STATISTICAL MODELING
Instructional goals
The course introduces the main concepts of probability and statistics, providing the methodological foundations for data collection and analysis.
Intended learning outcomes
Knowledge and understanding:
The course develops students' ability in collecting, analyzing and critically interpreting data related to economics, finance, management as well as everyday situations. The course also contributes to students' mathematical skills.
Applying knowledge and understanding:
The course provides the student the knowledge of a series of tools such as probabilistic models to model phenomena whose outcomes are uncertain, estimation techniques for understanding and prediction, hypothesis testing for decision making.
During the final exam, students are required to use mathematical thinking to formalize complex problems and to apply analytical tools to solve them.
Making judgements:
When facing complex problems, students are encouraged to apply analytical tools in an independent way and to give original interpretations to the results they obtain. This is also a requirement for the final exam.
Communication skill:
The course contributes to students' mathematical reasoning and ability to communicate in mathematical language.
Learning skills:
The knowledge in Probability and Statistics acquired during the course will
allow the student to autonomously understand and interpret new more advanced techniques and adapt them to the specific reference context.
Course Contents
Elements of probability theory and main probability models.
Descriptive statistics: data sets description and summarization; correlation in bivariate data sets.
Statistical inference: sampling statistics; point estimation and confidence intervals; hypothesis testing.
Reference Books
First part of the course:
1. Ross, Sheldon M. Introductory statistics. Elsevier/Academic Press.
Second part of the course:
2. Ross, Sheldon M. Introduction to probability and statistics for engineers and scientists. Elsevier/Academic Press.
Teaching Methods
Lectures with at least three intermediate tests.
Assessment Method
Students will be evaluated on the basis of the score obtained in several intermediate tests and in the final exam.
Intermediate tests will be given during classes, at least three times during the semester. Students will be required to answer multiple choice questions.
During the final exam, students will have to demonstrate their knowledge of the theoretical notions as well as their ability in using them for problem solving and result interpretation. The final exam will be written, but the teacher might require an oral integration.
The final exam will be evaulated in the usual 0-30 scale. intermediate tests can add up to 5 bonus points.
Thesis assignment criteria
Not relevant.
Week 1
Book 1 Ch 1: Introduction, data collection. Statistical models and parameters. The population and the sample.
Book 1 Ch 4: Basic probability, events, experiments, conditional probability, independence, uniform spaces and notions of combinatorics.
Week 2
Book 1 Ch 2-3: Descriptive statistics: tables, line plots, histograms, etc. Data examples. Summary statistics, mean, median, variance, standard deviation, covariance and correlation coefficient and percentiles
Week 3
Book 1 Ch 4 Bayes' formula.
Ch 5 Discrete random variables, Bernoulli sequences, Bernoulli and Binomial distributions.
Week 4
Book 1 Ch 5: Expectation and variance for discrete random variables. Transformations of discrete random variables. Linear transformations.
Joint distributions, covariance, correlation and independence. Hypergeometric and Poisson random variables.
Week 5
Book 2 Ch 4: Continuous random variables, densities and their features.
Expectations for continuous random variables.
Jointly continuous random variables.
Week 6
Book 2 Ch 4: Independence.
Book 2 Ch 5: Probability models: Binomial, Poisson, Uniform, Exponential, Normal.
Properties of normal random variables.
chi-square and T distributions.
Week 7
Book 2 Ch 6: Introduction to statistical inference. Distribution of Sample statistics. Main convergence theorems.
Week 8
Book 2 Ch 7: Maximum likelihood estimators, moment estimators. Estimators’ sampling properties MSE and bias).
Week 9
Book 2 Ch 7: Confidence intervals for the parameters of a normal population.
Week 10
Book 2 Ch 7: Confidence intervals for the difference of expectations.
Asymptotic confidence intervals based on Central Limit Theorem approximation.
Week 11
Book 2 Ch 8: Hypothesis testing.
Week 12
Review.