The Power of Sampling by Peter W. Glynn
Offered By: International Centre for Theoretical Sciences via YouTube
Course Description
Overview
Syllabus
Date: 14 August 2019, 16:00 to
Introduction to speaker
The Power of Sampling
What should a well-educated scientist know about sampling?
Thesis of Lecture:
According to Wikipedia:
Some History:
First sampling-based survey:
Second known instance of sampling
Today, statistical sampling is used everywhere
Such randomized trials form one setting where one can legitimately claim evidence of a causal effect
Key Philosophical Underpinning:
1936 US Presidential Election
Problems with Literary Digest survey:
Moral of the Story:
Subtle modifications in sampling can have a big impact
Why?
Many other such subtleties exist in applying sampling methods
Active research area:
Sampling in Computational Mathematics
High-dimensional Integration:
High-level Perspective:
History
Analysis of Monte Carlo Method:
If it's so slow, why is it so widely used?
The Numerical Alternative to Monte Carlo
Better integration rules:
Tracking discontinuities is easy in d = 1
Versatility of Monte Carlo Method:
"Curse of Dimensionality"
Result
What about Monte Carlo?
Example: Compute volume of region A c [0, 1]d
So, Monte Carlo is dimensionally insensitive...
Coding Flexibility and Visualization: Aan Example
Modify model so that time spent in just one state is non-exponential...
Monte Carlo Alternative:
A Key Difference between Statistical Sampling and Monte Carlo Sampling
Sampling in Synthesizing Distributed Controls
The agents typically need state information to make good decisions
Example: Assigning incoming jobs to servers on a server farm
Approach 1: Centralized controller assigns incoming jobs to shortest queue
Sampling plays a key role in many machine learning algorithms
Final words:
Q&A
Taught by
International Centre for Theoretical Sciences
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