feat(experimentation): Bayesian stats kernel

[gagantrivedi]

• I have read the Contributing Guide.
• I have added information to docs/ if required so people know about the feature. (deferred — internal module; docs land with the results UI.)
• I have filled in the "Changes" section below.
• I have filled in the "How did you test this code" section below.

Changes

Contributes to the experimentation results scorecard (v0.2). Pure stats module — no Django, ClickHouse or schema changes; the query, model and endpoints follow in stacked PRs.

• VariantStats — per-variant sufficient statistics (n, sum, sum_squares) with derived mean and clamped unbiased variance; the only data the warehouse needs to return per metric × variant.
• compare_to_control(control, treatment) — relative lift with delta-method variance, Normal posterior under a flat prior: 95% credible interval and chance_to_win = P(lift > 0); direction flips for "lower is better" metrics belong to the payload builder. Returns None when inference is undefined (an arm below two observations, or zero control mean); zero variance degenerates to certainty without dividing by zero.
• srm_p_value(observed, expected_shares) — chi-squared goodness-of-fit survival, exact for integer degrees of freedom using only the stdlib (erfc base case + the incomplete-gamma recurrence; no scipy). None when not computable.

How did you test this code?

• 19 example-based tests: hand-derived proportions case (lift/CI/chance to 1e-4), identical arms, zero-variance degenerate certainty, undefined-inference inputs, chi-squared reference values for 1, 2 and 3 dof (0.0455, e⁻¹, 0.04601), heavy imbalance below the 0.001 threshold, non-computable SRM inputs, variance clamping.
• pytest tests/unit/experimentation/ — 265 passed; ruff + mypy strict clean.

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3 Skipped Deployments

Project	Deployment	Actions	Updated (UTC)
docs	Ignored	Preview	Jun 12, 2026 9:01am
flagsmith-frontend-preview	Ignored	Preview	Jun 12, 2026 9:01am
flagsmith-frontend-staging	Ignored	Preview	Jun 12, 2026 9:01am

[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 98.56%. Comparing base (879046c) to head (a8ba0c8).

Additional details and impacted files

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  Coverage   98.56%   98.56%            
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  Files        1459     1461     +2     
  Lines       56134    56237   +103     
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+ Hits        55327    55430   +103     
  Misses        807      807            

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