Koroliouk D., Koroliuk V. S., Rosato N.
Equilibrium processes in biomedical data analysis: the Wright–Fisher model

The biological process of cooperative interaction with equilibrium state is described as a model of binary statistical experiments with the Wright–Fisher normalization, which sets the concentration of a certain characteristic. Such mathematical model is supposed to have the property of persistent regression, which means that all current elementary transitions depend on the mean concentration of the said characteristics in the previous state. Equilibrium state of the model is expressed in terms of the regression function given by a cubic parabola with three real roots. We construct the stochastic approximation of the model by autoregressive process with normal disturbances. Such an approach was developed for effective and calculable mathematical description of dynamic concentration for experiment planning, parameter evaluation, and verification of hypotheses of the mechanisms of action. © 2014, Springer Science+Business Media New York.

Keywords: binary statistical experiment, equilibrium state, normal autoregression, persistent regression, Wright–Fisher normalization, Regression analysis, Stochastic systems, Autoregression, Biomedical data analysis, Cooperative interactions, Equilibrium state, Mathematical descriptions, persistent regression, Statistical experiments, Stochastic approximations, Stochastic models

PDF

Cite:
Koroliouk, Koroliuk, Rosato. (2014). Equilibrium processes in biomedical data analysis: the Wright–Fisher model. Cybernetics and Systems Analysis, 50 (6), 80-86. doi: https://doi.org/10.1007/s10559-014-9680-y http://jnas.nbuv.gov.ua/article/UJRN-0001313828