Monte Carlo & Uncertainty Simulators

Bayesian Calibration via MCMC (Metropolis–Hastings) Simulator: Calibrate a CAE model parameter the Bayesian way: feed in a prior, a likelihood and observed d…

Compute 95% bootstrap confidence intervals for the mean and median in real time. Resample with replacement and vary N and B to watch the distribution converge.

Brownian motion simulator to verify Einstein's diffusion formula and explore parameters.

Buffon's needle simulator drops needles at random on a floor of parallel lines and estimates pi from the crossing probability P = 2L/(pi d). Vary needle count, length, line spacing and LCG seed.

Control Variates Simulator: Experience the control variates method, which boosts Monte Carlo accuracy almost for free. Using an auxiliary variable strongly c…

Analyze time-series signals with the Fast Fourier Transform. Tweak window functions, sampling frequency and signal components to feel aliasing and leakage.

Gibbs Sampling Simulator: Draw samples from a bivariate normal distribution with Gibbs sampling, the classic MCMC (Markov chain Monte Carlo) method. Adjust t…

Importance Sampling for tail probability estimation: reduce Monte Carlo variance by tuning proposal distributions. Interactive simulator for engineers.

Latin Hypercube Sampling vs Monte Carlo: stratified design sampling technique for improved integration accuracy and uncertainty quantification in CAE.

Two-state Markov chain simulator. Vary p, q to see the stationary distribution π=(q/(p+q), p/(p+q)), the t-step probability P_1(t), and 99% mixing time t_mix.

MCMC Metropolis-Hastings sampler for arbitrary 1D distributions. Tune proposal variance, analyze chain mixing, trace plots, and autocorrelation. Bayesian inference sampling.

Estimate π using random numbers! This Monte Carlo simulation drops points into a square to reveal the value of Pi through probability and error analysis.

Explore Monte Carlo methods: estimate π, test the Central Limit Theorem, perform integration, and simulate random processes with this interactive statistics simulator.

Morris Elementary Effects Method Simulator: Run the cheapest global sensitivity method — the Morris Elementary Effects (EE) screening — directly in your brow…

Polynomial Chaos Expansion (PCE) Simulator: For a Gaussian input X ~ N(μ, σ²) and the model Y = a₁X + a₂X², this tool builds a Hermite Polynomial Chaos Expan…

Quasi-Monte Carlo Simulator — Sobol Sequence: Integrate numerically with low-discrepancy sequences such as the Sobol and Halton sequences. Change the sample …

Simulate 2D random walks in real time. Visualize diffusion laws with MSD plots and switch between lattice, Gaussian, and Lévy flight modes.

Rejection sampling simulator for Monte Carlo methods. Visualize envelope-based sample generation from complex distributions. Learn proposal functions and acceptance rates.

A hands-on global sensitivity analysis tool that decomposes how input uncertainty drives output variance into main effects and interactions.

Central Limit Theorem Simulator: Repeatedly sample from uniform, exponential, bimodal, or skewed distributions. Vary sample size n and observe how sample mea…

Stratified Sampling Simulator: A tool for experiencing stratified sampling, a way to boost the accuracy of Monte Carlo integration for free. Split the interv…

Calculate measurement uncertainty with our free Monte Carlo analysis tool. Simulate error propagation and analyze results online instantly.