30456 - STATISTICS - MODULE 1 (THEORY AND METHODS)
Course taught in English
Go to class group/s: 13
Lezioni della classe erogate in presenza
In order to successfully attend the course it is recommended to possess a good knowledge of the basic notions of mathematics, in particular derivatives, integrals, logarithmic and exponential functions.
The aim of the course is to provide students with a first introduction to the main concepts of statistical thinking, both descriptive and inferential. The most relevant techniques for collecting and analyzing data are first explored. The course then introduces the fundamental principles of probability theory and random variables, as a basis for better understanding the point estimation theory. The focus is on analyzing real data, illustrating some of the methods and concepts with the help of the statistical software R.
The course focuses on the following main topics:
- Basic univariate exploratory data analysis: frequency distributions, graphical representations, summary statistics of centrality and variability.
- Basic bivariate exploratory data analysis: contingency tables, summary statistics of linear association, simple linear regression model.
- Probability: elementary set theory, events, algebras, axiomatic definition, conditional probability and elementary rules of calculus, Bayes' rule.
- Random variables: discrete and continuous distribution, expectation and moments, common families of distributions (Bernoulli, binomial, geometric, Poisson, uniform, normal, negative exponential).
- Functions of random variables.
- Random vectors: joint, marginal and conditional distributions, covariance and correlation coefficient, stochastic independence.
- Multivariate normal distribution.
- Sampling: population and sample, inferential process, sample variability and sampling error, statistics.
- Sample mean: expected value and variance.
- Sampling from a normal population: sample mean and sample variance properties.
- Central limit theorem and convergence in distribution. The Weak Law of Large Numbers and convergence in probability.
- Properties of estimators: unbiasedness, consistency and mean squared error. Asymptotic properties of estimators: weak and strong consistency.
- Understand the fundamentals of statistical thinking, both descriptive and inferential.
- Reproduce the basics of descriptive statistics to economic data analysis.
- Illustrate the main concepts of probability and point estimation theory.
- Analyze real dataset on different socio-economic phenomena, with the aid of an adequate computer software.
- Summarize and visualize information contained in real data sets.
- Study the relationship between relevant variables.
- Choose adequate probabilistic models to represent data and learn from it in a statistical setting.
- Estimate unknown population parameters based on sampling information.
- Interpret the obtained results.
- Face-to-face lectures
- Exercises (exercises, database, software etc.)
Teaching and learning activities for this course are divided into:
- Face-to-face lectures during which statistical methods are explained and discussed.
- Exercises on quantitative methods.
- Applications on real data using the statistical software R.
|Continuous assessment||Partial exams||General exam|
With the purpose of measuring the acquisition of the above-mentioned learning outcomes, the students’ assessment is based on two main components:
- Final written exam (90% of the final grade). The written exam consists of exercises and closed and/or open questions aimed to assess students’ ability to apply properly the statistical tools illustrated during the course, to summarize information contained in datasets, to study the relationship between variables, to choose adequate probability models as well as to estimate unknown parameters.
- Home assignments (10% of the final grade), consisting in a PC project aimed to test the students’ ability to analyze a real dataset with the statistical software R and discuss critically the output.
For both attending and non-attending students:
- S. M. ROSS, Probability and Statistics for Engineers and Scientists, Elsevier Press, Fifth Edition.
- Additional teaching materials are announced before the start of the course and indicated on the Bboard platform. The slides of the course and additional exercises are uploaded to the Bboard platform of the course.