6,648 research outputs found
Regularization and Bayesian Learning in Dynamical Systems: Past, Present and Future
Regularization and Bayesian methods for system identification have been
repopularized in the recent years, and proved to be competitive w.r.t.
classical parametric approaches. In this paper we shall make an attempt to
illustrate how the use of regularization in system identification has evolved
over the years, starting from the early contributions both in the Automatic
Control as well as Econometrics and Statistics literature. In particular we
shall discuss some fundamental issues such as compound estimation problems and
exchangeability which play and important role in regularization and Bayesian
approaches, as also illustrated in early publications in Statistics. The
historical and foundational issues will be given more emphasis (and space), at
the expense of the more recent developments which are only briefly discussed.
The main reason for such a choice is that, while the recent literature is
readily available, and surveys have already been published on the subject, in
the author's opinion a clear link with past work had not been completely
clarified.Comment: Plenary Presentation at the IFAC SYSID 2015. Submitted to Annual
Reviews in Contro
Symmetrized importance samplers for stochastic differential equations
We study a class of importance sampling methods for stochastic differential
equations (SDEs). A small-noise analysis is performed, and the results suggest
that a simple symmetrization procedure can significantly improve the
performance of our importance sampling schemes when the noise is not too large.
We demonstrate that this is indeed the case for a number of linear and
nonlinear examples. Potential applications, e.g., data assimilation, are
discussed.Comment: Added brief discussion of Hamilton-Jacobi equation. Also made various
minor corrections. To appear in Communciations in Applied Mathematics and
Computational Scienc
Possible solution to the riddle of HD 82943 multiplanet system: the three-planet resonance 1:2:5?
We carry out a new analysis of the published radial velocity data for the
planet-hosting star HD82943. We include the recent Keck/HIRES measurements as
well as the aged but much more numerous CORALIE data. We find that the CORALIE
radial velocity measurements are polluted by a systematic annual variation
which affected the robustness of many previous results. We show that after
purging this variation, the residuals still contain a clear signature of an
additional days periodicity. The latter variation leaves
significant hints in all three independent radial velocity subsets that we
analysed: the CORALIE data, the Keck data acquired prior to a hardware upgrade,
and the Keck data taken after the upgrade.
We mainly treat this variation as a signature of a third planet in the
system, although we cannot rule out other interpretations, such as long-term
stellar activity. We find it easy to naturally obtain a stable three-planet
radial-velocity fit close to the three-planet mean-motion resonance 1:2:5, with
the two main planets (those in the 1:2 resonance) in an aligned apsidal
corotation. The dynamical status of the third planet is still uncertain: it may
reside in as well as slightly out of the 5:2 resonance. We obtain the value of
days for its orbital period and of for its
minimum mass, while the eccentric parameters are uncertain.Comment: 18 pages, 5 tables, 18 figures; accepted for publication in MNRA
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
Distributed Parameter Estimation in Probabilistic Graphical Models
This paper presents foundational theoretical results on distributed parameter
estimation for undirected probabilistic graphical models. It introduces a
general condition on composite likelihood decompositions of these models which
guarantees the global consistency of distributed estimators, provided the local
estimators are consistent
Sequential Bayesian inference for implicit hidden Markov models and current limitations
Hidden Markov models can describe time series arising in various fields of
science, by treating the data as noisy measurements of an arbitrarily complex
Markov process. Sequential Monte Carlo (SMC) methods have become standard tools
to estimate the hidden Markov process given the observations and a fixed
parameter value. We review some of the recent developments allowing the
inclusion of parameter uncertainty as well as model uncertainty. The
shortcomings of the currently available methodology are emphasised from an
algorithmic complexity perspective. The statistical objects of interest for
time series analysis are illustrated on a toy "Lotka-Volterra" model used in
population ecology. Some open challenges are discussed regarding the
scalability of the reviewed methodology to longer time series,
higher-dimensional state spaces and more flexible models.Comment: Review article written for ESAIM: proceedings and surveys. 25 pages,
10 figure
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