The analysis of Balmer alpha beam emission spectra represents a challengingtask, both in terms of the wealth of information hidden in them, and in termsof complex spectral features. The shape of a spectrum depends on many localplasma parameters, such as magnetic field strength and direction, beamdensity, effective charge and deuteron density. This paper is concerned withthe deduction of local plasma deuteron densities from Balmer alpha emissionfrom plasma atoms following charge exchange with the beam atoms. The model wewill use is statistical, and is based on multi-layer perceptron neuralnetworks (Hertz et al 1991, Bishop 1995). The use of neural networks makes thedeconvolution task fully automatic and fast enough for real-time calculationof complete deuteron density profiles. It is shown that the spectra themselvesand local electron densities are the only data necessary for accurateinference of local deuteron densities. This result is partly inferred from asensitivity analysis of dependences on different plasma parameters. Propererror bars for the model predictions will be derived using Bayesianprobability theory.