[ИАД, осень 2026] Байесовское мультимоделирование I. Лекция 2

[ИАД, осень 2026] Байесовское мультимоделирование I. Лекция 2

[IAD, fall 2026] Bayesian multi-modeling I. Lecture 2

🎙 Machine Learning – Intelligent Systems 👥 8K 📅 October 2, 2026 ⏱ 75 min 👁 1 📄 tutorial 🧭 2026-10-02
Available in: English (current) Français

Keywords

maximum likelihoodbeta distributionDirichletsoftmaxvon Mises

Summary

The lecture begins with a Bayesian formulation of learning, where the goal is to uncover the process generating data. It then reviews the coin toss example, introducing Bernoulli distribution and maximum likelihood estimation (MLE). Properties of MLE are discussed including consistency, asymptotic normality, efficiency, and invariance. The link between MLE and Kullback-Leibler divergence is demonstrated. The instructor then covers measures of central tendency (mean, median, mode), skewness, and kurtosis, illustrating why they differ in skewed distributions. Empirical PDF estimation and kernel density smoothing are briefly described. Several probability distributions are introduced: Bernoulli and Beta with conjugate prior interpretation, softmax and multinomial, Dirichlet as a generalization of Beta, normal and Student’s t with heavy tails. Finally, circular distributions like von Mises and Kent are mentioned, highlighting their relevance to periodic data. The lecture is a comprehensive yet accessible review aimed at building foundations for Bayesian multimodeling.

145 words

Critical Evaluation

Value of the Information & Strength of the Argument

The lecture offers valuable pedagogical content by systematically revising fundamental concepts and connecting them to Bayesian inference. The argumentation is solid: mathematical derivations for MLE properties and KL divergence are presented clearly, and examples like the coin toss illustrate the intuition. The inclusion of less common topics such as circular distributions broadens the perspective. However, the lecture is more of a review than an original contribution; its value lies in synthesis and clarity rather than novelty.

Scientific Rigor, Source Quality, Title Accuracy

Scientific rigor is moderate; the instructor references textbooks (e.g., ‘How to Lie with Statistics’) and internal courses but provides no formal citations. The title matches the content, as it is a foundational lecture for a Bayesian multimodeling course. The material is standard and aligns with mainstream statistics, so reliability is high despite informal sourcing. The adéquation titre/contenu is adequate; the lecture is a faithful introduction to Bayesian concepts.

159 words

Title / Content Match

The title indicates a Bayesian multimodeling lecture; content matches as it covers core Bayesian concepts and distributions, though it is more of a review/revision lecture.

Quality & Reliability

7/10

The lecture provides a solid overview of foundational distributions and Bayesian inference, with clear derivations and examples. However, sources are informal (mentions of textbooks and courses) and no formal citations are given.

Key Moments

Cited Sources

  • How to Lie with Statistics — Mentioned as an example of using different central tendency measures.
  • Course by Andrey Gribovoy on applied statistics — Referenced for terminology on score function and other statistical concepts.

Contribution & Novelties

This lecture contributes by providing a structured review of probability distributions with an emphasis on their roles in Bayesian inference. It highlights the parametrization of softmax and Dirichlet with temperature, which is a less standard presentation. The connections between Bernoulli-Beta and multinomial-Dirichlet as conjugate pairs are clearly articulated, serving as a pedagogical bridge.

Pour aller plus loin :

91 words

Radar Profile

The radar profile shows a balanced lecture with high reliability and quantity of information, moderate technical level, and good quality. The strengths are in coverage and trustworthiness, while the technical depth is not extremely advanced, making it accessible to a broad audience.

Reliability 8/10