Reflective boundaries implementation

[myradio]

From the JOSS,

Reflecting boundary conditions can be used to improve reconstruction accuracy. For example, with data drawn from a log-normal distribution, a standard KDE will produce ‘leakage’ outside of the domain. To enforce the restriction that f(x < 0) = 0 (which must be known {a priori}), the kernel is redefined such that KH(x < 0) = 0, and re-normalized to preserve unitarity1 . This example is shown in Figure 1, with histograms in the upper panel and KDEs on the bottom.

Isn't this then absorbing boundary conditions? Or am I missing something?

[syrte]

Not sure if this is what you are asking: https://kalepy.readthedocs.io/en/latest/kde_api.html#reflecting-boundaries

[myradio]

Your link shows an example of how to use this feature in kalepy package.
My question regards what is doing under the hood when we use the option 'reflect=True', but I reckon I will have to dig myself. From what I read on the JOSS paper that explains what the package does, my first thinking is that what here is called reflective BC is actually absorbing BC.

[lzkelley]

Hi @myradio , I think you're right that the description in the paper is actually describing absorption. I'm not sure how/why this got mixed up in the paper - but thank you for pointing it out. The implementation however is actually that of reflection, which you can see here.

Does that clarify things?

[myradio]

Hi @lzkelley , Sorry for the delay. You are absolutely right!. Actually it is both things, right? After reflecting the data wrt the boundary as (the code you mentioned) , then you need to set to zero the pdf beyond the boundary. Thanks!