Uncovering Meaning Amidst Randomness! || A Beginner's Guide to Monte Carlo Integration

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🎲 Welcome to our deep dive into Monte Carlo Integration! 🎲
In this video, we're unraveling the mysteries of one of the most intriguing and powerful mathematical techniques used in various fields from finance to physics: Monte Carlo Integration. Perfect for students, professionals, and anyone with a curiosity for mathematics and computational methods!
🔍 What You'll Learn:
1. Monte Carlo Integration Explained: Understand the basics of Monte Carlo methods and how they apply to integration.
2. Real-World Applications: Discover how Monte Carlo Integration is used in real-world scenarios.
3. Step-by-Step Tutorial: Follow a simple, yet comprehensive guide on implementing Monte Carlo Integration with practical examples.
4. Comparisons and Advantages: Learn how Monte Carlo differs from traditional integration techniques and its unique advantages.
Common Pitfalls and Solutions: Get insights into common challenges and how to overcome them effectively.
📘 Chapters:
0:00 - Intro
1:45 - Simple Example
3:41 - Why MC Integration is Useful
6:48 - Quick Review of Expected Values
9:56 - Finding the EV of the MC Estimator
12:43 - Deriving the General MC Estimator
15:24 - Quick Review of Variance
17:06 - Finding the Variance of the MC Estimator
18:14 - Obtaining Zero Variance
19:25 - Sampling Custom Functions
20:01 - Inversion Method
22:56 - Rejection Method
24:59 - Complex Example
27:33 - Conclusion
🔗 Resources:
GitHub Repo (WIP, check dev branch for now): github.com/Sourish07/Monte-Ca...
All content on this channel is produced by and is the intellectual property of Sourish Kundu LLC.

Опубликовано:

15 июн 2024

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Комментарии : 11

@jsierra88 3 месяца назад

This is such a nice introduction to MC! Thank you.

@sourishk07 3 месяца назад

I'm really glad you enjoyed the video! Thanks for the comment

@sohamkundu9685 5 месяцев назад

Very good

@sourishk07 5 месяцев назад

Thanks for watching!

@Chak29 5 месяцев назад

this video is awesome! Idk if i missed it, but I am curios how you learned this, was it classes at uni, work, or a personal thing?

@sourishk07 5 месяцев назад

Thank you! I’m glad you enjoyed it. I initially learned this all on my own through reading different textbooks and articles. Later on though, one of my classes at Madison did cover it.

@undertaker7523 4 месяца назад

Please make that video on Ray tracing

@sourishk07 4 месяца назад

Thank you for expressing your interest! Ray tracing is one of my favorite topics and I can't wait to get started on that video!

@kevin-nf5ub 3 месяца назад

what application to no limit texas holdem would this have??

@sourishk07 3 месяца назад

Hey! Thanks for the question. From my rudimentary understanding of poker, there isn't necessarily a function that one needs to integrate. However, the concept of Monte Carlo simulations in general has huge applicability here. It could be used to estimate the likelihood of each hand winning or various other probabilities that would be useful to the players. You would simply simulate a large number of poker hands with a computer and watch the probability estimates converge to the true values.

@kevin-nf5ub 3 месяца назад

@@sourishk07Thanks Dr. K, I will be using this as a holy instrument to unleash the wrath of the almighty against local donkeys, fish, and heathens.