arXiv subjects

Sebastian Espinosa

Publications and source records attributed to Sebastian Espinosa.

5 recordsLinked to original sources

arXiv2025

The impact of the point spread function fitting radius on photometric uncertainty based on the Fisher information matrix

In point spread function (PSF) photometry, the selection of the fitting aperture radius plays a critical role in determining the precision of flux and background estimations. Traditional methods often rely on maximizing the signal-to-noise ratio (S/N) as a criterion for aperture selection. However, S/N-based approaches do not necessarily provide the optimal precision for joint estimation problems as they do not account for the statistical limits imposed by the Fisher information in the context of the Cram\'er-Rao lower bound (CRLB). This study aims to establish an alternative criterion for selecting the optimal fitting radius based on Fisher information rather than S/N. Fisher information serves as a fundamental measure of estimation precision, providing theoretical guarantees on the achievable accuracy for parameter estimation. By leveraging Fisher information, we seek to define an aperture selection strategy that minimizes the loss of precision. We conducted a series of numerical experiments that analyze the behavior of Fisher information and estimator performance as a function of the PSF aperture radius. Specifically, we revisited fundamental photometric models and explored the relationship between aperture size and information content. We compared the empirical variance of classical estimators, such as maximum likelihood and stochastic weighted least squares, against the theoretical CRLB derived from the Fisher information matrix. Our results indicate that aperture selection based on the Fisher information provides a more robust framework for achieving optimal estimation precision.

astro-ph.IM↗

arXiv2023

Optimal photometry of point sources: Joint source flux and background determination on array detectors -- from theory to practical implementation

In this paper we study the joint determination of source and background flux for point sources as observed by digital array detectors. We explicitly compute the two-dimensional Cramér-Rao absolute lower bound (CRLB) as well as the performance bounds for high-dimensional implicit estimators from a generalized Taylor expansion. This later approach allows us to obtain computable prescriptions for the bias and variance of the joint estimators. We compare these prescriptions with empirical results from numerical simulations in the case of the weighted least squares estimator (introducing an improved version, denoted stochastic weighted least-squares) as well as with the maximum likelihood estimator, finding excellent agreement. We demonstrate that these estimators provide quasi-unbiased joint estimations of the flux and background, with a variance that approaches the CRLB very tightly and are, hence, optimal, unlike the case of sequential estimation used commonly in astronomical photometry which is sub-optimal. We compare our predictions with numerical simulations of realistic observations, as well as with observations of a bona-fide non-variable stellar source observed with TESS, and compare it to the results from the sequential estimation of background and flux, confirming our theoretical expectations. Our practical estimators can be used as benchmarks for general photometric pipelines, or for applications that require maximum precision and accuracy in absolute photometry.

astro-ph.IM↗

arXiv2021

On the Exponential Approximation of Type II Error Probability of Distributed Test of Independence

This paper studies distributed binary test of statistical independence under communication (information bits) constraints. While testing independence is very relevant in various applications, distributed independence test is particularly useful for event detection in sensor networks where data correlation often occurs among observations of devices in the presence of a signal of interest. By focusing on the case of two devices because of their tractability, we begin by investigating conditions on Type I error probability restrictions under which the minimum Type II error admits an exponential behavior with the sample size. Then, we study the finite sample-size regime of this problem. We derive new upper and lower bounds for the gap between the minimum Type II error and its exponential approximation under different setups, including restrictions imposed on the vanishing Type I error probability. Our theoretical results shed light on the sample-size regimes at which approximations of the Type II error probability via error exponents became informative enough in the sense of predicting well the actual error probability. We finally discuss an application of our results where the gap is evaluated numerically, and we show that exponential approximations are not only tractable but also a valuable proxy for the Type II probability of error in the finite-length regime.

math.ST↗

arXiv2021

Finite-Length Bounds on Hypothesis Testing Subject to Vanishing Type I Error Restrictions

A central problem in Binary Hypothesis Testing (BHT) is to determine the optimal tradeoff between the Type I error (referred to as false alarm) and Type II (referred to as miss) error. In this context, the exponential rate of convergence of the optimal miss error probability -- as the sample size tends to infinity -- given some (positive) restrictions on the false alarm probabilities is a fundamental question to address in theory. Considering the more realistic context of a BHT with a finite number of observations, this paper presents a new non-asymptotic result for the scenario with monotonic (sub-exponential decreasing) restriction on the Type I error probability, which extends the result presented by Strassen in 2009. Building on the use of concentration inequalities, we offer new upper and lower bounds to the optimal Type II error probability for the case of finite observations. Finally, the derived bounds are evaluated and interpreted numerically (as a function of the number samples) for some vanishing Type I error restrictions.

cs.IT↗

arXiv2018

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.

astro-ph.IM↗