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I realize this may be better asked on Stack Overflow, but thought I would try to elicit a response here first.

Here is my problem

I am simulating a GAM from the posterior of the multivariate normal distribution based on examples from Simon Wood's GAM textbook.

I am able to easily obtain confidence intervals (CIs) for the maximum $X$ using the quantile() R function, but I would now like to obtain an estimates of the standard error (SE) for the different GAM bases that I choose. I don't think simply using sd() will work here. If not, then is there a way to somehow extract the SE from the CIs?

compbiostats
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  • post a MWE..... – generic_user Dec 05 '17 at 19:32
  • I based my analysis verbatim from https://stats.stackexchange.com/questions/190348/can-i-use-bootstrapping-to-estimate-the-uncertainty-in-a-maximum-value-of-a-gam/191489#191489 – compbiostats Dec 05 '17 at 19:52
  • Can't you just take the standard error of the mean of the maximum? – Gavin Simpson Dec 05 '17 at 22:00
  • @GavinSimpson Yes, this did occur to me, but I have not tried it because I don't know that it is the most statistically correct approach to take. Bootstrapping is easy to implement, but problematic for GAMs, as you have mentioned before, which is why I am opting for the current approach – compbiostats Dec 05 '17 at 22:53
  • Right, but you need some estimator of the maximum; you could take the mean of the simulated maxima as your point estimate and the standard error of that mean as your measure of uncertainty in that estimate. In the example from the linked Q, this may or may not be what you want if the distribution of simulated values is skewed. I think a lot of this comes down to what's your loss function? – Gavin Simpson Dec 05 '17 at 22:59
  • @GavinSimpson I have written a routine that finds X from a given Y, but I'm unsure how to modify your example from the linked question. Right now, R is giving me a CI of (100, 100), which makes absolutely no sense at all. – compbiostats Dec 06 '17 at 02:55
  • I think I will try your suggestion for the standard error. – compbiostats Dec 06 '17 at 02:56

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