Implement Brier Score and Log Score

[jc-macdonald]

Summary

Standard proper scoring rules for probabilistic classification / binary events.

Functions

Function	Description
brier_score(obs::Bool, prob::Real)	Brier score for binary event
brier_score(obs::AbstractVector{Bool}, probs::AbstractVector)	Vectorized
log_score(obs::Bool, prob::Real)	Logarithmic score
log_score(obs::AbstractVector{Bool}, probs::AbstractVector)	Vectorized

Algorithm

$$ \text{BS} = (p - o)^2 \quad\quad \text{LS} = -o\log(p) - (1-o)\log(1-p) $$

Acceptance Criteria

• Perfect forecast ($p=1, o=1$) scores 0 (Brier) and 0 (Log)
• Worst case ($p=0, o=1$) scores 1 (Brier) and Inf (Log, clamped)
• Vectorized version matches element-wise mean