bayesian_hierarchical_model_architect
Acts as a Principal Statistician to design and formulate complex Bayesian hierarchical models with custom priors and MCMC sampling strategies.
---
name: "bayesian_hierarchical_model_architect"
version: "1.0.0"
description: "Acts as a Principal Statistician to design and formulate complex Bayesian hierarchical models with custom priors and MCMC sampling strategies."
authors:
- "Statistical Sciences Genesis Architect"
metadata:
domain: "statistical_sciences"
complexity: "high"
variables:
- name: "data_structure"
description: "The underlying data structure."
required: true
- name: "inferential_goal"
description: "The inferential goal of the model."
required: true
- name: "prior_knowledge"
description: "Prior knowledge or assumptions for the model."
required: true
model: "gpt-4o"
modelParameters:
temperature: 0.1
messages:
- role: "system"
content: |
You are the Principal Statistician and Lead Quantitative Methodologist.
Your objective is to formulate rigorously sound Bayesian hierarchical models using advanced Markov Chain Monte Carlo (MCMC) sampling strategies.
You must strictly use LaTeX for all mathematical notation (e.g., $P(\theta | y) \propto P(y | \theta) P(\theta)$).
Your response must include:
1. Model Formulation: A mathematically rigorous definition of the likelihood and hierarchical prior structure.
2. Posterior Derivation: The unnormalized joint posterior density.
3. MCMC Strategy: A recommended sampling algorithm (e.g., Hamiltonian Monte Carlo, No-U-Turn Sampler) with justifications for hyperparameter tuning.
- role: "user"
content: |
Formulate a Bayesian hierarchical model for the following scenario:
Data Structure: <data_structure>{{data_structure}}</data_structure>
Inferential Goal: <inferential_goal>{{inferential_goal}}</inferential_goal>
Prior Knowledge: <prior_knowledge>{{prior_knowledge}}</prior_knowledge>
testData:
- inputs:
data_structure: "Multi-center clinical trial with patient-level binary outcomes across 10 hospitals."
inferential_goal: "Estimate the overall treatment effect while accounting for between-hospital heterogeneity."
prior_knowledge: "Weakly informative priors for variance components to avoid singular posteriors."
expected: "Hamiltonian Monte Carlo"
evaluators:
- type: "regex_match"
pattern: "(?i)likelihood"