Improvement on Monte Carlo estimation of HPD intervals. Issue 8 (2nd August 2020)

• Record Type: Journal Article
• Authors: Le, Hoa; Pham, Uyen; Nguyen, Phuong; Pham, The Bao
• Is Part Of: Communications in statistics. Volume 49:Issue 8(2020)
• Page Start: 2164
• Page End: 2180
• Publication Date: 2020-08-02
• Subjects: The highest density region -- The highest posterior density region -- The mean relative error -- The predictive interval; Mathematical statistics -- Periodicals; Mathematical statistics -- Data processing -- Periodicals; Digital computer simulation -- Periodicals; 519.5
• DOI: 10.1080/03610918.2018.1513141
• Languages: English
• ISSNs: 0361-0918

Abstract

Abstract: In Bayesian statistics, there have been several methods on estimating the highest probability posterior density (HPD) such as using Monte Carlo approach combined with mean relative error (ME) served as a measure of effectiveness in Chen and Shao (1999 ) and Chen, Shao and Ibrahim (2012 ) for the unimodal case and a simple application to Bayesian hierarchical model. In this paper, we firstly reconsider the former and then propose a new method based on probability density function with an algorithm in order to give an estimation for HPD intervals to improve on Monte Carlo in both unimodal and multimodal cases. We further show that our new method has made an improvement in producing credible intervals with the shortest length for some cases. The necessary theory is developed and illustrative examples are provided.