30401 - MATHEMATICS AND STATISTICS - MODULE 2 (STATISTICS)
Course taught in English
Go to class group/s: 25
Class-group lessons delivered on campus
To feel comfortable with some topics in this course, students should be familiar with differential and integral calculus.
The main aim of the course is to introduce students to probability theory, the logic of uncertainty, and statistics, which represent fundamental methodological tools for modern applications in Science and beyond. Students are expected to get familiar with key principles of probability theory and statistical thinking, both descriptive and inferential. Several examples and illustrations of concepts and methods will be provided, also with the help of the statistical software R.
- Combinatorics, probability measures and related elementary properties.
- Conditional probability and independence.
- Discrete and continuous random variables. Notable examples. Expected values.
- Joint distribution, independence, correlation, conditional distributions.
- Descriptive statistics, population and sampling, frequency tables, graphs, measures of location and spread.
- Distributions of sampling statistics and related asymptotic distributions.
- Point and interval parameter estimation.
- Hypothesis testing.
- Understand basic concepts of probability required for the use and interpretation of statistical methods.
Describe a dataset through adequate graphs, tables and statistics.
Identify if the structure of the data allows the application of basic statistical inferential methods.
Do inference on the mean of a population (point estimation/ prediction, interval estimation, hypothesis testing).
Understand the fundamental logic of estimation and hypothesis testing.
Understand the challenges derived from the presence of uncertainty in real-life situation.
Choose and apply adequate (basic) statistical tools to aid in the decision-making process by learning from available data.
Interpret charts, graphs and statistics and identify possible misrepresentations of data.
Question statements based on data, by analysing the statistical elements and the validity of the assumptions made.
- Face-to-face lectures
- Exercises (exercises, database, software etc.)
- Group assignments
- Interactive class activities (role playing, business game, simulation, online forum, instant polls)
Exercises (Exercises, database, software etc.):
Special sessions with exercises, examples and illustrations of concepts and methods, also with the help of statistical software R, will be provided.
Students may choose between the following two options:
- Two partial written exams (a mid-term and a final) that contribute to the final grade with a 50% weight each.
- A single general written exam (after the end of the course) that counts for 100% of the final mark.
The tests consist of exercises. They aim at ascertaining students' mastery of concepts and results discussed during lectures as well as an adequate knowledge of R.
In each test the maximum grade is 31.
The assessment method is the same for both attending and non-attending students.
Students who take the mid-term exam may still take the general exam instead of taking the final exam.
Importantly, access to the final (or second partial) exam follows the rules indicated in Section 7.6 of the Guide to the University.
The teaching material will be primarily that developed during the classes and distributed to the students in a PDF format after each class.
The course will use examples and extracts primarily from the first book listed below. It is advisable to acquire this book either in its original publication or its Italian translation (it is also available as an e-book), since it is an excellent modern resource to learn Probability and Statistics and why these are fundamental in anything that has to do with learning from data.
Early chapters from the second book provide an excellent more technical introduction to Probability. The introduction and some Appendices of the third book provide an excellent and accessible introduction to statistical machine learning and the use of Probability and Statistics for designing and analyzing algorithms. The fourth is a textbook whose syllabus correlates highly with the contents of this course. For a number of basic concepts the corresponding Wikipedia pages are a great resource. Please use that instead of random blogs, webpages or videos posted on youtube.
Spiegelhalter, The Art of Statistics: How to Learn from Data, Penguin, 2019, ISBN 978-1541618510 (available also in Italian translation)
- Grimmett and Stirzaker, Probability and Random Processes, Oxford, Fourth Edition, 2020, ISBN 978-0198847595
- Bishop, Pattern Recognition and Machine Learning, Springer, 2006, ISBN 978-0387310732
- S. ROSS, Introduction to Probability and Statistics for Engineers and Scientists, Fourth Edition, Academic Press, 2014