempstead: Harvester Wheatsheaf.
11. _, RUIZ, E. and SHEPHARD, N. (1994) Multivariate stochastic variance models. Rev. Econ. Stud. 61, 247-64.
12. DE JONG, P. (1989) Smoothing and interpolation with the state space model. J. Am. Stat. Assoc. 84, 1085-88.
13. _ and SHEPHARD, N. (1995) The simulation smoother for time series models. Biometrika 82, 339-50.
14. KALMAN, R. E. (1960) A new approach to linear filtering and prediction problems. J. Basic Eng., Trans. ASMA, Ser. D 82, 35-45.
15. PRIESTLEY, M. B. (1981) Spectral Analysis and Time Series. London: Academic.
16. RIPLEY, B. D. (1977) Modelling spatial patterns (with discussion). J. R. Stat. Soc. B 39, 172-212.
17. _ (1987) Stochastic Simulation. New York: Wiley.
18. ROBERTS, G. O. and SAHU, S. K. (1996) Rate of convergence of the Gibbs sampler by Gaussian approximation. Technical Report 96-21, Statistical Laboratory, University of Cambridge.
19. _ and _ (1997) Updating schemes, correlation structure, blocking and parameterization for the Gibbs sampler. J. R. Stat. Soc. B 59, 291-317.
20. SCHOTMAN, P. C. (1994) Priors for the AR(1) model: parameterisation issues and time series considerations. Economet. Theory 10, 579-95.
21. SHEPHARD, N. (1994) Partial non-Gaussian state space. Biometrika 81, 115-31.
22. _ (1996) Statistical aspects of ARCH and stochastic volatility. In Time Series Models in Econometrics, Finance and Other Fields (eds D. R. Cox, O. E. Barndorff-Nielson and D. V. Hinkley). London: Chapman and Hall, pp. 1-67.
23. _ and PITT, M. K. (1997) Likelihood analysis of non-Gaussian measurement time series. Biometrika 84, forthcoming.
24. TANNER, M. A. and WONG, W. H. (1987) The calculation of posterior distributions by data augmentation (with discussion). J. Am. Stat. Assoc. 82, 528-50.