Introduction to the basics of mathematical statistics and data analysis, including quantitative numerical experiments using suitable statistical software.
Curriculum
teacher profile teaching materials
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
Mutuazione: 20410555 ST410-STATISTICA in Scienze Computazionali LM-40 MARTINELLI FABIO
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.Attendance
OptionalType of evaluation
Written exam (30 points), Project (optional, 3 points), average of the exercise sheets (10 points). Final grade: max {written exam grade, 2/3 * exam + exercise sheets + project, 30}. teacher profile teaching materials
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
Mutuazione: 20410555 ST410-STATISTICA in Scienze Computazionali LM-40 MARTINELLI FABIO
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.Attendance
OptionalType of evaluation
Written exam (30 points), Project (optional, 3 points), average of the exercise sheets (10 points). Final grade: max {written exam grade, 2/3 * exam + exercise sheets + project, 30}.