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I am using a Neural Network to estimate Ecosystem Respiration (ER) and Gross Primary Productivity (GPP) from Net Ecosystem Exchange (NEE) observations where.

NEE = GPP + ER

I've used the model to fit a NEE response to four independent variables: Photon Flux Density (PPFD), Air & Soil Temps (Ta & Ts), and Soil Water (Sw). PPFD is the primary driver of photosynthesis (GPP) while the other factors have more complicated effects.

To estimate ER, I'm running the Network setting PPFD = 0, and leaving all others the same. Theoretically, GPP ~ 0 and NEE = ER as PPFD >> 0. I have some nighttime observations where GPP ~ 0 and NEE = ER, so I have some observations with which to validate my ER estimates. My goal is to extrapolate my ER estimates to cover the full time series.

I'm using bootstrapping method, explained in this paper (Dybowski & Roberts, 2001) to calculate the input dependent CI for the mean regression response and PI's for individual unseen inputs for estimates of NEE.

My question is how to calculate a prediction interval for the mean response of multiple unseen inputs? I want to present the mean estimated ER with some error bounds around it? I can easily calculate the prediction interval for each individual estimate of ER, but I'm a bit confused when it comes to aggregating those individual estimates. Should I simply estimate the PI using the mean of the unseen inputs?

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