Title: A Statistical Perspective on Inverse and Inverse Regression Problems,
Abstract: Inverse problems, where in broad sense the task is to learn from the noisy
response about some unknown function, usually represented as the argument of
some known functional form, has received wide attention in the general
scientific disciplines. How- ever, in mainstream statistics such inverse
problem paradigm does not seem to be as popular. In this article we provide a
brief overview of such problems from a statistical, particularly Bayesian,
perspective.
We also compare and contrast the above class of problems with the perhaps
more statistically familiar inverse regression problems, arguing that this
class of problems contains the traditional class of inverse problems. In course
of our review we point out that the statistical literature is very scarce with
respect to both the inverse paradigms, and substantial research work is still
necessary to develop the fields.