Bayesian statistical inference based on rounded data

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.

Keywords:

• Asymptotic normality
• Bayesian analysis
• consistency
• posterior distribution
• rounded data

Additional information

Funding

This work was supported by the Civil Aviation University of China under Grant 3122013C003; Civil Aviation University of China under Grant 2012QD11X; and National Natural Science Foundation of China under Grant 11571067.