An algorithmic framework is proposed to improve stochastic equations obtained with principle/method, \(\mathcal{P}.\) The framework is motivated by the way neurons are processing information. In each neuron, Data Evolves Creating Knowledge (DECK) transmitted to the next neuron for processing. In stochastic equations, DECK is observed when new information, i.e. obtained solutions, replace parameters and the remaining, evolved equations cannot be derived with \(\mathcal{P},\) deviate from zero and need adjustment. In statistical inference, the DECK principle was not allowed by Fisher due to the unique distribution used in MLE. However, equations’ adjustment with an evolved distribution due to DECK improved maximum likelihood and method of moments estimates, that are either biased or inconsistent. The Neyman–Scott (Econometrica 16(1):1–32, 1948) problem for the MLE of the common variance, \(\psi ,\) for m normal models which holds also for the moments’ estimate for all models, was not solved so far with Deep Learning, and is due to neglecting DECK and the adjustment of the \(\psi \) -equation and not the increasing number of the m means. The evolution of static moments and likelihood equations seen as layers, will allow statisticians to see the parallel with the improved layers of equations in Deep Learning, and should be used in other stochastic optimization problems.
