Integral

Creator
Creator
Seonglae ChoSeonglae Cho
Created
Created
2022 Apr 5 15:51
Editor
Edited
Edited
2025 Jun 2 15:39

Only a handful of specific integrals are analytically tractable

  • Substitution
  • Coordinate changing such as Polar coordinates
Integral Notion
 
 
 

The stochasticity trick of Monte Carlo method (
Importance sampling
)

Assume you have a difficult integral to compute
The Monte Carlo estimator for performs better than sampling from the original distribution when it has lower variance. For comparison, the variance of is , while the variance of is - with lower variance being preferable.
In short, Monte Carlo methods enable us to estimate any integral by random sampling. In
Bayesian Statistics
,
Evidence
is also form of integral so it becomes tractable.
 
 
 
 
 

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