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

Monday, May 7, 12

NUMERICAL PYTHON

http://www.enthought.com/

Monday, May 7, 12

FILE FORMATS

Monday, May 7, 12

EXAMPLE DATA

Monday, May 7, 12

EXAMPLE DATA

Monday, May 7, 12

TRANSFORMING DATA

Example log transform of population

Monday, May 7, 12

PLOTTING DATA

Monday, May 7, 12

INTERFACE WITH R

Monday, May 7, 12

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

Monday, May 7, 12

DATA NEVER SEEN IN THE SOCIAL SCIENCES

Swiss Astronomer Rudolf Wolf (1816-1893)

Monday, May 7, 12

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

Monday, May 7, 12

BAYESIAN ANALYSIS

p(r|data) ⇠ p(data|r)p(r) # n

1 3246

2 3449

3 2897

4 2841

5 3635

6 3923

Monday, May 7, 12

PYTHON

Monday, May 7, 12

CLIMATE EXAMPLE

Is there evidence of an oscillation here?More than one?

Monday, May 7, 12

BAYESIAN ANALYSIS BRETTHORST, 1988

data

model

Gaussian noise

Monday, May 7, 12

BAYESIAN ANALYSIS BRETTHORST, 1988

likelihood

Monday, May 7, 12

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

Monday, May 7, 12

NUMERICAL ANALYSIS

Monday, May 7, 12

BAYESIAN REGRESSION

order Log Likelihood

1 1.2

2 18.2

3 18.9

Monday, May 7, 12

BAYESIAN REGRESSION

order Log Posterior

1 -4.8

2 9.2

3 6.9

Automatic penalty for

more complex models

Monday, May 7, 12

THANKS!

Monday, May 7, 12