Mediaspace scheduled maintenance: Aug 25, 2026 07:00 - 12:00 AM. During this time, videos will be temporarily unavailable. Check status updates.

Lecture

Stochastic Simulation: Rare Events and Crude Monte Carlo

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 topic of stochastic simulation, focusing on rare events and the Crude Monte Carlo method. The instructor explains the importance of generating enough realizations and introduces the concept of thresholds. The lecture discusses the process of choosing parameters and the algorithm for adaptive cross-entropy. It also delves into the idea of introducing thresholds and the significance of closed-form expressions in simulations.

This video is available exclusively on Mediaspace for a restricted audience. Please log in to MediaSpace to access it if you have the necessary permissions.

Watch on Mediaspace

Instructor

Fabio Nobile

Official source

Related concepts (31)

Cross-entropy method

The cross-entropy (CE) method is a Monte Carlo method for importance sampling and optimization. It is applicable to both combinatorial and continuous problems, with either a static or noisy objective. The method approximates the optimal importance sampling estimator by repeating two phases: Draw a sample from a probability distribution. Minimize the cross-entropy between this distribution and a target distribution to produce a better sample in the next iteration.

Cyrillic script

The Cyrillic script (sᵻˈɹɪlᵻk ), Slavonic script or the Slavic script is a writing system used for various languages across Eurasia. It is the designated national script in various Slavic, Turkic, Mongolic, Uralic, Caucasian and Iranic-speaking countries in Southeastern Europe, Eastern Europe, the Caucasus, Central Asia, North Asia, and East Asia, and used by many other minority languages. around 250 million people in Eurasia use Cyrillic as the official script for their national languages, with Russia accounting for about half of them.

Genetic algorithm

In computer science and operations research, a genetic algorithm (GA) is a metaheuristic inspired by the process of natural selection that belongs to the larger class of evolutionary algorithms (EA). Genetic algorithms are commonly used to generate high-quality solutions to optimization and search problems by relying on biologically inspired operators such as mutation, crossover and selection. Some examples of GA applications include optimizing decision trees for better performance, solving sudoku puzzles, hyperparameter optimization, causal inference, etc.

Stochastic optimization

Stochastic optimization (SO) methods are optimization methods that generate and use random variables. For stochastic problems, the random variables appear in the formulation of the optimization problem itself, which involves random objective functions or random constraints. Stochastic optimization methods also include methods with random iterates. Some stochastic optimization methods use random iterates to solve stochastic problems, combining both meanings of stochastic optimization.

Stochastic

Stochastic (stəˈkæstɪk; ) refers to the property of being well described by a random probability distribution. Although stochasticity and randomness are distinct in that the former refers to a modeling approach and the latter refers to phenomena themselves, these two terms are often used synonymously. Furthermore, in probability theory, the formal concept of a stochastic process is also referred to as a random process.

Related lectures (8)

Renormalization: AQFT

Covers the concept of renormalization in Algebraic Quantum Field Theory.

Central Potentials in Quantum Physics

Explores central potentials in quantum physics, focusing on commutation relations and diagonalization processes.

Efficient Stochastic Numerical Methods

Explores efficient stochastic numerical methods for modeling and learning, covering topics like the Analytical Engine and kinase inhibitors.

Stochastic Simulation: Uncertainty Quantification Log in to Mediaspace to watch this video

Explores uncertainty quantification using Quasi Monte Carlo methods and discrepancy measures for integral approximation and volume estimation.

Stochastic Simulation: Markov Chains and Monte Carlo Log in to Mediaspace to watch this video