Ce cours apparaît dans les formations suivantes :
• Ecole Du Numérique (EDN) - Master 1 DATA Management In Biosciences - S1 - 3 ECTS

Pré requis

No prerequisite skills.
Take with you : attention, curiosity, and passion.

Objectifs du 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)

Contenu du cours

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

Modalités d'enseignement

Organisation du cours

The structure of the course highlight a methodology that is not simply to learn probability and statistics. The cours create an holistic perspective to understand living / biological systems.

Because we are both the instructor and students biological living systems, we will create connections between the discipline and our real-world problems, real epistemological dilemmas, real problems we would like to solve.

The cours is not a course that's off the beaten track, detached from reality or overly theoretical, but rather a connection to reality.The education method employed in this course is designed to foster active learning and critical thinking.

Students will engage in lectures, discussions, and practical exercises to grasp theoretical concepts and apply them to real-world problems. The course promotes collaborative learning, encouraging students to work together on assignments and projects, enhancing their problem-solving skills and teamwork abilities. Additionally, regular assessments and feedback mechanisms will help student progress and provide opportunities for improvement.

In one world: engagement.

THEORETICAL LEARNING

Presentation of slides using a video projector

Schematization on the board

ACTIVE LEARNING WITH THE INSTRUCTOR

Group exercise

Debate

Collective problem exploration

APPLICATIONS

A capstone project by groups at the middle of the semester

Méthodes pédagogiques

Évaluation