1,182 research outputs found

### Approximate Integrated Likelihood via ABC methods

We propose a novel use of a recent new computational tool for Bayesian
inference, namely the Approximate Bayesian Computation (ABC) methodology. ABC
is a way to handle models for which the likelihood function may be intractable
or even unavailable and/or too costly to evaluate; in particular, we consider
the problem of eliminating the nuisance parameters from a complex statistical
model in order to produce a likelihood function depending on the quantity of
interest only. Given a proper prior for the entire vector parameter, we propose
to approximate the integrated likelihood by the ratio of kernel estimators of
the marginal posterior and prior for the quantity of interest. We present
several examples.Comment: 28 pages, 8 figure

### Jeffreys priors for mixture estimation

While Jeffreys priors usually are well-defined for the parameters of mixtures
of distributions, they are not available in closed form. Furthermore, they
often are improper priors. Hence, they have never been used to draw inference
on the mixture parameters. We study in this paper the implementation and the
properties of Jeffreys priors in several mixture settings, show that the
associated posterior distributions most often are improper, and then propose a
noninformative alternative for the analysis of mixtures

### Approximate Bayesian inference in semiparametric copula models

We describe a simple method for making inference on a functional of a
multivariate distribution. The method is based on a copula representation of
the multivariate distribution and it is based on the properties of an
Approximate Bayesian Monte Carlo algorithm, where the proposed values of the
functional of interest are weighed in terms of their empirical likelihood. This
method is particularly useful when the "true" likelihood function associated
with the working model is too costly to evaluate or when the working model is
only partially specified.Comment: 27 pages, 18 figure

### Jeffreys priors for mixture estimation: properties and alternatives

While Jeffreys priors usually are well-defined for the parameters of mixtures
of distributions, they are not available in closed form. Furthermore, they
often are improper priors. Hence, they have never been used to draw inference
on the mixture parameters. The implementation and the properties of Jeffreys
priors in several mixture settings are studied. It is shown that the associated
posterior distributions most often are improper. Nevertheless, the Jeffreys
prior for the mixture weights conditionally on the parameters of the mixture
components will be shown to have the property of conservativeness with respect
to the number of components, in case of overfitted mixture and it can be
therefore used as a default priors in this context.Comment: arXiv admin note: substantial text overlap with arXiv:1511.0314

### Accelerating Metropolis-Hastings algorithms: Delayed acceptance with prefetching

MCMC algorithms such as Metropolis-Hastings algorithms are slowed down by the
computation of complex target distributions as exemplified by huge datasets. We
offer in this paper an approach to reduce the computational costs of such
algorithms by a simple and universal divide-and-conquer strategy. The idea
behind the generic acceleration is to divide the acceptance step into several
parts, aiming at a major reduction in computing time that outranks the
corresponding reduction in acceptance probability. The division decomposes the
"prior x likelihood" term into a product such that some of its components are
much cheaper to compute than others. Each of the components can be sequentially
compared with a uniform variate, the first rejection signalling that the
proposed value is considered no further, This approach can in turn be
accelerated as part of a prefetching algorithm taking advantage of the parallel
abilities of the computer at hand. We illustrate those accelerating features on
a series of toy and realistic examples.Comment: 20 pages, 12 figures, 2 tables, submitte

### Constraining the Warm Dark Matter Particle Mass through Ultra-Deep UV Luminosity Functions at z=2

We compute the mass function of galactic dark matter halos for different
values of the Warm Dark Matter (WDM) particle mass m_X and compare it with the
abundance of ultra-faint galaxies derived from the deepest UV luminosity
function available so far at redshift z~2. The magnitude limit M_UV=-13 reached
by such observations allows us to probe the WDM mass functions down to scales
close to or smaller than the half-mass mode mass scale ~10^9 M_sun. This
allowed for an efficient discrimination among predictions for different m_X
which turn out to be independent of the star formation efficiency adopted to
associate the observed UV luminosities of galaxies to the corresponding dark
matter masses. Adopting a conservative approach to take into account the
existing theoretical uncertainties in the galaxy halo mass function, we derive
a robust limit m_X>1.8 keV for the mass of thermal relic WDM particles when
comparing with the measured abundance of the faintest galaxies, while m_X>1.5
keV is obtained when we compare with the Schechter fit to the observed
luminosity function. The corresponding lower limit for sterile neutrinos
depends on the modeling of the production mechanism; for instance m_sterile > 4
keV holds for the Shi-Fuller mechanism. We discuss the impact of observational
uncertainties on the above bound on m_X. As a baseline for comparison with
forthcoming observations from the HST Frontier Field, we provide predictions
for the abundance of faint galaxies with M_UV=-13 for different values of m_X
and of the star formation efficiency, valid up to z~4.Comment: 14 pages, 3 figures. Accepted for publication in The Astrophysical
Journa

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