Virtual data and ANTIDATA http://omega.albany.edu:8008/antidata.pdf Carlos Rodriguez SUNY Albany. copyMEright by C. Rodriguez. Please copy me!

Inference

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

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

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:

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)

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

Posterior Inference Logistic Regression Racine’s data

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