Modification of posterior probability variable with frequency factor according to Bayes Theorem

Abstract

Probability theory is a branch of science that statistically analyzes random events. Thanks to this branch of science, machine learning techniques are used inferences for the prediction or recommendation system. One of the statistical methods at the forefront of these techniques is Bayesian theory. Bayes is a simple mathematical formula used to calculate conditional probabilities and obtain the best estimates. The two most important parts of the formula are the concepts of a priori probability and posterior/conditional probability. In a priori probability, the most rational assessment of the probability of an outcome is made based on the available data, while in posterior probability, the probability of the event occurring is calculated after considering all evidence or data. In this study, a new mathematical model is presented to calculate the posterior probability variable of Bayesian theory more precisely. According to this new mathematical model, equal priority probabilities of some variables should be recalculated according to frequency. Calculations are applied to two nodes. The first of these two nodes is the node consisting of the existing data, and the second is the queried node. The positive frequency value will be applied when the variables consisting of existing data and having the same a priori probabilities are found at the questioned node, and negative frequency value will be applied for the other variables. Thus, while calculating a standard probability value according to Bayesian Theory, frequency-based values are taken into account with the help of the newly created mathematical model. With the help of these frequencies, the modification of the system reveals more precise results according to these two basic principles. The results obtained were tested with the cross validation method and high accuracy rates were determined.