Adaptive Multidimensional Integration: VEGAS Enhanced

Abstract

We describe a new algorithm, VEGAS+, for adaptive multidimensional Monte Carlo integration. The new algorithm adds a second adaptive strategy, adaptive stratified sampling, to the adaptive importance sampling that is the basis for its widely used predecessor VEGAS. Both VEGAS and VEGAS+ are effective for integrands with large peaks, but VEGAS+ can be much more effective for integrands with multiple peaks or other significant structures aligned with diagonals of the integration volume. We give examples where VEGAS+ is 2-19 times more accurate than VEGAS. We also show how to combine VEGAS+ with other integrators, such as the widely available MISER algorithm, to make new hybrid integrators. For a different kind of hybrid, we show how to use integrand samples, generated using MCMC or other methods, to optimize VEGAS+ before integrating. We give an example where preconditioned VEGAS+ is more than 100 times as efficient as VEGAS+ without preconditio ing. Finally, we give examples where VEGAS+ is more than 10 times as efficient as MCMC for Bayesian integrals with D = 3 and 21 parameters. We explain why VEGAS+ will often outperform MCMC for small and moderate sized problems.

23 pages, 11 figures

References in corpus (3)

• The automated computation of tree-level and next-to-leading order differential cross sections, and their matching to parton shower simulations
• Bayesian Evidence for a Cosmological Constant using new High-Redshift Supernovae Data
• Model Evidence with Fast Tree Based Quadrature

Cited by in corpus (64)

• Non-Gaussianity and the induced gravitational wave background
• Updated constraints on axion-like particles from temporal information in supernova SN1987A gamma-ray data
• Implications of Pulsar Timing Array Data for Scalar-Induced Gravitational Waves and Primordial Black Holes: Primordial Non-Gaussianity $f_{\mathrm{NL}}$ Considered
• Generation of gravitational waves from freely decaying turbulence
• Primordial Non-Gaussianity $f_{\mathrm{NL}}$ and Anisotropies in Scalar-Induced Gravitational Waves
• MadNIS -- Neural Multi-Channel Importance Sampling
• Improved information criteria for Bayesian model averaging in lattice field theory
• Freezing-In Gravitational Waves
• Numerical 1-loop correction from a potential yielding ultra-slow-roll dynamics
• Complete analysis of the background and anisotropies of scalar-induced gravitational waves: primordial non-Gaussianity $f_{\mathrm{NL}}$ and $g_{\mathrm{NL}}$ considered
• The MadNIS Reloaded
• Efficient phase-space generation for hadron collider event simulation
• Resummation of Next-to-Leading Non-Global Logarithms at the LHC
• Improved ${\pi }^0,\eta ,{\eta }^{\prime }$ transition form factors in resonance chiral theory and their $a_{\mu }^{\mathrm{HLbL}}$ contribution
• Numerical integration of loop integrals through local cancellation of threshold singularities
• The Dark Ages' 21-cm Trispectrum
• Supernova Limits on Muonic Dark Forces
• Scalar-Induced Gravitational Waves from Ghost Inflation and Parity Violation
• Cosmology from the integrated shear 3-point correlation function: simulated likelihood analyses with machine-learning emulators
• The QCD Axion: Some Like It Hot
• Differentiable MadNIS-Lite
• A machine learning approach for efficient multi-dimensional integration
• Efficiently Exploring Multi-Dimensional Parameter Spaces Beyond the Standard Model
• Subtracting the kinetic Sunyaev-Zeldovich effect from the cosmic microwave background with surveys of large-scale structure
• Multi-variable integration with a variational quantum circuit
• Discovery prospects for heavy dark matter in KAGRA
• Identifying Strongly Lensed Gravitational Waves with the Third-generation Detectors
• The reconstructed CMB lensing bispectrum
• Multiple peaks in gravitational waves induced from primordial curvature perturbations with non-Gaussianity
• Local analytic sector subtraction for initial- and final-state radiation at NLO in massless QCD
• Normalizing flows for microscopic many-body calculations: an application to the nuclear equation of state
• Quantum entanglement correlations in double quark PDFs
• Pressure tuning of intrinsic and extrinsic sources to the anomalous Hall effect in CrGeTe${}_3$
• More Ingredients for an Altarelli Cocktail at MiniBooNE
• Machine Learning Post-Minkowskian Integrals
• Tadpoles and vacuum bubbles in light-front quantization
• Beyond universality in repulsive SU(N) Fermi gases
• Sound attenuation in the hyperhoneycomb Kitaev spin liquid
• Cold Quark Matter: Renormalization Group Improvement at next-to-next-to leading order
• Neutrinos from muon-rich ultra high energy electromagnetic cascades: The MUNHECA code
• New Approximation of Magnification Statistics for Random Microlensing of Magnified Sources
• Infinite Series Solution of the Time-Dependent Radiative Transfer Equation in Anisotropically Scattering Media
• Proton-box contribution to $a_{\mu }^{\mathrm{HLbL}}$
• Fast detection and reconstruction of merging Massive Black Hole Binary signals
• Wave Effects in Double-Plane Lensing
• NLO Oriented Event-Shape Distributions for Massive Quarks
• Unveiling atomic electron motion effects in $e^{+}{e}^{-}$ high energy collisions at NA64
• Tidal effects on primordial black hole capture in neutron stars
• Variance Reduction via Simultaneous Importance Sampling and Control Variates Techniques Using Vegas
• Flow Annealed Importance Sampling Bootstrap meets Differentiable Particle Physics
• Moment-functional based spectral density-functional theory
• Comment on: "Third-order corrections to the slow-roll expansion: Calculation and constraints with Planck, ACT, SPT, and BICEP/Keck [2025 PDU 47 101813]"
• Comprehensive analysis of dissipative effects in the induced gravitational waves
• Transport coefficients of dense nucleon matter at low temperature
• Focused Angular $N$-Body Event Generator (FANG)
• Indirect detection of long-lived particles in a rich dark sector with a dark vector portal
• Amplitude Surrogates for Multi-Jet Processes
• Boltzmann Equation Solver for Thermalization
• Constraining dimension-6 SMEFT with higher-order predictions for $pp\to tW$
• Identical particle and lepton mass effects in the decay $H\to Z^{\ast }(\to {\tau }^{+}{\tau }^{-})+Z^{\ast }(\to {\tau }^{+}{\tau }^{-})$
• Origin of pressure-induced anomalies in the nodal-line ferrimagnet Mn${}_3$Si${}_2$Te${}_6$
• NNLO QCD corrections to $\gamma \gamma \to Q\bar{Q}$ from Local Unitarity combined with Coulomb resummation and NLO EW effects
• Data-Driven Predictions for Dark Photon and Millicharged Particle Production
• Three-point intrinsic alignments of galaxies and haloes in the FLAMINGO simulations