Lectures related to Master's in Mechanical Engineering Structure

Physics Assistantship: Electromagnetism Coordination

Covers the coordination of physics assistantship for electromagnetism course.

Confidence Intervals: Student, Asymptotic Wald

Covers confidence intervals for Gaussian means, Student distribution, and Wald confidence intervals for maximum likelihood estimators.

Estimation and Confidence Intervals

Explores bias, variance, and confidence intervals in parameter estimation using examples and distributions.

Probability Distributions: Central Limit Theorem and Applications

Discusses probability distributions and the Central Limit Theorem, emphasizing their importance in data science and statistical analysis.

Introduction to Continuous Random Variables: Probability Distributions

Introduces continuous random variables and their probability distributions, emphasizing their applications in statistics and data science.

Scale-Free Networks: Power Laws and Preferential Attachment

Explores scale-free networks, power laws, preferential attachment, and network assortativity.

Continuous Random Variables: Basic Ideas

Explores continuous random variables and their properties, including support and cumulative distribution functions.

Copulas and Extreme Values

Explores copulas for measuring dependence strength in distributions and transforming variables to unit Fréchet margins.

Statistical Analysis of Network Data

Explores epidemics in network data, covering SIR model, basic reproductive ratio, percolation, directed networks, and maximum likelihood estimation.

Generalization Error

Explores generalization error in machine learning, focusing on data distribution and hypothesis impact.

Sampling Theory: Statistics for Mathematicians

Covers the theory of sampling, focusing on statistics for mathematicians.

Probability and Statistics

Covers inequalities, joint Gaussian distribution, risk estimation, and classification method testing in probability and statistics.

Multivariate Statistics: Wishart and Hotelling T²

Explores the Wishart distribution, properties of Wishart matrices, and the Hotelling T² distribution, including the two-sample Hotelling T² statistic.

Heavy-Tailed Distributions

Explores heavy-tailed distributions, the Hill estimator, convergence to Gaussian, and distribution comparison.

Advanced Probabilities: Random Variables & Expected Values

Explores advanced probabilities, random variables, and expected values, with practical examples and quizzes to reinforce learning.

Node Degree and Strength

Explores node degree and strength in network neuroscience, discussing random vs real networks and the challenges of fitting power laws to real data.

Sampling Distributions: Theory and Applications

Explores sampling distributions, estimators' properties, and statistical measures for data science applications.

Distributions & Interpolation Spaces

Covers distributions, interpolation spaces, convergence, and the concept of dual spaces.

Handling Network Data

Covers handling network data, types of graphs, centrality measures, and properties of real-world networks.

Estimators and Confidence Intervals

Explores bias, variance, unbiased estimators, and confidence intervals in statistical estimation.