## Well-posedness conditions in stochastic inversion problems. (arXiv:1806.03440v1 [math.ST])

Stochastic inversion problems arise when it is wanted to estimate the
probability distribution of a stochastic input from indirect observable and
noisy information and the limited knowledge of an operator that connects the
inputs to the observable output. While such problems are characterized by
strong identifiability conditions, well-posedness conditions of "signal over
noise" nature should be respected priori to collect observations. In addition
to well-known Hadamard' well-posedness condition, a new one is established
based on the predictive transmission of input uncertainty to output, which can
be interpreted as the result provided by a sensitivity analysis if the problem
were solved. This new condition should take part within the input model itself,
which adds a constraint in established frequentist or Bayesian methodologies of
stochastic inversion. While this article mainly deals with linearizable
operators, the lack of constrast typical of linear problems suggest that the
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