Estimation of a non-negative function

It is pointed out that the problem of estimating a function from the values of a finite number of functionals is often posed, at least partially, as an aesthetic problem rather than as a mathematical one.A particular problem of interpretation of experimental results, arising in the study of radiation source distribution in a plasma, is formulated mathematically in two different ways. Although the two formulations are different in character, they both rely on the idea of imposing a relative likelihood distribution on an appropriate function space; this is particularly fruitful when observational errors are taken into account.