  The Bayesian nonparametric inference and Dirichlet process are popular tools
in statistical methodologies. In this paper, we employ the Dirichlet process in
hypothesis testing to propose a Bayesian nonparametric chi-squared
goodness-of-fit test. In our Bayesian nonparametric approach, we consider the
Dirichlet process as the prior for the distribution of data and carry out the
test based on the Kullback-Leibler distance between the updated Dirichlet
process and the hypothesized distribution F0. We prove that this distance
asymptotically converges to the same chi-squared distribution as the
chi-squared test does. Similarly, a Bayesian nonparametric chi-squared test of
independence for a contingency table is provided. Also, by computing the
Kullback-Leibler distance between the Dirichlet process and the hypothesized
distribution, a method to obtain an appropriate concentration parameter for the
Dirichlet process is suggested.
