Monte Carlo Crash Course: Quasi-Monte Carlo
21 days ago
- #Variance Reduction
- #Monte Carlo
- #Sampling
- Monte Carlo integration is a fundamental tool for variance reduction and sampling difficult distributions.
- Variance in Monte Carlo estimators is inversely proportional to sample count, with error scaling as 1/√N.
- Negative correlation between samples can reduce variance, improving convergence rates.
- Poisson disk sampling generates perceptually random samples by enforcing minimum separation distances.
- Stratified sampling partitions the domain into regions, reducing variance by ensuring coverage.
- Dynamic stratification adjusts the number of regions based on sample count, optimizing performance in low dimensions.
- Adaptive sampling allocates more samples to high-variance regions, improving efficiency.
- Latin hypercube sampling stratifies dimensions independently, useful in high-dimensional spaces.
- Quasi-Monte Carlo (QMC) uses deterministic sequences for integration, offering faster convergence in low dimensions.
- Low-discrepancy sequences like Halton and Sobol’ minimize bias and improve QMC performance.
- Scrambling techniques enhance high-dimensional low-discrepancy sequences by reducing initial discrepancy.