Abstract
Complex scientific data is becoming the norm, many disciplines are growing immensely data-rich, and higher-dimensional measurements are performed to resolve complex relationships between parameters. Inherently multi-dimensional measurements can directly provide information on both the distributions of individual parameters and the relationships between them, such as in nuclear magnetic resonance and optical spectroscopy. However, when data originates from different measurements and comes in different forms, resolving parameter relationships is a matter of data analysis rather than experiment. We present a method for resolving relationships between parameters that are distributed individually and also correlated. In two case studies, we model the relationships between diameter and luminescence properties of quantum dots and the relationship between molecular weight and diffusion coefficient for polymers. Although it is expected that resolving complicated correlated relationships require inherently multi-dimensional measurements, our method constitutes a useful contribution to the modelling of quantitative relationships between correlated parameters and measurements. We emphasise the general applicability of the method in fields where heterogeneity and complex distributions of parameters are obstacles to scientific insight.
Highlights
Increasing the dimensions of an experiment allows the measurement of dependence between parameters
A ‘link’ between the measurements for different samples is provided through the conditional distribution py|x(x, y), interpreted physically as the distribution of y caused by unobserved parameters of the system other than x
We demonstrate a general-purpose mathematical method for estimating probabilistic relationships from measured distributions of individual parameters
Summary
Increasing the dimensions of an experiment allows the measurement of dependence between parameters. Introducing multi-dimensional nuclear magnetic resonance (NMR) has opened new possibilities for studying heterogeneous structures and complex phenomena by correlating different parameters describing transport properties and identifying different populations based on diffusion and relaxation properties [1, 2]. In optical (electronic) spectroscopy in the infrared, visible, and ultraviolet ranges, obtaining 2D spectra that describe correlations of excitation and detection wavelengths recently enabled the mapping of energy transfer.
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