PYTHON AND STATISTICAL INFERENCE - Bryant University
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PYTHON AND STATISTICAL INFERENCE Brian Blais Science and Technology Bryant University Monday, May 7, 12
Transcript of PYTHON AND STATISTICAL INFERENCE - Bryant University
PYTHON AND STATISTICAL INFERENCE
Brian BlaisScience and TechnologyBryant University
Monday, May 7, 12
WHAT IS PYTHON?Flexible,powerful language
Multiple programming paradigms
Easy, clean syntax
Large community of support
“Batteries included”
Free as in “free beer”
Free as in “free speech”
http://www.python.org
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NUMERICAL PYTHON
http://www.enthought.com/
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FILE FORMATS
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EXAMPLE DATA
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EXAMPLE DATA
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TRANSFORMING DATA
Example log transform of population
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PLOTTING DATA
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INTERFACE WITH R
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INFERENCE IN PHYSICS(Or Why I Don’t Do This Sort of Analysis Often)
•In the physical sciences one often has much more prior information about the causal structure in the problem•Often more concerned with parameter estimation and model comparison than correlation detection
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DATA NEVER SEEN IN THE SOCIAL SCIENCES
Swiss Astronomer Rudolf Wolf (1816-1893)
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ELONGATED DICE
1 cm
1 cm
(1 + r) cm
Surface Area Model
p1 = p2 = p5 = p6 =1 + r
6 + 4r
p3 = p4 =1
6 + 4r
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BAYESIAN ANALYSIS
p(r|data) ⇠ p(data|r)p(r) # n
1 3246
2 3449
3 2897
4 2841
5 3635
6 3923
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PYTHON
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CLIMATE EXAMPLE
Is there evidence of an oscillation here?More than one?
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BAYESIAN ANALYSIS BRETTHORST, 1988
data
model
Gaussian noise
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BAYESIAN ANALYSIS BRETTHORST, 1988
likelihood
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BAYESIAN ANALYSIS BRETTHORST, 1988
•integrate out the B1 and B2 (uniform priors)•we don’t know the noise level - integrate it out•interested only in the frequency
C(w) is the Schuster periodogram, related to the FFT
This is the “Student” t-distribution
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NUMERICAL ANALYSIS
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BAYESIAN REGRESSION
order Log Likelihood
1 1.2
2 18.2
3 18.9
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BAYESIAN REGRESSION
order Log Posterior
1 -4.8
2 9.2
3 6.9
Automatic penalty for
more complex models
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THANKS!
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