9,154 research outputs found
Bayesian Nonparametric Calibration and Combination of Predictive Distributions
We introduce a Bayesian approach to predictive density calibration and
combination that accounts for parameter uncertainty and model set
incompleteness through the use of random calibration functionals and random
combination weights. Building on the work of Ranjan, R. and Gneiting, T. (2010)
and Gneiting, T. and Ranjan, R. (2013), we use infinite beta mixtures for the
calibration. The proposed Bayesian nonparametric approach takes advantage of
the flexibility of Dirichlet process mixtures to achieve any continuous
deformation of linearly combined predictive distributions. The inference
procedure is based on Gibbs sampling and allows accounting for uncertainty in
the number of mixture components, mixture weights, and calibration parameters.
The weak posterior consistency of the Bayesian nonparametric calibration is
provided under suitable conditions for unknown true density. We study the
methodology in simulation examples with fat tails and multimodal densities and
apply it to density forecasts of daily S&P returns and daily maximum wind speed
at the Frankfurt airport.Comment: arXiv admin note: text overlap with arXiv:1305.2026 by other author
Auxiliary Likelihood-Based Approximate Bayesian Computation in State Space Models
A computationally simple approach to inference in state space models is
proposed, using approximate Bayesian computation (ABC). ABC avoids evaluation
of an intractable likelihood by matching summary statistics for the observed
data with statistics computed from data simulated from the true process, based
on parameter draws from the prior. Draws that produce a 'match' between
observed and simulated summaries are retained, and used to estimate the
inaccessible posterior. With no reduction to a low-dimensional set of
sufficient statistics being possible in the state space setting, we define the
summaries as the maximum of an auxiliary likelihood function, and thereby
exploit the asymptotic sufficiency of this estimator for the auxiliary
parameter vector. We derive conditions under which this approach - including a
computationally efficient version based on the auxiliary score - achieves
Bayesian consistency. To reduce the well-documented inaccuracy of ABC in
multi-parameter settings, we propose the separate treatment of each parameter
dimension using an integrated likelihood technique. Three stochastic volatility
models for which exact Bayesian inference is either computationally
challenging, or infeasible, are used for illustration. We demonstrate that our
approach compares favorably against an extensive set of approximate and exact
comparators. An empirical illustration completes the paper.Comment: This paper is forthcoming at the Journal of Computational and
Graphical Statistics. It also supersedes the earlier arXiv paper "Approximate
Bayesian Computation in State Space Models" (arXiv:1409.8363
Multilevel Sequential Monte Carlo with Dimension-Independent Likelihood-Informed Proposals
In this article we develop a new sequential Monte Carlo (SMC) method for
multilevel (ML) Monte Carlo estimation. In particular, the method can be used
to estimate expectations with respect to a target probability distribution over
an infinite-dimensional and non-compact space as given, for example, by a
Bayesian inverse problem with Gaussian random field prior. Under suitable
assumptions the MLSMC method has the optimal bound on the
cost to obtain a mean-square error of . The algorithm is
accelerated by dimension-independent likelihood-informed (DILI) proposals
designed for Gaussian priors, leveraging a novel variation which uses empirical
sample covariance information in lieu of Hessian information, hence eliminating
the requirement for gradient evaluations. The efficiency of the algorithm is
illustrated on two examples: inversion of noisy pressure measurements in a PDE
model of Darcy flow to recover the posterior distribution of the permeability
field, and inversion of noisy measurements of the solution of an SDE to recover
the posterior path measure
Universal bounds on current fluctuations
For current fluctuations in non-equilibrium steady states of Markovian
processes, we derive four different universal bounds valid beyond the Gaussian
regime. Different variants of these bounds apply to either the entropy change
or any individual current, e.g., the rate of substrate consumption in a
chemical reaction or the electron current in an electronic device. The bounds
vary with respect to their degree of universality and tightness. A universal
parabolic bound on the generating function of an arbitrary current depends
solely on the average entropy production. A second, stronger bound requires
knowledge both of the thermodynamic forces that drive the system and of the
topology of the network of states. These two bounds are conjectures based on
extensive numerics. An exponential bound that depends only on the average
entropy production and the average number of transitions per time is rigorously
proved. This bound has no obvious relation to the parabolic bound but it is
typically tighter further away from equilibrium. An asymptotic bound that
depends on the specific transition rates and becomes tight for large
fluctuations is also derived. This bound allows for the prediction of the
asymptotic growth of the generating function. Even though our results are
restricted to networks with a finite number of states, we show that the
parabolic bound is also valid for three paradigmatic examples of driven
diffusive systems for which the generating function can be calculated using the
additivity principle. Our bounds provide a new general class of constraints for
nonequilibrium systems.Comment: 19 pages, 13 figure
Lattice-Based Group Signatures: Achieving Full Dynamicity (and Deniability) with Ease
In this work, we provide the first lattice-based group signature that offers
full dynamicity (i.e., users have the flexibility in joining and leaving the
group), and thus, resolve a prominent open problem posed by previous works.
Moreover, we achieve this non-trivial feat in a relatively simple manner.
Starting with Libert et al.'s fully static construction (Eurocrypt 2016) -
which is arguably the most efficient lattice-based group signature to date, we
introduce simple-but-insightful tweaks that allow to upgrade it directly into
the fully dynamic setting. More startlingly, our scheme even produces slightly
shorter signatures than the former, thanks to an adaptation of a technique
proposed by Ling et al. (PKC 2013), allowing to prove inequalities in
zero-knowledge. Our design approach consists of upgrading Libert et al.'s
static construction (EUROCRYPT 2016) - which is arguably the most efficient
lattice-based group signature to date - into the fully dynamic setting.
Somewhat surprisingly, our scheme produces slightly shorter signatures than the
former, thanks to a new technique for proving inequality in zero-knowledge
without relying on any inequality check. The scheme satisfies the strong
security requirements of Bootle et al.'s model (ACNS 2016), under the Short
Integer Solution (SIS) and the Learning With Errors (LWE) assumptions.
Furthermore, we demonstrate how to equip the obtained group signature scheme
with the deniability functionality in a simple way. This attractive
functionality, put forward by Ishida et al. (CANS 2016), enables the tracing
authority to provide an evidence that a given user is not the owner of a
signature in question. In the process, we design a zero-knowledge protocol for
proving that a given LWE ciphertext does not decrypt to a particular message
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