1. Virtual data and ANTIDATA
Carlos Rodriguez SUNY Albany.
copyMEright by C. Rodriguez. Please copy me!

2. Inference

5. Geometrization of Inferenceq*
Truth: t(x)
Model: { p(x|q)}
Geometrization of Inference

6. Embedding in Hilbert Space
Fisher Information metric automagically induced on the tangent bundle !

7. The Volume Form as Prior
A hypothesis space M is said to be regular when (M,g) is a smooth orientable riemannian manifold. A k-dim regular M has volume form:
In arbitrary (orientation preserving) theta coordinates the volume of (M,g) is:

8. Ex: Simple Logistic Regression
Racine’s data
Dose (log g/ml) x
No. of animals n
No. of deaths y
-0.863 5
-0.296 1
-0.053 3
0.727
independent.
log (odds of death) = a + b x
logit(p) = log p/(1-p)
Need: Ignorance Prior on (a,b)

9. Ignorance for Logistic Regression
Racine’s data
MCMC: 1000 samples
mean a = 0.091
sd = 3.94
corr[a,b] = 0.56
Mean b = 0.14
sd = 9.36
Ignorance for Logistic Regression

10. Posterior Inference Logistic Regression Racine’s data

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13. To Herb