What are methods that combines/regress on frequent low quality estimates (laden with bias+noise) with infrequent high quality estimates to yield estimates that have lower uncertainty?
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$\begingroup$ If you can assign some rough numeric value to quality, one possibility is to use that number to weight the data. $\endgroup$– James PhillipsCommented Jun 28, 2017 at 9:38
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This type of regression has a name in the litterature: it is called multi-fidelity (or multi-level) regression. This subject is of particular interest in the context of global optimization of costly computer codes and obviously in the case of the study of computer codes with several levels of approximation with different levels of cost.
It assumes, as you said, that you have multiple ways of estimating a same underlying function which you want approximate using regression.
Basically, the idea developed in most of the model is to use co-kriging (aka Gaussian Process Regression for multivariate functions) to regress on each level of approximation
A good way to enter the topic can be
Also, one of the latest advances on the subject may be found here.
