Penalized splines for smooth representation of high-dimensional Monte Carlo datasets

Abstract Detector response to a high-energy physics process is often estimated by Monte Carlo simulation. For purposes of data analysis, the results of this simulation are typically stored in large multi-dimensional histograms, which can quickly become both too large to easily store and manipulate and numerically problematic due to unfilled bins or interpolation artifacts. We describe here an application of the penalized spline technique (Marx and Eilers, 1996) [1] to efficiently compute B-spline rep... Title of program: Photospline Catalogue Id: AEPK_v1_0 Nature of problem An algorithm to smoothly represent histogram, including mathematical operations and convolutions. Using histograms of Monte Carlo simulation for likelihood fitting can be unstable due to binning artifacts from statistical fluctuations and hard bin-to-bin transitions. This package provides a toolkit for using penalized spline fits on extremely large multi-dimensional datasets to reduce or eliminate such issues. Versions of this program held in the CPC repository in Mendeley Data AEPK_v1_0; Photospline; 10.1016/j.cpc.2013.04.008 This program has been imported from the CPC Program Library held at Queen's University Belfast (1969-2018)摘要 高能物理过程中的探测器响应通常通过蒙特卡洛模拟（Monte Carlo simulation）进行估算。出于数据分析需求，该模拟的结果通常存储于大型多维直方图中，但这类直方图极易出现两类问题：一是体积过大，难以便捷存储与操作；二是因空箱或插值伪影引发数值层面的问题。本文介绍了惩罚样条技术（penalized spline technique，Marx与Eilers，1996）[1]的一种应用，用于高效计算B样条（B-spline）的…… 程序名称：Photospline 目录编号：AEPK_v1_0 问题本质 本算法用于实现直方图的平滑表示，涵盖数学运算与卷积操作。基于蒙特卡洛模拟直方图开展似然拟合时，因统计涨落带来的分箱伪影以及生硬的分箱间跃迁，常会导致拟合过程不稳定。本工具包提供了在超大型多维数据集上应用惩罚样条拟合的功能，以缓解乃至消除上述问题。 孟德雷数据（Mendeley Data）中CPC库收录的本程序版本：AEPK_v1_0；Photospline；10.1016/j.cpc.2013.04.008 本程序源自贝尔法斯特女王大学维护的CPC程序库（1969-2018）