Measures of epistemic utility are used by formal epistemologists to make determinations of epistemic betterness among cognitive states. The Brier rule is the most popular choice (by far) among formal epistemologists for such a measure. In this paper, however, we show that the Brier rule is sometimes seriously wrong about whether one cognitive state is epistemically better than another. In particular, there are cases where an agent gets evidence that definitively eliminates a false hypothesis (and the probabilities assigned to the other hypotheses stay in the same ratios), but where the Brier rule says that things have become epistemically worse. Along the way to this 'elimination experiment' counter-example to the Brier rule as a measure of epistemic utility, we identify several useful monotonicity principles for epistemic betterness. We also reply to several potential objections to this counter-example.

In the present paper we explore various approaches of computing model likelihoods from the MCMC output for mixture and switching models, among them the candidate's formula, importance sampling, reciprocal importance sampling and bridge sampling. We demonstrate that the candidate's formula is sensitive to label switching. It turns out that the best method to estimate the model likelihood is the bridge sampling technique, where the MCMC sample is combined with an iid sample from an importance density. The importance density is constructed in an unsupervised manner from the MCMC output using a mixture of complete data posteriors. Whereas the importance sampling estimator as well as the reciprocal importance sampling estimator are sensitive to the tail behaviour of the importance density, we demonstrate that the bridge sampling estimator is far more robust in this concern. Our case studies range from from selecting the number of classes in a mixture of multivariate normal distributions, testing for the inhomogeneity of a discrete time Poisson process, to testing for the presence of Markov switching and order selection in the MSAR model. (author's abstract) / Series: Forschungsberichte / Institut für Statistik

In the present paper we discuss the problem of estimating model likelihoods from the MCMC output for a general mixture and switching model. Estimation is based on the method of bridge sampling (Meng and Wong, 1996), where the MCMC sample is combined with an iid sample from an importance density. The importance density is constructed in an unsupervised manner from the MCMC output using a mixture of complete data posteriors. Whereas the importance sampling estimator as well as the reciprocal importance sampling estimator are sensitive to the tail behaviour of the importance density, we demonstrate that the bridge sampling estimator is far more robust in this concern. Our case studies range from computing marginal likelihoods for a mixture of multivariate normal distributions, testing for the inhomogeneity of a discrete time Poisson process, to testing for the presence of Markov switching and order selection in the MSAR model. (author's abstract) / Series: Report Series SFB "Adaptive Information Systems and Modelling in Economics and Management Science"

In model-based clustering mixture models are used to group data points into clusters. A useful concept introduced for Gaussian mixtures by Malsiner Walli et al. (Stat Comput 26:303-324, 2016) are sparse finite mixtures, where the prior distribution on the weight distribution of a mixture with K components is chosen in such a way that a priori the number of clusters in the data is random and is allowed to be smaller than K with high probability. The number of clusters is then inferred a posteriori from the data. The present paper makes the following contributions in the context of sparse finite mixture modelling. First, it is illustrated that the concept of sparse finite mixture is very generic and easily extended to cluster various types of non-Gaussian data, in particular discrete data and continuous multivariate data arising from non-Gaussian clusters. Second, sparse finite mixtures are compared to Dirichlet process mixtures with respect to their ability to identify the number of clusters. For both model classes, a random hyper prior is considered for the parameters determining the weight distribution. By suitable matching of these priors, it is shown that the choice of this hyper prior is far more influential on the cluster solution than whether a sparse finite mixture or a Dirichlet process mixture is taken into consideration.

Este trabalho visa apresentar métodos de categorização de variáveis explicativas contínuas em Análise de Sobrevivência. Do ponto de vista clínico, agrupar pacientes em grupos de risco distintos é importante para agilizar tomadas de decisões; entretanto, perda de informação e outros problemas estatísticos podem ocorrer. Portanto, métodos para seleção de pontos de corte e correção dos possíveis problemas gerados pela categorização são criticamente avaliados. Para a aplicação e comparação dos métodos são utilizados dados do Instituto do Coração do Hospital das Clínicas da Faculdade de Medicina da Universidade de São Paulo (InCor - FMUSP), em que a variável fração de ejeção é dicotomizada e tricotomizada. / This dissertation aims to present methods of categorization for continuous variables in Survival Analysis. From a clinical point of view, grouping patients into distinct risk groups is important for accelerating decision-making; however, loss of information and other statistical problems may occur. Therefore, methods for selecting cutpoints and correcting problems generated by categorization are critically evaluated. For the application and comparison of the methods, the dataset from Heart Institute - University of Sao Paulo Medical School (InCor FMUSP) is used, in which the variable ejection fraction is dichotomized and trichotomized.

Este trabalho visa apresentar métodos de categorização de variáveis explicativas contínuas em Análise de Sobrevivência. Do ponto de vista clínico, agrupar pacientes em grupos de risco distintos é importante para agilizar tomadas de decisões; entretanto, perda de informação e outros problemas estatísticos podem ocorrer. Portanto, métodos para seleção de pontos de corte e correção dos possíveis problemas gerados pela categorização são criticamente avaliados. Para a aplicação e comparação dos métodos são utilizados dados do Instituto do Coração do Hospital das Clínicas da Faculdade de Medicina da Universidade de São Paulo (InCor - FMUSP), em que a variável fração de ejeção é dicotomizada e tricotomizada. / This dissertation aims to present methods of categorization for continuous variables in Survival Analysis. From a clinical point of view, grouping patients into distinct risk groups is important for accelerating decision-making; however, loss of information and other statistical problems may occur. Therefore, methods for selecting cutpoints and correcting problems generated by categorization are critically evaluated. For the application and comparison of the methods, the dataset from Heart Institute - University of Sao Paulo Medical School (InCor FMUSP) is used, in which the variable ejection fraction is dichotomized and trichotomized.