Showing papers by "Siva Sivaganesan published in 1989"
TL;DR: In this paper, the authors consider the problem of robustness or sensitivity of given Bayesian posterior criteria to specification of the prior distribution, including the posterior mean, variance and probability of a set (for credible regions and hypothesis testing).
Abstract: We consider the problem of robustness or sensitivity of given Bayesian posterior criteria to specification of the prior distribution. Criteria considered include the posterior mean, variance and probability of a set (for credible regions and hypothesis testing). Uncertainty in an elicited prior, $\pi_0$, is modelled by an $\varepsilon$-contamination class $\Gamma = \{\pi = (1 - \varepsilon)\pi_0 + \varepsilon q, q \in Q\}$, where $\varepsilon$ reflects the amount of probabilistic uncertainty in $\pi_0$, and $Q$ is a class of allowable contaminations. For $Q = \{$all unimodal distributions$\}$ and $Q = \{\text{all symmetric unimodal distributions}\}$, we determine the ranges of the various posterior criteria as $\pi$ varies over $\Gamma$.
131 citations
TL;DR: In this article, the sensitivity or robustness of posterior mean to uncertainties in the specification of the prior distribution is considered, and the range of the posterior mean as prior varies over this class, and give an example involving normal distributions.
Abstract: The sensitivity or robustness of posterior mean to uncertainties in the specification of the prior distribution is considered. We model the uncertainty in an elicited prior ttq, which we assume unimodal, by means of a e-contaminated class of priors Γ= {π= (1-e) U q + ες : q e Q } where ε is the amount of uncertainty in ttq and Q is the set of all contaminations q which make the resulting prior π = (l-e)iT0 + eq unimodal with the same mode as that of T q . Then, we find the range of the posterior mean as prior varies over this class, and give an example involving normal distributions.
16 citations