JuliaMath / JuliaMath/MeasureTheory.jl
Density at an infinite sequence
- Dominant language
- Julia
- Stars
- 401
- Forks
- 31
- PR merge metrics
- No merged PRs in 30d
Description
This is a little unintuitive for me. So `testvalue`, which is I think a point on the sample space of `Chain`, cannot be passed to the `logdensity` function without some processing. Would it make more sense for `Chain` to be a family of measures that must be conditioned on a fixed number of steps (here, 10), in order to uniquely define a measure?
_Originally posted by @sethaxen in https://github.com/cscherrer/MeasureTheory.jl/pull/137#discussion_r688925975_
My original response:
> I agree it's unintuitive, but I think it's more a difficulty of the math than a problem with the implementation. It's a little like working with irrational numbers. Everything is well-defined, but you can never look at or do computations with the full set of decimal digits. Or even better a Gaussian process - the GP itself is a continuous function, but we can only ever evaluate it on a finite set of values.
Thinking some more about this, given a continuous function `f` on the reals, we usually compute (approximate, really) `f(π)` by looking at `f` on values near `π`. And we can compute the log-density of a GP on some continuous function using integration.
We can't have an empirically observed infinite sequence, but we can define things like this programmatically. And yet as currently implemented, the density of a `Chain` on any infinite sequence converges to zero.
This leads to the question, are we really implementing this correctly? @mschauer you've had helpful insights on similar problems, any thoughts on this?
Contributor guide
No contributing guide indexed for this repository
Assessment
This issue has not been assessed yet.