# Re: [R] Prediction interval of Y using BMA

From: Spencer Graves <spencer.graves_at_pdf.com>
Date: Sun 16 Jul 2006 - 14:23:27 EST

From what I've heard, the primary reason for using Bayesian Model Averaging (BMA) is to get better predictions, both better point estimates and better estimates of the uncertainties. I could not find a function to compute that.

However, if you've got point estimates of predictions, I can give you a formula for the variance of the prediction error:

var(Y|x) = var(E(Y|x,i)over i)+E(var(Y|x,i)over i),

where Y is the response variable, and 'i' indicates which model. This is a companion to the formula for the predictions:

E(Y|x) = E(E(Y|x,i)over i).

If you've got a function to compute E(Y|x,i) and compute their expectation over i, it should not be too difficult to modify that function to also compute var(Y|x,i) and then to compute both E(var(Y|x,i)over i) and var(E(Y|x,i)over i). Then if distributions are roughly normal, you've got what you need.

```	  Does this make sense?
Hope this helps.
Spencer Graves
```

p.s. I've copied the maintainer for the BMA package on this email. I hope he will correct any misstatement in these comments and update us on any relevant capabilities we may have missed.

Nicolas.Meyer@chru-strasbourg.fr wrote:
> Hello everybody,
>
> In order to predict income for different time points, I fitted a linear
> model with polynomial effects using BMA (bicreg(...)). It works fine, the
> results are consistent with what we are looking for.
> Now, we would like to predict income for a future time point t_next and of
> course draw the prediction interval around the estimated value for this
> point t_next. I've found the formulae for the ponctual estimation of t_next
> but I cannot succeed in finding the formula to compute the prediction
> interval based on BMA sets of models, which requires the adequate variance.
> The paper of Hoeting et al. on BMA gives the posterior variance of a
> parameter but what I want is the posterior variance of a predicted Y and not
> the posterior variance of a beta, since the goal here is not to build an
> explanatory model but an accurately predictive model.
> Is there a way to get around it with the function of the BMA package or does
> anybody has indication on where to find the formulae ? I searched the web
> for hours but nothing like this is to be found.
> Any help will be appreciated.
>
>
>
>
> Nicolas Meyer
> Département de Santé Publique
> Unité de Biostatistique et Méthodologie
> 03 88 11 63 58
> nicolas.meyer@chru-strasbourg.fr <mailto:nicolas.meyer@chru-strasbourg.fr>
>
> La conjecture de Feynman :
> "To report a significant result and reject the null in favor of an
> alternative hypothesis is meaningless unless the alternative hypothesis has
> been stated before the data was obtained"
> "The meaning of it all", 1998.
>
>
> [[alternative HTML version deleted]]
>
>
>
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