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Lecture

Discrepancy Function: Estimation and Applications

In course

MATH-414: Stochastic simulation

The student who follows this course will get acquainted with computational tools used to analyze systems with uncertainty arising in engineering, physics, chemistry, and economics. Focus will be on sampling methods as Monte Carlo, quasi Monte Carlo, Mark ...

Description

This lecture covers the concept of discrepancy function estimation and its applications in various fields. Starting with the basics of Monte Carlo methods, the instructor explains the idea behind constructing estimators and introduces the Quasi Monte Carlo method. The lecture then delves into the construction of discrepancy functions and their significance in generating new sets with low discrepancy. Examples of point sets and lattice structures are discussed to illustrate the practical implications of discrepancy functions.

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Instructor

Fabio Nobile

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Related concepts (29)

Monte Carlo method

Monte Carlo methods, or Monte Carlo experiments, are a broad class of computational algorithms that rely on repeated random sampling to obtain numerical results. The underlying concept is to use randomness to solve problems that might be deterministic in principle. They are often used in physical and mathematical problems and are most useful when it is difficult or impossible to use other approaches. Monte Carlo methods are mainly used in three problem classes: optimization, numerical integration, and generating draws from a probability distribution.

Markov chain Monte Carlo

In statistics, Markov chain Monte Carlo (MCMC) methods comprise a class of algorithms for sampling from a probability distribution. By constructing a Markov chain that has the desired distribution as its equilibrium distribution, one can obtain a sample of the desired distribution by recording states from the chain. The more steps that are included, the more closely the distribution of the sample matches the actual desired distribution. Various algorithms exist for constructing chains, including the Metropolis–Hastings algorithm.

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