Quantification of uncertainty for Stochastic Approximation.

Summary Stochastic Approximation is an iterative procedure for computing a zero θ of a function that is not explicit but defined as an expectation. It is, for example, a numerical tool for computing maximum likelihood in "regular" latent data models. If the definition of the statistical model is tainted with an uncertainty τ , of which only an a priori dπ(τ ) is known, then the zeros depend on τ and the natural question is to explore their distribution when τ ∼ dπ. In this paper, we propose an iterative algorithm based on a Stochastic Approximation scheme that,in the limit, computes θ (τ) for any τ and produces a characterization of its distribution. and weenounce sufficient conditions for the convergence of this algorithm.