8,043 research outputs found
Dynamical maximum entropy approach to flocking
Peer reviewedPublisher PD
Joint state-parameter estimation of a nonlinear stochastic energy balance model from sparse noisy data
While nonlinear stochastic partial differential equations arise naturally in
spatiotemporal modeling, inference for such systems often faces two major
challenges: sparse noisy data and ill-posedness of the inverse problem of
parameter estimation. To overcome the challenges, we introduce a strongly
regularized posterior by normalizing the likelihood and by imposing physical
constraints through priors of the parameters and states. We investigate joint
parameter-state estimation by the regularized posterior in a physically
motivated nonlinear stochastic energy balance model (SEBM) for paleoclimate
reconstruction. The high-dimensional posterior is sampled by a particle Gibbs
sampler that combines MCMC with an optimal particle filter exploiting the
structure of the SEBM. In tests using either Gaussian or uniform priors based
on the physical range of parameters, the regularized posteriors overcome the
ill-posedness and lead to samples within physical ranges, quantifying the
uncertainty in estimation. Due to the ill-posedness and the regularization, the
posterior of parameters presents a relatively large uncertainty, and
consequently, the maximum of the posterior, which is the minimizer in a
variational approach, can have a large variation. In contrast, the posterior of
states generally concentrates near the truth, substantially filtering out
observation noise and reducing uncertainty in the unconstrained SEBM
Maximum a posteriori estimation through simulated annealing for binary asteroid orbit determination
This paper considers a new method for the binary asteroid orbit determination
problem. The method is based on the Bayesian approach with a global
optimisation algorithm. The orbital parameters to be determined are modelled
through an a posteriori distribution made of a priori and likelihood terms. The
first term constrains the parameters space and it allows the introduction of
available knowledge about the orbit. The second term is based on given
observations and it allows us to use and compare different observational error
models. Once the a posteriori model is built, the estimator of the orbital
parameters is computed using a global optimisation procedure: the simulated
annealing algorithm. The maximum a posteriori (MAP) techniques are verified
using simulated and real data. The obtained results validate the proposed
method. The new approach guarantees independence of the initial parameters
estimation and theoretical convergence towards the global optimisation
solution. It is particularly useful in these situations, whenever a good
initial orbit estimation is difficult to get, whenever observations are not
well-sampled, and whenever the statistical behaviour of the observational
errors cannot be stated Gaussian like.Comment: Accepted for publication in Monthly Notices of the Royal Astronomical
Societ
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