Probabilistic Programming

Overview

Probabilistic programming combines the power of programming languages with probabilistic modeling, enabling developers to build and train complex probabilistic models using high-level abstractions.

Core Concepts

• Bayesian Inference
  • Prior and Posterior Distributions
  • Likelihood Functions
  • Conjugate Priors
• MCMC Methods
  • Metropolis-Hastings Algorithm
  • Gibbs Sampling
  • Hamiltonian Monte Carlo
• Probabilistic Models
  • Hierarchical Models
  • Mixture Models
  • State Space Models

Tools and Frameworks

• PyMC3
  • Model Specification
  • Inference Methods
  • Diagnostics and Visualization
• Other Frameworks
  • Stan
  • Edward
  • Pyro

Applications

• Scientific Computing
  • Uncertainty Quantification
  • Experimental Design
  • Model Comparison
• Machine Learning
  • Bayesian Neural Networks
  • Probabilistic Topic Models
  • Time Series Analysis

Additional Resources

• Using PyMC3 for MCMC - A comprehensive tutorial on using PyMC3 for Markov Chain Monte Carlo simulations
• PyMC3 Documentation - Official documentation and examples
• Stan User Guide - Comprehensive guide to probabilistic programming with Stan