Statistical Computing & Empirical Methods Using R Programming

Course: Statistical Computing & Empirical Methods
Timeline: October 2024 – December 2024
Institution: University of Bristol
Author: Thrisha Rajkumar

This repository contains coursework for the Statistical Computing & Empirical Methods unit, blending foundational statistical techniques, empirical data exploration, and predictive modeling using R.

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Project Highlights

1. Supervised Learning & Predictive Modelling

• Developed Decision Tree and Random Forest classifiers for predicting loan approvals.
• Addressed missing data, encoded categorical variables, and engineered features.
• Tuned models via grid search with 10-fold cross-validation.
• Achieved:
  • AUC = 0.7949
  • F1 Score = 0.70

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2. Data Wrangling & Exploratory Data Analysis (EDA)

• Cleaned multi-source financial data (13,824 rows, 63 indicators).
• Performed joins, renaming, and grouping by income/region.
• Created insightful plots to explore patterns:

Income Distribution

Credit History vs Loan Status

Regional Financial Flow (Violin Plot)

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3. Statistical Simulation & Computing

• Estimated λ for exponential distribution using Maximum Likelihood Estimation (MLE).
• Bootstrapped 1,000 samples to construct confidence intervals: CI = [0.0191, 0.0207].
• Simulated 100,000 trials of discrete variables.
• Demonstrated Central Limit Theorem (CLT) using 50,000 sample means.

CLT Density Plot

Exponential λ Visualization

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📊 Dataset Sources

1. Loan Approval Data

• Kaggle – Finance Loan Approval Prediction
• Includes demographic and financial attributes for binary classification.
• Note: Data files (train.csv, test.csv) are not included due to licensing. Please download them directly from Kaggle.

2. Simulated Exponential Data

• Generated internally using rexp() in R for bootstrapping & CLT demonstrations.

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📁 Folder Structure

Statistical-Computing-R/
│
├── notebooks/                 # R Markdown reports
│   ├── SectionA_Code_Output.Rmd
│   ├── SectionB_Analysis.Rmd
│   └── SectionC_Methodology.Rmd
│
├── reports/                   # Final PDF submissions
│   ├── Section-A.pdf
│   ├── Section-B.pdf
│   └── Section-C.pdf
│
├── images/                    # Visuals used in README
│   ├── applicant_income_histogram.png
│   ├── loan_status_by_credit.png
│   ├── loan_prediction_metrics.png
│   ├── clt_distribution.png
│   ├── exponential_distribution_lambda.png
│   └── eda_violinplot_timeseries.png
│
├── setup.txt                  # Installation and usage instructions
└── README.md                  # This file

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🛠 How to Run

Step 1 – Install Required Packages

install.packages(c("tidyverse", "rpart", "randomForest", "caret", "boot",
                   "ggplot2", "e1071", "reshape2", "knitr"))

Step 2 – Run Models

# Load dataset
train <- read.csv("train.csv")

# Decision Tree
library(rpart)
tree_model <- rpart(Loan_Status ~ ., data = train, method = "class")

# Random Forest
library(randomForest)
rf_model <- randomForest(Loan_Status ~ ., data = train, ntree = 100)

Step 3 – Bootstrap & CLT

library(boot)
lambda_hat <- function(x, i) 1 / mean(x[i])
boot_data <- rexp(1000, rate = 0.02)
boot_lambda <- boot(data = boot_data, statistic = lambda_hat, R = 1000)
boot.ci(boot_lambda, type = "perc")

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📑 Documentation

Section	Description
A	Code and outputs for EDA and wrangling
B	Descriptive analysis and distribution modeling
C	Simulation-based inference, bootstrapping, MLE

All reports are in the /reports/ folder.

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🧠 Skills Demonstrated

• R Programming (Tidyverse, ggplot2, caret, rpart, randomForest)
• Data Wrangling & Joining
• Predictive Modelling & Evaluation
• Statistical Estimation (MLE, Bootstrapping)
• Central Limit Theorem Demonstration
• Reproducible Analysis with R Markdown

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📜 License

This repository is for academic and educational purposes under the University of Bristol.
Reuse is permitted with citation of author and coursework context.