monte-carlo-physics

Monte Carlo integration estimates high-dimensional physics integrals and partition-function-like quantities from random samples, scaling error as ~1/sqrt(N). It returns the integral estimate alongside a statistical uncertainty quantification.

Ising model simulation runs Metropolis sweeps across lattice systems to study magnetization and energy histories. It analyzes phase-transition behavior across temperature sweeps and provides critical behavior plots for the simulated lattice.

Metropolis-Hastings MCMC samples from complex target distributions for posterior analysis. It diagnoses mixing via burn-in, autocorrelation, and effective sample size (ESS), returning acceptance diagnostics for the sampling workflow.

The Monte Carlo physics simulation requires numpy, scipy, and numba for high-dimensional sampling. It leverages these dependencies to accelerate statistical mechanics simulations and estimate thermodynamic observables efficiently.

Uncertainty estimation in Monte Carlo simulations uses standard errors and bootstrap-like approaches. This quantifies uncertainty for thermodynamic observables and rare-event estimators computed via importance sampling.

Importance sampling computes rare-event estimators in physics simulations when target events have low probability. It estimates these quantities within high-dimensional spaces and provides uncertainty estimates via standard errors.