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Bayesian adaptively updated Hamiltonian Monte Carlo with an application to high-dimensional BEKK GARCH models

Bayesian adaptively updated Hamiltonian Monte Carlo with an application to high-dimensional BEKK... Abstract Hamiltonian Monte Carlo (HMC) is a recent statistical procedure to sample from complex distributions. Distant proposal draws are taken in a sequence 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 Adaptively Updated HMC (AUHMC), 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 AUHMC 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 AUHMC. Simulation examples and an application of the BEKK GARCH model show the practical usefulness of the new posterior sampler. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Studies in Nonlinear Dynamics & Econometrics de Gruyter

Bayesian adaptively updated Hamiltonian Monte Carlo with an application to high-dimensional BEKK GARCH models

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Publisher
de Gruyter
Copyright
Copyright © 2013 by the
ISSN
1081-1826
eISSN
1558-3708
DOI
10.1515/snde-2013-0020
Publisher site
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Abstract

Abstract Hamiltonian Monte Carlo (HMC) is a recent statistical procedure to sample from complex distributions. Distant proposal draws are taken in a sequence 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 Adaptively Updated HMC (AUHMC), 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 AUHMC 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 AUHMC. Simulation examples and an application of the BEKK GARCH model show the practical usefulness of the new posterior sampler.

Journal

Studies in Nonlinear Dynamics & Econometrics – de Gruyter

Published: Sep 1, 2013

References

  • Sampling from the Posterior Distribution in Generalized Linear Mixed Models and
    Gamerman
  • Comparison of Generalized Hybrid Monte Carlo Methods with and Without Momentum Flip of
    Akhmatskaya
  • Practical Markov Chain Monte Carlo
    Geyer
  • using Hamiltonian dynamics In Handbook of Markov Chain Monte Carlo edited by
    Neal
  • Tuning the Hybrid Monte Carlo Algorithm
    Gupta
  • Understanding the Metropolis Algorithm
    Chib
  • Practical Markov Chain Monte Carlo
    Geyer
  • Bayesian Comparison of Bivariate ARCH - type Models for the Main Exchange Rates in of
    Osiewalski
  • Analytical Quasi Maximum Likelihood Inference in Multivariate Volatility Models
    Hafner
  • On the Shape of Posterior Densities and Credible Sets in Instrumental Variable Regression Models with Reduced Rank : An Application of Flexible Sampling Methods using of
    Hoogerheide
  • Likelihood of Non Gaussian Time Series
    Pitt
  • Efficient Molecular Dynamics and Hybrid Monte Carlo Algorithms for Path Integrals The of
    Tuckerman
  • Optimal Scaling of Discrete Approximations to of the Methodology
    Roberts
  • Classical and Bayesian Analysis of Univariate and Multivariate Stochastic Volatility Models
    Liesenfeld
  • using Hamiltonian dynamics In Handbook of Markov Chain Monte Carlo edited by
    Neal
  • Geometric Numerical Integration Illustrated by the Method
    Hairer
  • Probabilistic Inference Using Markov Chain Monte Carlo Technical Report of University of
    Neal
  • Efficient Molecular Dynamics and Hybrid Monte Carlo Algorithms for Path Integrals The of
    Tuckerman
  • Large Scale Conditional Covariance Matrix Modeling Estimation Testing Academia Economic
    Ding
  • Adaptive Radial - Based Direction Sampling : Some Flexible and Robust Monte Carlo Integration of
    Bauwens
  • Hybrid Monte Carlo
    Duane
  • Convex Verlag
    Kurdila
  • Manifold Monte Carlo with Discussion of the Series
    Girolami
  • Convex Verlag
    Kurdila
  • Metropolis and in
    Roberts
  • Understanding the Metropolis Algorithm
    Chib
  • Classical and Bayesian Analysis of Univariate and Multivariate Stochastic Volatility Models
    Liesenfeld
  • Probabilistic Inference Using Markov Chain Monte Carlo Technical Report of University of
    Neal
  • On the Shape of Posterior Densities and Credible Sets in Instrumental Variable Regression Models with Reduced Rank : An Application of Flexible Sampling Methods using of
    Hoogerheide
  • Simulating Dynamics New University
    Leimkuhler
  • Monte Carlo Statistical nd ed New York
    Robert
  • Comparison of Generalized Hybrid Monte Carlo Methods with and Without Momentum Flip of
    Akhmatskaya
  • Bayesian Model Choice Asymptotics Exact Calculations of the
    Gelfand
  • Monte Carlo Strategies in Scientific New York Series in
    Liu
  • Bayesian Comparison of Bivariate ARCH - type Models for the Main Exchange Rates in of
    Osiewalski
  • Optimal Tuning of the Hybrid Monte - Carlo Algorithm Working Paper arXiv math PR
    Beskos
  • Kroner Multivariate Simultaneous Generalized ARCH
    Engle
  • Metropolis and in
    Roberts
  • Contemporary Bayesian
    Geweke
  • Likelihood of Non Gaussian Time Series
    Pitt
  • Adaptive Radial - Based Direction Sampling : Some Flexible and Robust Monte Carlo Integration of
    Bauwens
  • Bayesian Auxiliary Variable Models for Binary and Multinomial Regression Bayesian
    Holmes
  • Bayesian Auxiliary Variable Models for Binary and Multinomial Regression Bayesian
    Holmes
  • Bayesian Model Choice Asymptotics Exact Calculations of the
    Gelfand
  • Large Scale Conditional Covariance Matrix Modeling Estimation Testing Academia Economic
    Ding
  • Bayesian Approach to Relaxing Parameter Restrictions in Multivariate GARCH Models TEST An Official of the Spanish of and
    Hudson
  • Geometric Numerical Integration Illustrated by the Method
    Hairer
  • Optimal Scaling of Discrete Approximations to of the Methodology
    Roberts
  • Tailored Randomized Block with Application to DSGE Models of
    Chib
  • Bayesian Approach to Relaxing Parameter Restrictions in Multivariate GARCH Models TEST An Official of the Spanish of and
    Hudson
  • Simulating Dynamics New University
    Leimkuhler
  • Kroner Multivariate Simultaneous Generalized ARCH
    Engle
  • Dynamic Conditional Correlation Simple Class of Multivariate Generalized Autoregressive Conditional Heteroskedasticity Models of
    Engle
  • Matrix Differential Calculus with Applications in New York
    Magnus
  • Hybrid Monte Carlo
    Duane
  • Modelling Volatility Asymmetries Bayesian Analysis of a Class of Tree Structured Multivariate GARCH Models
    Dellaportas
  • Monte Carlo Strategies in Scientific New York Series in
    Liu
  • Matrix Differential Calculus with Applications in New York
    Magnus
  • Fitting Vast Dimensional Time - Varying Covariance Models working paper
    Engle
  • Tuning the Hybrid Monte Carlo Algorithm
    Gupta
  • Contemporary Bayesian
    Geweke
  • Modelling Volatility Asymmetries Bayesian Analysis of a Class of Tree Structured Multivariate GARCH Models
    Dellaportas
  • Dynamic Conditional Correlation Simple Class of Multivariate Generalized Autoregressive Conditional Heteroskedasticity Models of
    Engle
  • Sampling from the Posterior Distribution in Generalized Linear Mixed Models and
    Gamerman
  • Analytical Quasi Maximum Likelihood Inference in Multivariate Volatility Models
    Hafner
  • Tailored Randomized Block with Application to DSGE Models of
    Chib
  • Manifold Monte Carlo with Discussion of the Series
    Girolami
  • Monte Carlo Statistical nd ed New York
    Robert
  • Fitting Vast Dimensional Time - Varying Covariance Models working paper
    Engle
  • Optimal Tuning of the Hybrid Monte - Carlo Algorithm Working Paper arXiv math PR
    Beskos