We consider the problem of Bayesian inference about the centre of symmetry of a symmetric density on the real line based on independent identically distributed observations. A result of Diaconis and Freedman shows that the posterior distribution of the location parameter may be inconsistent if (symmetrized) Dirichlet process prior is used for the unknown distribution function. We choose a symmetrized Polya tree prior for the unknown density and independently choose according to a continuous and positive prior density on the real line. Suppose that the parameters of Polya tree depend only on the level m of the tree and the common values rm’s are such that ∑∞ m=1 r−1=2 m ¡∞. Then it is shown that for a large class of true symmetric densities, including the trimodal distribution of Diaconis and Freedman, the marginal posterior

This paper considers the problem of choosing between an existing component whose reliability is well established and a new component that has an unknown reliability. In some scenarios, the designer may have some initial beliefs about the new component’s reliability. The designer may also have the opportunity to obtain more information and to update these beliefs. Then, based on these updated beliefs, the designer must make a decision between the two components. This paper examines the statistical approaches for updating reliability assessments and the decision policy that the designer uses. We consider four statistical approaches for modeling the uncertainty about the new component and updating assessments of its reliability: a classical approach, a precise Bayesian approach, a robust Bayesian approach, and an imprecise probability approach. The paper investigates the impact of different approaches on the decision between the components and compares them. In particular, given that the test results are random, the paper considers the likelihood of making a correct decision with each statistical approach under different scenarios of available information and true reliability. In this way, the emphasis is on practical comparisons of the policies rather than on philosophical arguments.

Research on using Bayesian networks to enhance digital forensic investigations has yet to evaluate the quality of the output of a Bayesian network. This evaluation can be performed by assessing the sensitivity of the posterior output of a forensic hypothesis to the input likelihood values of the digital evidence. This paper applies Bayesian sensitivity analysis techniques to a Bayesian network model for the well-known Yahoo! case. The analysis demonstrates that the conclusions drawn from Bayesian network models are statistically reliable and stable for small changes in evidence likelihood values.

Sets of probability measures which form neighbourhoods of classical probability measures are studied. An application of Jeffrey’s rule of conditioning to forming neighbourhoods of probability measures is proposed. Neighbourhoods that are closed for generalized conditioning according to this rule are characterized. They are shown to be exactly convex and bi-elastic neighbourhoods.