Predictive Time-Dependent Model Through the Conjunction of Bayes Theorem and Mitchell Criteria

This study aimed to construct a predictive model based on the Bayes theorem and Mitchell criteria. The Bayes theorem is expressed as integrals of convolution by using test probabilistic distribution functions. By assuming a set of inputs, are derived a set of probabilities whose main structure conserves the one of Bayes theorem. Therefore, the projection onto the territory of Mitchell criteria allows to build set of algorithms for the calculation of probabilities of central events (or the main stochastic variable of study for a certain time). In this way, a formalism and an algorithm were proposed. The central objective is the estimation of any variable in terms of Bayesian probabilities. From the results of this paper, probabilistic distribution functions are obtained along a lapse of time. Thus, for a subsequent time of a prediction, the probabilities of prediction were small compared to the previous ones. Because of this approach, prediction was limited due to the Bayesian probabilities as well as random numbers.

I. Introduction

It is well-known that basic sciences and engineering need robust models to carry out estimations and predictions with minimal deviations [1], [2]. On finds in literature, numerous approaches for a wide spectrum of applications. Notable applications are found in physics, chemistry, medicine, genetics, and hardware (micro and nanotechnology) [3], [4]. The mathematical component in its different formulations predominates in all those fields of study.