Rasch model

[dustinvtran]

A simple implementation of the Rasch model in item response theory. (also see #346)

python rasch_model.py
## Iteration    1 [  0%]: Loss = 5476.080
## Iteration  250 [ 10%]: Loss = 3062.469
## Iteration  500 [ 20%]: Loss = 3072.561
## Iteration  750 [ 30%]: Loss = 3062.746
## Iteration 1000 [ 40%]: Loss = 3062.882
## Iteration 1250 [ 50%]: Loss = 3058.824
## Iteration 1500 [ 60%]: Loss = 3067.787
## Iteration 1750 [ 70%]: Loss = 3061.325
## Iteration 2000 [ 80%]: Loss = 3060.995
## Iteration 2250 [ 90%]: Loss = 3060.363
## Iteration 2500 [100%]: Loss = 3063.963
## MSE between true traits and inferred posterior mean:
## 0.202594817092

Plot of the true traits by the inferred posterior means.

Reviewer suggestions:

Would love it if you took a look @mdzeig. Otherwise I'll just merge it.

[mdzeig]

Checked the code. Everything looks good. Some time soonish, I will update add hyper priors for the threshold parameter to get things into state that IRT people will use. Thanks!

[dustinvtran]

sure, that would be awesome