54,281 research outputs found
Computational statistics using the Bayesian Inference Engine
This paper introduces the Bayesian Inference Engine (BIE), a general
parallel, optimised software package for parameter inference and model
selection. This package is motivated by the analysis needs of modern
astronomical surveys and the need to organise and reuse expensive derived data.
The BIE is the first platform for computational statistics designed explicitly
to enable Bayesian update and model comparison for astronomical problems.
Bayesian update is based on the representation of high-dimensional posterior
distributions using metric-ball-tree based kernel density estimation. Among its
algorithmic offerings, the BIE emphasises hybrid tempered MCMC schemes that
robustly sample multimodal posterior distributions in high-dimensional
parameter spaces. Moreover, the BIE is implements a full persistence or
serialisation system that stores the full byte-level image of the running
inference and previously characterised posterior distributions for later use.
Two new algorithms to compute the marginal likelihood from the posterior
distribution, developed for and implemented in the BIE, enable model comparison
for complex models and data sets. Finally, the BIE was designed to be a
collaborative platform for applying Bayesian methodology to astronomy. It
includes an extensible object-oriented and easily extended framework that
implements every aspect of the Bayesian inference. By providing a variety of
statistical algorithms for all phases of the inference problem, a scientist may
explore a variety of approaches with a single model and data implementation.
Additional technical details and download details are available from
http://www.astro.umass.edu/bie. The BIE is distributed under the GNU GPL.Comment: Resubmitted version. Additional technical details and download
details are available from http://www.astro.umass.edu/bie. The BIE is
distributed under the GNU GP
Approximate Inference for Constructing Astronomical Catalogs from Images
We present a new, fully generative model for constructing astronomical
catalogs from optical telescope image sets. Each pixel intensity is treated as
a random variable with parameters that depend on the latent properties of stars
and galaxies. These latent properties are themselves modeled as random. We
compare two procedures for posterior inference. One procedure is based on
Markov chain Monte Carlo (MCMC) while the other is based on variational
inference (VI). The MCMC procedure excels at quantifying uncertainty, while the
VI procedure is 1000 times faster. On a supercomputer, the VI procedure
efficiently uses 665,000 CPU cores to construct an astronomical catalog from 50
terabytes of images in 14.6 minutes, demonstrating the scaling characteristics
necessary to construct catalogs for upcoming astronomical surveys.Comment: accepted to the Annals of Applied Statistic
Uncertainty quantification for radio interferometric imaging: II. MAP estimation
Uncertainty quantification is a critical missing component in radio
interferometric imaging that will only become increasingly important as the
big-data era of radio interferometry emerges. Statistical sampling approaches
to perform Bayesian inference, like Markov Chain Monte Carlo (MCMC) sampling,
can in principle recover the full posterior distribution of the image, from
which uncertainties can then be quantified. However, for massive data sizes,
like those anticipated from the Square Kilometre Array (SKA), it will be
difficult if not impossible to apply any MCMC technique due to its inherent
computational cost. We formulate Bayesian inference problems with
sparsity-promoting priors (motivated by compressive sensing), for which we
recover maximum a posteriori (MAP) point estimators of radio interferometric
images by convex optimisation. Exploiting recent developments in the theory of
probability concentration, we quantify uncertainties by post-processing the
recovered MAP estimate. Three strategies to quantify uncertainties are
developed: (i) highest posterior density credible regions; (ii) local credible
intervals (cf. error bars) for individual pixels and superpixels; and (iii)
hypothesis testing of image structure. These forms of uncertainty
quantification provide rich information for analysing radio interferometric
observations in a statistically robust manner. Our MAP-based methods are
approximately times faster computationally than state-of-the-art MCMC
methods and, in addition, support highly distributed and parallelised
algorithmic structures. For the first time, our MAP-based techniques provide a
means of quantifying uncertainties for radio interferometric imaging for
realistic data volumes and practical use, and scale to the emerging big-data
era of radio astronomy.Comment: 13 pages, 10 figures, see companion article in this arXiv listin
PPF - A Parallel Particle Filtering Library
We present the parallel particle filtering (PPF) software library, which
enables hybrid shared-memory/distributed-memory parallelization of particle
filtering (PF) algorithms combining the Message Passing Interface (MPI) with
multithreading for multi-level parallelism. The library is implemented in Java
and relies on OpenMPI's Java bindings for inter-process communication. It
includes dynamic load balancing, multi-thread balancing, and several
algorithmic improvements for PF, such as input-space domain decomposition. The
PPF library hides the difficulties of efficient parallel programming of PF
algorithms and provides application developers with the necessary tools for
parallel implementation of PF methods. We demonstrate the capabilities of the
PPF library using two distributed PF algorithms in two scenarios with different
numbers of particles. The PPF library runs a 38 million particle problem,
corresponding to more than 1.86 GB of particle data, on 192 cores with 67%
parallel efficiency. To the best of our knowledge, the PPF library is the first
open-source software that offers a parallel framework for PF applications.Comment: 8 pages, 8 figures; will appear in the proceedings of the IET Data
Fusion & Target Tracking Conference 201
- …