Bayesian MCP

A Model Calling Protocol (MCP) server for Bayesian reasoning, inference, and belief updating. This tool enables LLMs to perform rigorous Bayesian analysis and probabilistic reasoning.

Features

• Bayesian Inference: Update beliefs with new evidence using MCMC sampling
• Model Comparison: Compare competing models using information criteria
• Predictive Inference: Generate predictions with uncertainty quantification
• Visualization: Create visualizations of posterior distributions
• MCP Integration: Seamlessly integrate with any LLM that supports MCP

Installation

Development Installation

Clone the repository and install dependencies:

git clone https://github.com/wrenchchatrepo/bayesian-mcp.git
cd bayesian-mcp
pip install -e .

Requirements

• Python 3.9+
• PyMC 5.0+
• ArviZ
• NumPy
• Matplotlib
• FastAPI
• Uvicorn

Quick Start

Starting the Server

# Run with default settings
python bayesian_mcp.py

# Specify host and port
python bayesian_mcp.py --host 0.0.0.0 --port 8080

# Set log level
python bayesian_mcp.py --log-level debug

The server will start and listen for MCP requests on the specified host and port.

API Usage

The Bayesian MCP server exposes several functions through its API:

1. Create Model

Create a new Bayesian model with specified variables.

# MCP Request
{
    "function_name": "create_model",
    "parameters": {
        "model_name": "my_model",
        "variables": {
            "theta": {
                "distribution": "normal",
                "params": {"mu": 0, "sigma": 1}
            },
            "likelihood": {
                "distribution": "normal",
                "params": {"mu": "theta", "sigma": 0.5},
                "observed": [0.1, 0.2, 0.3, 0.4]
            }
        }
    }
}

2. Update Beliefs

Update model beliefs with new evidence.

# MCP Request
{
    "function_name": "update_beliefs",
    "parameters": {
        "model_name": "my_model",
        "evidence": {
            "data": [0.1, 0.2, 0.3, 0.4]
        },
        "sample_kwargs": {
            "draws": 1000,
            "tune": 1000,
            "chains": 2
        }
    }
}

3. Make Predictions

Generate predictions using the posterior distribution.

# MCP Request
{
    "function_name": "predict",
    "parameters": {
        "model_name": "my_model",
        "variables": ["theta"],
        "conditions": {
            "x": [1.0, 2.0, 3.0]
        }
    }
}

4. Compare Models

Compare multiple models using information criteria.

# MCP Request
{
    "function_name": "compare_models",
    "parameters": {
        "model_names": ["model_1", "model_2"],
        "metric": "waic"
    }
}

5. Create Visualization

Generate visualizations of model posterior distributions.

# MCP Request
{
    "function_name": "create_visualization",
    "parameters": {
        "model_name": "my_model",
        "plot_type": "trace",
        "variables": ["theta"]
    }
}

Examples

The examples/ directory contains several examples demonstrating how to use the Bayesian MCP server:

Linear Regression

A simple linear regression example to demonstrate parameter estimation:

python examples/linear_regression.py

A/B Testing

An example of Bayesian A/B testing for conversion rates:

python examples/ab_test.py

Supported Distributions

The Bayesian engine supports the following distributions:

• normal: Normal (Gaussian) distribution
• lognormal: Log-normal distribution
• beta: Beta distribution
• gamma: Gamma distribution
• exponential: Exponential distribution
• uniform: Uniform distribution
• bernoulli: Bernoulli distribution
• binomial: Binomial distribution
• poisson: Poisson distribution
• deterministic: Deterministic transformation

MCP Integration

This server implements the Model Calling Protocol, making it compatible with a wide range of LLMs and frameworks. To use it with your LLM:

import requests

response = requests.post("http://localhost:8000/mcp", json={
    "function_name": "create_model",
    "parameters": {
        "model_name": "example_model",
        "variables": {...}
    }
})

result = response.json()

License

MIT

Credits

Based on concepts and code from the Wrench AI framework.