Related papers: Bias in the Cepheid PL relation
In Bayesian statistics, one's prior beliefs about underlying model parameters are revised with the information content of observed data from which, using Bayes' rule, a posterior belief is obtained. A non-trivial example taken from the…
(Abridged) I cross-correlate the OGLE database of Cepheids in the Large and Small Magellanic Clouds (MCs) with the second incremental release of the 2MASS JHK survey, and the DENIS IJK point source catalog towards the MCs. Of the 3384…
Bernstein-von Mises results (BvM) establish that the Laplace approximation is asymptotically correct in the large-data limit. However, these results are inappropriate for computational purposes since they only hold over most, and not all,…
Classical Cepheids remain a cornerstone of the cosmic distance scale, and thus characterizing the dependence of their light amplitude on metallicity is important. Period-amplitude diagrams constructed for longer-period classical Cepheids in…
In this paper we present randomization methods to enhance the accuracy of the central limit theorem (CLT) based inferences about the population mean $\mu$. We introduce a broad class of randomized versions of the Student $t$-statistic, the…
Preference learning in Large Language Models (LLMs) has advanced significantly, yet existing methods remain limited by modest performance gains, high computational costs, hyperparameter sensitivity, and insufficient modeling of global…
Many practical optimization problems lack strong convexity. Fortunately, recent studies have revealed that first-order algorithms also enjoy linear convergences under various weaker regularity conditions. While the relationship among…
Large Language Models (LLMs) have shown capabilities close to human performance in various analytical tasks, leading researchers to use them for time and labor-intensive analyses. However, their capability to handle highly specialized and…
We prove lower bounds on the error incurred when approximating any oscillating function using piecewise polynomial spaces. The estimates are explicit in the polynomial degree and have optimal dependence on the meshwidth and frequency when…
The RR Lyrae distance scale is reviewed. In particular, we discuss theoretical and empirical methods currently adopted in the literature. Moreover, we also outline pros and cons of optical and near-infrared mean magnitudes to overcome some…
On the basis of new theoretical results useful predictions concerning the Period-Luminosity (PLR) and Period-Luminosity-Color (PLCR) relations both for optical and infrared magnitudes are presented. It is shown that, following the…
When analyzing incomplete data, is it better to use multiple imputation (MI) or full information maximum likelihood (ML)? In large samples ML is clearly better, but in small samples ML's usefulness has been limited because ML commonly uses…
Classical Cepheids are well-known and widely used distance indicators. As distance and extinction are usually degenerate, it is important to develop suitable methods to robustly anchor the distance scale. Here, we introduce a near-infrared…
Informally, a model is calibrated if its predictions are correct with a probability that matches the confidence of the prediction. By far the most common method in the literature for measuring calibration is the expected calibration error…
The accuracy of extragalactic distance measurements ultimately depends on robust, high-precision determinations of the distances to the galaxies in the local volume. Following our detailed study addressing possible publication bias in the…
Polaris the Cepheid has been observed for centuries, presenting surprises and changing our view of Cepheids and stellar astrophysics, in general. Specifically, understanding Polaris helps anchor the Cepheid Leavitt law, but the distance…
Detecting community structure is fundamental to clarify the link between structure and function in complex networks and is used for practical applications in many disciplines. A successful method relies on the optimization of a quantity…
The error bound property for a solution set defined by a set-valued mapping refers to an inequality that bounds the distance between vectors closed to a solution of the given set by a residual function. The error bound property is a…
\textit{Mallows model} is a widely-used probabilistic framework for learning from ranking data, with applications ranging from recommendation systems and voting to aligning language models with human preferences~\cite{chen2024mallows,…
This paper provides an analysis of the tradeoff between asymptotic bias (suboptimality with unlimited data) and overfitting (additional suboptimality due to limited data) in the context of reinforcement learning with partial observability.…