Surveying and declaring disease freedom in wildlife is difficult because information on population size and spatial distribution is often inadequate. We describe and demonstrate a novel spatial model of wildlife disease-surveillance data for predicting the probability of freedom of bovine tuberculosis (caused by Mycobacterium bovis) in New Zealand, in which the introduced brushtail possum (Trichosurus vulpecula) is the primary wildlife reservoir. Using parameters governing home-range size, probability of capture, probability of infection and spatial relative risks of infection we employed survey data on reservoir hosts and spillover sentinels to make inference on the probability of eradication. Our analysis revealed high sensitivity of model predictions to parameter values, which demonstrated important differences in the information contained in survey data of host-reservoir and spillover-sentinel species. The modelling can increase cost efficiency by reducing the likelihood of prematurely declaring success due to insufficient control, and avoiding unnecessary costs due to excessive control and monitoring.

We have been oversold on the base rate fallacy in probabilistic judgment from an empirical, normative, and methodological standpoint. At the empirical level, a thorough examination of the base rate literature (including the famous lawyer–engineer problem) does not support the conventional wisdom that people routinely ignore base rates. Quite the contrary, the literature shows that base rates are almost always used and that their degree of use depends on task structure and representation. Specifically, base rates play a relatively larger role in tasks where base rates are implicitly learned or can be represented in frequentist terms. Base rates are also used more when they are reliable and relatively more diagnostic than available individuating information. At the normative level, the base rate fallacy should be rejected because few tasks map unambiguously into the narrow framework that is held up as the standard of good decision making. Mechanical applications of Bayes's theorem to identify performance errors are inappropriate when (1) key assumptions of the model are either unchecked or grossly violated, and (2) no attempt is made to identify the decision maker's goals, values, and task assumptions. Methodologically, the current approach is criticized for its failure to consider how the ambiguous, unreliable, and unstable base rates of the real world are and should be used. Where decision makers' assumptions and goals vary, and where performance criteria are complex, the traditional Bayesian standard is insufficient. Even where predictive accuracy is the goal in commonly defined problems, there may be situations (e.g., informationally redundant environments) in which base rates can be ignored with impunity. A more ecologically valid research program is called for. This program should emphasize the development of prescriptive theory in rich, realistic decision environments.

Objectives: Due to potential advantages (e.g., using all available evidence), Bayesian methods have been proposed to assist healthcare decision making. This review provides a detailed description of how Bayesian methods have been applied to economic evaluations of patient level data. The results serve both as a reference and as a means by which to examine the appropriate application of Bayesian methods to inform decision making.

Methods: MEDLINE, EMBASE, and Cochrane Economic Evaluation databases were searched to identify studies, published up to November 2007, meeting three inclusion criteria: (i) the study conducted an economic evaluation, (ii) sampling uncertainty was incorporated using Bayesian methods, (iii) the likelihood function was informed by patient level data from a single source. Data were collected on key study characteristics (e.g., prior distribution, likelihood function, presentation of uncertainty).

Results: The search identified 366 potentially relevant studies, from which 103 studies underwent full-text review. Sixteen studies met the inclusion criteria. Half of the studies used uninformative priors; most studies incorporated the potential dependence between costs and effects, and presented cost-effectiveness acceptability curves. Results were sensitive to changes in the priors and likelihoods.

Conclusions: Limited use of informative priors, among the included studies, gives policy makers little guidance on one of the main benefits of Bayesian methods, the ability to integrate all available evidence to capture the uncertainty inherent in decision making.

Bayesian statistics provide effective techniques for analyzing data and translating the results to inform decision making. This paper provides an elementary tutorial overview of the WinBUGS software for performing Bayesian statistical analysis. Background information on the computational methods used by the software is provided. Two examples drawn from the field of medical decision making are presented to illustrate the features and functionality of the software.

A desirable element of cost-effectiveness analysis (CEA) modeling is a systematic way to relate uncertainty about input parameters to uncertainty in the computational results of the CEA model. Use of Bayesian statistical estimation and Monte Carlo simulation provides a natural way to compute a posterior probability distribution for each CEA result. We demonstrate this approach by reanalyzing a previously published CEA evaluating the incremental cost-effectiveness of tissue plasminogen activator compared to streptokinase for thrombolysis in acute myocardial infarction patients using data from the GUSTO trial and other auxiliary data sources. We illustrate Bayesian estimation for proportions, mean costs, and mean quality-of-life weights. The computations are performed using the Bayesian analysis software WinBUGS, distributed by the MRC Biostatistics Unit, Cambridge, England.

For the construction of bonus-malus systems, we propose to show how to apply, thanks to simple mathematics, a parametric method encompassing those encountered in the literature. We also compare this parametric method with a non-parametric one that has not yet been used in the actuarial literature and that however permits a simple formulation of the stationary and transition probabilities in a portfolio whenever we have the intention to construct a bonus-malus system with finite number of classes.

This paper discusses the distribution of tumor size at detection derived within the framework of a new stochastic model of carcinogenesis. This distribution assumes a simple limiting form, with age at detection tending to infinity which is found to be a generalization of the distribution that arises in the length-biased sampling. Two versions of the model are considered with reference to spontaneous and induced carcinogenesis; both of them show similar asymptotic behavior. When the limiting distribution is applied to real data analysis its adequacy can be tested through testing the conditional independence of the size, V, and the age, A, at detection given A > t*, where the value of t* is to be estimated from the given sample. This is illustrated with an application to data on premenopausal breast cancer. The proposed distribution offers the prospect of the estimation of some biologically meaningful parameters descriptive of the temporal organization of tumor latency. An estimate of the model stability to the prior distribution of tumor size and some other stability results for the Bayes formula are given.

In this paper, we will cover the bonus-malus system in automobile insurance. Bonus-malus systems are based on the distribution of the number of car accidents. Therefore, the modelling and fitting of that distribution are considered. Fitting of data is done using the Poisson inverse Gaussian distribution, which shows a good fit. Building the bonus system is done by minimizing the insurer's risk, according to Lemaire's (1985) bonus system.