Comparison of fuzzy Bayesian hypotheses tests

In this study, the effect of Bayesian approach to hypothesis testing by using different prior distributions will be measured with Fuzzy hypothesis. In the hypothesis test, the data to be derived from Poisson and Exponential distribution are used, while the distribution of the parameters related to these two distributions's parameter is assumed to be Gamma distribution. Gamma, Weibull, Normal and Exponential distributions as prior information distribution and Jeffreys' prior and Uniform distribution as noninformation prior were used. One of the important points in this thesis is that Bayesian probabilities are calculated by mathematical notation of the uncertainties provided by Fuzzy hypotheses. The superiority of fuzzy hypotheses in the Bayesian hypothesis test compared to the classical Bayesian approach gives both a flexibility in weighting the hypotheses in the posterior distributions and a mathematical background. One of the other important points is that although the Bayesian approach has an important place in statistical analysis, it is an undesirable method in terms of process load compared to the alternatives. Non Information prior such as Jeffreys prior is used a sensitivity analysis that the frequency approach giving similar results. Using this sensitivity analysis, we compared the performance against the first and second types of errors, which show in the hypothesis test and the power of the test, by using the information prior. As a result of these comparisons, it has been seen that the use some of the prior information distributions in the small size of sample data sets has made the decision maker the right decision.