Bayesian statistical inference based on rounded data. Issue 1 (2nd January 2020) - Zhao, Ningning; Bai, Zhidong
Abstract: Rounded observations are omnipresent in continuous populations due to the precision of the recording or storage mechanism. The rounding error is usually ignored in statistical inferences. However, along with more and more large samples being employed in statistical inferences, the influences of the rounding error are significant, especially on hypothesis testing. This paper analyze the influences of the rounding error on Bayesian statistical inferences and propose a corresponding posterior density function based on rounded data, which can correct rounding error efficiently. Moreover, the properties of consistency and asymptotic normality of the posterior distribution obtained by the method proposed in this paper are proved.