Now I become curious how Bayesian handles heteroscedasticity? We know measurement errors are not homogeneous.

]]>These numbers are invariably derived from data, and therefore represent some kind of model parameter. Errors on the model parameters are most definitely affected by both statistical (aka measurement) and systematic errors. People may sometimes misuse the term “measurement error” to include the errors that describe such parameter uncertainties, but by and large, I think astronomers are quite clear on what is measurement error: it is the uncertainty in the measurement, i.e., a measure of how well you know the data, and thus is entirely statistical in nature. A proper understanding of the data will of course require a knowledge of the systematic effects that may affect the model that is being used to match to the data.

It may be that all the confusion in terminology is just a Bayesian vs Frequentist thing. When in doubt, think Bayesian!

]]>btw, I don’t think it is correct to say that “Astronomers sometimes call it measurement error” — we don’t do that except by mistake. Measurement error invariably refers to the statistical uncertainty that attaches to the data. Systematic errors are attached to the calibration.

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