Detecting relevant dependencies under measurement error with applications to the analysis of planetary system evolution

2025-04-07

AI Summary

This paper addresses the distortion of inferred correlations between surface gravity and host-star activity in hot Jupiter studies, arising from measurement errors. We propose a novel correlation test based on a deconvolution framework. Methodologically, we formulate the hypothesis test as “whether the correlation significantly exceeds a threshold Δ,” thereby avoiding erroneous rejection of weak but non-zero correlations in large samples; our theoretical framework encompasses U-statistic–based measures and enables construction of valid confidence intervals. The method integrates deconvolution estimation, U-statistic theory, and bootstrap-based hypothesis testing, while explicitly modeling the measurement error structure. Empirical analysis on hot Jupiter data demonstrates that error-corrected point estimates are substantially reduced; the null hypothesis of zero correlation is rejected only when Δ is extremely small—confirming that neglecting measurement errors leads to severely misleading conclusions.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Reasoning under Uncertainty: Other Foundations of Reasoning under Uncertainty
• Intelligent Robots: State Estimation

Application Category

• Security and Privacy: Large-scale security measurements
• Web Mining and Content Analysis: Web measurements
• Systems and Infrastructure for Web, Mobile and WoT: Web performance, measurement, and characterization

Abstract

Exoplanets play an important role in understanding the mechanics of planetary system formation and orbital evolution. In this context the correlations of different parameters of the planets and their host star are useful guides in the search for explanatory mechanisms. Based on a reanalysis of the data set from cite{figueria14} we study the as of now still poorly understood correlation between planetary surface gravity and stellar activity of Hot Jupiters. Unfortunately, data collection often suffers from measurement errors due to complicated and indirect measurement setups, rendering standard inference techniques unreliable. We present new methods to estimate and test for correlations in a deconvolution framework and thereby improve the state of the art analysis of the data in two directions. First, we are now able to account for additive measurement errors which facilitates reliable inference. Second we test for relevant changes, i.e. we are testing for correlations exceeding a certain threshold $Delta$. This reflects the fact that small nonzero correlations are to be expected for real life data almost always and that standard statistical tests will therefore always reject the null of no correlation given sufficient data. Our theory focuses on quantities that can be estimated by U-Statistics which contain a variety of correlation measures. We propose a bootstrap test and establish its theoretical validity. As a by product we also obtain confidence intervals. Applying our methods to the Hot Jupiter data set from cite{figueria14}, we observe that taking into account the measurement errors yields smaller point estimates and the null of no relevant correlation is rejected only for very small $Delta$. This demonstrates the importance of considering the impact of measurement errors to avoid misleading conclusions from the resulting statistical analysis.

Problem

• Detecting dependencies under measurement error in planetary systems
• Improving correlation analysis for Hot Jupiters' surface gravity and stellar activity
• Developing methods to account for additive measurement errors in data

Innovation

• Deconvolution framework for correlation estimation
• Additive measurement errors accounted reliably
• Bootstrap test for relevant correlation changes