Bayesian MCP

# Bayesian MCP: Project Overview This document provides a high-level overview of the Bayesian MCP project, its architecture, and its capabilities. ## Project Vision Bayesian MCP is designed to bring rigorous Bayesian reasoning capabilities to large language models (LLMs) through the Model Calling Protocol (MCP). The project aims to enable LLMs to: 1. Perform probabilistic reasoning with proper uncertainty quantification 2. Update beliefs systematically based on evidence 3. Make predictions that account for uncertainty 4. Compare alternative hypotheses rigorously 5. Create accurate visualizations of probability distributions By offering these capabilities through an MCP interface, we allow LLMs to overcome their limitations in statistical reasoning and enable them to make better-informed decisions under uncertainty. ## Architecture The Bayesian MCP server is structured as follows: ``` bayesian-mcp/ ├── src/ │ ├── bayesian_engine/ # Core Bayesian inference engine │ │ ├── engine.py # Main implementation of Bayesian models │ │ └── distributions.py # Utility functions for distributions │ ├── mcp/ # MCP server implementation │ │ ├── server.py # FastAPI server implementation │ │ └── handlers.py # Request handlers for MCP functions │ ├── schemas/ # Pydantic models for API validation │ │ └── mcp_schemas.py # Schema definitions │ └── utils/ # Utility functions │ └── plotting.py # Visualization utilities ├── examples/ # Example clients │ ├── linear_regression.py # Linear regression example │ └── ab_test.py # A/B testing example └── bayesian_mcp.py # Main entry point ``` ## Core Components ### Bayesian Engine The heart of the system is the Bayesian engine, which leverages PyMC for probabilistic modeling and inference. It provides: - Creation of Bayesian models with various probability distributions - Posterior inference using Markov Chain Monte Carlo (MCMC) methods - Extraction of posterior statistics and summaries - Prediction generation from posterior distributions - Model comparison using information criteria (WAIC, LOO) ### MCP Server The MCP server provides an HTTP interface that adheres to the Model Calling Protocol. It exposes Bayesian capabilities through a standardized API that LLMs can interact with. ### Visualization Tools The system includes robust visualization capabilities powered by ArviZ, enabling the creation of: - Trace plots to diagnose MCMC convergence - Posterior distribution plots to visualize belief uncertainty - Forest plots for parameter comparison - Pair plots for correlation analysis - Custom visualizations for specific model types ## Key Features ### 1. Model Creation and Updating Users can create Bayesian models with complex dependency structures and update them with new evidence: ```python # Create a linear regression model create_model_request = { "function_name": "create_model", "parameters": { "model_name": "linear_regression", "variables": { "intercept": {"distribution": "normal", "params": {"mu": 0, "sigma": 10}}, "slope": {"distribution": "normal", "params": {"mu": 0, "sigma": 10}}, "sigma": {"distribution": "halfnormal", "params": {"sigma": 5}}, "likelihood": { "distribution": "normal", "params": {"mu": "intercept + slope * x", "sigma": "sigma"}, "observed": [3.1, 4.5, 5.3, 7.8, 9.1] } } } } # Update with new data update_request = { "function_name": "update_beliefs", "parameters": { "model_name": "linear_regression", "evidence": {"x": [1.0, 2.0, 3.0, 4.0, 5.0]} } } ``` ### 2. Hypothesis Comparison The system enables rigorous comparison of competing hypotheses: ```python # Compare two models compare_request = { "function_name": "compare_models", "parameters": { "model_names": ["model_1", "model_2"], "metric": "waic" } } ``` ### 3. Dynamic Visualization Users can generate a variety of visualizations to better understand their models: ```python # Create a trace plot visualization_request = { "function_name": "create_visualization", "parameters": { "model_name": "my_model", "plot_type": "trace", "variables": ["theta"] } } ``` ## Use Cases The Bayesian MCP server can be applied to numerous domains: 1. **Data Science**: Parameter estimation, regression analysis, classification 2. **Business**: A/B testing, customer lifetime value prediction 3. **Finance**: Risk assessment, portfolio optimization 4. **Healthcare**: Treatment effect estimation, disease progression modeling 5. **Research**: Hypothesis testing, experimental design 6. **Education**: Teaching Bayesian concepts with visualizations ## Future Directions Planned enhancements include: 1. **Model Templates**: Pre-defined models for common use cases 2. **Automatic Model Selection**: Recommending model structures from data 3. **Sensitivity Analysis**: Assessing robustness to prior specifications 4. **Hierarchical Models**: Supporting multi-level models 5. **Causal Inference**: Adding tools for causal reasoning ## Integration with Wrench AI This project complements the Wrench AI framework by providing a specialized MCP server focused on Bayesian reasoning. While it can be used independently, it's designed to work seamlessly within the Wrench AI ecosystem, adding powerful probabilistic reasoning capabilities to the existing agent architecture.