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The two layer feed-forward neural net (the perceptton) may be regarded as a generalization of a multiple logistic regression model with multivariate output, if the threshold function is interpreted as a generalised linear model link. The multi-layer perceptton can be, and has been, used as a highly structured and parameterised non-linear model of expectation behaviour. The usual back propagation rules for training a neural net are equivalent to fairly simple methods for minimizing the error sum of squares at the outputs, ie. OLS. Then: has been little work done which uses the multi-layer perceptron as a statistical trend model in which the error distributions at the output nodes are statistically specified. For such nonlinear models, OLS will be inefficient as well as biased. However, an appropriate specification of the stochastic error structure will lead to either weighted least squares or maximum likelihood estimates, which may be achieved ether directly or by iteratively reweighted least squares. This general statistical approach allows the precision of trained weights to be estimated, as well as the correlation between these weights in the variance-covariance matrix. Such a feature is useful in examining the conjecture that different layers of the MLP have characterised different aspects of the training data set Statistical methods can then also be used to prune the topology of the network using a step-wise approach.

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ECS LLC operates a wastewater collection and treatment facility for their client Northern Oil&Gas, Inc. in Myton, Utah. The facility receives fracking and produced wastewater from various pumping stations, and then treats the water for disposal at the injection well located on site. Electrocoagulation followed by two clarifiers and 5 micron filter was used. Since many particles float or just "swim" inside the clarifier we performed a flocculation -flotation pilot study followed by full scale installation of the flocculation flotation --the GEM Systems. This manuscript summarizes the results of the pilot studies and operational performance and problems of the full scale 600 GPM GEM Systems