Analysis of scattered higher dimensional data using generalized Fourier interpolation

TL;DR

This paper introduces a spectral Fourier interpolation method for analyzing high-dimensional scattered data, especially useful when data are only available as discrete events, with applications in physics and comparisons to traditional methods.

Contribution

It presents a novel non-grid spectral approach for higher-dimensional data analysis, demonstrating efficiency and near-optimal performance in extracting model parameters.

Findings

Method approaches the Cramer-Rao bound in some cases

Performance surpasses conventional procedures in examples

Efficient for discrete event data analysis

Abstract

A method based on orthogonal function series interpolation of the square root probability density to analyze higher dimensional scattered data is presented. The method is targeted for the use-case when the model and/or data are available only as discrete events. While fast and efficient algorithms are well known for pseudo-spectral (grid node based) methods, this work focuses on a spectral (non grid based) approach. A typical application is the extraction of physics model parameters from events detected in high energy particle collisions. Several examples are provided and the performance is compared to existing conventional procedures. In some cases the method can be shown to behave as an optimal observable of the data, exemplified by the ability to approach the Cramer-Rao bound.