Programme

Random variables and their distribution, moment generating function, mean variance and covariance.
Random sampling model and statistical model.
Statistics: concept, examples, sufficient statistics.
Point estimators: definition and desired properties, moments, maximum likelihood and Bayes.
Computational methods: Newton-Raphson, EM algorithm
Improving an estimator: Rao-Blackwell, UMVU estimator, full statistic, Lehman-Scheff ́e II and Cramer-Rao
Confidence intervals: intuitive, pivotal quantity, IC for Bayes and asymptotic IC.
Hypothesis testing: likelihood ratio, pivotal quantity test (Z and T test), duality with IC, UMP, Neyman-Pearson and Karlin-Rubin tests.
Non-parametric methods: goodness-of-fit, contingency table, Kolmogorov-Smirnov and ranking tests.
Analysis of variance (ANOVA) and F.
Regression: linear, multiple linear, generalized linear and Logistic / Poisson

Core Documentation

Statistical Inference, Casella e Berger, 2nd Edition, Duxbury Advanced Series.

Additional reference:
Luca Leuzzi, Enzo Marinari, Giorgio Parisi
CALCOLO DELLE PROBABILITÀ: un trattatello per principianti volenterosi

Type of delivery of the course

Lectures will take place in a lecture room either on the blackboard or on a tablet

Attendance

Optional

Type of evaluation

During the course students will have to solve three exercises sheets focused on different parts of the program. The final exam will consist of four exercises, each one with two or three questions of theoretical and/or practical character. The final score will be the maximum between the score of the final exam and 2/3 x score final exam + average score of the exercises sheets.

Programme

Random variables and their distribution, moment generating function, mean variance and covariance.
Random sampling model and statistical model.
Statistics: concept, examples, sufficient statistics.
Point estimators: definition and desired properties, moments, maximum likelihood and Bayes.
Computational methods: Newton-Raphson, EM algorithm
Improving an estimator: Rao-Blackwell, UMVU estimator, full statistic, Lehman-Scheff ́e II and Cramer-Rao
Confidence intervals: intuitive, pivotal quantity, IC for Bayes and asymptotic IC.
Hypothesis testing: likelihood ratio, pivotal quantity test (Z and T test), duality with IC, UMP, Neyman-Pearson and Karlin-Rubin tests.
Non-parametric methods: goodness-of-fit, contingency table, Kolmogorov-Smirnov and ranking tests.
Analysis of variance (ANOVA) and F.
Regression: linear, multiple linear, generalized linear and Logistic / Poisson

Core Documentation

Statistical Inference, Casella e Berger, 2nd Edition, Duxbury Advanced Series.

Additional reference:
Luca Leuzzi, Enzo Marinari, Giorgio Parisi
CALCOLO DELLE PROBABILITÀ: un trattatello per principianti volenterosi

Type of delivery of the course

Lectures will take place in a lecture room either on the blackboard or on a tablet

Attendance

Optional

Type of evaluation

During the course students will have to solve three exercises sheets focused on different parts of the program. The final exam will consist of four exercises, each one with two or three questions of theoretical and/or practical character. The final score will be the maximum between the score of the final exam and 2/3 x score final exam + average score of the exercises sheets.

Programme

Random variables and their distribution, moment generating function, mean variance and covariance.
Random sampling model and statistical model.
Statistics: concept, examples, sufficient statistics.
Point estimators: definition and desired properties, moments, maximum likelihood and Bayes.
Computational methods: Newton-Raphson, EM algorithm
Improving an estimator: Rao-Blackwell, UMVU estimator, full statistic, Lehman-Scheff ́e II and Cramer-Rao
Confidence intervals: intuitive, pivotal quantity, IC for Bayes and asymptotic IC.
Hypothesis testing: likelihood ratio, pivotal quantity test (Z and T test), duality with IC, UMP, Neyman-Pearson and Karlin-Rubin tests.
Non-parametric methods: goodness-of-fit, contingency table, Kolmogorov-Smirnov and ranking tests.
Analysis of variance (ANOVA) and F.
Regression: linear, multiple linear, generalized linear and Logistic / Poisson

Core Documentation

Statistical Inference, Casella e Berger, 2nd Edition, Duxbury Advanced Series.

Additional reference:
Luca Leuzzi, Enzo Marinari, Giorgio Parisi
CALCOLO DELLE PROBABILITÀ: un trattatello per principianti volenterosi

Type of delivery of the course

Lectures will take place in a lecture room either on the blackboard or on a tablet

Attendance

Optional

Type of evaluation

During the course students will have to solve three exercises sheets focused on different parts of the program. The final exam will consist of four exercises, each one with two or three questions of theoretical and/or practical character. The final score will be the maximum between the score of the final exam and 2/3 x score final exam + average score of the exercises sheets.