AMathematical tool to measure uncertinity is?

Answer 1

Tools to Measure Uncertainty
Optimization, optimization, optimization.

Easiest approach: falsification of hypotheses using finite-dimensional optimization.

Math tools to probe infinite-dimensional problems:

Functional analysis, nonsmooth analysis, convex analysis

Optimization in infinite-dimensional spaces: Fenchel and Lagrangian duality, linear and nonlinear programming

Probability, and nonparametric and robust statistics

A general-purpose approach that gives conservative bounds:

set misfit tolerance using sum of bound on systematic data errors, and probabilistic bound on stochastic data errors

bound systematic errors from mis-modeling (Cauchy-Schwarz, mixed norm inequalities, modulus of continuity--sometimes a posteriori bounds are sharper)

find extrema of functional of interest among all models that satisfy the data "adequately" and meet the a priori constraints (when problem cannot be solved exactly, sometimes still can be bounded using duality--bracket uncertainty)

Some statistically optimal procedures for finding confidence intervals are in the class of estimators this gives.

The misfit measure can be tailored for the geometry of the observation functionals, the systematic errors, the constraints, and the functional to be estimated.

Often l2 measure of misfit (as in least-squares) is not optimal (even can be statistically inconsistent).

This approach can be quite demanding computationally.

Answer 2

a mathematical tool use for measuring uncertinity is formulating an equation.

Answer 3

Is probably random

Answer 4

statistics

Answer 5

a t-test