Monte Carlo methods and sampling for computing

Information

• Lecturer: Dr. Francesco Banterle.
• Period: 2nd Term

Abstract

This course introduces students to Monte Carlo methods and sampling techniques with a focus on visual computing. These are crucial to accelerating the computations of a variety of computational simulations where we need to draw high-quality samples or to integrate a complex multi-dimensional function such as physically-based rendering for computing the radiance of buildings, estimating the price of options, or how epidemics spread out. At the end of this course, students will have both theoretical and practical tools that they can apply to a variety of problems to achieve high-quality solutions. During the course, students will see and study successful examples of this beautiful theory to visual computing; e.g., visual processing, computational finance and biology.

Lectures

• Introduction; code.
• Monte-Carlo Estimation; code.
• Monte-Carlo Integration; code.
• Uniform Random Numbers; code.
• Non Uniform Random Numbers; code.
• Variance Reduction techniques; code.
• Quasi Monte-Carlo; code.
• Monte-Carlo Applications.

Books

• Monte-Carlo: theory, method and examples by Art Owen.
• Physically-Based Rendering by Matt Pharr, Wenzel Jakob, and Greg Humphreys.

Exam

At this link, there is a list of programming projects and publications (seminar) for the exam.