MATLAB: Neural network: probability of prediction

Deep Learning Toolboxneural networkpredictionprobabilityprobability predictionstatistics

I have been using the neural network toolbox to predict the next value in a time series. This works, however I would like to know what is the probability of Matlab's neural network prediction.
E.g.: let's say we have time series [1 2 3 4 5]. The neural network would maybe predict the next value in the chain will be 5.9 (as an example).
Is there any (easy) way to derive the probability of this prediction? I would like to be able to tell something like this: it is predicted that the expected value of the next step will be 5.9 with a probability of 78%. It would be even better if I could get the entire probability distribution of the next value, or at least also the standard deviation. I hope anyone can help.
My point is that having a prediction without a probability does not help a lot, there might be a lot of uncertainty about this prediction. If one would forecast it is going to rain tomorrow this would give little information. If one would say it is going to rain with 95% probability than I know how to handle.

Best Answer

The only way I know of to obtain error bars for a neural net output is to
 1. Assume an input probability distribution 
 2. Assume an input variance
 3. Create many random realizations
 4. Calculate the resulting spread of the prediction
Hope this helps.
Greg
Related Question