Ranges of Posterior Measures for Priors with Unimodal Contaminations

Sivaganesan, Siva; Berger, James O.

doi:10.1214/aos/1176347148

Cited by 112 publications

(56 citation statements)

References 28 publications

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“…A specific choice for A is the class of -contamination prior distributions, widely studied in the literature on Bayesian robustness (see among others Berger and Berliner [4], Sivaganesan and Berger [22]). It is defined as…”

Section: Robust Sequential Criterionmentioning

confidence: 99%

“…In our specific set up this would make the comparison with the fixed prior approach less interesting. From a technical point of view, in order to calculate the inferior bound of the posterior probability involved in criterion (4), the results of Sivaganesan and Berger [22] can be exploited, as discussed in details in Brutti et al [10] with reference to the normal case.…”

Section: Robust Sequential Criterionmentioning

confidence: 99%

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Robust Bayesian monitoring of sequential trials

Brutti

Santis

Gubbiotti

2013

METRON

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In sequential experiments the sample size is not planned in advance. Data are progressively collected and a stopping rule based on the observed results is defined in order to terminate the study. In a Bayesian framework, it is straightforward to monitor an ongoing experiment looking at the posterior probability that a parameter of interest θ , belongs to a given set. Specifically, in this paper we focus on the context of phase II clinical trials, where θ represents treatment efficacy. The Bayesian stopping rule we adopt involves the posterior probability that θ exceeds a clinically relevant threshold. Moreover, we introduce a robust version of this criterion by replacing the single prior distribution with a class of prior distributions. A simulation study is performed to compare the average sample sizes of the robust sequential approach both with the sample sizes of the non robust approach and of the non sequential approach. An interesting result is that, when the class of prior distributions is sufficiently narrow, the average sample sizes of the robust sequential approach can be smaller than the non sequential sample sizes.

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Section: Robust Sequential Criterionmentioning

confidence: 99%

Section: Robust Sequential Criterionmentioning

confidence: 99%

Robust Bayesian monitoring of sequential trials

Brutti

Santis

Gubbiotti

2013

METRON

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show abstract

“…The proof follows by representing a unimodal density as a mixture of uniforms (Lemma 3.2.1 in Sivaganesan and Berger, 1989) and applying Lemma A.1 in Sivaganesan and Berger (1989).…”

Section: Sensitivity Studymentioning

confidence: 99%

Measuring sensitivity in a bonus–malus system

Gómez¹,

Hernández²,

Pérez³

et al. 2002

Insurance: Mathematics and Economics

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In performing Bayesian analysis of a bonus-malus system (BMS) it is normal to choose a parametric structure, π 0 (λ), in the insurer's portfolio. According to Bayesian sensitivity analysis the structure function can be modelled by specifying a class Γ of priors instead of a single prior. In this paper, we examine the ranges of the relativities, i.e. δ π = E[λπ(λ|data)]/E[λπ(λ)], π ∈ Γ . We illustrate our method with data from [Astin Bulletin 10 (3) (1979) 274].

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“…The most attractive ε-contaminated class of priors is given by (Berger, 1985;Sivaganesan, 1988;Sivaganesan, 1989, among others),…”

Section: Robustness Of the Esscher Principle With Respect To The Priormentioning

confidence: 99%

The Esscher premium principle in risk theory: a Bayesian sensitivity study

Gómez–Déniz

Hernández-Bastida

Polo

1999

Insurance: Mathematics and Economics

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In this paper the Esscher premium calculation principle is applied to the non-compound collective model in a robust Bayesian context. We consider that uncertainty with regard to the prior distribution can be represented by the assumption that the unknown prior distribution belongs to a class of distributions and examine the ranges of the Bayesian premium when the priors belong to such a class. The assessment of the influence of the prior is termed sensitivity analysis or robustness analysis.

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Ranges of Posterior Measures for Priors with Unimodal Contaminations

Cited by 112 publications

References 28 publications

Robust Bayesian monitoring of sequential trials

Robust Bayesian monitoring of sequential trials

Measuring sensitivity in a bonus–malus system

The Esscher premium principle in risk theory: a Bayesian sensitivity study

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