2,432 research outputs found
Forest resampling for distributed sequential Monte Carlo
This paper brings explicit considerations of distributed computing
architectures and data structures into the rigorous design of Sequential Monte
Carlo (SMC) methods. A theoretical result established recently by the authors
shows that adapting interaction between particles to suitably control the
Effective Sample Size (ESS) is sufficient to guarantee stability of SMC
algorithms. Our objective is to leverage this result and devise algorithms
which are thus guaranteed to work well in a distributed setting. We make three
main contributions to achieve this. Firstly, we study mathematical properties
of the ESS as a function of matrices and graphs that parameterize the
interaction amongst particles. Secondly, we show how these graphs can be
induced by tree data structures which model the logical network topology of an
abstract distributed computing environment. Thirdly, we present efficient
distributed algorithms that achieve the desired ESS control, perform resampling
and operate on forests associated with these trees
Particle Gibbs Split-Merge Sampling for Bayesian Inference in Mixture Models
This paper presents a new Markov chain Monte Carlo method to sample from the
posterior distribution of conjugate mixture models. This algorithm relies on a
flexible split-merge procedure built using the particle Gibbs sampler. Contrary
to available split-merge procedures, the resulting so-called Particle Gibbs
Split-Merge sampler does not require the computation of a complex acceptance
ratio, is simple to implement using existing sequential Monte Carlo libraries
and can be parallelized. We investigate its performance experimentally on
synthetic problems as well as on geolocation and cancer genomics data. In all
these examples, the particle Gibbs split-merge sampler outperforms
state-of-the-art split-merge methods by up to an order of magnitude for a fixed
computational complexity
Distributed Particle Filters for Data Assimilation in Simulation of Large Scale Spatial Temporal Systems
Assimilating real time sensor into a running simulation model can improve simulation results for simulating large-scale spatial temporal systems such as wildfire, road traffic and flood. Particle filters are important methods to support data assimilation. While particle filters can work effectively with sophisticated simulation models, they have high computation cost due to the large number of particles needed in order to converge to the true system state. This is especially true for large-scale spatial temporal simulation systems that have high dimensional state space and high computation cost by themselves. To address the performance issue of particle filter-based data assimilation, this dissertation developed distributed particle filters and applied them to large-scale spatial temporal systems. We first implemented a particle filter-based data assimilation framework and carried out data assimilation to estimate system state and model parameters based on an application of wildfire spread simulation. We then developed advanced particle routing methods in distributed particle filters to route particles among the Processing Units (PUs) after resampling in effective and efficient manners. In particular, for distributed particle filters with centralized resampling, we developed two routing policies named minimal transfer particle routing policy and maximal balance particle routing policy. For distributed PF with decentralized resampling, we developed a hybrid particle routing approach that combines the global routing with the local routing to take advantage of both. The developed routing policies are evaluated from the aspects of communication cost and data assimilation accuracy based on the application of data assimilation for large-scale wildfire spread simulations. Moreover, as cloud computing is gaining more and more popularity; we developed a parallel and distributed particle filter based on Hadoop & MapReduce to support large-scale data assimilation
Population annealing: Theory and application in spin glasses
Population annealing is an efficient sequential Monte Carlo algorithm for
simulating equilibrium states of systems with rough free energy landscapes. The
theory of population annealing is presented, and systematic and statistical
errors are discussed. The behavior of the algorithm is studied in the context
of large-scale simulations of the three-dimensional Ising spin glass and the
performance of the algorithm is compared to parallel tempering. It is found
that the two algorithms are similar in efficiency though with different
strengths and weaknesses.Comment: 16 pages, 10 figures, 4 table
Getting Started with Particle Metropolis-Hastings for Inference in Nonlinear Dynamical Models
This tutorial provides a gentle introduction to the particle
Metropolis-Hastings (PMH) algorithm for parameter inference in nonlinear
state-space models together with a software implementation in the statistical
programming language R. We employ a step-by-step approach to develop an
implementation of the PMH algorithm (and the particle filter within) together
with the reader. This final implementation is also available as the package
pmhtutorial in the CRAN repository. Throughout the tutorial, we provide some
intuition as to how the algorithm operates and discuss some solutions to
problems that might occur in practice. To illustrate the use of PMH, we
consider parameter inference in a linear Gaussian state-space model with
synthetic data and a nonlinear stochastic volatility model with real-world
data.Comment: 41 pages, 7 figures. In press for Journal of Statistical Software.
Source code for R, Python and MATLAB available at:
https://github.com/compops/pmh-tutoria
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