This repository contains solutions for different Statistics courseworks at Imperial College London (2021-2024).
- Investigated the impact of a stimulant on heart rate, analyzing its relationship with BMI and treatment groups.
- Performed exploratory data analysis, generating summaries and visualizations to understand trends and distributions.
- Implemented and compared linear regression and Gamma GLM models, assessing model fit and estimating the treatment effect with confidence intervals.
- Conducted a simulation study to evaluate the power of detecting treatment effects and provided a clear summary for both statisticians and non-experts.
📜 Coursework Specification
📝 Coursework Report
- Manually simulated an AR(4) process, exploring pseudo-cyclical behavior and dominant frequencies using different parameter settings.
- Implemented spectral estimation methods, including periodograms and direct spectral estimators, to analyze frequency components.
- Investigated bias in spectral estimators, running simulations to compare periodogram and cosine-tapered direct estimates.
- Analyzed real-world sea level data, estimating spectral densities and identifying dominant frequencies using direct spectral estimation.
- Developed and compared AR models using Yule-Walker and maximum likelihood estimation, selecting the best model based on predictive performance.
- Forecasted future sea level values, computing prediction intervals to quantify uncertainty in the forecasts.
📜 Coursework Specification
📓 Coursework Notebook | 🔗 View in nbviewer | 📝 View PDF
- Developed Monte Carlo estimation techniques to compute marginal likelihoods and perform model selection.
- Implemented sampling algorithms, including Random Walk Metropolis (RWMH), Metropolis-Adjusted Langevin Algorithm (MALA), and Unadjusted Langevin Algorithm (ULA), to generate posterior distributions.
- Built a Gibbs sampler by deriving full conditionals for a 2D posterior.
📜 Coursework Specification
📓 Coursework Notebook | 🔗 View in nbviewer | 📝 View PDF
- Implemented Monte Carlo integration to estimate an improper integral, analyzing variance and optimizing the choice of sampling distribution.
- Derived and applied probability transformations, using uniform random variables to generate samples from a power-law distribution.
- Estimated the MLE for galaxy mass distributions and studied its variability through Monte Carlo simulations.
- Designed and tested a hypothesis to distinguish between competing power-law models, estimating statistical power and performing an empirical test on real data.
📜 Coursework Specification | 🛠️ Typos
📝 Coursework Report
📂 Coursework Files