CI based on delta method vs sampling method

[parksw3]

This might be something that's worth explaining/mentioning in the manuscript.

I saw your CI code in expgrowthfit and implemented it in fitsir as well and noticed that delta method and sampling method give significantly different results for CI.

You can try running the following code to see the difference:

harbin2 <- setNames(harbin, c("times", "count"))
ff <- fitsir(harbin2, type="death", method="BFGS")
plot(ff, level=0.95) ## delta
plot(ff, level=0.95, method="sample") ## sampling method

If you use lower level (e.g. level=0.1), sampled CI even misses the mean maximum likelihood trajectory.

If you want to see all samples, you can try running

predict(ff, level=0.95, method="sample", debug=TRUE)

If you want to see the actual code (should be identical to your code if I didn't make any mistakes), it's inside predict function under fitsir-methods.R.

There's something about non-linearity...

[parksw3]

I wonder how this "problem" translates to CIs in expgrowthfit...