Rather than using z-scoring, one can use log probabilities to measure prediction accuracy. They are computed by (μ−xσ)2−log(σ)−12log(2π).
A downside is that they are not scale invariant, but instead the unit you measure x in leads to a constant offset. I don’t know whether one can come up with a scale invariant version. (I think no, because changing the scale is symmetric with changing the prediction accuracy? Though if one has some baseline prediction, one can use that to define the scale.)
Rather than using z-scoring, one can use log probabilities to measure prediction accuracy. They are computed by (μ−xσ)2−log(σ)−12log(2π).
A downside is that they are not scale invariant, but instead the unit you measure x in leads to a constant offset. I don’t know whether one can come up with a scale invariant version. (I think no, because changing the scale is symmetric with changing the prediction accuracy? Though if one has some baseline prediction, one can use that to define the scale.)