Estimating Statistical Properties in Grouped Measurements
Intro In this post, we’ll explore a statistical problem: estimating population means and their uncertainties from hierarchically structured data or so called grouped measurements. While averaging measurements may seem straightforward, the presence of natural groupings in data introduces important statistical considerations that require careful treatment. To illustrate the practical significance of this problem, let’s examine how hierarchically structured measurements - where individual observations are naturally clustered into groups - arise across diverse real-world applications. Multiple-Instance Learning (MIL) represents an important machine learning paradigm specifically designed for analyzing such grouped or clustered data structures. The following scenarios showcase a few situations where measurements naturally organize into clusters of varying sizes: ...