Add LKJ
#1066
Add LKJ
#1066
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@@ Coverage Diff @@
## master #1066 +/- ##
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+ Coverage 79.45% 80.62% +1.17%
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Files 112 113 +1
Lines 5514 5611 +97
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+ Hits 4381 4524 +143
+ Misses 1133 1087 -46
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Hi, could you post a screenshot of the docstring of |
^Updated. |
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Do you know in which sense is this "uniform" if eta=1? |
| # Section 3.2 in LKJ (2009 JMA) | ||
| # 1. Initialization | ||
| R = ones(typeof(η), d, d) | ||
| β = η + 0.5d - 1 |
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Maybe
| β = η + 0.5d - 1 | |
| β = η + d/2 - 1 |
or should this have some oftype?
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β won't be promoted to whatever η is?
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η = 1f0
d = 4
julia> typeof(η), typeof(η + 0.5d - 1)
(Float32, Float64)
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Right, thanks. Since Beta suffers from #960 it doesn't end up mattering, unfortunately.
| # 2. | ||
| for k in 2:d - 1 | ||
| # (a) | ||
| β -= 0.5 |
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One could test that importance sampling is successful, e.g. for R ~ LKJ(eta) and U ~ LKJ(1) and some functional f |
The density is constant in R. The determinant term collapses to 1 and you just have f(R; η) = c₀. |
Fair enough. I can add that. |
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Yes, I can see that, but I suspect there is something to say what that distribution actually is. Or in other words, what is the reference measure for the densities? |
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@mschauer It's a density with respect to Lebesgue measure, so uniform here just means the density is one over the Lebesgue measure of the support. The m = d(d-1)/2 free elements of a correlation matrix live in a subset of [-1, 1]ᵐ that has finite and strictly positive Lebesgue measure. So not some measure zero submanifold that requires a funky dominating measure to define a density. More here and here. Consequently though, the log integrating constant here is currently off by a sign. Fixing that now. |
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Thank you, this is nice. What is the price we pay for the test in terms of time? |
0.21 seconds |
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Thanks for all of the help on this, as usual. Let me know what else you want to see for this to be considered for merging. |
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Looks great to me. @johnczito maybe add a reference in the testset from the last commit to indicate where the stan test set comes from (documentation link or something) |
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Awesome, the tests were green before, so I'll just merge it here, thanks! |
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I now believe that it is uniform in the constraint space of correlation matrices!
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@mschauer Nice! And that's a code snippet I'll definitely be stealing... |
This PR adds the LKJ distribution, which is a distribution over correlation matrices. It can be found in other statistical computing platforms (here, here, or here, for instance).
Note: One of the unit tests runs a hypothesis test, so this PR adds
HypothesisTests.jlas an extra testing dependency in the.toml. Let me know if I have done this incorrectly, or if I should exclude this change for now.