Add feature to save MCMCChains objects as JSON

[shravanngoswamii]

Save MCMCChains objects as:

• JSON
• StanCSV
• ArviZ InferenceObjects See here.

Partially completes #499

[codecov]

Codecov Report

❌ Patch coverage is 61.11111% with 21 lines in your changes missing coverage. Please review.
✅ Project coverage is 88.37%. Comparing base (6b95633) to head (bc5bfe8).

Files with missing lines	Patch %	Lines
src/fileio.jl	0.00%	17 Missing ⚠️
ext/MCMCChainsJSONExt.jl	89.18%	4 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##             main     #502      +/-   ##
==========================================
+ Coverage   88.35%   88.37%   +0.02%     
==========================================
  Files          20       21       +1     
  Lines        1365     1402      +37     
==========================================
+ Hits         1206     1239      +33     
- Misses        159      163       +4     

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[github-actions]

MCMCChains.jl documentation for PR #502 is available at:
https://TuringLang.github.io/MCMCChains.jl/previews/PR502/

[devmotion]

The documented way to define JSON (de)serialization for custom types seems to be to define JSON.lower: https://juliaio.github.io/JSON.jl/dev/writing/#Custom-Type-Serialization-with-lower

[shravanngoswamii]

Thank you, @devmotion! I have updated the extension to define JSON.lower for custom types.

[yebai]

note that ArivZ conversion already exist, see https://github.com/arviz-devs/ArviZ.jl/blob/ffd94133ba9f081930b32af05dc901bd19dfd42e/ext/ArviZMCMCChainsExt.jl#L103

[yebai]

cc @nsiccha as this will implement StanCSV.