79044 - Statistical Models for Actuarial Sciences

Learning outcomes

By the end of the course, students will be able to specify and estimate statistical models for analyzing different types of response variables, namely binary variables, count variables, and rates. In particular, students will be able to: - apply and interpret statistical models appropriate to the nature of the data; - use specialized statistical software for applied studies in actuarial science.

Course contents

Introduction to Statistical Models in Machine Learning

• Objectives of statistical learning: inference and prediction using statistical models and machine-learning algorithms.
• Learning methods: parametric and nonparametric models. Supervised and unsupervised learning. Regression and classification problems.
• Assessing the accuracy of predictive models: the bias–variance trade-off.
• Loss functions and evaluation metrics for predictive models.
• Predictive accuracy and overfitting.

Statistical Models for Machine Learning

• Generalized linear models (GLMs): Gaussian, Poisson, gamma, logistic, and multinomial models.
• Regularization methods: ridge, lasso, and elastic net.
  
• Decision trees for regression and classification.
• Naive Bayes methods.

Selection and Evaluation of Statistical Models for Machine Learning

• Model-selection criteria: AIC and BIC.
• Resampling methods: cross-validation and bootstrap.
• Evaluation of regression models: MSE, RMSE, MAE, and R^2.
• Evaluation of classification models: confusion matrix, accuracy and error rate, sensitivity and specificity, ROC curves and AUC, precision and recall, F-score, cross-entropy, and Brier score.
• The problem of imbalanced classes.

Ensemble Methods

• Bagging.
• Random forests.
• Boosting.
• Stacking.

 

Readings/Bibliography

Textbook:

• James G., Witten D., Hastie T., Tibshirani R. (2021) An Introduction to Statistical Learning with Applications in R, 2nd edition, Springer-Verlag.
  Available online.

Supplementary readings:

• Murphy K. P. (2022) Probabilistic Machine Learning: An Introduction, MIT Press.
  Available online.
• Wüthrich, M.V., Merz, M. (2023) Statistical Foundations of Actuarial Learning and its Applications, Springer.
  Available online.

Additional teaching materials (slides, exercises, etc.) prepared by the instructor are available on Virtuale.

Teaching methods

• Lectures.
• Practical classes and laboratory sessions in which real-world data will be analyzed using R software.

Although attendance is not mandatory, active participation in classes is strongly recommended.

Given the type of activities and teaching methods used, attendance at this training activity requires all students to first complete modules 1 and 2 of the e-learning training course on safety in the workplace.

Assessment methods

Assessment consists of two parts:

1. Data analysis project. Working in groups of no more than three, students must prepare a report on the application of statistical methods and models to prediction in a real-world case study. The report must describe the problem under investigation, the data used, the methods adopted, the model-evaluation procedures, and the resulting predictions. The project will be discussed during the examination.
2. Oral examination. The oral examination will cover the course content and assess students’ understanding of the main theoretical, methodological, and applied concepts addressed in the course.

The use of AI in the data analysis project is permitted, provided that it is explicitly disclosed, limited in scope, and used only as a support tool. It may not replace the student’s original and critical contribution.

Assessment criteria: grades will be awarded according to the following scale:
<18 insufficient
18–23 sufficient
24–26 fair
27–28 good
29–30 very good
30 with honours excellent

Students with specific learning disorders or temporary or permanent disabilities: students are advised to contact the University's dedicated support office in good time. The office will propose any appropriate accommodations for eligible students. These accommodations must be submitted to the course instructor for approval at least 15 days in advance. The instructor will assess their appropriateness, taking into account the intended learning outcomes of the course.

Examination registration: all students must register for the exam through the AlmaEsami platform in accordance with the general rules established by the University.

 

Office hours

See the website of Luca Scrucca