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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 introduce a modified Metropolis-adjusted Langevin algorithm (MALA) sampler that features two tuning parameters: the usual step size parameter and an interpolation parameter that accommodates the dimension of the target distribution. We theoretically study the efficiency of this algorithm by making use of the local- and global- balance concepts introduced in Zanella (2017). Although the traditional MALA is shown to be optimal to sample from infinite-dimensional targets, in practice, the modified MALA remains the most appealing option (even for high-dimensional targets).
Simulation studies and numerical experiments corroborate our findings. In particular, the efficiency of the modified MALA compares favorably to that of competing algorithms in various Bayesian logistic regression contexts. There is no extra computational cost associated to the new sampler.
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