MCMC proposal bug-fixes and small refactor

[odunbar]

…ogic

Purpose

• Closes [audit 2026-07-09] overly Symmetrised proposals in MCMC #447

To-do

Content

• Fix the issue where proposals default (via copied boilerplate) to RWM log-ratio framework that is incompatible with asymmetric densities.
• This also requires a bug-fix in the Barker proposal (which assumes decorrelated sampling, so we use the cholesky factors to whiten)
• In their place, we define the proper log ratio by using a correct transition density "q(u|u') - q(u'|u)"
• We have a small refactor, to define the Markov kernel, as a Struct. This allows for kernels that can be represented by Distributions.jl, we make a single location to define the kernel, then rand(kernel) produces a proposal, and logpdf(kernel) produces the transition log-density. For kernels that aren't representable by Distributions.jl (i.e. Barker) we store the relevant parameters in the kernel, and use similar interface for readability via methods _barker_rand(kernel) and _barker_logpdf(kernel) with the analytical formulas inside.
• We have unit tests that will catch future bugs in the proposals. We ensure that some analytic posteriors are recovered well

MISC

• we also improved the stepsize criteria to a bisection method rather than a doubling approach

---

• I have read and checked the items on the review checklist.

[codecov]

Codecov Report

❌ Patch coverage is 97.08738% with 3 lines in your changes missing coverage. Please review.
✅ Project coverage is 95.19%. Comparing base (26d7455) to head (ba7a3b4).

Files with missing lines	Patch %	Lines
src/MarkovChainMonteCarlo.jl	97.08%	3 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##             main     #448      +/-   ##
==========================================
+ Coverage   95.16%   95.19%   +0.02%     
==========================================
  Files          12       12              
  Lines        2441     2495      +54     
==========================================
+ Hits         2323     2375      +52     
- Misses        118      120       +2     

☔ View full report in Codecov by Harness.
📢 Have feedback on the report? Share it here.

🚀 New features to boost your workflow:

• ❄️ Test Analytics: Detect flaky tests, report on failures, and find test suite problems.