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Applied Bayesian Data Analysis Using State-Space Models

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Data Analysis
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Abstract

This paper reviews the Bayesian approach to parameter estimation in nonlinear nonnormal state-space models with posterior computations performed by Gibbs sampling. Fitting of nonlinear nonnormal state-space models is an important task in various scientific disciplines. The ease with which the Bayesian approach can now be implemented via BUGS, a recently developed, user-friendly, and freely available software package, should have a major impact on applied research. This is illustrated using examples from three different areas of currently active research: econonometrics, fisheries, and physics.

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References

  • ANDERSEN, T. CHUNG, H., and SORENSEN, B. (1990): Efficient Method of Moments Estimation of a Stochastic Volatility Model: A Monte Carlo study. Journal of Econometrics, 91, 61–87.

    Google Scholar 

  • BEST, N.G., COWLES, M.K., and VINES, S.K. (1995): CODA Manual Version 0.30. Cambridge, UK: MRC Biostatistics Unit.

    Google Scholar 

  • BERLINER, L.M. (1991): Likelihood and Bayesian Prediction of Chaotic Systems. J. Am. Stat. Assoc., 86, 938–952.

    Article  Google Scholar 

  • CARLIN, B.P., POLSON, N.G., and STOFFER, D.S. (1992): A Monte Carlo Approach to Nonnormal and Nonlinear State-space Modeling. J. Amer. Statist. Assoc, 87, 493–500.

    Article  Google Scholar 

  • DERISO, R.B. (1980): Havesting Strategies and Parameter Estimation for an Age-structured Model. Can. J. Fish. Aquat. Sci. 37, 268–282.

    Article  Google Scholar 

  • DEVANEY, R.L. (1989): Introduction to Chaotic Dynamical Systems, Benjamin-Cummings, Menlo Park, CA.

    Google Scholar 

  • DURBIN, J. and KOOPMAN, S.J. (2000): Time Series Analysis of Non-Gaussian Observations Based on State Space Models from Both Classical and Bayesian Perspectives (with Discussion). Journal of the Royal Statistical Society Series B, 62, 3–56.

    Article  Google Scholar 

  • FAHRMEIR, L. and TUTZ, G. (1994): Multivariate Statistical Modelling Based on Generalized Linear Models. Springer, New York.

    Google Scholar 

  • FRIDMAN, M. and HARRIS, L. (1998): A Maximum Likelihood Approach for Non-Gaussian Stochastic Volatility Models. Journal of Business and Economic Statistics, 16, 284–291.

    Google Scholar 

  • GILKS, W.R. and WILD, P. (1992): Adaptive Rejection Sampling for Gibbs Sampling. Applied Statistics, 41, 337–48.

    Article  Google Scholar 

  • GILKS, W.R., RICHARDSON, S., and SPIEGELHALTER, D.J. (1996): Markov Chain Monte Carlo in Practice. Chapman & Hall, London.

    Google Scholar 

  • Gilks, W.R., Roberts, G.O., and Sahu, S.K. (1998): Adaptive Markov Chain Monte Carlo through Regeneration. MCMC preprint server.

    Google Scholar 

  • HARVEY, A. (1990): Forecasting, Structural Time Series Models and the Kalman Filter. Cambridge University Press, New York.

    Google Scholar 

  • JACQUIER, E, POLSON, N.G., and ROSSI, P.E. (1994): Bayesian Analysis of Stochastic Volatility Models. Journal of Business and Economic Statistics, 12, 371–389.

    Google Scholar 

  • KALMAN, R.E. (1960): A New Approach to Linear Filtering and Prediction Problems. J. Basic Eng., 82, 34–45.

    Google Scholar 

  • KIM, S., SHEPHARD, N., and CHIB, S. (1998): Stochastic Volatility: Likelihood Inference and Comparison with ARCH Models. Review of Economic Studies, 65, 361–393.

    Article  Google Scholar 

  • KIMURA, D.K., BALSIGER, J.W., and ITO, D.H. (1996): Kalman Filtering the Delay-Difference Equation: Practical Approaches and Simulations. Fishery Bull. 94, 678–691.

    Google Scholar 

  • MCSHARRY, P.E. and SMITH, L.A. (1999): Better Nonlinear Models from Noisy Data: Attractors with Maximum Likelihood. Phys. Rev. Lett., 83, 4285–4288.

    Article  Google Scholar 

  • MEYER, R. and MILLAR, R.B. (1999a): Bayesian Stock Assessment Using a State-Space Implementation of the Delay Difference Model. Canadian Journal of Fisheries and Aquatic Sciences, 56, 37–52.

    Google Scholar 

  • MEYER, R. and MILLAR, R.B. (1999b): BUGS in Bayesian Stock Assessments. Canadian Journal of Fisheries and Aquatic Sciences, 56, 1078–1086.

    Google Scholar 

  • MEYER, R. and CHRISTENSEN, N.L. (2000): Bayesian Reconstruction of Chaotic Dynamical Systems, Technical Report STAT0002. Department of Statistics, University of Auckland.

    Google Scholar 

  • Applied Bayesian Data Analysis Using State-Space Models 271

    Google Scholar 

  • MEYER, R. and YU, J. (2000): Routine and Robust Bayesian Analysis of Stochastic Volatility Models, Technical Report STAT0003. Department of Statistics, University of Auckland.

    Google Scholar 

  • NEAL, R.M. (1997): Markov Chain Monte Carlo Methods Based on ‘Slicing’ the Density Function. Technical Report No. 9722. Department of Statistics, University of Toronto.

    Google Scholar 

  • RITTER, C. and TANNER, M.A. (1992): Facilitating the Gibbs Sampler: the Gibbs Stopper and the Griddy-Gibbs Sampler. J. R. Stat. Soc. Ser. B, 59, 291–317.

    Google Scholar 

  • SHEPHARD, N. and PITT, M.K. (1997): Likelihood Analysis of Non-Gaussian Measurement Time Series. Biometrika, 84, 653–667.

    Article  Google Scholar 

  • SPIEGELHALTER, D.J., THOMAS, A., BEST, N., and GILKS, W.R. (1996): BUGS 0.5, Bayesian Inference Using Gibbs Sampling. Manual (version ii) Cambridge, UK: MRC Biostatistics Unit.

    Google Scholar 

  • TAUCHEN, G. and PITTS, M. (1983): The Price Variability-Volume Relationship on Speculative Markets. Econornetrica, 51, 485–505.

    Article  Google Scholar 

  • WEST, M. and HARRISON, P.J. (1997): Bayesian Forecasting and Dynamic Models. Springer, New York.

    Google Scholar 

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Meyer, R. (2000). Applied Bayesian Data Analysis Using State-Space Models. In: Gaul, W., Opitz, O., Schader, M. (eds) Data Analysis. Studies in Classification, Data Analysis, and Knowledge Organization. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-58250-9_21

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  • DOI: https://doi.org/10.1007/978-3-642-58250-9_21

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-67731-4

  • Online ISBN: 978-3-642-58250-9

  • eBook Packages: Springer Book Archive

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