Data|Statistics|Research|Consultancy

Advanced Statistical Methods

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

  • 1
    Multivariate analysis of complex dataset
  • 2
    Time series forecasting project
  • 3
    Machine learning model development and evaluation
  • 4
    Bayesian analysis implementation
  • 5
    Advanced 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

Applied Multivariate Statistical Analysis

by Richard A. Johnson and Dean W. Wichern

View Book Details

Time Series Analysis: Forecasting and Control

by George E. P. Box, Gwilym M. Jenkins, Gregory C. Reinsel, and Greta M. Ljung

View Book Details

The Elements of Statistical Learning

by Trevor Hastie, Robert Tibshirani, and Jerome Friedman

View Book Details

Bayesian Data Analysis

by Andrew Gelman, John B. Carlin, Hal S. Stern, David B. Dunson, Aki Vehtari, and Donald B. Rubin

View Book Details

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