Empirical Bayesian Method in the Problem of a Harmonic Signal Detecting in the Gaussian Noise

2021 ◽  
Author(s):  
Igor Omelchuk ◽  
Igor Prokopenko ◽  
Yuliia Petrova ◽  
Olena Omelchuk
Keyword(s):  
Gaussian Noise ◽  
Bayesian Method ◽  
Harmonic Signal ◽  
Empirical Bayesian ◽  
Empirical Bayesian Method

scholarly journals The Bühlmann–Straub Estimation of Claim Means in Random B-F Reserve Model

2020 ◽  
Vol 2020 ◽  
pp. 1-11
Author(s):  
Zhang Yi ◽  
Wen Limin ◽  
Li Zhilong
Keyword(s):  
Prior Distribution ◽  
Personal Experience ◽  
Bayesian Method ◽  
Historical Data ◽  
Credibility Theory ◽  
Empirical Bayesian ◽  
Sample Distribution ◽  
Empirical Bayesian Method ◽  
Chain Ladder ◽  
Bayesian Estimators

In the B-F reserve model, it is a very critical step to estimate the claim means of the accident year. However, the traditional method uses the prior estimators of the claim means based on the personal experience of actuaries or historical data. This method inevitably carries the subjectivity of the actuary himself. In this paper, a stochastic B-F model is established, and a prior distribution is constructed for the claim means in the accident year. The idea of the credibility theory is used to derive the linear Bayesian estimators of claim means. Finally, the empirical Bayesian method is used to estimate the first two moments of the prior distribution, and the empirical Bayesian estimators of the claim means and the corresponding reserves are derived. The estimators obtained in this paper do not depend on the specific forms of the sample distribution and the prior distribution and can be used directly in practice. In the numerical simulation, our estimates are compared with the traditional B-F estimates and the chain ladder estimates. It is verified that the estimates given in this paper have small mean square error.

scholarly journals Bayesian Analysis of Inverted Kumaraswamy Mixture Model with Application to Burning Velocity of Chemicals

2021 ◽  
Vol 2021 ◽  
pp. 1-18
Author(s):  
Farzana Noor ◽  
Saadia Masood ◽  
Mehwish Zaman ◽  
Maryam Siddiqa ◽  
Raja Asif Wagan ◽  
...  
Keyword(s):  
Bayesian Analysis ◽  
Mixture Model ◽  
Bayesian Method ◽  
Burning Velocity ◽  
Likelihood Estimation ◽  
Empirical Bayesian ◽  
Squared Error ◽  
Linex Loss ◽  
Empirical Bayesian Method ◽  
Better Than

Burning velocity of different chemicals is estimated using a model from mixed population considering inverted Kumaraswamy (IKum) distribution for component parts. Two estimation techniques maximum likelihood estimation (MLE) and Bayesian analysis are applied for estimation purposes. BEs of a mixture model are obtained using gamma, inverse beta prior, and uniform prior distribution with two loss functions. Hyperparameters are determined through the empirical Bayesian method. An extensive simulation study is also a part of the study which is used to foresee the characteristics of the presented model. Application of the IKum mixture model is presented through a real dataset. We observed from the results that Linex loss performed better than squared error loss as it resulted in lower risks. And similarly gamma prior is preferred over other priors.

scholarly journals An approximate empirical Bayesian method for large-scale linear-Gaussian inverse problems

2018 ◽  
Vol 34 (9) ◽  
pp. 095001 ◽  
Author(s):  
Qingping Zhou ◽  
Wenqing Liu ◽  
Jinglai Li ◽  
Youssef M Marzouk
Keyword(s):  
Inverse Problems ◽  
Large Scale ◽  
Bayesian Method ◽  
Empirical Bayesian ◽  
Empirical Bayesian Method

scholarly journals Social geography of AIDS in Brazil: identifying patterns of regional inequalities

2014 ◽  
Vol 30 (2) ◽  
pp. 259-271 ◽  
Author(s):  
Tatiana Rodrigues de Araujo Teixeira ◽  
Renata Gracie ◽  
Monica Siqueira Malta ◽  
Francisco I. Bastos
Keyword(s):  
Bayesian Method ◽  
Moving Average ◽  
Social Geography ◽  
Regional Disparities ◽  
Mortality Pattern ◽  
Empirical Bayesian ◽  
Aids Epidemic ◽  
The North ◽  
Empirical Bayesian Method ◽  
Related Mortality

The trend towards decline and stabilization of the AIDS epidemic in Brazil should be analyzed carefully, since aggregate data can mask regional or local inequalities in such a large and diverse country. The current study reevaluates the epidemic’s spatial dissemination and the AIDS-related mortality pattern in Brazil. The study considered all AIDS cases diagnosed in individuals over 18 years of age and living in Brazil, as well as AIDS deaths recorded in 1998-2008. Three-year moving average rates were estimated, and a spatial analysis was conducted using a local empirical Bayesian method. The epidemic was only found to be expanding in the North and Northeast regions, while declining in the rest of the country, especially in the Southeast. According to the findings, the apparent stabilization of AIDS mortality tends to mask regional disparities. Social determinants of health and regional disparities should be taken into account in program development and policymaking.

Empirical Bayesian Strategy for Sampling Plans with Warranty Under Truncated Censoring

2016 ◽  
Vol 23 (05) ◽  
pp. 1650021 ◽  
Author(s):  
Jyun-You Chiang ◽  
Y. L. Lio ◽  
Tzong-Ru Tsai
Keyword(s):  
Bayesian Method ◽  
Design Procedure ◽  
Parameter Determination ◽  
Time Cost ◽  
Empirical Bayesian ◽  
Sampling Plans ◽  
Test Cost ◽  
Empirical Bayesian Method ◽  
Warranty Cost ◽  
The Cost

To reach an optimal acceptance sampling decision for products, whose lifetimes are Burr type XII distribution, sampling plans are developed with a rebate warranty policy based on truncated censored data. The smallest sample size and acceptance number are determined to minimize the expected total cost, which consists of the test cost, experimental time cost, the cost of lot acceptance or rejection, and the warranty cost. A new method, which combines a simple empirical Bayesian method and the genetic algorithm (GA) method, named the EB-GA method, is proposed to estimate the unknown distribution parameter and hyper-parameters. The parameters of the GA are determined through using an optimal Taguchi design procedure to reduce the subjectivity of parameter determination. An algorithm is presented to implement the EB-GA method. The application of the proposed method is illustrated by an example. Monte Carlo simulation results show that the EB-GA method works well for parameter estimation in terms of small bias and mean square error.

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