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Scatter in log-space: converting between dex and percentage

3 minute read


Those of us who work in astrophysics frequently analyze the logarithms of quantities of interest due to their large dynamic range. Thus, a lot of predictive modeling tasks that we work on aim to predict \(\log_{10}(X)\) rather than \(X\) itself. Two of the main summary statistics that we use to describe the predictive power of a model are the scatter and bias of the residuals. If working in log-space, the residuals are \(\mathcal{R} = \log_{10}(X_\mathrm{pred}) - \log_{10}(X_\mathrm{true})\). It’s quite common that the the scatter is then reported as the standard deviation of the residuals: