[m-murphy]

I think they mean either what is E[x| y] (standard regression point estimate) along with a confidence interval (this assumes that the mean is a meaningful quantity), or the interval s.t. F(x | y) -- the PDF of x -- is between .025 and .975 (the 95% predictive interval centered around .5). The point is that the width of the confidence interval around the point estimate of the mean converges to 0 as you add more data because you have more information to estimate this point estimate, while the predictive interval does not, it converges to the interval composed of the aleatoric uncertainty of the data generating distribution of x conditioned on the measured covariates y

[borroka]

That's exactly what I was talking about. The nature of the uncertainly intervals is made even more nebulous when not using formal notation, something I was guilty of doing in my comment--even if I used the word "loosely" for that purpose.

If you think about linear regression, it makes sense, given the assumptions of linear regression, that confidence interval E[x|y] is narrower around the mean of x and y.

If I had to choose between the two, confidence intervals in a forecasting context are less useful in the context of decision-making, while prediction intervals are, in my opinion, always needed.

[bo1024]

Ah, that makes sense. The word expectation was really throwing me off, along with the fact that, in the kind of forecasting setting of this post, the mean and confidence interval (used in the correct sense) are not meaningful, while the quantile or 'predictive interval' are meaningful.