Bayesian Inference for Binomial Probability and Psychometrics Techniques

This paper introduces a new concept of distribution called circular distribution. The total area of the circle is defined as the distribution density of the binomial probability which consists of . This probabilistic sum is assumed to be equal to , the area of a unit circle. In a binomial distribution where the probability of success is equal to one minus the probability of failure: , the probability of failure sector may be further sectioned in parts (sections) as required by the probability of failure subspace. Using the Laplace Rule of Success as the basis for deriving the prior for probability of success, the probability distribution density for success, failure and subspace of failure in a successive binomial partition may be accomplished. This circular distribution differs from the Gaussian distribution in that the graphical representation is a circle, not a bell shape curve. The bell shape curved may also be used to express the Normality of the distribution in the long run. However, for purposes of determining prior for Bayesian inference, the circular distribution may be used for visual aid and convenience in calculating binomial probability. There are several theories used in this paper. Primus, the Bayesian probability is a binomial probability. A binomial probability is defined by the probability with two categories of answer. Secundus, the Laplace Rule of Succession is a definitional rule of binomial probability. The two category answer choice is defined by two choices: success and failure. The LaPlace Rule of Success expresses the ratio of observed success to the total number of observation. Tertius, the Buddha's psychometric technique is explained and used as an illustrative model for generating Bayesian prior