Probability I Probability II Statistical Inference Techniques I Statistical Inference Techniques II Regression Methods

General objectives: 1. Capacity for analysis and synthesis. 2. To model and solve problems. 3. Oral and written communication skills. Specific objectives: 1. To know the basic techniques of resampling methods 2. To know and use statistical software to work with resampling techniques.

1. Introduction to Computationally Supported Resampling Methods in R 1.1. Resampling Fundamentals: History and Basic Principles 1.2. Computational Tools in R: Introduction to the R Environment and Relevant Statistical Packages 1.3. Types of Resampling: Differences and Applications of Parametric and Nonparametric Bootstrap 2. Introduction to Jackknife and Permutation Tests 2.1. Jackknife Theory: Concepts and Applications 2.2. Permutation Tests: Fundamentals and How to Perform Them in R 3. Concepts Related to Empirical Distribution 3.1. Definition and Properties: What It Is and How to Use It 3.2. Constructing the Empirical Distribution in R: Methods and Functions 3.3. Practical Applications: Using the Empirical Distribution in Data Analysis 4. Estimating Standard Errors and Bias Using Resampling 4.1. Concepts of Standard Error and Bias: Definitions and Relevance 4.2. Resampling Methods for Estimation 4.3. Implementation in R: Practical Examples and Case Studies 5. Resampling in Linear Models and Time Series 5.1. Application in Linear Models: Techniques and Examples in R 5.2. Resampling in Time Series: Challenges and Solutions 6. Confidence Intervals and Hypothesis Testing Based on Resampling 6.1. Constructing Confidence Intervals: Resampling-Based Methods 6.2. Performing Hypothesis Testing: Nonparametric Approaches 6.3. Practical Examples in R: Application to Real-World Datasets 7. Applications in Machine Learning: Bagging and Boosting 7.1. Fundamentals of Bagging: Concepts and How to Implement It in R 7.2. Introduction to Boosting: Theory and Practical Applications 7.3. Advantages of Ensemble Methods: Improving Accuracy and Reducing Overfitting 7.4. Practical exercises: Applying bagging and boosting to machine learning projects

Theory (4 ECTS). Theoretical classes with support material available on the Web. Practice (2 ECTS) problem-solving classes. Computing practices. Presentations and debates.