- Unit Coordinator: Agnieszka Kulawik
- ECTS Credits: 6
- Semester: 1
- Year: 2
- Campus: University of Silesia in Katowice
- Language: English
- Aims:
The aim of the Statistics unit is to get a deep knowledge on constructing statistical models and making statistical analysis, and to improve the skills of using statistical computer packages.
- Content:
1. Organising statistical analysis: collecting and data, their analysis and graphical description.
2. Linear and non-linear statistical models – estimation theory and statistical hypotheses testing.
3. Applications of linear and non-linear statistical models in econometrics and financial mathematics.
4. Parametric tests of significance involving two or more samples.
5. Conformity tests.
6. Non-parametric tests of significance involving two or more samples.
7. Applications of statistical computer software to estimation and statistical testing.
- Unit Coordinator: Rémi Catellier
- Programme: InterMaths
- ECTS Credits: 6
- Semester: 1
- Year: 1
- Campus: University of Côte d'Azur
- Language: English
- Delivery: In-class
- Aims:
The purpose of the course is to teach the basics of the theory of stochastic processes, which has become a standard tool in the modelling of biological neural networks.
The course will focus in particular on the Brownian motion, on stochastic calculus and on diffusion processes, with the integrate and fire model as a benchmark example.
Markov property and martingale theory will be also addressed in this framework, with possible extensions to some jump processes like those used in ion channel models.
- Content:
• Brownian motion
• Stochastic Calculus
• Diffusion Processes
• Markov Property
• Martingales
• Integrate and fire model
• Ion channel models - Pre-requisites:
Probability with measure theory
- Unit Coordinator: Cédric Bernardin
- ECTS Credits: 6
- Semester: 1
- Year: 2
- Campus: University of Côte d'Azur
- Language: English
- Aims:
The purpose of the course is to teach the basics of the theory of stochastic processes, which has become a standard tool in the modelling of biological neural networks.
The course will focus in particular on the Brownian motion, on stochastic calculus and on diffusion processes, with the integrate and fire model as a benchmark example.
Markov property and martingale theory will be also addressed in this framework, with possible extensions to some jump processes like those used in ion channel models.
- Content:
- Brownian motion
- Stochastic Calculus
- Diffusion Processes
- Markov Property
- Martingales
- Integrate and fire model
- Ion channel models
- Pre-requisites:
Probability with measure theory
- Unit Coordinator: François Delarue
- ECTS Credits: 6
- Semester: 1
- Year: 2
- Campus: University of Côte d'Azur
- Language: English
- Aims:
The course has two purposes. The first one is to provide the basic knowledge in stochastic control, control for discrete and continuous processes, dynamic programming principle, dynamic programming equation, Hamilton-Jacobi-Bellman equation.
The second part of the course will address interacting particle systems, as some of them are now currently used in the modelling of large neural networks. Applications to self-organisation and phase transition in neuroscience will be considered and, in connection with the first part of course, some learning methods will be discussed as well.
- Content:
- Stochastic control
- Dynamic programming principle
- HJB equation, interacting particle system
- Mean field models
- Learning methods
- Pre-requisites:
Probability with measure theory, optimization, stochastic calculus
