π GitHub Repository
Project Page:
github.com/SaiSampathKedari/MonteCarlo-Statistical-Methods
MonteCarlo-Statistical-Methods
A visual and practical guide to Monte Carlo techniques, focused on understanding rather than memorizing.
Each method is implemented from scratch and explored through intuitive diagrams, animations, and diagnostic tools.
These foundations support real applications in robotics, dynamics, and reinforcement learning, from Bayesian filters to sampling-based planning and uncertainty-aware control.
Table of Contents
- Overview
- Sampling Visualizations
- Importance Sampling
- Control Variates
- Brownian Motion
- Markov Chain Monte Carlo
- Notebook Gallery
- PDF Chapter Library
- Project Structure
- About Me
Overview
This repository builds Monte Carlo ideas from first principles using:
- Random variable generation: inverse transform, acceptβreject, importance sampling
- Monte Carlo estimation: WLLN, SLLN, CLT
- Variance reduction: control variates, Brownian motion scaling
- Markov Chain Monte Carlo: MH, AM, DR, DRAM
- Full diagnostics: burn-in, mixing, autocorrelation, integrated autocorrelation, ESS
Each topic is supported by clean visualizations and self-contained Jupyter notebooks.
Sampling Visualizations
Inverse Transform sampling (left) and AcceptβReject sampling (right).
Importance Sampling
Proposal vs likelihood alignment and resulting posterior for Importance Sampling.
Control Variates
Variance comparison (left) and correlation structure enabling control variates (right).
Brownian Motion
Random-walk scaling to Brownian motion and simulated sample paths.
Markov Chain Monte Carlo
The repository implements four MCMC algorithms on both 2D Gaussian and banana-shaped targets:
- MetropolisβHastings (MH)
- Adaptive Metropolis (AM)
- Delayed Rejection (DR)
- Delayed Rejection Adaptive Metropolis (DRAM)
All diagnostics: burn-in, mixing, autocorrelation, integrated autocorrelation, and ESS, are derived in the MH diagnostics notebook and reused across the remaining algorithms.
Below is a DRAM example on the banana-shaped target.
Target and Laplace Initialization
DRAM Sample Exploration
Mixing Behavior
Autocorrelation Diagnostics
Notebook Gallery
Chapter 2: Sampling
Chapter 3: Importance Sampling
Chapter 4: Variance Reduction
Chapter 6: Stochastic Processes
Chapter 5: MCMC
- MH Diagnostics
- Adaptive Metropolis β Gaussian
- Adaptive Metropolis β Banana
- Delayed Rejection β Gaussian
- Delayed Rejection β Banana
- DRAM β Gaussian
- DRAM β Banana
PDF Chapter Library
Full write-ups:
reports/ch02_general_transforms.pdfreports/ch02_accept_reject.pdfreports/ch03_01_ImportantSampling_Motivation_weights.pdfreports/ch03_02_ImportanceSampling_MC_vs_IS_Variance_Comparison.pdfreports/ch03_03_ImportanceSampling_Rare_event_Estimation.pdfreports/ch03_04_SelfNormalized_ImportantSampling.pdfreports/ch04_01_ControlVariate_Foundations-and-Intution.pdfreports/ch04_02_Brownian_Motion.pdfreports/ch04_03_ControlVariate_example1.pdfreports/ch05_01_MarkovChain_Intro.pdfreports/ch05_02_Irreducibility.pdfreports/ch05_07_Metropolis-Hastings.pdf
Project Structure
MonteCarlo-Statistical-Methods/
β
βββ animations/
βββ images/
β βββ sampling/
β βββ importance_sampling/
β βββ variance_reduction/
β βββ stochastic_processes/
β βββ mcmc/
β βββ exponential/
βββ notebooks/
β βββ ch02_sampling/
β βββ ch03_importance_sampling/
β βββ ch04_variance_reduction/
β βββ ch05_mcmc/
β βββ ch06_stochastic_processes/
βββ reports/
βββ src/
βββ README.md
βββ index.md
βββ pyproject.toml
About Me
I study and implement methods in optimization, control, robotics, Bayesian inference, and probabilistic reasoning.
- GitHub: https://github.com/SaiSampathKedari
- LinkedIn: https://linkedin.com/in/sai-sampath-kedari
- X: https://x.com/SSampathKedari
- Email: sampath@umich.edu
π€ About Me
Interested in robotics, control, and probabilistic methods for intelligent systems.
π« Email: sampath@umich.edu
: linkedin.com/in/sai-sampath-kedari
π : @SaiSampathK
: github.com/SaiSampathKedari