DALMINE
Overview
Date/time interval
Syllabus
Course Objectives
After this course, the student knows elements of applied probability theory, including discrete and continuous random variables and elements of statistical inference, including estimation, confidence intervals,
hypothesis testing and regression models, including the linear and the non linear case. They are able to use R (or another statistical software) to solve these problems
Course Prerequisites
Mathematical Analysis: Calculus, including derivatives and integrals.
Notions about matrix algebra and multiple integrals.
Teaching Methods
Lectures and exercises.
Lab for R (or another software).
A case study developed in group work.
Assessment Methods
-----------------
Mode A
-----------------
For those who can attend and prepare continuously, through intermediate tests and carrying out a group case study.
I) Intermediate tests.
- a self-assessment test in an R environment
- two computerized intermediate tests which require the use of R.
Access to the second test is allowed to those who obtain a mark of at least 15/30 in the first test.
The two intermediate tests together are passed with an average of at least 18/30.
The weights of each question within a test are initially equal as the 2 tests have the same weight.
Who has not attempted or passed the first intermediate exam, can try again in one (and only one, at your
choice) of the two sessions of the ordinary winter session.
II) Case study on regression. Group implementation of a case study on the topic of regression applied
to a data set provided by the teachers.
The paper illustrating the case study developed and the R script with the calculations carried out must be delivered before the group presentation of the same (preferably accompanied by slides).
More details will be provided in class.
III) Presentation and discussion of the case study. Group presentation in front of the class and discussion on contents, results and methodologies used.
Following the oral discussion of the project carried out, each member of the group will be asked a question regarding the methods used in the case study.
The whole class participates in the discussion of each group.
-----------------
B mode
-----------------
In ordinary appeal with a single computerized test and an oral exam in the same appeal.
The required preparation includes the ability to both write using R (or other software) and speak. The oral test focuses on the discussion of the methods covered in the course and evaluates the understanding of the language, formalism and concepts at a descriptive and interpretative level.
Contents
Random experiments.
Introduction to probability.
Conditional Probability, independence.
Bayes' theorem.
Discrete Random Variables. Expectation, variance, moments.
Bernoulli, Binomial, Begative Binomial, Hypergeometric, Poisson and Geometric distributions.
Continuous random variables. Existence of moments.
Uniform, Gaussian, Negative Exponential, Gamma, Chi-square distribution.
Poisson process.
Central limit theorem.
Statistical inference.
Estimation: unbiasedness, consistency and efficiency.
The sample mean, percentage and variance.
Laws of large numbers.
Confidence Intervals.
Test of Hypoteses: P-value.
Decision approach: 1st and 2nd type errors.
Significance and power.
Testing the mean and asymptotically Gaussian tests.
Testing for a proportion.
Testing for a variance.
Testing for mean differences and variance ratios.
Covariance and correlation.
Least squares and regression.
Coefficient of determination.
Tests and Confidence Intervals for regression coefficients.
Confidence Intervals for the response variable.
Confidence Intervals for regression forecasts.
Generalised linear models.
Outline of non-linear regression models and models for binary and categorical vartables.
Lasso and Ridge models.
Model selection, cross-validation, residual analysis and model testing
Online Resources
More information
Material provided by the teacher through the E-Learning Moodle page.