Lecture

Probability and Statistics

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In course

MATH-232: Probability and statistics (for IC)

Cours d'introduction à la théorie des probabilités et aux statistiques. ...

Description

This lecture covers the fundamental concepts of probability and statistics, providing mathematical tools for the study of random events, network modeling, stochastic algorithms, and more. Topics include distributions, expectation, variance, statistical inference, likelihood, and combinatorics. The course also discusses the importance of understanding material rather than memorization during exams.

Instructors (2)

Emmanuel Abbé

Teaching & PhD PhD Students Denys Pushkin, Ortal Yona Senouf, Vladyslav Shashkov Past EPFL PhD Students Elisabetta Cornacchia, Aryo Lotfi Courses Reasoning in artificial intelligence MATH-700 Large language models have raised the potential of artificial intelligence in various applications, including science and mathematics, but their reasoning capabilities remain under investigations. This class focuses on defining, measuring and improving the reasoning capabilities of such AI models. Awa

Raphaël Jean Berthier

Official source

Ontological neighbourhood

Statistics

Statistical inference: Mathematical statistics, Statistical hypothesis testing

Related concepts (32)

Probability density function

In probability theory, a probability density function (PDF), density function, or density of an absolutely continuous random variable, is a function whose value at any given sample (or point) in the sample space (the set of possible values taken by the random variable) can be interpreted as providing a relative likelihood that the value of the random variable would be equal to that sample.

Conditional probability distribution

In probability theory and statistics, given two jointly distributed random variables and , the conditional probability distribution of given is the probability distribution of when is known to be a particular value; in some cases the conditional probabilities may be expressed as functions containing the unspecified value of as a parameter. When both and are categorical variables, a conditional probability table is typically used to represent the conditional probability.

Probability distribution

In probability theory and statistics, a probability distribution is the mathematical function that gives the probabilities of occurrence of different possible outcomes for an experiment. It is a mathematical description of a random phenomenon in terms of its sample space and the probabilities of events (subsets of the sample space). For instance, if X is used to denote the outcome of a coin toss ("the experiment"), then the probability distribution of X would take the value 0.5 (1 in 2 or 1/2) for X = heads, and 0.

Binomial coefficient

In mathematics, the binomial coefficients are the positive integers that occur as coefficients in the binomial theorem. Commonly, a binomial coefficient is indexed by a pair of integers n ≥ k ≥ 0 and is written It is the coefficient of the xk term in the polynomial expansion of the binomial power (1 + x)n; this coefficient can be computed by the multiplicative formula which using factorial notation can be compactly expressed as For example, the fourth power of 1 + x is and the binomial coefficient is the coefficient of the x2 term.

Bayes factor

The Bayes factor is a ratio of two competing statistical models represented by their evidence, and is used to quantify the support for one model over the other. The models in questions can have a common set of parameters, such as a null hypothesis and an alternative, but this is not necessary; for instance, it could also be a non-linear model compared to its linear approximation. The Bayes factor can be thought of as a Bayesian analog to the likelihood-ratio test, although it uses the (integrated) marginal likelihood rather than the maximized likelihood.

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Related concepts (32)

Probability density function

Conditional probability distribution

Probability distribution

Binomial coefficient

Bayes factor