191,862 research outputs found
Ensemble Transport Adaptive Importance Sampling
Markov chain Monte Carlo methods are a powerful and commonly used family of
numerical methods for sampling from complex probability distributions. As
applications of these methods increase in size and complexity, the need for
efficient methods increases. In this paper, we present a particle ensemble
algorithm. At each iteration, an importance sampling proposal distribution is
formed using an ensemble of particles. A stratified sample is taken from this
distribution and weighted under the posterior, a state-of-the-art ensemble
transport resampling method is then used to create an evenly weighted sample
ready for the next iteration. We demonstrate that this ensemble transport
adaptive importance sampling (ETAIS) method outperforms MCMC methods with
equivalent proposal distributions for low dimensional problems, and in fact
shows better than linear improvements in convergence rates with respect to the
number of ensemble members. We also introduce a new resampling strategy,
multinomial transformation (MT), which while not as accurate as the ensemble
transport resampler, is substantially less costly for large ensemble sizes, and
can then be used in conjunction with ETAIS for complex problems. We also focus
on how algorithmic parameters regarding the mixture proposal can be quickly
tuned to optimise performance. In particular, we demonstrate this methodology's
superior sampling for multimodal problems, such as those arising from inference
for mixture models, and for problems with expensive likelihoods requiring the
solution of a differential equation, for which speed-ups of orders of magnitude
are demonstrated. Likelihood evaluations of the ensemble could be computed in a
distributed manner, suggesting that this methodology is a good candidate for
parallel Bayesian computations
Analysis and optimization of weighted ensemble sampling
We give a mathematical framework for weighted ensemble (WE) sampling, a
binning and resampling technique for efficiently computing probabilities in
molecular dynamics. We prove that WE sampling is unbiased in a very general
setting that includes adaptive binning. We show that when WE is used for
stationary calculations in tandem with a coarse model, the coarse model can be
used to optimize the allocation of replicas in the bins.Comment: 22 pages, 3 figure
Sampling diffusive transition paths
We address the problem of sampling double-ended diffusive paths. The ensemble
of paths is expressed using a symmetric version of the Onsager-Machlup formula,
which only requires evaluation of the force field and which, upon direct time
discretization, gives rise to a symmetric integrator that is accurate to second
order. Efficiently sampling this ensemble requires avoiding the well-known
stiffness problem associated with sampling infinitesimal Brownian increments of
the path, as well as a different type of stiffness associated with sampling the
coarse features of long paths. The fine-feature sampling stiffness is
eliminated with the use of the fast sampling algorithm (FSA), and the
coarse-feature sampling stiffness is avoided by introducing the sliding and
sampling (S&S) algorithm. A key feature of the S&S algorithm is that it enables
massively parallel computers to sample diffusive trajectories that are long in
time. We use the algorithm to sample the transition path ensemble for the
structural interconversion of the 38-atom Lennard-Jones cluster at low
temperature.Comment: 13 pages 5 figure
Steady-state simulations using weighted ensemble path sampling
We extend the weighted ensemble (WE) path sampling method to perform rigorous
statistical sampling for systems at steady state. The straightforward
steady-state implementation of WE is directly practical for simple landscapes,
but not when significant metastable intermediates states are present. We
therefore develop an enhanced WE scheme, building on existing ideas, which
accelerates attainment of steady state in complex systems. We apply both WE
approaches to several model systems confirming their correctness and efficiency
by comparison with brute-force results. The enhanced version is significantly
faster than the brute force and straightforward WE for systems with WE bins
that accurately reflect the reaction coordinate(s). The new WE methods can also
be applied to equilibrium sampling, since equilibrium is a steady state
- …