People often perform poorly on stock-flow reasoning tasks, with many (but not all) participants appearing to erroneously match the accumulation of the stock to the inflow – a response pattern attributed to the use of a “correlation heuristic”. Efforts to improve understanding of stock-flow systems have been limited by the lack of a principled approach to identifying and measuring individual differences in reasoning strategies. We present a principled inferential method known as Hierarchical Bayesian Latent Mixture Models (HBLMMs) to analyze stock-flow reasoning. HBLMMs use Bayesian inference to classify different patterns of responding as coming from multiple latent populations. We demonstrate the usefulness of this approach using a dataset from a stock-flow drawing task which compared performance in a problem presented in a climate change context, a problem in a financial context, and a problem in which the financial context was used as an analogy to assist understanding in the climate problem. The hierarchical Bayesian model showed that the proportion of responses consistent with the “correlation heuristic” was lower in the financial context and financial analogy context than in the pure climate context. We discuss the benefits of HBLMMs and implications for the role of contexts and analogy in improving stock-flow reasoning.

We present a classification methodology that jointly assigns to a decision maker a best-fitting decision strategy for a set of choice data as well as a best-fitting stochastic specification of that decision strategy. Our methodology utilizes normalized maximum likelihood as a model selection criterion to compare multiple, possibly non-nested, stochastic specifications of candidate strategies. In addition to single strategy with “error” stochastic specifications, we consider mixture specifications, i.e., strategies comprised of a probability distribution over multiple strategies. In this way, our approach generalizes the classification framework of Bröder and Schiffer (2003a). We apply our methodology to an existing dataset and find that some decision makers are best fit by a single strategy with varying levels of error, while others are best described as using a mixture specification over multiple strategies.

Population seroprevalence can be estimated from serosurveys by classifying quantitative measurements into positives (past infection/vaccinated) or negatives (susceptible) according to a fixed assay cut-off. The choice of assay cut-offs has a direct impact on seroprevalence estimates. A time-resolved fluorescence immunoassay (TRFIA) was used to test exposure to human parvovirus 4 (HP4). Seroprevalence estimates were obtained after applying the diagnostic assay cut-off under different scenarios using simulations. Alternative methods for estimating assay cut-offs were proposed based on mixture modelling with component distributions for the past infection/vaccinated and susceptible populations. Seroprevalence estimates were compared to those obtained directly from the data using mixture models. Simulation results showed that when there was good distinction between the underlying populations all methods gave seroprevalence estimates close to the true one. For high overlap between the underlying components, the diagnostic assay cut-off generally gave the most biased estimates. However, the mixture model methods also gave biased estimates which were a result of poor model fit. In conclusion, fixed cut-offs often produce biased estimates but they also have advantages compared to other methods such as mixture models. The bias can be reduced by using assay cut-offs estimated specifically for seroprevalence studies.

Insurers have been concerned about surrenders for a long time especially in saving business, where huge sums are at stake. The emergence of the European directive Solvency II, which promotes the development of internal risk models (among which a complete unit is dedicated to surrender risk management), strengthens the necessity to deeply study and understand this risk. In this paper, we investigate the topics of segmenting and modelling surrenders in order to better take into account the main risk factors impacting policyholders' decisions. We find that several complex aspects must be specifically dealt with to predict surrenders, in particular the heterogeneity of behaviour as well as the context faced by the insured. Combining them, we develop a new methodology that seems to provide good results on given business lines, and that moreover can be adapted for other products with little effort.

This paper considers the modelling of claim durations for existing claimants under income protection insurance policies. A claim is considered to be terminated when the claimant returns to work. Data used in the analysis were provided by the Life and Risk Committee of the Institute of Actuaries of Australia. Initial analysis of the data suggests the presence of a long-run probability, of the order of 7%, that a claimant will never return to work. This phenomenon suggests the use of mixed parametric regression models as a description of claim duration which include the prediction of a long-run probability of not returning to work. A series of such parametric mixture models was investigated, and it was found that the generalised F mixture distribution provided a good fit to the data and also highlighted the impact of a number of statistically significant predictors of claim duration.

The estimation of probabilistic deformable template models incomputer vision or of probabilistic atlases in Computational Anatomyare core issues in both fields.A first coherent statistical framework where the geometrical variability ismodelled as a hiddenrandom variable has been given by [S. Allassonnière et al., J. Roy. Stat. Soc.69 (2007) 3–29]. They introduce a Bayesian approach and mixture of them to estimate deformable template models.A consistent stochastic algorithm has been introduced in [S. Allassonnière et al. (in revision)] to face the problem encountered in [S. Allassonnière et al., J. Roy. Stat. Soc.69 (2007) 3–29] for theconvergence of the estimation algorithm for the one component model inthe presence of noise.We propose here to go on in this direction of using some “SAEM-like”algorithm to approximate the MAP estimator in the general Bayesian setting ofmixture of deformable template models.We also prove the convergence of our algorithm toward a criticalpoint of the penalised likelihood of the observations andillustrate this with handwritten digit images and medical images.

The aim is to study the asymptotic behavior of estimators and testsfor the components of identifiable finite mixture models ofnonparametric densities with a known number of components.Conditions for identifiability of the mixture components andconvergence of identifiable parameters are given.The consistency and weak convergence of the identifiable parametersand test statistics are presented for several models.

This paper deals with the likelihood ratio test (LRT) for testing hypotheseson the mixing measure in mixture models with or without structural parameter. The main result gives the asymptotic distribution of the LRTstatisticsunder some conditions that are proved to be almost necessary.A detailed solution is given for two testing problems: thetest of a single distribution against any mixture, with application to Gaussian, Poisson andbinomial distributions; the test of the number of populations in afinite mixture with or without structural parameter.