JuliaMath / JuliaMath/MeasureTheory.jl

Density at an infinite sequence

Open
#138 1 comment 0 reactions 0 assignees View on GitHub
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.

Get new issues in your inbox

A short digest of beginner-friendly GitHub issues.