**Statistical Measures of
Uncertainty in Inverse Problems**

**Inverse Problems as
Statistics**

**Forward Problems in
Geophysics**

**Elements of the Statistical
View**

**Deterministic and
Statistical Perspectives: Connections**

**Linear Forward Problems,
contd.**

**Ex: Sampling w/ systematic
and random error**

**Backus-Gilbert ^{++}:
Necessary conditions**

**Backus-Gilbert ^{++}:
Sufficient Conditions**

**Minimax is Bayes for least
favorable prior**

**Common Risk: Mean Distance
Error (MDE)**

**Minimax Estimation of Linear
parameters:
Hilbert Space, Gaussian error**

**Consistency in Linear
Inverse Problems**