Although Nematodirus battus is a serious threat to the health and survival of young lambs, there are few options to control this parasite. Bayesian Monte Carlo Markov Chain modelling with a zero-inflated Poisson distribution was used to estimate the heritability of egg counts in both June and July for each of five consecutive cohorts of 200 Scottish Blackface lambs. In one of the 10 analyses, the results failed the diagnostic tests. In seven of the analyses, there was no convincing evidence that the variation in egg counts was heritable. In the 2 years of high infection, the heritability was approximately 0.4 in June but the estimates lacked precision and the 95% highest posterior density credible intervals ranged from just above zero to 0.7. Selective breeding for resistance to N. battus will be difficult because genetically resistant or susceptible lambs cannot be consistently identified by phenotypic markers.

Can the output of human cognition be predicted from the assumption that it is an optimal response to the information-processing demands of the environment? A methodology called rational analysis is described for deriving predictions about cognitive phenomena using optimization assumptions. The predictions flow from the statistical structure of the environment and not the assumed structure of the mind. Bayesian inference is used, assuming that people start with a weak prior model of the world which they integrate with experience to develop stronger models of specific aspects of the world. Cognitive performance maximizes the difference between the expected gain and cost of mental effort. (1) Memory performance can be predicted on the assumption that retrieval seeks a maximal trade-off between the probability of finding the relevant memories and the effort required to do so; in (2) categorization performance there is a similar trade-off between accuracy in predicting object features and the cost of hypothesis formation; in (3) casual inference the trade-off is between accuracy in predicting future events and the cost of hypothesis formation; and in (4) problem solving it is between the probability of achieving goals and the cost of both external and mental problem-solving search. The implemention of these rational prescriptions in neurally plausible architecture is also discussed.

This paper addresses the Bayesian estimation of the shape parameter of Pareto distributions, and its application to premium calculation of large claims excess of loss (XL) reinsurance contracts. It studies the use of the generalized inverse Gaussian (GIG) as a Pareto prior conjugate, a family that contains as a particular case the gamma distribution. An exact credibility formula is deduced allowing the calculation of individual reinsurance premiums. These are premiums suited to the excesses history of a sole portfolio. A family of predictive distributions for the excesses is derived. We apply our exact credibility model to a sample of excesses arisen in ten Spanish portfolios of liability motor insurance from year 1992 to year 2001.

Interest in Bayesian analyses has increased recently, in part as a response to policy makers wanting sound scientific bases for health technology assessments, and associated healthcare funding decisions. This paper provides a brief and simplified description of Bayesian reasoning. Bayes is illustrated in a clinical setting of an expert helping a woman understand the potential risk of passing on an inheritable disease (hemophilia) to her next child, based on disease occurrence in two living children. The illustration describes fundamental concepts and derivations, such as Bayes theorem, likelihood functions, prior probability, and posterior probability. A second illustration shows the use of Bayes for interpreting clinical trial results. The uncertainty in the clinical effect before and after the trial analyses has been completed is characterized by the Bayes prior and posterior probabilities, respectively. Techniques are also shown for estimating the potential loss (e.g., in lives lost) for making the wrong decision with and without knowledge of the trial results, an estimation that cannot be carried out using techniques of hypotheses testing associated with the frequentist school of statistics. Information from Bayes analysis then may be used to help policy makers decide, or justify, whether the analyses provides a sufficient basis for making a treatment recommendation, or whether there remains a need to request more information. Subsequent papers in this volume offer additional examples and clarification of the use of Bayes in clinical practice and in interpretation of clinical studies.