Implement Statistical Primitives for Differential Expression Analysis

[ianfd]

Description

Add fundamental statistical functions and distributions to support differential expression (DE) analysis for single-cell data.

Objectives

• Implement core statistical building blocks needed for DE analysis
• Optimize for performance with sparse matrix operations
• Ensure numerical stability for single-cell data characteristics

Key Components to Implement

Statistical Tests

• Mann-Whitney U test implementation
• Student's and Welch's t-test implementations
• Negative binomial distribution and testing
• Zero-inflated model support

Multiple Testing Correction

• Benjamini-Hochberg procedure
• Bonferroni correction
• Storey's q-value estimation

Effect Size Calculation

• Hedges'G
• Fold change computation functionality
• Cohens'D

Utility Functions

• Parallelized hypothesis testing
• Specialized sparse matrix operations for statistical calculations

Integration Points

• Functions should operate directly on nalgebra sparse matrix types
• Implementations should support both f32 and f64 precision
• APIs should be consistent with existing single-algebra functions

Technical Notes

• Consider integrating with existing matrix traits like MatrixSum, MatrixVariance
• Implement traits for different statistical test categories for polymorphic usage
• Use generics for type flexibility