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A Framework for Loss Scale Determination in General Bayesian Updating

Abstract Number:

1137 

Submission Type:

Contributed Abstract 

Contributed Abstract Type:

Poster 

Participants:

YU JIN SEO (1), Seung Jun Park (2), Pamela Kim Salonga (2), Kyeong Eun Lee (2), Gyuhyeong Goh (2)

Institutions:

(1) N/A, N/A, (2) Department of Statistics, Kyungpook National University, N/A

Co-Author(s):

Seung Jun Park  
Department of Statistics, Kyungpook National University
Pamela Kim Salonga  
Department of Statistics, Kyungpook National University
Kyeong Eun Lee  
Department of Statistics, Kyungpook National University
Gyuhyeong Goh  
Department of Statistics, Kyungpook National University

First Author:

YU JIN SEO  
N/A

Presenting Author:

YU JIN SEO  
N/A

Abstract Text:

General Bayesian updating (GBU) is a framework for updating prior beliefs about the parameter of interest to a posterior distribution via a loss function without imposing the distribution assumption on data. In recent years, the asymptotic distribution of the loss-likelihood bootstrap (LLB) sample has been a standard for determining the loss scale parameter which controls the relative weight of the loss function to the prior in GBU. However, the existing method fails to consider the prior distribution since it relies on the asymptotic equivalence between GBU and LLB. To address this limitation, we propose a new finite-sample-based approach to loss scale determination using the Bayesian generalized method of moments (BGMM) as a reference. We develop an efficient algorithm that determines the loss scale parameter by minimizing the Kullback-Leibler divergence between the exact posteriors of GBU and BGMM. We prove the convexity of our objective function to ensure a unique solution. Asymptotic properties of the proposed method are established to demonstrate its generalizability. We demonstrate the performance of our proposed method through a simulation study and a real data application.

Keywords:

General Bayesian updating |Loss-likelihood bootstrap |Generalized method of moments|Kullback-Leibler divergence |Monte Carlo Newton-Raphson method|

Sponsors:

Korean International Statistical Society

Tracks:

Miscellaneous

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