This course provides a comprehensive introduction to statistical methods essential for the analysis of experimental data. The focus is on developing a strong understanding of fundamental probability and statistical concepts, and their practical application in data analysis. Students will learn to select and implement appropriate statistical techniques to extract meaningful insights from data, validate experimental results.
Students will be able to:
• Understand and apply fundamental concepts of probability and statistics.
• Describe and utilize various probability density functions (PDFs) and cumulative distribution functions (CDFs).
• Calculate and interpret conditional and joint probabilities.
• Apply the Law of Large Numbers and the Central Limit Theorem to real-world problems.
• Understand and apply Bayesian Statistics
• Understand and implement maximum likelihood estimation.
• Perform chi-square tests for goodness-of-fit and independence.
• Evaluate the goodness-of-fit of statistical models.
• Effectively communicate statistical results and interpretations.
Students will be able to:
• Understand and apply fundamental concepts of probability and statistics.
• Describe and utilize various probability density functions (PDFs) and cumulative distribution functions (CDFs).
• Calculate and interpret conditional and joint probabilities.
• Apply the Law of Large Numbers and the Central Limit Theorem to real-world problems.
• Understand and apply Bayesian Statistics
• Understand and implement maximum likelihood estimation.
• Perform chi-square tests for goodness-of-fit and independence.
• Evaluate the goodness-of-fit of statistical models.
• Effectively communicate statistical results and interpretations.
scheda docente
materiale didattico
2. Probability Distributions (10h): Probability density functions (PDFs) and cumulative distribution functions (CDFs). Conditional probability, joint distributions, and marginal distributions. Bayes' theorem.
3. Key Probability Distributions and Limit Theorems (5h): common probability distributions (e.g., normal, binomial, Poisson). The Law of Large Numbers and its applications. The Central Limit Theorem and its significance.
4. Maximum Likelihood Estimation (8h): Introduction to likelihood functions. Principles and methods of maximum likelihood estimation. Application of maximum likelihood estimation.
5. Chi-Square Tests (8h): Chi-square distribution and its properties. Chi-square goodness-of-fit tests. Chi-square tests for independence.
6. Goodness-of-Fit Testing (8h): Methods for assessing the fit of statistical models to data. Interpretation of goodness-of-fit results. Practical application of goodness of fit tests.
7. Practice (15h)
“Bayesian Reasoning in Data Analysis” – G. D’Agostini
Programma
1. Introduction to Probability and Statistics (6h): basic concepts of probability, random variables, and statistical inference. Descriptive statistics: measures of central tendency and dispersion. Introduction to data types and distributions.2. Probability Distributions (10h): Probability density functions (PDFs) and cumulative distribution functions (CDFs). Conditional probability, joint distributions, and marginal distributions. Bayes' theorem.
3. Key Probability Distributions and Limit Theorems (5h): common probability distributions (e.g., normal, binomial, Poisson). The Law of Large Numbers and its applications. The Central Limit Theorem and its significance.
4. Maximum Likelihood Estimation (8h): Introduction to likelihood functions. Principles and methods of maximum likelihood estimation. Application of maximum likelihood estimation.
5. Chi-Square Tests (8h): Chi-square distribution and its properties. Chi-square goodness-of-fit tests. Chi-square tests for independence.
6. Goodness-of-Fit Testing (8h): Methods for assessing the fit of statistical models to data. Interpretation of goodness-of-fit results. Practical application of goodness of fit tests.
7. Practice (15h)
Testi Adottati
“A Modern Introduction to Probability and Statistics” – F.M. Dekking, C. Kraaikamp, H.P Lopuhaä, L. E. Meester“Bayesian Reasoning in Data Analysis” – G. D’Agostini
Modalità Frequenza
Attendance is not compulsoryModalità Valutazione
The exam consists of a written test which may be followed, if necessary, by an oral interview