An Approximate Bayesian Selection of Statistical Model Based on Fuzzy Interval Data

Abstract

In recent years, Bayesian theory has come to be used in a wide range of fields. In the IT field, Bayesian theory is used to enable highly efficient searches, and this theory is also used to sort unsolicited e-mails. There are many research reports focusing on Bayesian theory, and they aim to construct a framework for Bayesian statistical analysis. In this paper, we propose an approximate Bayesian selection method for statistical models based on fuzzy interval data obtained from ordinary real number space. Here, we formulate the method using the concept of the probability of fuzzy events defined by Zadeh. In this paper, we refer to the interval data whose boundary is vague as fuzzy interval data. Fuzzy interval data are characterized using membership functions, but the integration of the product of this function and the probability density function causes the complexity of calculation. However, our method treating the middle points of the membership functions as the representative points can almost solve such problems. Here, the standard normal distribution, normal distribution, student’s t-distribution, Gamma distribution, and Weibull distribution are targeted as the selection of statistical models. Furthermore, numerical examples are shown to explain the proposed method concretely. We set the situation where the trapezoidal membership function is obtained as an asymmetrical type instead of a symmetrical type and show that the proposed method can deal flexibly. As a result, we were able to show the usefulness of our proposed method.