# making a single prediction based on multiple predictions with associated uncertainties (eg ensemble models)

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...

• If you add multiple uncertain events... the result will be even more uncertain. I think you are looking for something other than "add". Oct 19 '20 at 13:02
• 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. Oct 19 '20 at 13:07
• I suppose what I wrote only makes sense when you cannot perfectly trust the reported uncertainty of a specific model. Oct 19 '20 at 13:08
• 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. Oct 19 '20 at 13:11
• yep that's what I am currently doing, was just wondering if there is anything more statistically correct. Oct 19 '20 at 13:13