SC/0074 - PROBABILITA' E INFERENZA STATISTICA
Academic Year 2021/2022
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CLAUDIO CONVERSANO (Tit.)
- Teaching style
- Lingua Insegnamento
|[60/79] APPLIED COMPUTER SCIENCE AND DATA ANALYTICS||[79/00 - Ord. 2021] PERCORSO COMUNE||6||48|
The course aims to illustrate the basic concepts of data analysis and inference, also providing the basic techniques for data analysis and inductive processes from sample data to the population, with emphasis on potential economic applications. The final objective is to prepare students for the more advanced statistical methods typically encountered in major courses on multivariate and computational statistics.
Expected learning outcome (knowledge and understanding)
Students will know common statistical procedures, rules of probability, probability models and inferential procedures. Students will understand the rationale behind these techniques.
Expected learning outcomes (applying knowledge and understanding)
Students are expected to understand which statistical technique(s) may be useful for the problem at hand. They will be able to synthesize a dataset using graphical, tabular and numerical measures; to formalize problems involving uncertainty using probability calculus, to perform a statistical test to decide about un uncertain parameter of the population.
Mathematics at the level of a first-year course for undergraduate students in Computer Science.
Part 1 (Descriptive Statistics)
The statistical survey and its main phases. Statistical sources. Statistical units. Population and sample.
Quantitative and qualitative statistical variables.
The graphical representation of data.
Measures of central tendency and variability. Shape of a distribution.
Bivariate joint frequency distributions. Two-way contingency table. Joint, marginal and conditional frequencies. Statistical independence in general and Chi-square index.
Analysis of linear correlation; the Pearson correlation coefficient. The statistical interpolation: the method of least squares.
Part 2 (Elements of probability theory)
What is probability? Events, logical operations on events.
Elementary theorems of probability theory. Conditional probability and Bayes Theorem.
Random variables. Distribution of probability, cumulative distribution function.
Mathematical expectation and variance of a random variable. Chebycev inequality.
Discrete random variables: Uniform, Bernoulli, Binomial, Hypergeometric, Poisson.
Continuous random variables: Uniform, Normal.
Functions of random variables, in particular linear function. Bivariate random variables. Joint probability distributions, marginal and conditional (discrete case only). Stochastic independence. Functions of random vectors, in particular linear function. Central Limit Theorem.
Part 3 (Sampling and statistical inference)
Population and sample. Some statistics and their sampling distribution. Sample mean and variance. Outline of sampling techniques.
Parameter estimation. Main properties of point estimators.
Interval estimate. Confidence intervals for large samples.
Hypothesis testing. Outline on the construction of a test: the decision-making approach. Test statistics, type I and type II errors, power of a test and the Neyman-Pearson strategy.
Hypothesis testing for mean and proportions and their comparison (paired and unpaired samples).
Theoretical lectures (36 hours) and practice sessions (12 hours). Total credit: 6 CFU.
Verification of learning
31 Points are given as follows:
- written exam to be made using the Moodle platform composed of some quiz, excercises of descriptive statistics, probability and inference and one exercise to be solved using the R software.
To be announced soon