Bayesian econometrics

Sequential Monte Carlo (SMC) methods: pure filter

R code for BF and SIS

More R code

Sequential Monte Carlo (SMC) methods: parameter learning

1. Sampling importance resampling: review

2. First order normal dynamic linear model (DLM)

      a.  Sequential Importance Sampling (SIS)
      b.  Sequential importance resampling (SIR)
      c. Auxiliary particle filter (APF)
      d. APF and parameter learning

3. Stochastic volatility model

      a. Sequential “brute-force” MCMC (S-MCMC) versus APF
      b. S-MCMC versus APF and parameter learning

4. Nonlinear normal dynamic model

      a. APF and parameter learning

5. Markov switching stochastic volatility model

      a. APF and parameter learning


A few references

1. Andrieu, C. and Doucet, A. (2002). Particle filters for partially observed state space models. Journal of Royal Statistical Society, B, 64, 827-836.

2. Carvalho, C., Johannes, M., Lopes, H. and Polson, N. (2008) Particle learning and smoothing. University of Chicago Graduate School of Business.

3. Carvalho, C. and Lopes, H. (2007) Simulation-based sequential analysis of Markov switching stochastic volatility models, Computational Statistics and Data Analysis, 51, 4526-4542.

4. Carvalho, C., Lopes, H. and Polson, N. (2008) Particle Mixture Modeling. University of Chicago Graduate School of Business

5. Doucet, A., N. de Freitas, and N. Gordon, 2001, Sequential Monte Carlo Methods in Practice, Springer, New York.

6. Fearnhead, P. (2002). Markov chain Monte Carlo, sufficient statistics, and particle filters. Journal of Computational and Graphical Statistics, 11, 848-862.

7. Fearnhead, P. and Clifford, P. (2003). On-line inference for hidden Markov models via particle filters. Journal of the Royal Statistical Society, Series B, 65, 887-899.

8. Geweke, J. (1989) Bayesian inference in econometric models using Monte Carlo integration. Econometrica, 57, 1317-39.

9. Gilks, W. and Berzuini, C. (2001). Following a moving target: Monte Carlo inference for dynamic Bayesian models. Journal of Royal Statistical Society, Series B, 63, 127-146.

10. Gilks, W. R. and Wild, P. (1992) Adaptive rejection sampling for Gibbs sampling. Applied Statistics, 41, 337-48. Computational Statistics and Data Analysis, 51, 4526-42.

11. Gordon, N., D. Salmond, and A. Smith, 1993, Novel Approach to Nonlinear/Non-Gaussian Bayesian State Estimation, IEE Proceedings, F-140, 107-113.

12. Godsill, S.J., Doucet, A. and West, M. (2004). Monte Carlo smoothing for nonlinear time series. Journal of the American Statistical Association, 99, 156-168.

13. Liu, J. and West, M. (2001). Combined parameters and state estimation in simulation-based filtering. In Sequential Monte Carlo Methods in Practice. Springer-Verlag New York.

14. Pitt, M. and N. Shephard, 1999, Filtering via Simulation: Auxiliary Particle Filter, Journal of the American Statistical Association, 94, 590-599.

15. Polson, N.G., Stroud, J. and Muller, P. (2008). Practical filtering with sequential parameter learning. Journal of the Royal Statistical Society, Series B, 70, 413-428.

16. Smith, A. F. M. and Gelfand, A. E. (1992) Bayesian statistics without tears: a sampling-resampling perspective. American Statistician, 46, 84-8.

17. Storvik, G., (2002). Particle filters in state space models with the presence of unknown static parameters. IEEE. Trans. of Signal Processing, 50, 281-289.