5,838 research outputs found
General combination rules for qualitative and quantitative beliefs
Martin and Osswald \cite{Martin07} have recently proposed many
generalizations of combination rules on quantitative beliefs in order to manage
the conflict and to consider the specificity of the responses of the experts.
Since the experts express themselves usually in natural language with
linguistic labels, Smarandache and Dezert \cite{Li07} have introduced a
mathematical framework for dealing directly also with qualitative beliefs. In
this paper we recall some element of our previous works and propose the new
combination rules, developed for the fusion of both qualitative or quantitative
beliefs
On the physics of fizzing: How bubble bursting controls droplets ejection
Bubbles at a free surface surface usually burst in ejecting myriads of
droplets. Focusing on the bubble bursting jet, prelude for these aerosols, we
propose a simple scaling for the jet velocity and we unravel experimentally the
intricate roles of bubble shape, capillary waves, gravity and liquid
properties. We demonstrate that droplets ejection unexpectedly changes with
liquid properties. In particular, using damping action of viscosity,
self-similar collapse can be sheltered from capillary ripples and continue
closer to the singular limit, therefore producing faster and smaller
droplets.These results pave the road to the control of the bursting bubble
aerosols
On the utility of Metropolis-Hastings with asymmetric acceptance ratio
The Metropolis-Hastings algorithm allows one to sample asymptotically from
any probability distribution . There has been recently much work devoted
to the development of variants of the MH update which can handle scenarios
where such an evaluation is impossible, and yet are guaranteed to sample from
asymptotically. The most popular approach to have emerged is arguably the
pseudo-marginal MH algorithm which substitutes an unbiased estimate of an
unnormalised version of for . Alternative pseudo-marginal algorithms
relying instead on unbiased estimates of the MH acceptance ratio have also been
proposed. These algorithms can have better properties than standard PM
algorithms. Convergence properties of both classes of algorithms are known to
depend on the variability of the estimators involved and reduced variability is
guaranteed to decrease the asymptotic variance of ergodic averages and will
shorten the burn-in period, or convergence to equilibrium, in most scenarios of
interest. A simple approach to reduce variability, amenable to parallel
computations, consists of averaging independent estimators. However, while
averaging estimators of in a pseudo-marginal algorithm retains the
guarantee of sampling from asymptotically, naive averaging of acceptance
ratio estimates breaks detailed balance, leading to incorrect results. We
propose an original methodology which allows for a correct implementation of
this idea. We establish theoretical properties which parallel those available
for standard PM algorithms and discussed above. We demonstrate the interest of
the approach on various inference problems. In particular we show that
convergence to equilibrium can be significantly shortened, therefore offering
the possibility to reduce a user's waiting time in a generic fashion when a
parallel computing architecture is available
Perfect simulation for the Feynman-Kac law on the path space
This paper describes an algorithm of interest. This is a preliminary version
and we intend on writing a better descripition of it and getting bounds for its
complexity
A note on convergence of the equi-energy sampler
In a recent paper `The equi-energy sampler with applications statistical
inference and statistical mechanics' [Ann. Stat. 34 (2006) 1581--1619], Kou,
Zhou & Wong have presented a new stochastic simulation method called the
equi-energy (EE) sampler. This technique is designed to simulate from a
probability measure , perhaps only known up to a normalizing constant. The
authors demonstrate that the sampler performs well in quite challenging
problems but their convergence results (Theorem 2) appear incomplete. This was
pointed out, in the discussion of the paper, by Atchad\'e & Liu (2006) who
proposed an alternative convergence proof. However, this alternative proof,
whilst theoretically correct, does not correspond to the algorithm that is
implemented. In this note we provide a new proof of convergence of the
equi-energy sampler based on the Poisson equation and on the theory developed
in Andrieu et al. (2007) for \emph{Non-Linear} Markov chain Monte Carlo (MCMC).
The objective of this note is to provide a proof of correctness of the EE
sampler when there is only one feeding chain; the general case requires a much
more technical approach than is suitable for a short note. In addition, we also
seek to highlight the difficulties associated with the analysis of this type of
algorithm and present the main techniques that may be adopted to prove the
convergence of it
On nonlinear Markov chain Monte Carlo
Let be the space of probability measures on a measurable
space . In this paper we introduce a class of nonlinear Markov
chain Monte Carlo (MCMC) methods for simulating from a probability measure
. Nonlinear Markov kernels (see [Feynman--Kac Formulae:
Genealogical and Interacting Particle Systems with Applications (2004)
Springer]) can be
constructed to, in some sense, improve over MCMC methods. However, such
nonlinear kernels cannot be simulated exactly, so approximations of the
nonlinear kernels are constructed using auxiliary or potentially
self-interacting chains. Several nonlinear kernels are presented and it is
demonstrated that, under some conditions, the associated approximations exhibit
a strong law of large numbers; our proof technique is via the Poisson equation
and Foster--Lyapunov conditions. We investigate the performance of our
approximations with some simulations.Comment: Published in at http://dx.doi.org/10.3150/10-BEJ307 the Bernoulli
(http://isi.cbs.nl/bernoulli/) by the International Statistical
Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm
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