15,710 research outputs found
Performance analysis of the Least-Squares estimator in Astrometry
We characterize the performance of the widely-used least-squares estimator in
astrometry in terms of a comparison with the Cramer-Rao lower variance bound.
In this inference context the performance of the least-squares estimator does
not offer a closed-form expression, but a new result is presented (Theorem 1)
where both the bias and the mean-square-error of the least-squares estimator
are bounded and approximated analytically, in the latter case in terms of a
nominal value and an interval around it. From the predicted nominal value we
analyze how efficient is the least-squares estimator in comparison with the
minimum variance Cramer-Rao bound. Based on our results, we show that, for the
high signal-to-noise ratio regime, the performance of the least-squares
estimator is significantly poorer than the Cramer-Rao bound, and we
characterize this gap analytically. On the positive side, we show that for the
challenging low signal-to-noise regime (attributed to either a weak
astronomical signal or a noise-dominated condition) the least-squares estimator
is near optimal, as its performance asymptotically approaches the Cramer-Rao
bound. However, we also demonstrate that, in general, there is no unbiased
estimator for the astrometric position that can precisely reach the Cramer-Rao
bound. We validate our theoretical analysis through simulated digital-detector
observations under typical observing conditions. We show that the nominal value
for the mean-square-error of the least-squares estimator (obtained from our
theorem) can be used as a benchmark indicator of the expected statistical
performance of the least-squares method under a wide range of conditions. Our
results are valid for an idealized linear (one-dimensional) array detector
where intra-pixel response changes are neglected, and where flat-fielding is
achieved with very high accuracy.Comment: 35 pages, 8 figures. Accepted for publication by PAS
Family and parenting characteristics associated with marijuana use by Chilean adolescents
OBJECTIVE: Family involvement and several characteristics of parenting have been suggested to be protective factors for adolescent substance use. Some parenting behaviors may have stronger relationships with adolescent behavior while others may have associations with undesirable behavior among youth. Although it is generally acknowledged that families play an important role in the lives of Chilean adolescents, scant research exists on how different family and parenting factors may be associated with marijuana use and related problems in this population which has one of the highest rates of drug use in Latin America.
METHODS: Using logistic regression and negative binomial regression, we examined whether a large number of family and parenting variables were associated with the possibility of Chilean adolescents ever using marijuana, and with marijuana-related problems. Analyses controlled for a number of demographic and peer-related variables.
RESULTS: Controlling for other parenting and family variables, adolescent reports of parental marijuana use showed a significant and positive association with adolescent marijuana use. The multivariate models also revealed that harsh parenting by fathers was the only family variable associated with the number of marijuana-related problems youth experienced.
CONCLUSION: Of all the family and parenting variables studied, perceptions of parental use of marijuana and harsh parenting by fathers were predictors for marijuana use, and the experience of marijuana-related problems. Prevention interventions need to continue emphasizing the critical socializing role that parental behavior plays in their children's development and potential use of marijuana.https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3109755/https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3109755/Accepted manuscrip
Dark energy, Ricci-nonflat spaces, and the Swampland
It was recently pointed out that the existence of dark energy imposes highly
restrictive constraints on effective field theories that satisfy the Swampland
conjectures. We provide a critical confrontation of these constraints with the
cosmological framework emerging from the Salam-Sezgin model and its string
realization by Cvetic, Gibbons, and Pope. We also discuss the implication of
the constraints for string model building.Comment: Matching version to be published in PL
Analysis of the Bayesian Cramer-Rao lower bound in astrometry: Studying the impact of prior information in the location of an object
Context. The best precision that can be achieved to estimate the location of
a stellar-like object is a topic of permanent interest in the astrometric
community.
Aims. We analyse bounds for the best position estimation of a stellar-like
object on a CCD detector array in a Bayesian setting where the position is
unknown, but where we have access to a prior distribution. In contrast to a
parametric setting where we estimate a parameter from observations, the
Bayesian approach estimates a random object (i.e., the position is a random
variable) from observations that are statistically dependent on the position.
Methods. We characterize the Bayesian Cramer-Rao (CR) that bounds the minimum
mean square error (MMSE) of the best estimator of the position of a point
source on a linear CCD-like detector, as a function of the properties of
detector, the source, and the background.
Results. We quantify and analyse the increase in astrometric performance from
the use of a prior distribution of the object position, which is not available
in the classical parametric setting. This gain is shown to be significant for
various observational regimes, in particular in the case of faint objects or
when the observations are taken under poor conditions. Furthermore, we present
numerical evidence that the MMSE estimator of this problem tightly achieves the
Bayesian CR bound. This is a remarkable result, demonstrating that all the
performance gains presented in our analysis can be achieved with the MMSE
estimator.
Conclusions The Bayesian CR bound can be used as a benchmark indicator of the
expected maximum positional precision of a set of astrometric measurements in
which prior information can be incorporated. This bound can be achieved through
the conditional mean estimator, in contrast to the parametric case where no
unbiased estimator precisely reaches the CR bound.Comment: 17 pages, 12 figures. Accepted for publication on Astronomy &
Astrophysic
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