Benchmark

This page records a real benchmark run comparing runMCMC(...; fast_blocks=true) and runMCMC(...; fast_blocks=false) for the same target-scale question:

• N = 50,000 individuals
• target P = 2,000,000 markers
• target chain length L = 2000

Date of run: February 26, 2026.

Goal

Estimate wall-clock MCMC time for a single-trait BayesC run at target scale, and compare fast-block vs standard BayesC.

Environment

• Platform: UCD farm cluster (Slurm)
• Julia: 1.12.1
• Model: y1 = intercept + geno
• Data: synthetic dense Float32 genotype matrix and synthetic phenotype
• Settings:
  • method="BayesC"
  • memory_guard=:warn
  • outputEBV=false
  • output_heritability=false

Fast-Block Benchmark (fast_blocks=true)

Design

• Slurm job: 30951323
• Warmup run before timed cases
• Timed grid:
  • P ∈ {100,000, 200,000}
  • input chain_length ∈ {223, 446}
  • REPS = 2
• Because fast_blocks=true and N=50,000:
  • block_size = floor(sqrt(50000)) = 223
  • outer iterations are floor(chain_length / 223) (1 or 2 in timed runs)
• Extrapolation:
  1. For each P, fit t_mcmc = a + b * outer
  2. Convert target to outer iterations: floor(2000 / 223) = 8
  3. Fit target time vs P using P = 100,000 and P = 200,000, then extrapolate to P = 2,000,000

Measured t_mcmc (seconds)

Extrapolated Target Time

• SUMMARY_EST target_seconds = 3449.100
• target_hours = 0.958 (about 57.5 minutes)
• Replicate-based range: about 3274 to 3624 seconds (0.91 to 1.01 hours)

Standard BayesC Benchmark (fast_blocks=false)

Design

• Slurm job: 30951596
• Warmup run before timed cases
• Timed grid:
  • P ∈ {100,000, 200,000}
  • chain_length ∈ {2, 4}
  • REPS = 2
• Extrapolation:
  1. For each P, fit t_mcmc = a + b * chain_length
  2. Predict t_mcmc at chain_length = 2000
  3. Fit those predicted times vs P and extrapolate to P = 2,000,000

Measured t_mcmc (seconds)

Extrapolated Target Time

• SUMMARY_EST target_seconds = 735340.060
• target_hours = 204.261 (about 8.5 days)
• Replicate-based range: about 701539 to 769141 seconds (194.9 to 213.7 hours)

Summary Comparison

Approximate speedup from block mode in this benchmark setup: about 213x.

Notes and Interpretation

• These are empirical estimates from short-chain calibration runs, not exact guarantees.
• For fast_blocks=true, chain interpretation is two-level (outer iterations + inner block repeats).
• The two Slurm jobs landed on different CPU node types, so absolute times include some hardware variance.
• Even with that caveat, the gap between block and non-block is very large for this target-scale scenario.