MultilevelMonteCarlo.jl

Tools for (single-level) Monte Carlo and multilevel Monte Carlo estimation in Julia.

Features

• MLMC estimation — fixed and adaptive sample allocation with online variance tracking (Welford/Chan)
• Sample storage — collect raw fine/coarse samples and export to NetCDF
• PDF & CDF estimation — kernel density and maximum-entropy density estimation from MLMC samples
• Rank histograms — Gregory inverse-CDF resampling and PIT histograms for ensemble validation
• Vector QoI — estimators for vector-valued quantities of interest (e.g. trajectories)

Installation

using Pkg
Pkg.add(url="https://github.com/sintefmath/MultilevelMonteCarlo.jl")

Quick start

using MultilevelMonteCarlo

# Define levels (cheap → expensive), a QoI, and a parameter sampler
levels = Function[
    params -> params + 0.2 * randn(),
    params -> params + 0.02 * randn(),
    params -> Float64(params),
]
qoi_functions = Function[identity]
draw_parameters() = 2.0 + 0.5 * randn()

# Run MLMC estimation
result = mlmc_estimate(levels, qoi_functions, draw_parameters;
                       epsilon=0.05, initial_samples=100)

Documentation

See the full documentation for examples on projectile motion, sample storage, PDF/CDF estimation, and rank histograms.