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Sampling in Computational Mathematics
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Classroom Contents
The Power of Sampling by Peter W. Glynn
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- 1 Date: 14 August 2019, 16:00 to
- 2 Introduction to speaker
- 3 The Power of Sampling
- 4 What should a well-educated scientist know about sampling?
- 5 Thesis of Lecture:
- 6 According to Wikipedia:
- 7 Some History:
- 8 First sampling-based survey:
- 9 Second known instance of sampling
- 10 Today, statistical sampling is used everywhere
- 11 Such randomized trials form one setting where one can legitimately claim evidence of a causal effect
- 12 Key Philosophical Underpinning:
- 13 1936 US Presidential Election
- 14 Problems with Literary Digest survey:
- 15 Moral of the Story:
- 16 Subtle modifications in sampling can have a big impact
- 17 Why?
- 18 Many other such subtleties exist in applying sampling methods
- 19 Active research area:
- 20 Sampling in Computational Mathematics
- 21 High-dimensional Integration:
- 22 High-level Perspective:
- 23 History
- 24 Analysis of Monte Carlo Method:
- 25 If it's so slow, why is it so widely used?
- 26 The Numerical Alternative to Monte Carlo
- 27 Better integration rules:
- 28 Tracking discontinuities is easy in d = 1
- 29 Versatility of Monte Carlo Method:
- 30 "Curse of Dimensionality"
- 31 Result
- 32 What about Monte Carlo?
- 33 Example: Compute volume of region A c [0, 1]d
- 34 So, Monte Carlo is dimensionally insensitive...
- 35 Coding Flexibility and Visualization: Aan Example
- 36 Modify model so that time spent in just one state is non-exponential...
- 37 Monte Carlo Alternative:
- 38 A Key Difference between Statistical Sampling and Monte Carlo Sampling
- 39 Sampling in Synthesizing Distributed Controls
- 40 The agents typically need state information to make good decisions
- 41 Example: Assigning incoming jobs to servers on a server farm
- 42 Approach 1: Centralized controller assigns incoming jobs to shortest queue
- 43 Sampling plays a key role in many machine learning algorithms
- 44 Final words:
- 45 Q&A
