In a homogeneous jury, in which each vote is correct with the same probability, and each pair of votes correlates with the same correlation coefficient, there exists a correlation-robust voting quota, such that the probability of a correct verdict is independent of the correlation coefficient. For positive correlation, an increase in the correlation coefficient decreases the probability of a correct verdict for any voting rule below the correlation-robust quota, and increases that probability for any above the correlation-robust quota. The jury may be less competent under the correlation-robust rule than under simple majority rule and less competent under simple majority rule than a single juror alone. The jury is always less competent than a single juror under unanimity rule.

Deterministic simulation models are used to guide decision-making and enhance understanding of complex systems such as disease transmission, population dynamics, and tree plantation growth. Bayesian inference about parameters in deterministic simulation models can require the pooling of expert opinion. One class of approaches to pooling expert opinion in this context is supra-Bayesian pooling, in which expert opinion is treated as data for an ultimate decision maker. This article details and compares two supra-Bayesian approaches|\event updating" and \parameter updating". The suitability of each approach in the context of deterministic simulation models is assessed based on theoretical properties, performance on examples, and the selection and sensitivity of required hyperparameters. In general, we favor a parameter updating approach because it uses more intuitive hyperparameters, it performs sensibly on examples, and because the alternative event updating approach fails to exhibit a desirable property (relative propensity consistency) in all cases. Inference in deterministic simulation models is an increasingly important statistical and practical problem, and supra-Bayesian methods represent one viable option for achieving a sensible pooling of expert opinion. 1.

We present an algorithm functioning as a supervisor module in a multi expert decision making machine. It uses the Bayes theory in order to estimate the biases of individual expert opinions. These are then used to calibrate and conciliate expert opinions to one opinion. We present a framework for simulating decision strategies using expert opinions whose properties are easily modifiable. By using real data coming from a person authentication system using image and speech data we were able to confirm that the proposed supervisor improves the quality of individual expert decisions by reaching success rates of 99.5 %.

The use of domain knowledge in a learner can greatly improve the models it produces.

Elicitation is a key task for subjectivist Bayesians. While skeptics hold that it cannot (or perhaps should not) be done, in practice it brings statisticians closer to their clients and subjectmatter-expert colleagues. This paper reviews the state-of-the-art, reflecting both the experience of statisticians and the fruits of a long line of psychological research into how people represent uncertain information cognitively, and how they respond to questions about that information. In a discussion of the elicitation process, the first issue to address is what it means for an elicitation to be successful, i.e. what criteria should be employed? Our answer is that a successful elicitation faithfully represents the opinion of the person being elicited. It is not necessarily “true ” in some objectivistic sense, and cannot be judged that way. We see elicitation as simply part of the process of statistical modeling. Indeed in a hierarchical model it is ambiguous at which point the likelihood ends and the prior begins. Thus the same kinds of judgment that inform statistical modeling in general also inform elicitation of prior distributions.