Inferring the shape of data: a probabilistic framework for analysing experiments in the natural sciences
Inferring the shape of data: a probabilistic framework for analysing experiments in the natural sciences
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推断数据的形状：分析自然科学实验的概率框架
DOI：
10.1098/rspa.2022.0177
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发表时间：
2022
期刊：
影响因子：
--
通讯作者：
Kinz-Thompson, Colin D.
中科院分区：
文献类型：
--
作者：
Ray, Korak Kumar;Verma, Anjali R.;Gonzalez, Ruben L.;Kinz-Thompson, Colin D.
对许多不同类型的实验进行数据分析的一个关键步骤是在维度数据集中识别具有理论上定义的形状的特征；这一过程的例子包括在多维分子光谱中找到峰值或在荧光显微镜图像中找到发射体。识别这些特征涉及确定数据的整体形状是否与预期形状一致；然而，通常不清楚如何定量地作出这一确定。在实践中，许多分析方法使用主观的、启发式的方法，这使得随后的任何结果的验证变得复杂--特别是随着数据的数量和维度的增加。在这里，我们通过使用贝叶斯规则来计算数据具有几种潜在形状中的任何一种的概率，从而给出这个问题的概率解。这种概率方法可以用来客观地比较不同理论描述数据集的程度，识别数据集之间的变化，并使用称为基于贝叶斯推理的模板搜索的推论方法来检测数据中的特征；提供了几个证明原则的例子。总而言之，这个数学框架就像一个自动化的“引擎”，能够通过计算执行目前通过视觉检查跨科学做出的分析决定。
A critical step in data analysis for many different types of experiments is the identification of features with theoretically defined shapes in-dimensional datasets; examples of this process include finding peaks in multi-dimensional molecular spectra or emitters in fluorescence microscopy images. Identifying such features involves determining if the overall shape of the data is consistent with an expected shape; however, it is generally unclear how to quantitatively make this determination. In practice, many analysis methods employ subjective, heuristic approaches, which complicates the validation of any ensuing results—especially as the amount and dimensionality of the data increase. Here, we present a probabilistic solution to this problem by using Bayes’ rule to calculate the probability that the data have any one of several potential shapes. This probabilistic approach may be used to objectively compare how well different theories describe a dataset, identify changes between datasets and detect features within data using a corollary method called Bayesian Inference-based Template Search; several proof-of-principle examples are provided. Altogether, this mathematical framework serves as an automated ‘engine’ capable of computationally executing analysis decisions currently made by visual inspection across the sciences.