Point Process Simulation Dashboard

An interactive web application for simulating and analyzing spatial point processes using Markov Chain Monte Carlo (MCMC) methods with Birth-Death-Migration algorithms.

📸 Screenshots

Simulated Configurations

Number of Points Statistics

MCMC Performance Metrics

Overview

Implements several spatial point process densities (Poisson, Strauss, Saturated, Hardcore) and a Birth-Death-Move MCMC sampler. The interactive dashboard allows users to:

• Configure point process parameters
• Run MCMC simulations with customizable chain length and burn-in periods
• Visualize spatial configurations
• Analyze convergence properties through acceptance rates and autocorrelation functions

Installation

Prerequisites

• pip or uv package manager

Using uv (Recommended)

# Install uv if you haven't already
pip install uv
# Create a virtual environment
uv venv
source .venv/bin/activate  # On Windows: .venv\Scripts\activate

# Install the project in editable (development) mode
uv pip install -e .

Using pip

# Create a virtual environment
python -m venv .venv
source .venv/bin/activate  # On Windows: .venv\Scripts\activate

# Install the project in editable (development) mode
pip install -e .

Usage

Launch the Web Application

streamlit run scripts/app.py

The application will open in your default web browser at http://localhost:8501.

Core Components

src/samplers/bdm.py - MCMC Engine

• BirthDeathMigration: Main MCMC simulator class
• HistoryTracker: Simulation history logging
• ConfigEvaluator: Real-time metric computation

src/densities/ — Point Process Models

• Contains all implemented point process densities (e.g. Strauss, Poisson, Hardcore, Saturated Strauss)
• Each density is implemented as a class extending a common base interface

scripts/app.py - Web Interface

• Streamlit-based interactive dashboard

scripts/performance_tester.py — Performance Profiler

• Script for running and storing cProfile results of the BDM algorithm
• Helps identify performance bottlenecks and benchmark optimizations

Configuration

Point Process Parameters

• R (Interaction Radius): Distance threshold for point interactions (0.0 - 2.0)
  • Note: Values > √2 ≈ 1.41 may have limited effect due to unit square geometry
• β (Intensity): Base intensity parameter controlling point density (1.0 - 500.0)
• γ (Interaction Strength): Repulsion strength between nearby points (0.0 - 1.0)
  • γ = 0: Complete inhibition (hardcore process)
  • γ = 1: No interaction (Poisson process)
• s (Saturation): Maximum number of neighbors contributing to interaction

All simulations are constrained to the unit square [0,1]² spatial domain.

MCMC Parameters

• Iterations: Number of MCMC steps after burn-in
• Warm-up: Burn-in period to reach equilibrium
• Move Probabilities: Relative frequencies of birth/death/migration moves

Development

Adding New Point Processes

1. Implement the new density class in src/densities/ (create a new file if needed, or add to an existing one).
2. Add parameter controls in app.py.
3. Update visualization methods as needed.

Support

For questions, issues, or contributions, please open an issue on the project repository.