Add LogDensityProblems interface

[codecov[bot]]

Codecov Report

Patch coverage: 100.00% and project coverage change: -0.15 :warning:

Comparison is base (5f8e688) 86.46% compared to head (e9e4c5a) 86.31%.

Additional details and impacted files

```diff @@ Coverage Diff @@ ## main #286 +/- ## ========================================== - Coverage 86.46% 86.31% -0.15% ========================================== Files 37 37 Lines 3288 3282 -6 ========================================== - Hits 2843 2833 -10 - Misses 445 449 +4 ``` | [Impacted Files](https://codecov.io/gh/ptiede/Comrade.jl/pull/286?src=pr&el=tree&utm_medium=referral&utm_source=github&utm_content=comment&utm_campaign=pr+comments&utm_term=Paul+Tiede) | Coverage Δ | | |---|---|---| | [lib/ComradeAHMC/src/ComradeAHMC.jl](https://codecov.io/gh/ptiede/Comrade.jl/pull/286?src=pr&el=tree&utm_medium=referral&utm_source=github&utm_content=comment&utm_campaign=pr+comments&utm_term=Paul+Tiede#diff-bGliL0NvbXJhZGVBSE1DL3NyYy9Db21yYWRlQUhNQy5qbA==) | `95.23% <100.00%> (-0.60%)` | :arrow_down: | | [src/bayes/bayes.jl](https://codecov.io/gh/ptiede/Comrade.jl/pull/286?src=pr&el=tree&utm_medium=referral&utm_source=github&utm_content=comment&utm_campaign=pr+comments&utm_term=Paul+Tiede#diff-c3JjL2JheWVzL2JheWVzLmps) | `94.44% <100.00%> (+0.32%)` | :arrow_up: | | [src/inference/pullbacks.jl](https://codecov.io/gh/ptiede/Comrade.jl/pull/286?src=pr&el=tree&utm_medium=referral&utm_source=github&utm_content=comment&utm_campaign=pr+comments&utm_term=Paul+Tiede#diff-c3JjL2luZmVyZW5jZS9wdWxsYmFja3Muamw=) | `0.00% <0.00%> (-36.37%)` | :arrow_down: | | [src/models/modelimage/cache.jl](https://codecov.io/gh/ptiede/Comrade.jl/pull/286?src=pr&el=tree&utm_medium=referral&utm_source=github&utm_content=comment&utm_campaign=pr+comments&utm_term=Paul+Tiede#diff-c3JjL21vZGVscy9tb2RlbGltYWdlL2NhY2hlLmps) | `75.00% <0.00%> (-5.00%)` | :arrow_down: | | [src/models/modelimage/nuft.jl](https://codecov.io/gh/ptiede/Comrade.jl/pull/286?src=pr&el=tree&utm_medium=referral&utm_source=github&utm_content=comment&utm_campaign=pr+comments&utm_term=Paul+Tiede#diff-c3JjL21vZGVscy9tb2RlbGltYWdlL251ZnQuamw=) | `74.41% <0.00%> (-0.59%)` | :arrow_down: | | [src/observations/observations.jl](https://codecov.io/gh/ptiede/Comrade.jl/pull/286?src=pr&el=tree&utm_medium=referral&utm_source=github&utm_content=comment&utm_campaign=pr+comments&utm_term=Paul+Tiede#diff-c3JjL29ic2VydmF0aW9ucy9vYnNlcnZhdGlvbnMuamw=) | `70.00% <0.00%> (-0.18%)` | :arrow_down: | Help us with your feedback. Take ten seconds to tell us [how you rate us](https://about.codecov.io/nps?utm_medium=referral&utm_source=github&utm_content=comment&utm_campaign=pr+comments&utm_term=Paul+Tiede). Have a feature suggestion? [Share it here.](https://app.codecov.io/gh/feedback/?utm_medium=referral&utm_source=github&utm_content=comment&utm_campaign=pr+comments&utm_term=Paul+Tiede)

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