Bayesian updating with correlated data

I’m looking for some readings on the topic of correlation between data used for Bayesian inversion. There are a lot of discussions about the correlations between the parameters being used for updating, but I didn’t find much on the correlation between the data points.

The reason why I’m interested in that is because when working on health monitoring systems, multiple data sources are installed to establish the performance of a structural component. Now, this data is highly correlated. I think assuming the data points to be independent, we’re overestimating the information we gain from this data.

I’d be glad if someone could point out some good readings on a similar topic.

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