Bayesian and robust Bayesian analysis in a general setting

Karimnezhad, Ali; Parsian, Ahmad

doi:10.1080/03610926.2018.1482344

Cited by 4 publications

(5 citation statements)

References 30 publications

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“…Table 1 presents some examples of the GB loss. The following theorem is the corollary of Theorem 3.1. in Karimnezhad and Parsian (2018).…”

Section: Collective Bayes and Prgm Premiums Under The Gb Loss Functionmentioning

confidence: 99%

“…The quality of an estimator is measured by the expected value of a loss function. There are a lot of different loss functions considered in the literature (see Heilmann (1989), Gómez-Déniz (2008), Boratyńska (2008) and Karimnezhad and Parsian (2018) for more references). Its choice depends on the severity of the error related to overestimation or underestimation.…”

Section: Introductionmentioning

confidence: 99%

“…Again under-and over-estimation are not penalized equally. We will use the generalized Bregman loss (GB loss) function introduced by Karimnezhad and Parsian (2018) (for definition see Section 2). The class of GB loss functions contains different losses (weighted, symmetric, asymmetric, precautionary).…”

Section: Introductionmentioning

confidence: 99%

“…Examples of GB loss functions and collective, Bayes and PRGM premiums (for more examples and details seeKarimnezhad and Parsian (2018)) …”

mentioning

confidence: 99%

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Robust Bayesian insurance premium in a collective risk model with distorted priors under the generalised Bregman loss

Boratyńska

2021

Statistics in Transition New Series

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The article presents a collective risk model for the insurance claims. The objective is to estimate a premium, which is defined as a functional specified up to unknown parameters. For this purpose, the Bayesian methodology, which combines the prior knowledge about certain unknown parameters with the knowledge in the form of a random sample, has been adopted. The generalised Bregman loss function is considered. In effect, the results can be applied to numerous loss functions, including the square-error, LINEX, weighted squareerror, Brown, entropy loss. Some uncertainty about a prior is assumed by a distorted band class of priors. The range of collective and Bayes premiums is calculated and posterior regret Γ-minimax premium as a robust procedure has been implemented. Two examples are provided to illustrate the issues considered -the first one with an unknown parameter of the Poisson distribution, and the second one with unknown parameters of distributions of the number and severity of claims.

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“…Table 1 presents some examples of the GB loss. The following theorem is the corollary of Theorem 3.1. in Karimnezhad and Parsian (2018).…”

Section: Collective Bayes and Prgm Premiums Under The Gb Loss Functionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…Examples of GB loss functions and collective, Bayes and PRGM premiums (for more examples and details seeKarimnezhad and Parsian (2018)) …”

mentioning

confidence: 99%

See 2 more Smart Citations

Robust Bayesian insurance premium in a collective risk model with distorted priors under the generalised Bregman loss

Boratyńska

2021

Statistics in Transition New Series

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“…Zhang (2004) used Bregman divergence to study statistical behavior and consistency of classification methods. Recently, Bregman divergence was used to obtain a class of loss function in order for robust Bayesian prediction according to Karimnezhad and Parsian (2018).…”

Section: Bayesian Sensitivity Analysis With Bregman Divergencementioning

confidence: 99%

Testing for Random Effects in Compound Risk Models via Bregman Divergence

Jeong¹

2020

ASTIN Bull.

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Abstract The generalized linear model (GLM) is a statistical model which has been widely used in actuarial practices, especially for insurance ratemaking. Due to the inherent longitudinality of property and casualty insurance claim datasets, there have been some trials of incorporating unobserved heterogeneity of each policyholder from the repeated observations. To achieve this goal, random effects models have been proposed, but theoretical discussions of the methods to test the presence of random effects in GLM framework are still scarce. In this article, the concept of Bregman divergence is explored, which has some good properties for statistical modeling and can be connected to diverse model selection diagnostics as in Goh and Dey [(2014) Journal of Multivariate Analysis, 124, 371–383]. We can apply model diagnostics derived from the Bregman divergence for testing robustness of a chosen prior by the modeler to possible misspecification of prior distribution both on the naive model, which assumes that random effects follow a point mass distribution as its prior distribution, and the proposed model, which assumes a continuous prior density of random effects. This approach provides insurance companies a concrete framework for testing the presence of nonconstant random effects in both claim frequency and severity and furthermore appropriate hierarchical model which can explain both observed and unobserved heterogeneity of the policyholders for insurance ratemaking. Both models are calibrated using a claim dataset from the Wisconsin Local Government Property Insurance Fund which includes both observed claim counts and amounts from a portfolio of policyholders.

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A general guide in Bayesian and robust Bayesian estimation using Dirichlet processes

Karimnezhad

Zarepour

2019

Metrika

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Bayesian and robust Bayesian analysis in a general setting

Cited by 4 publications

References 30 publications

Robust Bayesian insurance premium in a collective risk model with distorted priors under the generalised Bregman loss

Robust Bayesian insurance premium in a collective risk model with distorted priors under the generalised Bregman loss

Testing for Random Effects in Compound Risk Models via Bregman Divergence

A general guide in Bayesian and robust Bayesian estimation using Dirichlet processes

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