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Activity Number:
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350
- Bayesian Modeling and Simulation
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Type:
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Contributed
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Date/Time:
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Wednesday, August 5, 2020 : 10:00 AM to 2:00 PM
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Sponsor:
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Section on Statistical Computing
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Abstract #309650
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Title:
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Efficiency of Globally-Balanced, Gradient-Based Proposal Distributions in Metropolis-Hastings Algorithms
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Author(s):
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Mylène Bédard* and Gabriel Boisvert-Beaudry
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Companies:
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Université De Montréal and Université de Montréal
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Keywords:
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Bayesian logistic regression;
efficiency;
global and local balances;
informed proposal distribution;
Markov chain Monte Carlo;
Metropolis-adjusted Langevin algorithm
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Abstract:
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Statistical models to study real-world phenomena have been increasing both in terms of complexity and dimensionality. Such models generally produce densities that cannot be treated analytically; MCMC methods have thus become a device of choice to obtain samples from these complicated probability distributions. We present a generalized Metropolis-adjusted Langevin algorithm (MALA) sampler. The informed proposal distribution of this new sampler features two tuning parameters: the usual step size parameter, plus a parameter gamma that may be adjusted to accommodate the dimension of the target distribution. We theoretically study the efficiency of the sampler by making use of the local- and global-balance concepts introduced in Zanella (2017). Although the usual MALA (gamma=1) is shown to be optimal for infinite-dimensional targets, in practice, the generalized MALA (1< gamma< 2) remains the most appealing option, even for high-dimensional target distributions. Simulation studies and numerical experiments are presented to illustrate our findings. We apply the new sampler to a Bayesian logistic regression context and show that its efficiency compares favorably to competing algorithms.
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Authors who are presenting talks have a * after their name.
