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I have a question regarding whether or not a certain type of statistical model exists. What I need to model is an error of measurement, and not measurement error in the sense of what I've generally come across in my learning of statistics. If this situation is indeed a simple case of measurement error, and model typically used to deal with measurement error is appropriate, please correct me, as I really need to understand this content (PhD student in social science).

I have a data-set consisting of acoustic measurements of speech taken from digital recordings. In this data-set, certain measurements are incorrect. There are 3 dependent variables, and for all of them, some values may not be representative of the reality they are supposed to measure. This is because the measurements are made by a computer algorithm that is not perfect, and as such a certain percentage of the values in all three dependent variables will be wrong: let's be conservative and say 5% of measurements are outside the range of a possibly correct value given knowledge of general acoustics and known properties of human speech.

The only option I see right now is to remove the multivariate outliers outside a certain Mahalanobis distance from the center of the space. This could be used in conjunction with expert knowledge of the phenomenon to make a cutoff at the reasonable value. I would then treat values outside the space as missing data and use a Bayesian imputation method to account for the cells I've deleted.

What I'd like to know is if there is a type of model I could run that would automatically detect likely measurement errors and reduce their weighting and/or mitigate their influence on the model. Any suggestions of models or concepts to look into would be greatly appreciated, especially in the form of academic papers or books.

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    $\begingroup$ What is your understanding of measurement error models and why is your case not under its scope? $\endgroup$
    – Tim Mak
    Jun 16, 2020 at 5:55
  • $\begingroup$ My understanding was that measurement error was that it came from the sampling of a population, and you needed to account for the standard error in the modelling. Not an outright faulty measurement. $\endgroup$
    – sjp
    Jun 16, 2020 at 18:02
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    $\begingroup$ I think what you described is known as sample variation. Have you checked out the Wikipedia article on measurement error models? The usual assumption in these models is that the observed $x$ is simply the true $x^*$ plus an error term, often assumed to be Gaussian. Given that you seem to be comfortable with Bayesian modeling. It's straightforward to replace the Gaussian with something more appropriate for your scenario. $\endgroup$
    – Tim Mak
    Jun 17, 2020 at 2:39
  • $\begingroup$ Thanks so much for the information, I will look into it and see if I can apply this to my data. The problem I foresee having is that the errors won't be distributed around the actual value measured. $\endgroup$
    – sjp
    Jun 17, 2020 at 17:53

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