Bayesian Adaptive Hamiltonian Monte Carlo with an Application to High-Dimensional BEKK GARCH Models
Hamiltonian Monte Carlo (HMC) is a recent statistical procedure to sample from complex distributions. Distant proposal draws are taken in a equence of steps following the Hamiltonian dynamics of the underlying parameter space, often yielding superior mixing properties of the resulting Markov chain. However, its performance can deteriorate sharply with the degree of irregularity of the underlying likelihood due to its lack of local adaptability in the parameter space. Riemann Manifold HMC (RMHMC), a locally adaptive version of HMC, alleviates this problem, but at a substantially increased computational cost that can become prohibitive in high-dimensional scenarios. In this paper we propose the Adaptive HMC (AHMC), an alternative inferential method based on HMC that is both fast and locally adaptive, combining the advantages of both HMC and RMHMC. The benefits become more pronounced with higher dimensionality of the parameter space and with the degree of irregularity of the underlying likelihood surface. We show that AHMC satisfies detailed balance for a valid MCMC scheme and provide a comparison with RMHMC in terms of effective sample size, highlighting substantial efficiency gains of AHMC. Simulation examples and an application of the BEKK GARCH model show the usefulness of the new posterior sampler.
|Date of creation:||21 Jun 2011|
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- Bauwens, L. & Bos, C.S. & van Dijk, H.K. & van Oest, R.D., 2003.
"Adaptive radial-based direction sampling; Some flexible and robust Monte Carlo integration methods,"
Econometric Institute Research Papers
EI 2003-22, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
- Bauwens, Luc & Bos, Charles S. & van Dijk, Herman K. & van Oest, Rutger D., 2004. "Adaptive radial-based direction sampling: some flexible and robust Monte Carlo integration methods," Journal of Econometrics, Elsevier, vol. 123(2), pages 201-225, December.
- BAUWENS, Luc & BOS, Charles S. & VAN DIJK, Herman K. & VAN OEST, Rutger D., "undated". "Adaptive radial-based direction sampling: some flexible and robust Monte Carlo integration methods," CORE Discussion Papers RP 1731, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
- Neil Shephard & Kevin Sheppard & Robert F. Engle, 2008.
"Fitting vast dimensional time-varying covariance models,"
Economics Series Working Papers
403, University of Oxford, Department of Economics.
- Robert Engle & Neil Shephard & Kevin Shepphard, 2008. "Fitting vast dimensional time-varying covariance models," OFRC Working Papers Series 2008fe30, Oxford Financial Research Centre.
- Chib, Siddhartha & Ramamurthy, Srikanth, 2010. "Tailored randomized block MCMC methods with application to DSGE models," Journal of Econometrics, Elsevier, vol. 155(1), pages 19-38, March.
- Hafner, C.M. & Herwartz, H., 2003.
"Analytical quasi maximum likelihood inference in multivariate volatility models,"
Econometric Institute Research Papers
EI 2003-21, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
- Christian Hafner & Helmut Herwartz, 2008. "Analytical quasi maximum likelihood inference in multivariate volatility models," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 67(2), pages 219-239, March.
- Engle, Robert F. & Kroner, Kenneth F., 1995. "Multivariate Simultaneous Generalized ARCH," Econometric Theory, Cambridge University Press, vol. 11(01), pages 122-150, February.
- Osiewalski, Jacek & Pipien, Mateusz, 2004. "Bayesian comparison of bivariate ARCH-type models for the main exchange rates in Poland," Journal of Econometrics, Elsevier, vol. 123(2), pages 371-391, December.
- P. Dellaportas & I. D. Vrontos, 2007. "Modelling volatility asymmetries: a Bayesian analysis of a class of tree structured multivariate GARCH models," Econometrics Journal, Royal Economic Society, vol. 10(3), pages 503-520, November.
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