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Table of Content

• I. Migraine
• 1. Description and stages
• 2. Epidemiology
• 3. Diagnosis
• 4. Quality of life
• 5. Economic burden
• 6. Electronic diaries in Migraine tracking
• II. Data
• 1st dataset
• Preprocessing
• 2nd dataset
• Preprocessing
• III. Approach
• 1. A Markov Model
• 2. A Bayeasian Approach
• 3. A Hierarchical Model
• IV. Markov Chain Monte Carlo methods
• 1. Markov Chain Monte Carlo
• Process
• Burn-in and thinning
• 2. Gibbs Sampling
• 3. Metropolis-Hastings
• 4. Hamiltonian Monte Carlo
• Example for a one-dimensional variable
• 5. No-U-Turn Sampler (NUTS)
• V. Application
• 1. Model
• Model's specifications
• Data input
• Sampling with 1st dataset
• Sampling with 2nd dataset
• 2. Convergence
• 3. Generating transition matrix
• VI. Discussion
• VII. References
• VIII. Appendix
• A. Posterior distribution - Expansion and simplification
• B. Model convergence
• C. Models code
• JAGS model
• STAN model
• D. Original δ
• E. Comparison of generated delta from JAGS and STAN
• F. Distribution of generated δs

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