220,570 research outputs found
Accelerating HEP simulations with Neural Importance Sampling
Many high-energy-physics (HEP) simulations for the LHC rely on Monte Carlo
using importance sampling by means of the VEGAS algorithm. However, complex
high-precision calculations have become a challenge for the standard toolbox,
as this approach suffers from poor performance in complex cases. As a result,
there has been keen interest in HEP for modern machine learning to power
adaptive sampling. While previous studies have shown the potential of
normalizing-flow-powered neural importance sampling (NIS) over VEGAS, there
remains a gap in accessible tools tailored for non-experts. In response, we
introduce Z\"uNIS, a fully automated NIS library designed to bridge this
divide, while at the same time providing the infrastructure to customise the
algorithm for dealing with challenging tasks. After a general introduction on
NIS, we first show how to extend the original formulation of NIS to reuse
samples over multiple gradient steps while guaranteeing a stable training,
yielding a significant improvement for slow functions. Next, we introduce the
structure of the library, which can be used by non-experts with minimal effort
and is extensivly documented, which is crucial to become a mature tool for the
wider HEP public. We present systematic benchmark results on both toy and
physics examples, and stress the benefit of providing different survey
strategies, which allows higher performance in challenging cases. We show that
Z\"uNIS shows high performance on a range of problems with limited fine-tuning.Comment: 31 pages, 11 figure
Metropolis Sampling
Monte Carlo (MC) sampling methods are widely applied in Bayesian inference,
system simulation and optimization problems. The Markov Chain Monte Carlo
(MCMC) algorithms are a well-known class of MC methods which generate a Markov
chain with the desired invariant distribution. In this document, we focus on
the Metropolis-Hastings (MH) sampler, which can be considered as the atom of
the MCMC techniques, introducing the basic notions and different properties. We
describe in details all the elements involved in the MH algorithm and the most
relevant variants. Several improvements and recent extensions proposed in the
literature are also briefly discussed, providing a quick but exhaustive
overview of the current Metropolis-based sampling's world.Comment: Wiley StatsRef-Statistics Reference Online, 201
On the flexibility of the design of Multiple Try Metropolis schemes
The Multiple Try Metropolis (MTM) method is a generalization of the classical
Metropolis-Hastings algorithm in which the next state of the chain is chosen
among a set of samples, according to normalized weights. In the literature,
several extensions have been proposed. In this work, we show and remark upon
the flexibility of the design of MTM-type methods, fulfilling the detailed
balance condition. We discuss several possibilities and show different
numerical results
Bayesian Methods for Analysis and Adaptive Scheduling of Exoplanet Observations
We describe work in progress by a collaboration of astronomers and
statisticians developing a suite of Bayesian data analysis tools for extrasolar
planet (exoplanet) detection, planetary orbit estimation, and adaptive
scheduling of observations. Our work addresses analysis of stellar reflex
motion data, where a planet is detected by observing the "wobble" of its host
star as it responds to the gravitational tug of the orbiting planet. Newtonian
mechanics specifies an analytical model for the resulting time series, but it
is strongly nonlinear, yielding complex, multimodal likelihood functions; it is
even more complex when multiple planets are present. The parameter spaces range
in size from few-dimensional to dozens of dimensions, depending on the number
of planets in the system, and the type of motion measured (line-of-sight
velocity, or position on the sky). Since orbits are periodic, Bayesian
generalizations of periodogram methods facilitate the analysis. This relies on
the model being linearly separable, enabling partial analytical
marginalization, reducing the dimension of the parameter space. Subsequent
analysis uses adaptive Markov chain Monte Carlo methods and adaptive importance
sampling to perform the integrals required for both inference (planet detection
and orbit measurement), and information-maximizing sequential design (for
adaptive scheduling of observations). We present an overview of our current
techniques and highlight directions being explored by ongoing research.Comment: 29 pages, 11 figures. An abridged version is accepted for publication
in Statistical Methodology for a special issue on astrostatistics, with
selected (refereed) papers presented at the Astronomical Data Analysis
Conference (ADA VI) held in Monastir, Tunisia, in May 2010. Update corrects
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Split Sampling: Expectations, Normalisation and Rare Events
In this paper we develop a methodology that we call split sampling methods to
estimate high dimensional expectations and rare event probabilities. Split
sampling uses an auxiliary variable MCMC simulation and expresses the
expectation of interest as an integrated set of rare event probabilities. We
derive our estimator from a Rao-Blackwellised estimate of a marginal auxiliary
variable distribution. We illustrate our method with two applications. First,
we compute a shortest network path rare event probability and compare our
method to estimation to a cross entropy approach. Then, we compute a
normalisation constant of a high dimensional mixture of Gaussians and compare
our estimate to one based on nested sampling. We discuss the relationship
between our method and other alternatives such as the product of conditional
probability estimator and importance sampling. The methods developed here are
available in the R package: SplitSampling
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