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Let's say I have a set of predictions $y_i$ and associated uncertainties $\sigma_i$ and the predictions are all normally distributed. How can I "add" these up to make some final prediction. ie predictions with low uncertainty are more trustworthy etc...

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  • $\begingroup$ If you add multiple uncertain events... the result will be even more uncertain. I think you are looking for something other than "add". $\endgroup$ Oct 19 '20 at 13:02
  • $\begingroup$ yep apologies, I meant more along the lines of if you have N models that make a prediction, and these return N uncertainties. If 1 model had uncertainty 0 you would just pick that one for example. But realistically none have 0 uncertainty, what theory do you use to best combine the predictions to get the most "accurate" result in terms of minimizing uncertainty while not completely ignoring the other models results. $\endgroup$ Oct 19 '20 at 13:07
  • $\begingroup$ I suppose what I wrote only makes sense when you cannot perfectly trust the reported uncertainty of a specific model. $\endgroup$ Oct 19 '20 at 13:08
  • $\begingroup$ First thing that comes to mind is just a simple average of all the predictions, you could use the uncertainties as weights in the calculation. $\endgroup$ Oct 19 '20 at 13:11
  • $\begingroup$ yep that's what I am currently doing, was just wondering if there is anything more statistically correct. $\endgroup$ Oct 19 '20 at 13:13

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