56,847 research outputs found
Bayes and empirical Bayes: do they merge?
Bayesian inference is attractive for its coherence and good frequentist
properties. However, it is a common experience that eliciting a honest prior
may be difficult and, in practice, people often take an {\em empirical Bayes}
approach, plugging empirical estimates of the prior hyperparameters into the
posterior distribution. Even if not rigorously justified, the underlying idea
is that, when the sample size is large, empirical Bayes leads to "similar"
inferential answers. Yet, precise mathematical results seem to be missing. In
this work, we give a more rigorous justification in terms of merging of Bayes
and empirical Bayes posterior distributions. We consider two notions of
merging: Bayesian weak merging and frequentist merging in total variation.
Since weak merging is related to consistency, we provide sufficient conditions
for consistency of empirical Bayes posteriors. Also, we show that, under
regularity conditions, the empirical Bayes procedure asymptotically selects the
value of the hyperparameter for which the prior mostly favors the "truth".
Examples include empirical Bayes density estimation with Dirichlet process
mixtures.Comment: 27 page
A new model for deflagration fronts in reactive fluids
We present a new way of modeling deflagration fronts in reactive fluids, the
main emphasis being on turbulent thermonuclear deflagration fronts in white
dwarfs undergoing a Type Ia supernova explosion. Our approach is based on a
level set method which treats the front as a mathematical discontinuity and
allows full coupling between the front geometry and the flow field. With only
minor modifications, this method can also be applied to describe contact
discontinuities. Two different implementations are described and their
physically correct behaviour for simple testcases is shown. First results of
the method applied to the concrete problems of Type Ia supernovae and chemical
hydrogen combustion are briefly discussed; a more extensive analysis of our
astrophysical simulations is given in (Reinecke et al. 1998, MPA Green Report
1122b).Comment: 11 pages, 13 figures, accepted by A&A, corrected and extended
according to referee's comment
Merging of globular clusters within inner galactic regions. I. Do they survive the tidal interaction?
The main topic of this paper is the investigation of the modes of interaction
of globular clusters (GCs) moving in the inner part of a galaxy. This is
tackled by means of high-resolution N-body simulations, whose first results are
presented in this article. Our simulations dealt with primordial very massive
(order of 10^7 solar masses) GCs that were able to decay, because of dynamical
friction, into the inner regions of triaxial galaxies on a time much shorter
than their internal relaxation time. To check the disruptive role of both tidal
forces and GC-GC collisions, we maximised the tidal interaction considering GCs
on quasi-radial orbits.
The available CPU resources allowed us to follow 8 oscillations of the GCs
along their orbits and the main findings are: i) clusters with an initial high
enough King concentration parameter (c>=1.2), preserve up to 50% of their
initial mass; ii) the inner density distribution of the survived clusters keep
a King model profile; iii) GC-GC collisions have a negligible effect with
respect to that caused by the passage through the galactic center; iv) the
orbital energy dissipation due to the tidal interaction is of the same order of
that caused by dynamical friction; v) complex sub-structures like "ripples" and
"clumps" formed, as observed around real clusters.
These findings support the validity of the hypothesis of merging of GCs in
the galactic central region, with modes that deserve further careful
investigations.Comment: LaTeX 2e, AASTeX v5.x, 23 pages with 14 figures. Accepted for
publication on the Astrophysical Journal. Final version with major change
An area law for entanglement from exponential decay of correlations
Area laws for entanglement in quantum many-body systems give useful
information about their low-temperature behaviour and are tightly connected to
the possibility of good numerical simulations. An intuition from quantum
many-body physics suggests that an area law should hold whenever there is
exponential decay of correlations in the system, a property found, for
instance, in non-critical phases of matter. However, the existence of quantum
data-hiding state--that is, states having very small correlations, yet a volume
scaling of entanglement--was believed to be a serious obstruction to such an
implication. Here we prove that notwithstanding the phenomenon of data hiding,
one-dimensional quantum many-body states satisfying exponential decay of
correlations always fulfil an area law. To obtain this result we combine
several recent advances in quantum information theory, thus showing the
usefulness of the field for addressing problems in other areas of physics.Comment: 8 pages, 3 figures. Short version of arXiv:1206.2947 Nature Physics
(2013
Foundations for Behavioural Model Elaboration Using Modal Transition Systems
Modal Transition Systems (MTS) are an extension of Labelled Transition Systems
(LTS) that have been shown to be useful to reason about system behaviour in the
context of partial information. MTSs distinguish between required, proscribed
and unknown behaviour and come equipped with a notion of refinement that supports
incremental modelling where unknown behaviour is iteratively elaborated
into required or proscribed behaviour.
A particularly useful notion in the context of software and requirements engineering
is that of “merge”. Merging two consistent models is a process that should
result in a minimal common refinement of both models where consistency is defined
as the existence of one common refinement. One of the current limitations
of MTS merging is that a complete and correct algorithm for merging has not
been developed. Hence, an engineer attempting to merge partial descriptions may
be prevented to do so by overconstrained algorithms or algorithms that introduce
behaviour that does not follow from the partial descriptions being merged. In
this thesis we study the problems of consistency and merge for the existing MTSs
semantics - strong and weak semantics - and provide a complete characterization
of MTS consistency as well as a complete and correct algorithm for MTS merging
using these semantics.
Strong and weak semantics require MTS models to have the same communicating
alphabet, the latter allowing the use of a distinguished unobservable action. In
this work we show that the requirement of fixing the alphabet for MTS semantics
and the treatment of observable actions are limiting if MTSs are to support
incremental elaboration of partial behaviour models. We present a novel observational
semantics for MTS, branching alphabet semantics, inspired by branching
LTS equivalence, which supports the elaboration of model behaviour including
the extension of the alphabet of the system to describe behaviour aspects that
previously had not been taken into account. Furthermore, we show that some
unintuitive refinements allowed by weak semantics are avoided, and prove a number
of theorems that relate branching refinement with alphabet refinement and
consistency. These theorems, which do not hold for other semantics, support the
argument for considering branching alphabet as a sound semantics to support
behaviour model elaboration
Dark matter self-interactions from a general spin-0 mediator
Dark matter particles interacting via the exchange of very light spin-0
mediators can have large self-interaction rates and obtain their relic
abundance from thermal freeze-out. At the same time, these models face strong
bounds from direct and indirect probes of dark matter as well as a number of
constraints on the properties of the mediator. We investigate whether these
constraints can be consistent with having observable effects from dark matter
self-interactions in astrophysical systems. For the case of a mediator with
purely scalar couplings we point out the highly relevant impact of
low-threshold direct detection experiments like CRESST-II, which essentially
rule out the simplest realization of this model. These constraints can be
significantly relaxed if the mediator has CP-violating couplings, but then the
model faces strong constraints from CMB measurements, which can only be avoided
in special regions of parameter space.Comment: 20 pages, 5 figures + appendices. v2: Matches published version. v3:
fixed typographical mistake in eq. (2.8). v4: fixed typographical mistake in
eq. (C.4
Dark matter self-interactions from a general spin-0 mediator
Dark matter particles interacting via the exchange of very light spin-0
mediators can have large self-interaction rates and obtain their relic
abundance from thermal freeze-out. At the same time, these models face strong
bounds from direct and indirect probes of dark matter as well as a number of
constraints on the properties of the mediator. We investigate whether these
constraints can be consistent with having observable effects from dark matter
self-interactions in astrophysical systems. For the case of a mediator with
purely scalar couplings we point out the highly relevant impact of
low-threshold direct detection experiments like CRESST-II, which essentially
rule out the simplest realization of this model. These constraints can be
significantly relaxed if the mediator has CP-violating couplings, but then the
model faces strong constraints from CMB measurements, which can only be avoided
in special regions of parameter space.Comment: 20 pages, 5 figures + appendices. v2: Matches published version. v3:
fixed typographical mistake in eq. (2.8). v4: fixed typographical mistake in
eq. (C.4
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