Insegnamento mutuato da: B000365 - STATISTICA Corso di Laurea in MATEMATICA Curricula APPLICATIVO
Is a basic course in Statistics that develops the fundamentals of Inference and Modelling.
Students of B027563 (6 credits) must attend part of the course. The specific topics are indicated by (*) in the detailed list of arguments below.
Wasserman, L. (2004). All of statistics. Springer-Verlag, New York.
Marchetti, G. M, Lupparelli, M (2020). Statistica: teoria e modelli. Dispense.
KNOWLEDGE AND UNDERSTANDING
We present and discuss the basic models for the study of statistics. A central theme is the theory of statistical inference. Inference is applied to problems of random sampling from a population defined by single or multiple random variables. The study of dependence will be treated with some care distinguishing when the main goal is prediction or explanation. In this last case we study the process of building statistical models in the presence of mixed continuous and binary variables, including possibly quadratic terms and interactions.
APPLYING KNOWLEDGE AND UNDERSTANDING
In statistics are crucial: the application of models to real problems, the model interpretation and the communication of results. Therefore, the course is based not only on theory but also on applications to data from various fields : Economics, Social Sciences, Biology or Computer Science. Statistical computing will be carried out using one of the best statistical data analysis software, the language R. The student will be able to find the most appropriate models for given set of data with the capacity of defending the chosen methods.
Develop model-building skills including evaluation of assumptions and interpretation of model-fitting
Learn and apply the basic mathematical theory of statistics
Develop verbal communication skills for discussing conclusions and limitations of statistical evidence; present data analysis appropriately.
Calcolo delle Probabilità
Standard lectures, Exercises from the textbook, computer practicals on real problems using the R language
Frequency to lectures, practice and lab: Recommended .
Homework is assigned each week to the students mainly based on the exercises from the textbook. For the students attending regularly to classes the exercises. The final exam is oral. For students regularly attending the classes final score will be calculated based on a weighted average of the score for the homeworks (33%) and the oral (67%).If the students have not attended the lectures and not done the homeworks the oral includes questions concerning exercises from the textbook.
The lectures cover 12 weeks.
The topics for the students with 6 credits are labeled with (*)
Statistical models, sampling i.i.d. (*)
Dependence probability models (*)
Estimation: estimators, mean square error, confidence intervals (*)
Likelihood. One-sample and two-sample models. (*)
Properties of maximum likelihood estimators (MLE) (*)
Proofs of the asymptotic properties of the MLE.
Tests. P-values. Likelihood Ratio Test. Profile likelihood. Application to confidence interval
Simple linear regression model. Least squares. Properties. Standard error. Confidence intervals. Some common tests (*)
Multiple regression models. Least-squares partial regression coefficients. Deviance. Covariates and factors. Interactions (*)
Linear logistic regression model. MLE. Deviance and tests. Odds-ratios.
Model selection. Penalized likelihoods. Cross-validation.
Introduction to graphical models. Directed acyclic graphs. Representation of independences. Conditional independence tests