veyepar: SymPy Stats - Uncertainty Modeling

Author(s):	Matthew Rocklin
Location	Ballroom (CDE)
Date	jul Wed 18	Days Raw Files
Start	14:45	First Raw Start	14:44
Duration	20:00	Offset	0:00:09
End	15:05	Last Raw End	15:30
Chapters	00:00 0:02:22 0:11:35 0:15:59 0:16:38
Total cuts_time	17 min.

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SymPy is a symbolic algebra package for Python. In SymPy.Stats we add a 
stochastic variable type to this package to form a language for uncertainty 
modeling. This allows engineers and scientists to symbolically declare the 
uncertainty in their mathematical models and to make probabilistic queries. We 
provide transformations from probabilistic statements like $P(X*Y > 3)$ or 
$E(X**2)$ into deterministic integrals. These integrals are then solved 
using SymPy's integration routines or through numeric sampling.

This talk touches on a few rising themes:
 * The rise in interest in uncertainty quantification and 
 * The use of symbolics in scientific computing 
 * Intermediate representation layers and multi-stage compilation

Historically solutions to uncertainty quantification problems have been 
expressed by writing Monte Carlo codes around individual problems. By creating 
a symbolic uncertainty language we allow the expression of the 
problem-to-be-solved to be written separately from the numerical technique. 
SymPy.stats  serves as an interface layer. The statistical programmer doesn't 
need to think about the details of numerical techniques and the computational 
methods programmer doesn't need to think about the particular domain-specific 
questions to be solved.

We have implemented multiple comptuational backends including purely symbolic 
(using SymPy's integration engine), sampling, and code generation.

In the talk we discuss these ideas with a few illustrative examples taken from 
basic probability and engineering. The following is one such example

http://sympystats.wordpress.com/2011/07/02/a-lesson-in-data-assimilation-using-sympy/

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