# Achievement

## Uncertainty of inputs to a finite dimensional map

### Project

Program for Interdisciplinary Mathematics, Ecology, and Statistics (PRIMES)

### University

Colorado State University

(Fort Collins, CO)

## Research Achievements

### Uncertainty of inputs to a finite dimensional map

An IGERT trainee considers the inverse problem of quantifying the uncertainty of inputs to a finite dimensional map, e.g. determined implicitly by solution of a nonlinear system, given specified uncertainty in a linear functional of the output of the map. He describes his problem probabilistically, so that the uncertainty in the quantity of interest is represented by a random variable with a known distribution,. He derives an efficient method for determining the unique solution to the problem of inverting through a many-to-one map by inverting into a quotient space representation of the input space which combines a forward sensitivity analysis with the Implicit Function Theorem. He then derives an efficient computational measure theoretic approach to further invert into the entire input space resulting in an approximate probability measure on the input space.

- “Research Achievements”
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