Advanced Statistical Methods
Explore advanced statistical techniques including multivariate analysis, time series analysis, and machine learning applications.
Course Introduction
Advanced Statistical Methods builds upon foundational statistical knowledge to explore sophisticated analytical techniques used in modern research and data science. This course covers multivariate methods, time series analysis, machine learning approaches, and other advanced statistical techniques. Students will develop the skills to tackle complex data analysis challenges and extract meaningful insights from multidimensional data.
Course Content
Module 1: Multivariate Analysis
- Multivariate data visualization
- Principal Component Analysis (PCA)
- Factor Analysis
- Discriminant Analysis
- Canonical Correlation Analysis
Module 2: Time Series Analysis
- Time series components and decomposition
- Stationarity and transformations
- ARIMA modeling
- Spectral analysis
- State space models and Kalman filtering
Module 3: Machine Learning Methods
- Supervised vs. unsupervised learning
- Classification and regression trees
- Random forests and boosting methods
- Support vector machines
- Neural networks and deep learning introduction
Module 4: Bayesian Statistics
- Bayesian inference principles
- Prior and posterior distributions
- Markov Chain Monte Carlo methods
- Bayesian hierarchical models
- Bayesian model selection and averaging
Module 5: Advanced Regression Techniques
- Generalized linear models
- Mixed effects models
- Nonlinear regression
- Quantile regression
- Regularization methods (Ridge, Lasso, Elastic Net)
Assignments
- 1Multivariate analysis of complex dataset
- 2Time series forecasting project
- 3Machine learning model development and evaluation
- 4Bayesian analysis implementation
- 5Advanced regression modeling case study
Case Studies
Case Study 1
Gene expression analysis using multivariate methods
Case Study 2
Economic forecasting with advanced time series models
Case Study 3
Medical diagnosis using machine learning algorithms
Case Study 4
Environmental data analysis with spatial-temporal models
Case Study 5
Customer behavior prediction using advanced regression
Datasets
Gene Expression Omnibus
Genomic data for multivariate analysis
Federal Reserve Economic Data (FRED)
Economic time series for forecasting
UCI Machine Learning Repository
Datasets for machine learning applications
ImageNet
Image database for deep learning applications
Recommended Textbooks
Time Series Analysis: Forecasting and Control
by George E. P. Box, Gwilym M. Jenkins, Gregory C. Reinsel, and Greta M. Ljung
View Book DetailsThe Elements of Statistical Learning
by Trevor Hastie, Robert Tibshirani, and Jerome Friedman
View Book DetailsBayesian Data Analysis
by Andrew Gelman, John B. Carlin, Hal S. Stern, David B. Dunson, Aki Vehtari, and Donald B. Rubin
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