Fix broken case when variables are multi-dimensional and add tests for AdvancedHMC extension and inference

[sunxd3]

Fix #71.

[codecov]

Codecov Report

Patch coverage has no change and project coverage change: -0.18% ⚠️

Comparison is base (35661f6) 72.16% compared to head (6a37dfd) 71.98%.

Additional details and impacted files

@@            Coverage Diff             @@
##           master      #89      +/-   ##
==========================================
- Coverage   72.16%   71.98%   -0.18%     
==========================================
  Files          16       16              
  Lines        1631     1635       +4     
==========================================
  Hits         1177     1177              
- Misses        454      458       +4     

Files Changed	Coverage Δ
src/BUGSExamples/BUGSExamples.jl	20.00% <0.00%> (-80.00%)	⬇️

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[github-actions]

Pull Request Test Coverage Report for Build 6213349923

• 0 of 4 (0.0%) changed or added relevant lines in 1 file are covered.
• No unchanged relevant lines lost coverage.
• Overall coverage decreased (-0.2%) to 71.988%

---

Changes Missing Coverage	Covered Lines	Changed/Added Lines	%
src/BUGSExamples/BUGSExamples.jl	0	4	0.0%

Totals
Change from base Build 6213090706:	-0.2%
Covered Lines:	1177
Relevant Lines:	1635

---

💛 - Coveralls

[sunxd3]

@yebai another look?

[yebai]

It appears these lines are the only AHMC specific code.

If so, can we improve this module by abstracting out the AHMC specific code into a lightweight separate extension? We can then convert this module into a generic JuliaBUGSMCMCChainsExt which can be shared by other samplers like AMH?

[sunxd3]

@yebai I moved the reference results to BUGSExamples, e.g.,

JuliaBUGS.jl/src/BUGSExamples/Volume_I/Seeds.jl

Lines 41 to 48 in 6a37dfd

	reference_results=(
	alpha0=(mean=-0.5499, std=0.1965),
	alpha1=(mean=0.08902, std=0.3124),
	alpha12=(mean=-0.841, std=0.4372),
	alpha2=(mean=1.356, std=0.2772),
	sigma=(mean=0.2922, std=0.1467),
	),
	)

Also created a function at

JuliaBUGS.jl/src/BUGSExamples/BUGSExamples.jl

Lines 55 to 61 in 6a37dfd

	function has_ground_truth(m::Symbol)
	if m in union(keys(VOLUME_I), keys(VOLUME_II))
	return haskey(getfield(BUGSExamples, m), :reference_results)
	else
	return false
	end
	end

Maybe something like

has_ground_truth(::Val{:seeds}) = true

# call
has_ground_truth(Val(:seeds))

is better?

For now, I'll merge this PR, we can improve in the future.