3,609 research outputs found
On Particle Learning
This document is the aggregation of six discussions of Lopes et al. (2010)
that we submitted to the proceedings of the Ninth Valencia Meeting, held in
Benidorm, Spain, on June 3-8, 2010, in conjunction with Hedibert Lopes' talk at
this meeting, and of a further discussion of the rejoinder by Lopes et al.
(2010). The main point in those discussions is the potential for degeneracy in
the particle learning methodology, related with the exponential forgetting of
the past simulations. We illustrate in particular the resulting difficulties in
the case of mixtures.Comment: 14 pages, 9 figures, discussions on the invited paper of Lopes,
Carvalho, Johannes, and Polson, for the Ninth Valencia International Meeting
on Bayesian Statistics, held in Benidorm, Spain, on June 3-8, 2010. To appear
in Bayesian Statistics 9, Oxford University Press (except for the final
discussion
Path storage in the particle filter
This article considers the problem of storing the paths generated by a
particle filter and more generally by a sequential Monte Carlo algorithm. It
provides a theoretical result bounding the expected memory cost by where is the time horizon, is the number of particles and
is a constant, as well as an efficient algorithm to realise this. The
theoretical result and the algorithm are illustrated with numerical
experiments.Comment: 9 pages, 5 figures. To appear in Statistics and Computin
A multi-resolution, non-parametric, Bayesian framework for identification of spatially-varying model parameters
This paper proposes a hierarchical, multi-resolution framework for the
identification of model parameters and their spatially variability from noisy
measurements of the response or output. Such parameters are frequently
encountered in PDE-based models and correspond to quantities such as density or
pressure fields, elasto-plastic moduli and internal variables in solid
mechanics, conductivity fields in heat diffusion problems, permeability fields
in fluid flow through porous media etc. The proposed model has all the
advantages of traditional Bayesian formulations such as the ability to produce
measures of confidence for the inferences made and providing not only
predictive estimates but also quantitative measures of the predictive
uncertainty. In contrast to existing approaches it utilizes a parsimonious,
non-parametric formulation that favors sparse representations and whose
complexity can be determined from the data. The proposed framework in
non-intrusive and makes use of a sequence of forward solvers operating at
various resolutions. As a result, inexpensive, coarse solvers are used to
identify the most salient features of the unknown field(s) which are
subsequently enriched by invoking solvers operating at finer resolutions. This
leads to significant computational savings particularly in problems involving
computationally demanding forward models but also improvements in accuracy. It
is based on a novel, adaptive scheme based on Sequential Monte Carlo sampling
which is embarrassingly parallelizable and circumvents issues with slow mixing
encountered in Markov Chain Monte Carlo schemes
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
A Constrained Path Monte Carlo Method for Fermion Ground States
We describe and discuss a recently proposed quantum Monte Carlo algorithm to
compute the ground-state properties of various systems of interacting fermions.
In this method, the ground state is projected from an initial wave function by
a branching random walk in an over-complete basis of Slater determinants. By
constraining the determinants according to a trial wave function
, we remove the exponential decay of signal-to-noise ratio
characteristic of the sign problem. The method is variational and is exact if
is exact. We illustrate the method by describing in detail its
implementation for the two-dimensional one-band Hubbard model. We show results
for lattice sizes up to and for various electron fillings and
interaction strengths. Besides highly accurate estimates of the ground-state
energy, we find that the method also yields reliable estimates of other
ground-state observables, such as superconducting pairing correlation
functions. We conclude by discussing possible extensions of the algorithm.Comment: 29 pages, RevTex, 3 figures included; submitted to Phys. Rev.
Langevin and Hamiltonian based Sequential MCMC for Efficient Bayesian Filtering in High-dimensional Spaces
Nonlinear non-Gaussian state-space models arise in numerous applications in
statistics and signal processing. In this context, one of the most successful
and popular approximation techniques is the Sequential Monte Carlo (SMC)
algorithm, also known as particle filtering. Nevertheless, this method tends to
be inefficient when applied to high dimensional problems. In this paper, we
focus on another class of sequential inference methods, namely the Sequential
Markov Chain Monte Carlo (SMCMC) techniques, which represent a promising
alternative to SMC methods. After providing a unifying framework for the class
of SMCMC approaches, we propose novel efficient strategies based on the
principle of Langevin diffusion and Hamiltonian dynamics in order to cope with
the increasing number of high-dimensional applications. Simulation results show
that the proposed algorithms achieve significantly better performance compared
to existing algorithms
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