Module effect 

Effect decomposition using Bayesian linear regression (spec §3.4.6).

This module decomposes timing differences into interpretable components:

• Uniform shift (μ): All quantiles move equally (e.g., branch timing)
• Tail effect (τ): Upper quantiles shift more than lower (e.g., cache misses)

Design Matrix (spec §3.4.6)

X = [1 | b_tail] where:

• Column 0: ones = [1, 1, …, 1] - uniform shift affects all quantiles equally
• Column 1: b_tail = [-0.5, -0.375, …, 0.5] - tail effect is antisymmetric

The tail basis is centered (sums to zero) so μ and τ are orthogonal.

Model

Δ = Xβ + ε, ε ~ N(0, Σ_n)

With the same conjugate Gaussian model as the Bayesian layer (spec §3.4.6).

Effect Pattern Classification (spec §3.4.6)

An effect component is “significant” if |effect| > 2×SE:

• UniformShift: Only μ is significant
• TailEffect: Only τ is significant
• Mixed: Both are significant
• Indeterminate: Neither is significant (classify by relative magnitude)

Structs

EffectDecomposition

Result of effect decomposition (internal, detailed).

EffectEstimate

Simplified effect estimate for public API.

Functions

classify_pattern

Classify the effect pattern based on posterior estimates (spec §3.4.6).

decompose_effect

Decompose timing differences into shift and tail effects (spec §3.4.6).