🧠 7089CEM: Statistical Methods for Data Science

This repository contains a complete analysis of MEG brain response data from a simulated neuromarketing experiment. The project combines nonlinear regression modelling and Bayesian inference techniques to investigate how the brain reacts to emotional versus neutral audio stimuli.

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📁 Repository Structure

File/Folder	Description
SMDS_CW.R	Main R script with structured code for data processing, modeling, and ABC
data/	Contains raw input files: X.csv, y.csv, and time.csv

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📊 Task 1: Exploratory Data Analysis (EDA)

🎯 Objective

Understand the structure and patterns in MEG responses under emotional and neutral audio stimuli.

📈 Visualizations

• Time series of MEG and audio signals
• Histograms, boxplots, and scatter plots by stimulus type
• Pearson correlation analysis

Insight: Emotional narration resulted in higher and more varied MEG responses, justifying a nonlinear modelling approach.

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🔁 Task 2: Nonlinear Regression Modelling

🧮 Models Evaluated

• Five polynomial regression models of varying complexity
• Estimated using least squares
• Evaluated using RSS, Log-Likelihood, AIC, BIC, and residual diagnostics

🧠 Best Model: Model 3

Polynomial terms: x1, x1², x1⁴, x2
Demonstrated best balance between fit and generalization.

🧪 Results Summary

Model	RSS	AIC	BIC	Residual Normality
Model 3	✅ Lowest	✅ Best	✅ Best	✅ Good fit
Model 4	Close	Slightly worse	Acceptable	Also valid
Others	❌ Poor fit	❌ Higher error	❌ Deviations	❌ Skewed residuals

Conclusion: Model 3 best captures the nonlinear brain response to audio stimuli.

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📦 Task 3: Approximate Bayesian Computation (ABC)

🔍 Goal

Estimate uncertainty in the top two most influential model parameters of Model 3.

🔧 Method

• Rejection sampling ABC
• Uniform priors (±30%) around least squares estimates
• 10,000 simulations; top 1% used to form posterior

📊 Outcomes

• Marginal and joint posterior distributions
• Parameters show weak correlation, but strong identifiability
• Posterior centers align closely with initial estimates

Insight: ABC confirmed robustness of Model 3 and provided interpretable uncertainty quantification.

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✨ Key Takeaways

• Emotional voice triggers stronger brain activity measurable by MEG.
• Nonlinear regression (Model 3) provides best fit for input-output relationship.
• ABC is a powerful tool to quantify uncertainty in complex models without explicit likelihoods.

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🧑‍💻 Author

Itorobong Akpan
MSc Data Science & Computational Intelligence
Coventry University, UK
📧 [email protected]
🔗 GitHub Profile

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