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Stochastic processes and time series
01TXMSM
A.A. 2020/21
Course Language
Inglese
Degree programme(s)
Master of science-level of the Bologna process in Data Science And Engineering - Torino
Course structure
| Teaching | Hours |
|---|---|
| Lezioni | 40 |
| Esercitazioni in aula | 20 |
| Esercitazioni in laboratorio | 20 |
Lecturers
| Teacher | Status | SSD | h.Les | h.Ex | h.Lab | h.Tut | Years teaching |
|---|---|---|---|---|---|---|---|
| Bibbona Enrico | Professore Associato | STAT-01/A | 20 | 0 | 20 | 0 | 2 |
Co-lectures
Context
| SSD | CFU | Activities | Area context | MAT/06 SECS-S/01 |
4 4 |
C - Affini o integrative C - Affini o integrative |
Attività formative affini o integrative Attività formative affini o integrative |
|---|
2020/21
The purpose of the course is to introduce the students to the main stochastic and statistical models suitable to describe dependent data, which can evolve over time or space, or that are connected via dependence structures more complex than pure independence or seriality. To this aim, the most relevant stochastic processes and time series models, in both discrete and continuous time, are described, together with some relevant hierarchical and network models.
The purpose of the course is to introduce the students to the main stochastic and statistical models suitable to describe dependent data, which can evolve over time or space, or that are connected via dependence structures more complex than pure independence or seriality. To this aim, the most relevant stochastic processes and time series models, in both discrete and continuous time are described, together with the statistical methodology used to infer the values of the parameters.
The course will be held with the method of flipped classrooms. Theoretical lectures will be delivered as video talks for self study (40-50 hours). Virtual classrooms (30-40 hours) will be organized for exercise sessions, group work on case studies, problem solving sessions and interactions with the instructors.
The goal is to introduce the most basic probabilistic, statistical and simulation tools to face problems where the data do not satisfy the assumption of independence. At the end of the course the student is expected to be able to identify adequate models fitting complex and dependent data, to estimate their parameters, to explore extensions when necessary, and to simulate the corresponding processes or networks, computing related useful quantities like, e.g., expected time to reach absorbing states, expected numbers of recurrences, or measures of variability. The ability to apply the gained knowledge will be verified through class exercises and analysis of simple case studies.
The student is expected to be able to identify adequate models for stochastic systems arising in practical problems in engineering and life sciences, assess their qualitative behavior (e.g. stationarity) and, when possible, compute their most useful quantities, for example, stationary distributions and expected time to reach absorbing states.
The student is expected to be able to fit the models to experimental data and to practically implement the algorithms needed for simulation and inference by himself.
Knowledge of calculus and basic education in probability theory and statistics roughly equivalent to 9 credits are the prerequisites for this course.
Knowledge of calculus and basic education in probability theory and statistics roughly equivalent to 9 credits are the prerequisites for this course.
• Counting and renewal processes - 10 hours;
• Markov chains in discrete and continuous time, and their asymptotics - 12 hours;
• Elementary martingales and Brownian motion - 6 hours;
• ARMA time series and their generalizations (including GARCH time series) - 8 hours;
• Spatial data on continuous and discrete domains - 6 hours;
• Statistics for continuous time processes - 8 hours;
• Multilevel (hierarchical) data and network dependencies - 10 hours;
• Statistical inference and simulation with R, with analysis of some case studies - 20 hours.
• Counting and renewal processes - 10 hours;
• Markov chains in discrete and continuous time, and their asymptotics - 20 hours;
• Elementary martingales and Brownian motion - 10 hours;
• Statistical inference for ODE models observed with noise - 6 hours;
• ARMA and GARCH time series - 6 hours;
• Likelihood or estimating functions based statistical inference for dependent data and Markov processes - 10 hours;
• Simulation of Markov Chains - 5 hours
• Bayesian statistical inference and basic MCMC methods for dependent data and Markov processes - 13 hours;
The hour's count is provisional and may be significantly adapted while the course is run. It is intended to include both the time for seeing the videolectures and the time for Virtual classrooms
In the first part of the course the lectures are held with the support of slides. Exercises are presented and solved in the class as well. In the final part of the course the lessons will mainly consist in activities carried out at the computer lab under the guidance of the teacher. Technical discussions during class lectures will also help to assess the acquired level of knowledge and ability at the different stages of the course.
The course will be held with the method of flipped classrooms. Theoretical lectures will be delivered as video talks for self-study (40-50 hours). Virtual classrooms (30-40 hours) will be organized for exercise sessions, group work on case studies, problem-solving sessions, and interactions with the instructors.
For each topic, the student is expected to listen to the video lectures and understand their content before participating to the VC.
Slides of the lectures, examples of R scripts and exercises with solutions will be available in the website of the course. A list of suggested books will be also provided by the teacher during the first lecture.
Lectures will be delivered as videos through the Exercise platform. Exercises will be proposed for each video lecture.
Reference to written material will be given during the Lectures.
The teaching material might include R code.
Modalità di esame: Prova scritta su carta con videosorveglianza dei docenti; Prova scritta tramite PC con l'utilizzo della piattaforma di ateneo;
L'esame sarà scritto e diviso in due parti.
La prima parte sarà un test a risposta multipla e varrà 8 punti.
Se il punteggio della prima parte sarà almeno pari a 4 si avrà accesso alla seconda parte che consisterà di esercizi tradizionali a risposta aperta. Il punteggio massimo assegnato alla seconda parte sarà di 24 punti.
Il punteggio totale si otterrà sommando i punteggi delle due parti. Punteggi superiori al 30 daranno diritto alla lode.
Exam: Paper-based written test with video surveillance of the teaching staff; Computer-based written test using the PoliTo platform;
The exam is written and divided into two parts.
The first part is a multiple-choice test and weights for a maximum of 6 points.
The student that gets at least 3 points on this part, is admitted to the second part, which consists of traditional exercises with open-ended questions.
The maximum score that can be obtained in the second part is 26.
If the student is admitted to the second part, his/her score is calculated by adding up the scores of the two parts. If the result is greater then 30 the final score is 30L.
Modalità di esame: Prova scritta (in aula); Prova scritta su carta con videosorveglianza dei docenti; Prova scritta tramite PC con l'utilizzo della piattaforma di ateneo;
L'esame sarà scritto e diviso in due parti.
La prima parte sarà un test a risposta multipla e varrà 8 punti.
Se il punteggio della prima parte sarà almeno pari a 4 si avrà accesso alla seconda parte che consisterà di esercizi tradizionali a risposta aperta. Il punteggio massimo assegnato alla seconda parte sarà di 24 punti.
Il punteggio totale si otterrà sommando i punteggi delle due parti. Punteggi superiori al 30 daranno diritto alla lode.
Exam: Written test; Paper-based written test with video surveillance of the teaching staff; Computer-based written test using the PoliTo platform;
The exam is written and divided into two parts.
The first part is a multiple-choice test and weights for a maximum of 6 points.
The student that gets at least 3 points on this part, is admitted to the second part, which consists of traditional exercises with open-ended questions.
The maximum score that can be obtained in the second part is 26.
If the student is admitted to the second part, his/her score is calculated by adding up the scores of the two parts. If the result is greater then 30 the final score is 30L.