Fix some errors and datatype issues in examples

[sunxd3]

No description provided.

[github-actions]

Benchmark results on macOS (aarch64)

BridgeStan not found at location specified by $BRIDGESTAN environment variable, downloading version 2.6.1 to /Users/runner/.bridgestan/bridgestan-2.6.1
Done!

Stan results:

Model	Parameters	Density Time (µs)	Density+Gradient Time (µs)
rats	65	5.425	7.625
pumps	12	0.911765	1.04342
bones	13	87.729	99.125
oxford	244	11.833	13.792
epil	303	38.083	42.333
lsat	1006	105.105	145.0
schools	133	241.666	377.229
beetles	2	0.799778	0.900548
air	5	0.943548	1.05383

JuliaBUGS results:

Model	Parameters	Density Time (µs)	Density+Gradient Time (µs)
rats	65	103.0	324.208
pumps	12	14.291	21.875
bones	33	584.5	443.666
oxford	244	404.458	587.521
epil	303	332.271	789.521
lsat	1006	2721.75	3594.75
schools	133	3147.79	10427.5
beetles	2	9.354	11.5625
air	5	7.625	9.167

---

Benchmark results on Ubuntu (x64)

BridgeStan not found at location specified by $BRIDGESTAN environment variable, downloading version 2.6.1 to /home/runner/.bridgestan/bridgestan-2.6.1
Done!

Stan results:

Model	Parameters	Density Time (µs)	Density+Gradient Time (µs)
rats	65	5.2198	7.501
pumps	12	0.971167	1.1838
bones	13	71.835	89.178
oxford	244	13.5555	17.583
epil	303	26.83	33.574
lsat	1006	164.118	205.887
schools	133	510.945	748.286
beetles	2	0.842143	0.99669
air	5	0.663045	0.833

JuliaBUGS results:

Model	Parameters	Density Time (µs)	Density+Gradient Time (µs)
rats	65	68.188	89.147
pumps	12	12.5435	6.62
bones	33	420.996	185.798
oxford	244	355.197	209.824
epil	303	298.135	277.952
lsat	1006	1918.86	1187.4
schools	133	2446.8	3350.24
beetles	2	7.407	3.51913
air	5	6.55	2.34358

[coveralls]

Pull Request Test Coverage Report for Build 13560991363

Warning: This coverage report may be inaccurate.

This pull request's base commit is no longer the HEAD commit of its target branch. This means it includes changes from outside the original pull request, including, potentially, unrelated coverage changes.

• For more information on this, see Tracking coverage changes with pull request builds.
• To avoid this issue with future PRs, see these Recommended CI Configurations.
• For a quick fix, rebase this PR at GitHub. Your next report should be accurate.

Details

• 0 of 0 changed or added relevant lines in 0 files are covered.
• No unchanged relevant lines lost coverage.
• Overall coverage remained the same at 81.99%

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Totals
Change from base Build 13514768036:	0.0%
Covered Lines:	1607
Relevant Lines:	1960

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💛 - Coveralls