Bayesian Inference Exercise Enhancing a Medical Diagnosis S…

Bayesian Inference Exercise Enhancing a Medical Diagnosis System

Use Case:

You are part of a healthcare AI startup developing an intelligent diagnostic system. Your goal is to enhance the systems accuracy using Bayesian Inferencean approach that combines prior knowledge with new patient data to predict the likelihood of disease. This system must dynamically update its diagnostic predictions as it encounters new cases.

Youll build a Bayesian model using Python, apply it to a medical dataset (e.g., the UCI Heart Disease dataset), and validate its performance with real-world diagnostic outcomes.

Learning Objectives:

• Understand and apply Bayesian inference in real-world predictive modeling.
• Use domain knowledge to define priors and update beliefs with new evidence.
• Gain practical experience with probabilistic programming using PyMC3 or similar libraries.
• Validate and refine models using statistical and diagnostic performance metrics.

Instructions:

1. Data Collection

• Use the UCI Heart Disease dataset or a comparable public health dataset containing:
• Patient symptoms
• Medical history
• Diagnosed conditions
• Perform preprocessing (clean missing values, encode categorical variables, etc.).

2. Prior Knowledge Integration

• Conduct a brief literature review to determine the prior probabilities of various heart conditions or diseases.
• Cite medical studies or datasets used to determine these priors.
• Clearly explain assumptions and how priors are mathematically incorporated.

3. Bayesian Model Development

• Use PyMC3, PyMC, or TensorFlow Probability to implement your model.
• Your model should:
• Use patient symptoms and history as input features.
• Output the posterior probability of a diagnosis.
• Update dynamically as new data points are introduced.

4. Model Validation

• Reserve a validation/test subset (e.g., 20% of the data).
• Evaluate model performance using metrics such as:
• Predictive accuracy
• Log-likelihood
• Confusion matrix
• ROC/AUC if applicable
• Compare predictions with actual diagnoses.

5. Iteration and Refinement

• Based on validation results:
• Adjust prior distributions
• Modify likelihood functions
• Re-train and re-evaluate the model

6. Final Report

• Submit a well-structured report that includes:
• Introduction to the problem and use case
• Description of dataset and priors
• Explanation of the Bayesian model and assumptions
• Summary of validation and results
• Discussion of findings and potential improvements
• Conclusion and next steps

Submission Requirements

Deliverables:

Python Code File (.ipynb or .py):

• Modular, well-commented code.
• Includes data processing, model development, training, and validation.
• Use markdown or comments to explain each section.

Final Report (.pdf or .docx):

• Include figures such as posterior distributions, ROC curves, and performance tables.
• Use APA citation style.

Sample Data Set:

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