Abstract
A quantitative analysis of any environment older than the instrumental record relies on proxies. Uncertainties associated with proxy reconstructions are often underestimated, which can lead to artificial conflict between different proxies, and between data and models. In this paper, using ordinary least squares linear regression as a common example, we describe a simple, robust and generalizable method for quantifying uncertainty in proxy reconstructions. We highlight the primary controls on the magnitude of uncertainty, and compare this simple estimate to equivalent estimates from Bayesian, nonparametric and fiducial statistical frameworks. We discuss when it may be possible to reduce uncertainties, and conclude that the unexplained variance in the calibration must always feature in the uncertainty in the reconstruction. This directs future research toward explaining as much of the variance in the calibration data as possible. We also advocate for a “data‐forward” approach, that clearly decouples the presentation of proxy data from plausible environmental inferences.
Highlights
Ancient environments cannot be observed directly, so paleo-environmental reconstructions rely on indirect proxy approaches
In this paper we show that statistical uncertainty in proxy reconstructions is mostly due to the magnitude of scatter around the calibration line
Our aim is to explore the factors that control the magnitude of uncertainty in reconstructions, and to provide a simple, robust and generalizable approach that can be used to estimate the uncertainty associated with any paleo-environmental proxy reconstruction
Summary
Ancient environments cannot be observed directly, so paleo-environmental reconstructions rely on indirect proxy approaches. A proxy is a characteristic of a material that can be measured, and is known to correlate with some aspect of the material's environment of formation. A paleo-environmental proxy reconstruction is complete only with a quantitative statement of its uncertainty (Taylor & Kuyatt, 1994). Our aim is to explore the factors that control the magnitude of uncertainty in reconstructions, and to provide a simple, robust and generalizable approach that can be used to estimate the uncertainty associated with any paleo-environmental proxy reconstruction. The first step in proxy reconstruction is to constrain a relationship between the proxy variable to be measured (P) and the environmental variable to be inferred (E) with a calibration data set consisting of paired values. The value of P depends on the value of E, so this relationship must be defined with a MCCLELLAND ET AL
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