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

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

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

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

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

Performance of steer progeny of sires differing in genetic potential for fatness and meat yield following post-weaning growth at different rates.: 1. Growth and live-animal composition

The present experiment, 'Regional Combinations', examined growth, and carcass- and meat-quality traits in the progeny of sires genetically diverse for fatness and meat yield when grown at different rates from weaning to feedlot entry. The present paper is the first of several papers describing results from the New South Wales site, one of four in the project. It reports the effects on growth and body composition of steers during backgrounding and feedlot finishing phases. A total of 43 sires within three carcass-class categories, defined as high potential for meat yield, for marbling or for both traits, was used, based on estimated breeding values for retail beef yield and intramuscular fat. Sires were drawn from Angus, Charolais, Limousin, Black Wagyu and Red Wagyu breeds, providing a range of carcass sire types across the three carcass classes. Matings were by artificial insemination to Hereford dams from a single herd. Steer progeny were grown at conventional (slow: ~0.5 kg/day) or accelerated (fast: ~0.7 kg/day) rates from weaning to feedlot entry weight, targeting group means of 400 kg. Accelerated and conventionally grown groups from successive calvings entered the feedlot at similar entry liveweights at the same time, then having identical management during the 100-day finishing phase before slaughter. Within finishing cohorts, fast backgrounding growth resulted in increased subcutaneous fatness at feedlot entry in steers of all carcass types. Slow growth during backgrounding resulted in faster (compensatory) growth in the feedlot in all classes and sire types. This increased the deposition of fat in slow-backgrounded steers compared with that in fast-backgrounded steers during feedlotting, and thus reduced the difference between the groups in P8 and rib fat at feedlot exit. However, there did appear to be an advantage in the level of compensation in the feedlot in favour of those sire types with a genetic propensity for faster growth. Backgrounding growth rate affected body composition and the rate of weight gain during finishing. Faster growth produced more subcutaneous fat during both backgrounding and finishing. Steer progeny groups clearly showed the expected responses in growth and body composition, on the basis of the genetic potential of their sires