Finite Partially Ordered Classification Models Based On Posterior Probability

Finite partially ordered classification models are useful for many statistical applications, including cognitive model. Finite partially ordered set is a natural model for cognitive problems, as it is more reasonable than others. Finite partially ordered classification models are useful in many aspects, such as those in automated medical diagnosis or bioinformatics. Our main work focuses on the classification of partially ordered models. A statistical framework is presented for data analysis of finite partially ordered classification models. We use Bayesian method and posterior probabilit.v to treat the classification problem. In response distribution parameter estimation, Gibbs sampling procedure is utilized. The parameters to be estimated are Bernoulli response parameters. We change the number of testing subjects in the up-set of y to adapt the Bernoulli response parameters. Partially ordered model is an important tool to treat this situation. Furthermore, an example in Tatsuoka (2002) will be used to illustrate our proposed procedure.Our research is an extension of the work done in sequential classification by Tatsuoka. We propose a new method and compare this method with Shannon entropy procedure. A method dealing with vague situation is presented in this paper. Sometimes we want to identify a student's ability, for example, whether the student has the ability or not. If a student doesn't correctly answer the question, we can't simply declare that he hasn't the ability, because maybe he has made a careless mistake.So we should see other aspects. If the classification is too strict, we won't get satisfactory result, In this paper Kullback-Leibler information is used to analyze the estimation of parameter and the model. Moreover, we bring forward a new idea of the situation that one item tests several abilities .