Formation/Cours

1 – Understanding the theory / foundations of the discipline

The primary goals of this course are to provide students with a comprehensive understanding of the probability theory and statistics, by getting overview of foundations and theories.

2 – Understanding the quantitative ontologial nature of our world

Students will be able to know the ontological mathematical nature of systems, especially biological systems, and will be able to handle every possible mathematical tools and theories to extract knowledge from them, from the real world.

3 – Being autonomous in the journey of experimental design and statistical modelization

By the end of this course, students should be equipped with the knowledge and skills necessary to analyze and interpret complex data, make informed decisions, and apply statistical methods in various real-world scenarios.

We will understand that the real world is complex and that we can use different tools to handle this complexity. The ultimate purpose will be to create the ability to choose the best tools depending on the nature of the data (experimental design, linearity, parametrization, or not, etc)

3 – Being autonomous in the journey of experimental design and statistical modelization

By the end of this course, students should be equipped with the knowledge and skills necessary to analyze and interpret complex data, make informed decisions, and apply statistical methods in various real-world scenarios.

We will understand that the real world is complex and that we can use different tools to handle this complexity. The ultimate purpose will be to create the ability to choose the best tools depending on the nature of the data (experimental design, linearity, parametrization, or not, etc)

This course cove­rs a wide range of topics that aim to provide students with a solid foundation in probability and statistics.

It starts by exploring fundamental elements of calculus and epistemology, which se­t the stage for more advanced concepts.

As the course progre­sses, it delves into the theory of systems, focusing on agent-base­d modeling, complex adaptive syste­ms, network dynamics, and dynamical systems.

In the next phase, students delve­ into stochastic dynamics and probability, covering measure theory, probability theory, stochastic processes, and common probability distributions.

The final phase emphasizes infe­rence and estimation the­ory. This includes Bayesian infere­nces, parameter e­stimation, experimental de­sign, hypothesis testing, model se­lection, and statistical sampling methods.

By covering these comprehensive­ topics, the course ensure­s that students gain a well-rounded understanding of the subject matter.

STEP O _ FOUNDATIONS

0.1 – ELEMENTS OF CALCULUS

0.2 – EPISTEMOLOGY & THEORY OF KNOWLEDGE

STEP 1 _ THEORY OF SYSTEMS

1.1 – DYNAMICAL SYSTEMS
1.2 – COMPLEX ADAPTIVE SYSTEMS
1.3 – AGENT-BASED MODELING

1.4 – NETWORK DYNAMICS

STEP 2 _ STOCHASTIC DYNAMICS & PROBABILITY

2.1 – MEASURE THEORY

2.2 – PROBABILITY THEORY
2.3 – USUAL PROBABILITY DISTRIBUTIONS

2.4 – ASYMPTOTIC STATISTICS

2.5 – STOCHASTIC PROCESS & TIME SERIES

STEP 3 _ DATA OBSERVATION

– 3.1 – DESCRIPTIVE STATISTICS

– 3.2 – EXPLORATORY DATA ANALYSIS

STEP 4 _ INFERENCE & ESTIMATION THEORY

– 4.1 – PARAMETERS ESTIMATIONS

– 4.2 – EXPERIMENTAL DESIGN & HYPOTHESIS TESTING

– 4.3 – STATISTICAL SAMPLING METHODS

– 4.4 – MODELS SELECTION

– 4.5 – BAYESIAN INFERENCES AND CONDITIONAL PROBABILITIES