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

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

Orbits for eighteen visual binaries and two double-line spectroscopic binaries observed with HRCAM on the CTIO SOAR 4m telescope, using a new Bayesian orbit code based on Markov Chain Monte Carlo

We present orbital elements and mass sums for eighteen visual binary stars of spectral types B to K (five of which are new orbits) with periods ranging from 20 to more than 500 yr. For two double-line spectroscopic binaries with no previous orbits, the individual component masses, using combined astrometric and radial velocity data, have a formal uncertainty of ~0.1 MSun. Adopting published photometry, and trigonometric parallaxes, plus our own measurements, we place these objects on an H-R diagram, and discuss their evolutionary status. These objects are part of a survey to characterize the binary population of stars in the Southern Hemisphere, using the SOAR 4m telescope+HRCAM at CTIO. Orbital elements are computed using a newly developed Markov Chain Monte Carlo algorithm that delivers maximum likelihood estimates of the parameters, as well as posterior probability density functions that allow us to evaluate the uncertainty of our derived parameters in a robust way. For spectroscopic binaries, using our approach, it is possible to derive a self-consistent parallax for the system from the combined astrometric plus radial velocity data ("orbital parallax"), which compares well with the trigonometric parallaxes. We also present a mathematical formalism that allows a dimensionality reduction of the feature space from seven to three search parameters (or from ten to seven dimensions - including parallax - in the case of spectroscopic binaries with astrometric data), which makes it possible to explore a smaller number of parameters in each case, improving the computational efficiency of our Markov Chain Monte Carlo code.Comment: 32 pages, 9 figures, 6 tables. Detailed Appendix with methodology. Accepted by The Astronomical Journa

Optimality of the Maximum Likelihood estimator in Astrometry

The problem of astrometry is revisited from the perspective of analyzing the attainability of well-known performance limits (the Cramer-Rao bound) for the estimation of the relative position of light-emitting (usually point-like) sources on a CCD-like detector using commonly adopted estimators such as the weighted least squares and the maximum likelihood. Novel technical results are presented to determine the performance of an estimator that corresponds to the solution of an optimization problem in the context of astrometry. Using these results we are able to place stringent bounds on the bias and the variance of the estimators in close form as a function of the data. We confirm these results through comparisons to numerical simulations under a broad range of realistic observing conditions. The maximum likelihood and the weighted least square estimators are analyzed. We confirm the sub-optimality of the weighted least squares scheme from medium to high signal-to-noise found in an earlier study for the (unweighted) least squares method. We find that the maximum likelihood estimator achieves optimal performance limits across a wide range of relevant observational conditions. Furthermore, from our results, we provide concrete insights for adopting an adaptive weighted least square estimator that can be regarded as a computationally efficient alternative to the optimal maximum likelihood solution. We provide, for the first time, close-form analytical expressions that bound the bias and the variance of the weighted least square and maximum likelihood implicit estimators for astrometry using a Poisson-driven detector. These expressions can be used to formally assess the precision attainable by these estimators in comparison with the minimum variance bound.Comment: 24 pages, 7 figures, 2 tables, 3 appendices. Accepted by Astronomy & Astrophysic

Self‐reported sleep patterns and quality amongst adolescents: cross‐sectional and prospective associations with anxiety and depression

Background Sleep problems are common in adolescence, and frequently comorbid with both anxiety and depression. Research studies have suggested a bidirectional relationship between sleep and psychopathology, which includes evidence that sleep interventions can alleviate symptoms of anxiety and depression. However, little is known about the nature of sleep problems amongst adolescents with anxiety and depression, and whether specific sleeping difficulties are involved in the longitudinal relationship between sleep, anxiety and depression. Method The sample was derived from the Avon Longitudinal Study of Parents and Children (ALSPAC), a population‐based, prospective, birth cohort study of children born in 1991–1992. Data were explored from a subset of participants who took part in a clinical assessment at age 15, on self‐report sleep patterns and quality, and diagnostic outcomes of anxiety and depression (N = 5,033). Subsequent diagnostic and symptom severity data on anxiety and depression at ages 17, 21 and 24 were also examined. Results Cross‐sectional and longitudinal analyses were conducted to explore the relationship between sleep problems, anxiety and depression. Results revealed that adolescents aged 15 with depression experience difficulties with both sleep patterns and sleep quality, whereas adolescents with anxiety only reported problems with sleep quality. A range of sleep variables at age 15 predicted the severity of anxiety and depression symptoms and the diagnoses of anxiety and depressive disorders at age 17, 21 and 24 years. Conclusions The results provide further insight into the nature of sleep problems amongst adolescents with anxiety and depression, and the prospective relationship between sleep disturbance and future psychopathology. These data suggest that targeting sleep difficulties during adolescence may have long‐term mental health benefits

Photocatalytic Formic Acid Conversion on CdS Nanocrystals with Controllable Selectivity for H2 or CO.

Formic acid is considered a promising energy carrier and hydrogen storage material for a carbon-neutral economy. We present an inexpensive system for the selective room-temperature photocatalytic conversion of formic acid into either hydrogen or carbon monoxide. Under visible-light irradiation (λ>420 nm, 1 sun), suspensions of ligand-capped cadmium sulfide nanocrystals in formic acid/sodium formate release up to 116±14 mmol H2 g(cat)(-1) h(-1) with >99% selectivity when combined with a cobalt co-catalyst; the quantum yield at λ=460 nm was 21.2±2.7%. In the absence of capping ligands, suspensions of the same photocatalyst in aqueous sodium formate generate up to 102±13 mmol CO g(cat)(-1) h(-1) with >95% selectivity and 19.7±2.7% quantum yield. H2 and CO production was sustained for more than one week with turnover numbers greater than 6×10(5) and 3×10(6), respectively.This work was supported by the Christian Doppler Research Association (Austrian Federal Ministry of Science, Research and Economy and the National Foundation for Research, Technology and Development), the OMV Group, the EPSRC (EP/H00338X/2 to ER), the Isaac Newton Trust, the German Research Foundation (MFK), and the Advanced Institute for Materials Research-Cambridge Joint Research Centre (KLO). XPS spectra were obtained at the National EPSRC XPS User's Service (NEXUS) at Newcastle University, an EPSRC Mid-Range Facility.This is the author accepted manuscript. The final version is available from Wiley via http://dx.doi.org/10.1002/anie.20150623

Status of Marine Turtles in British Columbia Waters: A Reassessment

Marine turtles in British Columbia have previously been considered off course stragglers. Here we document 20 new reports for Green Turtles, Chelonia mydas, and Leatherback Turtles, Dermochelys coriacea, for the province. Until recently there had been no concerted effort to acquire data on marine turtle abundance or frequency off British Columbia. Observations presented here allow a reassessment of marine turtle status in British Columbia waters. We suggest Green Turtles and Leatherbacks should be considered rare vagrants and uncommon seasonal residents, respectively, off British Columbia and that they are a natural part of the British Columbia marine environment

Altered Na/Ca exchange distribution and activity in ventricular myocytes from failing hearts

In mammalian cardiac ventricular myocytes, Ca efflux via Na/Ca exchange (NCX) occurs predominantly at T tubules. Heart failure is associated with disrupted t-tubular structure, but its effect on t-tubular function is less clear. We therefore investigated t-tubular NCX activity in ventricular myocytes isolated from rat hearts ∼18 wk after coronary artery ligation (CAL) or corresponding sham operation (Sham). NCX current (I(NCX)) and l-type Ca current (I(Ca)) were recorded using the whole cell, voltage-clamp technique in intact and detubulated (DT) myocytes; intracellular free Ca concentration ([Ca](i)) was monitored simultaneously using fluo-4. I(NCX) was activated and measured during application of caffeine to release Ca from sarcoplasmic reticulum (SR). Whole cell I(NCX) was not significantly different in Sham and CAL myocytes and occurred predominantly in the T tubules in Sham myocytes. CAL was associated with redistribution of I(NCX) and I(Ca) away from the T tubules to the cell surface and an increase in t-tubular I(NCX)/I(Ca) density from 0.12 in Sham to 0.30 in CAL myocytes. The decrease in t-tubular I(NCX) in CAL myocytes was accompanied by an increase in the fraction of Ca sequestered by SR. However, SR Ca content was not significantly different in Sham, Sham DT, and CAL myocytes but was significantly increased by DT of CAL myocytes. In Sham myocytes, there was hysteresis between I(NCX) and [Ca](i), which was absent in DT Sham but present in CAL and DT CAL myocytes. These data suggest altered distribution of NCX in CAL myocytes

Optimal observational scheduling framework for binary and multiple stellar systems

The optimal instant of observation of astrophysical phenomena for objects that vary on human time-sales is an important problem, as it bears on the cost-effective use of usually scarce observational facilities. In this paper we address this problem for the case of tight visual binary systems through a Bayesian framework based on the maximum entropy sampling principle. Our proposed information-driven methodology exploits the periodic structure of binary systems to provide a computationally efficient estimation of the probability distribution of the optimal observation time. We show the optimality of the proposed sampling methodology in the Bayes sense and its effectiveness through direct numerical experiments. We successfully apply our scheme to the study of two visual-spectroscopic binaries, and one purely astrometric triple hierarchical system. We note that our methodology can be applied to any time-evolving phenomena, a particularly interesting application in the era of dedicated surveys, where a definition of the cadence of observations can have a crucial impact on achieving the science goals.Comment: Accepted for publication to PASP. 23 pages, 2 Tables, 9 Figures, 2 Appendice