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Title: Exploring the Relationship Between Nutrition, Physical Activity, and Obesity Through Bayesian Predictive Modeling.

Objective: The primary goal of this project is to analyze the interplay between nutrition, physical activity, and obesity rates using Bayesian methods. We will employ advanced Bayesian techniques, including Leave-One-Out Cross-Validation (LOO-CV), posterior predictive checks, and model comparison, to build reliable predictive models and uncover significant lifestyle-related factors influencing obesity prevalence.

Research Question: How can Bayesian methods be used to predict the likelihood of obesity, and what are the most significant factors (such as caloric intake, age, income, gender, education, frequency of physical activity, and demographic variables) influencing this prediction?

Proposed Workflow

  1. Data Exploration and Preprocessing ● Handling Missing Data ● Normalize continuous variables such as caloric intake, sedentary time, and age. ● Encode categorical variables like gender, race/ethnicity, and education level. ● Create derived features, e.g.:Ratio of sedentary time to physical activity time, income-to-calorie-consumption ratio (proxy for affordability of healthier food).

  2. Model Development a. Bayesian Logistic Regression ● Use Bayesian logistic regression to predict the binary outcome: ○ Obese vs. Non-Obese. ● Model posterior distributions for predictors to quantify uncertainty. b. Bayesian Hierarchical Models (Multilevel Models) ● Account for grouped or hierarchical data: ○ Groups: Income brackets, Race/Ethnicity, or Education level. ● Hierarchical models can capture within-group variations (e.g., variations within the same income group).

  3. Model Comparison and Validation ● Cross-Validation: ○ Apply K-Fold Cross-Validation or Leave-One-Out Cross-Validation (LOO-CV) to evaluate model robustness. ● Posterior Predictive Checks: ○ Evaluate how well the model replicates observed data by simulating and performing posterior predictive checks to evaluate model fit.

  4. Insights and Visualization ● Identify the most significant predictors influencing obesity or BMI and visualize some actionable insights.