Thanks a bunch, looking forward to reading the paper. I am especially intrigued by the claim one can give stronger guarantees than say a simple random walk.
Re:Spurious Splines
by idealmedtech on Wednesday November 16, 2022 @12:15PM
(#33626715)
By "naive" random walk, I'm referring to how one would _implement_ a random walk that's restricted to a given range. The most straightforward way to do it is to "clip" any values that would exit the given range by simply coercing them to the bound, eg:
if next_value > upper_bound: next_value = upper_bound
if next_value < lower_bound: next_value = lower_bound
This works fine, but serves to concentrate probability mass near the boundaries, so it's no longer uniformly distributed. By reflecting across boundaries rather than coercing, you're effectively flattening that concentration. If you coerce, you also reduce the expected value, which may or may not be a desirable property.
We published a paper about such an application to modelling sensor error here: https://doi.org/10.1177/1932296817711297
The martingale comes up under the "simulator" section, starting in the paragraph "In our previous simulation study".