Correction to: Nature Communications https://doi.org/10.1038/s41467-020-19529-8, published online 13 November 2020.

The original version of this Article contained an error in Eq. (5) and the corresponding notation, and incorrectly read:

“Using the assumption that the residuals follow a normal distribution, Bayes' theorem and the scaled inverse χ2 prior, it can be shown [20] that the expected value of the posterior of \({\tilde{s}}_{i}^{2}\) is

$${\tilde{s}}_{i}^{2}=\frac{{d}_{0}{s}_{0}^{2}+{d}_{2}{s}_{i}^{2}}{{d}_{0}+{d}_{g}}.$$
(5)

Here, the hyperparameters \({s}_{0}^{2}\) and \({d}_{0}\) are estimated by fitting a scaled F-distribution with \({s}^{2} \sim {s}_{0}^{2}{F}_{d,{d}_{0}}\)”.

The correct form of Eq. (5) and the corresponding notation is:

“Using the assumption that the residuals follow a normal distribution, Bayes' theorem and the scaled inverse χ2 prior, it can be shown [20] that the expected value of the posterior of \({\sigma }_{i}^{2}\) given \({s}_{i}^{2}\) is

$${\tilde{s}}_{i}^{2}=\frac{{d}_{0}{s}_{0}^{2}+{d}_{2}{s}_{i}^{2}}{{d}_{0}+{d}_{2}}.$$
(5)

Here, the hyperparameters \({s}_{0}^{2}\) and \({d}_{0}\) are estimated by fitting a scaled F-distribution with \({s}_{i}^{2} \sim {s}_{0}^{2}{F}_{{d}_{2},{d}_{0}}\)”.

In addition, the original version of this Article contained an error in Fig. 1a (step 2), in which the letters of the word “temperature” were scrambled in the gray-white gradient bar.

This has been corrected in the PDF and HTML versions of the Article.