Show Matern kernel parameter effects in demo 4
To understand the add_fluctuations_matern()
parameter effects better, I added showcases of them to the 4th demo (getting_started_4_CorrelatedFields.ipynb
).
@gedenhof: could you have a look at the parameter explanations and check whether they are correct, please?
Also: I played around with the values for some time, but if you know better/more practice-oriented value combinations to showcase, please amend them.
Cheers, Lukas
Merge request reports
Activity
Looks good. You hit one minor misconception though, see below.
From the NOTE section:
The parameters of the amplitude model are assumed to be relative to a unit-less power spectrum, i.e. the parameters are assumed to be agnostic to changes in the volume of the target subdomain. This is in steep contrast to the non-parametric amplitude operator in :class:
~nifty8.library.correlated_fields.CorrelatedFieldMaker.add_fluctuations
.This does not mean that the correlation structure is independent of the volume. Only the hyper-parameters which one sets are. This is very convenient since users enlarge their space e.g. by adding more pixels and increasing the volume accordingly, will not need to change their priors. In the non-parametric correlated field model this is not the case. The hyper-parameters implicitly depend on the target space and are not invariant under an enlarged space.
Hmm, this is what I wanted to communicate, but I may not understand it well enough to formulate it correctly.
The hyper-parameters should be independent of the fields volume for both types of amplitude models by definition, right? As I understand it is only when some other property of the samples has to be conserved under volume changes that the hyper-parameters need to be adjusted alongside the volume for the non-parametric amplitude model. I wanted to state what quantity is conserved under volume changes by the Matern amplitude operator in a way less abstract than the note does, but did not put much thought into it.
Do you see a way to describe it less abstractly?
No, the hyper-parameters of the non-parametric field model implicitly change the prior on the correlation structure if one changes the volume of the space. They are not agnostic to the choice of pixelization!
In a description of the Matern kernel I would highlight exactly that: In contrast to the non-parametric model where the prior on the correlation structure implicitly changes with the volume of the target subspace, the Matern kernel's correlation structure parameterized by its hyper-parameters is agnostic to any change in volume of the target subspace.
added 464 commits
-
dc6350bd...4ec43f17 - 463 commits from branch
NIFTy_8
- 2774b09e - add matern fluctuations, note still explanation text still wrong
-
dc6350bd...4ec43f17 - 463 commits from branch
Hi Gordian,
in an effort to fix and finish outstanding merge requests, I am revisiting this one. Sorry for not replying earlier to your feedback!
As I would really like to get this out, I simply removed the erroneous note without replacement.
Do you think the text is correct in the current form?
@parras Could you please quickly check and merge?
mentioned in commit 10ef8340